A piezoelectric thin-film microactuator in the form of an asymmetrically laminated diaphragm is developed as an intracochlear hearing aid. Experimentally, natural frequencies of the microactuator bifurcate with respect to an applied bias voltage. To qualitatively explain the findings, we model the lead-zirconate-titanate (PZT) diaphragm as a doubly curved, asymmetrically laminated, piezoelectric shallow shell defined on a rectangular domain with simply supported boundary conditions. The von Karman type nonlinear strain–displacement relationship and the Donnell–Mushtari–Vlasov theory are used to calculate the electric enthalpy and elastic strain energy. Balance of virtual work between two top electrodes is also considered to incorporate an electric-induced displacement field that has discontinuity of in-plane strain components. A set of discretized equations of motion are obtained through a variational approach.
For the last decade, bistability behavior of micro-electrical-mechanical systems (MEMS) has attracted significant attention of researchers [1–17]. One unique phenomenon of these bistable devices is the ability to migrate from one equilibrium state to another via snap-through. The snap-through phenomenon could enable new applications for electrostatic MEMS actuators, such as switches [18–20], microvalves and microrelays [21–23], and band-pass filters . The study of snap-through also facilitates better designs against pull-in instability of electrostatic MEMS actuators. In fact, many MEMS structures are fabricated via high-temperature processes. Thermal stresses resulting from these processes often cause the MEMS structures to warp, thus producing a bistable system potentially for snap-through to occur.
In structural mechanics, snap-through instability is a well-studied topic . Snap-through instability could occur in one-dimensional structures (e.g., arches [25–27]) or two-dimensional structures (e.g., shells [28,29]). For MEMS devices, the study of snap-through instability is focused primarily on electrostatic actuators. For these systems, an applied voltage and a curved, elastic structure form an electrostatic load causing the snap-though. The constitutive equation of the structure follows Hooke's law. There are, however, many other modes of actuation in MEMS devices, such as piezoelectric and thermal actuations.
For a piezoelectric actuator, the applied voltage affects a curved structure via the converse piezoelectric effect. Distinct compared to electrostatic actuators, the applied voltage changes the stiffness and thus the stability of the structure, resulting in rich bistability behaviors. For example, for a bimorph buckled beam under distributed actuation, Maurini et al.  showed that depending on the magnitude and phase of axial actuation, the beam can have different numbers of equilibria and the stability of the equilibria change accordingly. Furthermore, the voltage–displacement curve of a bimorph curved beam of partial surface piezoelectric coverage subjected to bias voltages was observed separated into two disjoint portions before and after snap through in a finite element analysis conducted by Varelis and Saravanos; see Fig. 7 of Ref. . None of the above has been observed in electrostatic actuators.
The purpose of this paper is to study snap-through phenomenon of a piezoelectric MEMS actuator. The piezoelectric actuator takes the form of a two-dimensional diaphragm with initial warping, and the snap-through is induced via an applied voltage. This paper is motivated by the development of a lead-zirconate-titanate (PZT), thin-film, acoustic microactuator intended for an intra-cochlear hearing aid ; see Fig. 1. The microactuator consists of four parts: a silicon diaphragm, a bulk silicon substrate, a PZT thin-film layer, and a pair of electrodes. (Note that the four parts in Fig. 1 are not drawn to scale.) The diaphragm is anchored to the silicon substrate. The diaphragm can be formed, for example, by etching the silicon substrate from the bottom side to form a cavity under the diaphragm. On top of the silicon diaphragm is a layer of PZT thin film with a pair of bottom and top electrodes. When a driving voltage is applied to the electrodes, the PZT thin film extends and contracts flexing the diaphragm like a speaker.
The diaphragm of the microactuator, however, is not perfectly flat. In fact, it is warped into a thin shell due to thermal stresses induced in the fabrication process; see Fig. 14 of Ref. . As a result, the microactuator is likely to have multiple equilibrium positions to enable snap-through. The snap-through instability, if reached, may cause several concerns. First, when a PZT microactuator is used in cochlea, it may need to be poled regularly to maintain its piezoelectricity. If snap-through instability occurs during poling, it may affect the gain and bandwidth of the microactuator, as different equilibrium states imply different local stiffness and natural frequencies. There is also a risk that a standard 5 V power source could drive the micro-actuator into various domains of attraction under normal operation.
It is not a trivial task to study snap-through instability of such PZT thin-film micro-actuators. There are several major challenges that need to be overcome. First, there must be some preliminary experimental results suggesting that snap-though instability may have occurred in the operation of the PZT thin-film micro-actuator. In other words, theoretical modeling of the snap-through instability should be justified.
If the theoretical modeling is necessary, the second challenge that ensues is lack of existing models. Although general nonlinear piezoelectric shell lamination (multilayered) theories can be found in the literature [31,34–43], when used to derive models, various assumptions are considered. For example, a bimorph configuration is often assumed, where one or multiple elastic layers are symmetrically laminated across the thickness direction, with two identical piezoelectric layers being on the top and bottom surfaces, respectively [37–41,44,45]. (This configuration is referred to as “symmetric lamination” hereafter.) Such a bimorph configuration greatly simplifies modeling of piezoelectric actuation. One immediate example is that it allows for pure bending actuation, where the top and bottom piezoelectric layers extend and contract against each other, excluding in-plane stretching actuation. In fact, for an asymmetrically laminated bi-morph or mono-morph configuration, bending and stretching actuation are coupled with each other, e.g., see Ref. , and should be taken into account. Furthermore, for piezoelectric smart structures, the thickness of piezoelectric layers is often much thinner than elastic layers and assumed to be negligible, and so are their elastic properties [44,46,47]. However, as will be shown later in this paper, when the elastic properties of the piezoelectric layers are not negligible, the applied voltage affects the stiffness of a curved structure via the converse piezoelectric effect.
In reality, piezoelectric MEMS devices are often asymmetrically laminated to minimize fabrication complexity. Moreover, the piezoelectric and elastic layers are quite comparable in thickness to maximize actuation strength. For example, the intra-cochlear acoustic microactuator in Ref.  has multiple layers, including parylene, gold, chromium, PZT, platinum, titanium, silicon nitride, silicon oxide, and a second parylene layer. The layers above and below the PZT thin film total about 0.5 μm and 1.1 μm, respectively, while the PZT thin film itself is about 1 μm in thickness. By all measures, the PZT actuator diaphragm is asymmetrically laminated and the thickness of the PZT thin film is not negligible.
The third challenge is that a realistic PZT thin-film microactuator employs partial electrodes to maximize actuator displacement; see Ref. . The use of partial electrodes results in discontinuous electric fields when the voltage is applied. Studies of electro-mechanical coupling with continuous electric fields are available in the literature [42,43]. Studies of discontinuous electric fields, however, remain largely open.
When asymmetric lamination and partial electrode coverage or more general configurations are considered, finite element methods are predominantly used [31,35–38,42,43]. Although finite element methods facilitate studying general configurations, physical insights are often lost during the process.
From the discussions above, it is evident that existing theoretical studies of piezoelectric shells are not adequate for the design and development of piezoelectric MEMS actuators. Snap-through instability of PZT thin-film microactuators, induced by an applied voltage, has not been extensively studied despite its potential impact.
For the rest of the paper, we first present preliminary experimental results that suggest occurrence of snap-through instability in the PZT thin-film microactuator. The experimental results demonstrate that vibration modes bifurcate when the applied voltage exceeds a threshold. We then develop a mathematical model to qualitatively explain the bifurcation. Specifically, we model the PZT diaphragm as a doubly curved, asymmetrically laminated, piezoelectric shallow shell defined on a rectangular domain with simply supported boundary conditions. Assumptions and coordinate systems of the shell model are introduced and explained. Kinematic relations and constitutive equations are introduced to formulate electric enthalpy and elastic strain energy of the shell model. Virtual work done by the boundary membrane forces and bending moments are derived and simplified. A particular shape function of in-plane displacement fields that satisfy, in the sense of weak form, a set of continuity and equilibrium equations along the boundary of two partial electrodes is derived to incorporate the discontinuous electric fields resulting from the partial electrodes. Finally, variational forms of the potential and kinetic energy are derived, and discretized equations of motion are obtained through Hamilton's principle and the Rayleigh-Ritz method using a set of admissible shape functions and the particular shape function.
Preliminary Experiment Study
The PZT thin-film microactuator shown in Fig. 1 has been fabricated and tested [32,49]. The diaphragm has a size of 0.8 mm by 0.8 mm and a thickness of 2–3 μm. Moreover, the diaphragm has a bottom electrode and two top electrodes (i.e., one inner and one outer) as illustrated in Fig. 1. Detailed description of the test specimen can be found in Refs.  and  and is not repeated here. The experiment was done in an aqueous environment. The PZT thin-film microactuator was submerged in water. A voltage drove the microactuator and a laser Doppler vibrometer measured the velocity of the vibrating diaphragm. A spectrum analyzer processed the driving voltage and measured velocity to obtain a frequency response function (FRF) that characterizes the PZT thin-film microactuator. Detailed description of the experimental setup can also be found in Refs.  and  and is not repeated here again.
With the test specimen and the experimental setup, we conducted a preliminary experiment to investigate possible snap-through instability of the PZT thin-film microactuator. For the first step, a considerable direct current (DC) bias voltage (e.g., 2 V) was applied across the outer and bottom electrodes for a sufficiently long time (>20 min.). In the meantime, the inner electrode remained floating. The hypothesis was that the bias voltage could deflect the actuator diaphragm from one stable equilibrium configuration to another if the bias voltage was large enough. The next step was to remove the DC voltage, and a swept sine measurement was subsequently conducted. For the swept sine measurement, a small voltage (in the order of mV) was applied across the inner and bottom electrodes. At the same time, the outer electrode remained floating. The purpose of the swept sine measurement was to obtain FRFs, from which natural frequencies of the microactuator diaphragm could be extracted experimentally. The hypothesis was that natural frequencies reflected the linearized stiffness coefficients around a stable equilibrium position. If snap-through instability occurred, the actuator diaphragm would move to a different stable equilibrium position. Therefore, the linearized stiffness coefficients would change and so would the natural frequencies. These two steps were repeated by increasing or decreasing the DC bias voltage hoping to maneuver the actuator diaphragm from one stable equilibrium position to another and then back.
Figure 2 shows the measured natural frequencies versus the DC bias voltage varied between 5 V and −5 V. Measured FRFs are also included Fig. 2 for comparison. The experiment started with a zero DC biased voltage (see section 1 in Fig. 2). In the measured FRF, there was only one significant resonance peak with a natural frequency around 24 kHz. As the DC biased voltage increased from 0 to 2.5 V, the resonance peak remained unchanged. When the DC bias voltage exceeded 2.5 V, the FRF changed abruptly (see section 2 in Fig. 2). Specifically, the 24 kHz resonance peak disappeared and two new resonance peaks emerged, one around 34 kHz and the other around 20 kHz. These two resonance peaks did not change significantly when the DC bias voltage was increased to 3.5 V (see section 3 in Fig. 2), indicating the PZT diaphragm had migrated from the initial stable equilibrium position to another stable equilibrium position.
In the second part of the experiment, the DC-biased voltage was reduced and removed. The two resonance peaks remained at around 33 kHz and 19 kHz. In other words, the PZT diaphragm stayed in the second stable equilibrium position and did not return to its initial stable equilibrium state. The measured FRF remained the same even when the biased voltage was reversed (i.e., negative DC bias). When the DC-biased voltage was reduced to −4 V, the FRF experienced another abrupt change. The two resonance peaks at 33 kHz and 19 kHz disappeared. Instead, one new resonance peak appeared at 31 kHz (see section 4 in Fig. 2). The natural frequency and FRF were not affected as the biased voltage was further decreased (see section 5 in Fig. 2) or increased (see section 6 in Fig. 2), indicating the PZT diaphragm migrated from the second stable equilibrium position to a third stable equilibrium position.
In summary, the natural frequencies of the PZT diaphragm bifurcate when the DC bias voltage exceeds a threshold. Moreover, unlike the snap-through observed in electrostatic actuators or elastic structures, the trend of bifurcation is not reversible, suggesting something unique occurred to the piezoelectric actuator. The only tangible explanation is that the DC bias voltage has created bending moments and in-plane stresses that migrate the PZT diaphragm from one stable equilibrium to another via snap-through, and the mechanism that kept it from going back to its original state remains to be investigated. These experimental results indicate that snap-through instability is highly possible for a PZT, thin-film, diaphragm-type microactuator. A detailed mathematical model to analyze snap-through of piezoelectric thin shells is critically needed.
Figure 3 shows the shallow shell model to be developed in this paper. The shell model consists of three layers. The middle layer 2 is a piezoelectric layer, representing the PZT thin film. Layer 1 is an elastic layer representing all materials below the PZT thin film, such as the bottom electrode, silicon nitride, silicon oxide, and silicon. Layer 3 is an elastic layer representing all materials above the PZT thin film, such as the top electrode and parylene coating. Moreover, layer 3 consists of an inner electrode and an outer electrode neighboring to each other. (For the PZT microactuator in Fig. 1, the gap between the inner and outer electrodes is 20 μm.) For the rest of the paper, quantities related to the ith layer are denoted by a superscript (i) or a subscript i. Furthermore, a special notation is reserved for a reference surface, known as the modulus-weighted midsurface , which will be defined later in this section. Finally, quantities without any subscript or superscript are related to the shell laminate, which consists of all three layers.
In developing the shallow shell laminate model, the following assumptions and definitions are made:
The diaphragm of the PZT micro-actuator is warped due to thermal stresses induced in the fabrication process. Rigorously speaking, the micro-actuator should be modeled as a thermally buckled plate. However, it is a difficult task to estimate the induced thermal stresses. As a first attempt, the micro-actuator is simplified as a shell laminate model which is assumed to be initially stress free, and yet curved with constant curvature Rx and Ry (spherical type). The constant curvatures are used to account for the warping.
For the PZT micro-actuator model in Fig. 3, the actuator domain Ω consists of an inner electrode domain Ω– and an outer electrode domain Ω+. Furthermore, Ω is considered as a rectangular domain defined as and enclosed by an outer boundary , where a and b represent the domain widths. By the same token, Ω– is defined as , and enclosed by an inner boundary , where and represent the four vertices of the domain. The outer electrode domain is then , and is enclosed by and an inner boundary , which coincides with .
For each layer, there exists a local coordinate system with orthogonal curvilinear coordinates ; see Fig. 3(b). Furthermore, all three layers are shallow shells satisfying the following assumptions .
The orthogonal curvilinear surface coordinates can be replaced with the rectangular coordinates ; see Fig. 3(b).
The Lamé parameters of a shallow shell equal unity, i.e., , where i = 1, 2, 3. Furthermore, the radii of curvature of each layer are equal, i.e., , where . As a result, the differential volume of each layer can be approximated by .
- (4)A global coordinate system with coordinates is defined, where the x and y coordinates are identical to those in the local coordinate systems , while the coordinate is obtained by shifting the transverse coordinate ; see Fig. 3(b). is used to determine the modulus-weighted midsurface , which serves as a reference to account for the variation of modulus and Poisson's ratio in each layer across the thickness direction. The position of can be determined by a standard moment analysis. Let be the distance from the midsurface of the ith layer to . Thenwhere is the vertical distance from to is the conventional membrane stiffness, and , hi and νi are the Young's modulus, thickness, and Poisson's ratio of the ith layer, respectively. It is convenient to set the origin of the global coordinate system to coincide with a reference point on such that the distance becomes zero. Consequently,(1)(2)
All three layers adopt a geometric nonlinear strain–displacement relationship used in von Karman plates. Moreover, the Donnell–Mushtari–Vlasov theory is used to simplify the model, which is well justified by the shell laminate being shallow . The interested reader is referred to Ref.  for the details of the Donnell-Mushtari-Vlasov (DMV) theory.
Love's assumptions are made in the kinematic relations for the shell laminate. Consequently, the following kinematic relations can be obtained .
- (a)Let be the displacement vector of the modulus-weighted midsurface, where u, v, and w are the displacement in the x, y, and z directions, respectively, and T indicates transpose. Also, let be the angular rotation vector, where βx and βy are the angles of rotation of the laminate, and βz are the normal deformations of the laminate across the thickness. Consider an arbitrary point P in the laminate, located at in the global coordinate system. Let be the displacement vector of P. Then(4)
- (b)Love's assumptions imply that . Furthermore, the laminate's strains in the transverse direction vanish, i.e., . As a result, the laminate's rotational angles β and curvatures κ can be simplified by the DMV theory, i.e.,where , and c = 2 if and c = 1 otherwise.(5)
- (c)Following the procedure in Ref. , the in-plane strains of the laminate can be written in the global coordinate system aswhere , S are the laminate's in-plane strains and S0 are the membrane strains of the modulus-weighted mid-surface. To transform the laminate's in-plane strains to the ith layer's local coordinate system, Eq. (3) is substituted into Eq. (6), leading to(6)where and and are the ith layer's in-plane strains and membrane strains of the midsurface, respectively. Finally, the normal stresses σ33 are negligible in all three layers.(7)
The electric potential inside the piezoelectric layer is assumed to vary linearly across the thickness direction. In addition, the in-plane electric fields Ex and Ey are neglected and only the transverse electric field Ez is considered.
The shell laminate model is developed using a” local” to” global” procedure. Formulas of individual layers are derived in each local coordinate system and in terms of quantities associated with each layer , such as the membrane strains of the ith layer (layer level). The shell laminate is then obtained by assembling individual layers and transforming all the quantities to the modulus-weighted midsurface in the global coordinate system (laminate level).
Kinematics and Electric Fields
In this section, the kinematic relations in the layer level are transformed to the global coordinate system , and then added together to derive those in the laminate level.
where and are a 3 × 3 identity and zero matrix, respectively.
where is the electric bias voltage between the top and bottom electrodes.
In this section, a generalized form of constitutive equations of the piezoelectric and elastic layers will be obtained in terms of stress and moment resultants as follows.
Piezoelectric and Elastic Layers.
where Dz is the electric displacement in the thickness direction, e31 is the piezoelectric constant, and ε33 is the dielectric constant.
To obtain for the outer electrode, one simply needs to replace the superscript − in Eq. (22) with +.
Laminate Boundary Forces and Moments.
where and .
Variation of Potential and Kinetic Energies and Virtual Work
Variation of Electric Enthalpy and Elastic Strain Energy.
After a variational process, Eq. (31) will lead to a set of electromechanical equations of mechanical motion that governs the displacement vector and a set of charge equations of electrostatics that governs the electric potential . Since the shell laminate is an actuator, the electric field is prescribed. As a result, the electric potential is no longer a degree-of-freedom (DOF) but a control variable, rendering . Therefore, only the first two integrals in Eq. (31) will be considered throughout the rest of the paper.
Variation of Kinetic Energy.
Virtual Work Along Boundaries.
By the same token, let us define and as the boundary displacement and slope components in the individual n − t coordinate systems at ∂Ω− and ∂Ω+, respectively. Comparing Figs. 3 and 4, it can be seen that the inner electrode boundary ∂Ω− has the same normal and tangential direction as , and thus shares the same sign convention as ub. Therefore, to obtain at and , one simply needs to replace the components in Eq. (35) with equivalent counterparts of superscripts −. The normal and tangential directions along ∂Ω+, on the other hand, have an opposite sign. Therefore, except for since the transverse direction is the same.
By the same token, let us define and as the boundary force and moment components in the individual n − t coordinate systems at ∂Ω− and ∂Ω+, respectively. Again referred to Fig. 4, the boundary forces and moments components along ∂Ω− and ∂Ω+ are the same in their individual local n − t coordinate systems. Therefore, except for and .
The virtual work along ∂Ω− or ∂Ω+ can be obtained by simply replacing , ub, and fb in Eq. (37) with ∂Ω− or or , and or .
Variational Formulation and Discretization
where N is the number of terms retained, and are two sets of shape functions defined on Ω− and Ω−, respectively, and and are the generalized coordinates.
Shape Function Expansion
and and are their generalized coordinates.
where . Note that the integrals are evaluated at and that um, vm, w, βy, κxx, κyy, and κxy do not appear in Eq. (47) because they are assumed to be continuous across . Also, in deriving Eq. (47), Eq. (2) has been used to eliminate the membrane strains from the last integral.
Determination of the final forms of and depends on the boundary condition at , which will be demonstrated in Sec. 9.
A Reference System
As a final remark, the reference system is not chosen to model the microactuator that yields the result in Fig. 2. Due to uneven etch rates, exact diaphragm geometry of the microactuator is rather complex. It has a uniform circular membrane area at the center but a slightly tapered residual silicon region between the circular membrane and the rectangular anchor; see Fig. 6 in Ref. . The piezoelectric thin film is also not uniform. The inner electrode is not rectangular because it needs to extend to outside for electric connection; the outer electrode is not a rectangular ring, because it needs to give way to the inner electrode connection; see Fig. 9 in Ref. . All things considered, it is impractical to model the real microactuator tested. Instead, the reference system is chosen to study snap through for two reasons. First, elastic shells on rectangular domains with simply supported boundary conditions are better studied for snap-through phenomena. Second, shape functions to discretize the equation of motion are easier to select.
Discretized Equation of Motion
where and m is the mass per unit area of the shell laminate. Definition of the nonlinear operators , and is provided in Appendix.
where K is the linear stiffness, Q is the quadratic stiffness, Γ is the cubic stiffness, Snle is the nonlinear softening or stiffening coefficient (depending on the signs of and ) due to the electric potential, F is the electric force coefficient due to the converse piezoelectric effect, and B is the electric force coefficient due to boundary conditions. The solution procedure to derive Eq. (58) and definition of all coefficients in Eq. (58) can be found in Appendix.
There are two things worth noting in Eq. (58). First, due to the von Karman-type strain displacement relation, the converse piezoelectric effect leads to nonlinear softening or stiffening effect as manifested by the coefficients and . In other words, an applied voltage can change the stiffness of the shell laminate. Furthermore, these coefficients would vanish if the elastic properties of the piezoelectric layer had been ignored, which was assumed in many studies for piezoelectric smart structures, e.g., in Refs. , , and . Second, it is also worth noting that the presence of the inner and outer electrodes has a similar effect with and , as manifested by the coefficients Snle. As seen in Eq. (58), if the electric potentials on the inner and outer electrodes are equal, or , i.e., the shell laminate is uniformly actuated, the Snle terms will then vanish. In other words, the coefficient Snle indicates a specialty of nonuniform or distributed actuation of piezoelectric shells or plates, which largely remains unexplored.
In this paper, we reported the experimental findings of a PZT thin-film microactuator that was submerged in water. We have also developed a mathematical model hoping to qualitatively explain the experimental findings. With the presentations above, we reach the following conclusions.
Experimental results indicate that natural frequencies of the microactuator bifurcate when the applied DC bias voltage reaches specific thresholds. The bifurcation indicates a change of local stiffness and thus a migration between stable equilibrium states of the microactuator. Furthermore, the bifurcation is irreversible, unlike those seen in electrostatic actuators or elastic curve structures. A snap-through phenomenon specific to nonlinear piezoelectric actuators is hypothesized to facilitate the migration when the threshold DC bias voltage is reached.
To explore the possibility of snap-through induced by a DC bias voltage, we develop a multilayered, asymmetrically laminated, doubly curved, geometrically nonlinear, shallow shell model. The model is applied to a rectangular domain with simply boundary conditions and two partial electrodes, specifically, an inner electrode and an outer electrode. Discretized equations of motion are derived via a variational formulation and assumed shapes of displacement fields.
The geometrical nonlinearity couples in-plane displacements with transverse displacement in the derived equations of motion. In-plane equation of motion is algebraic, implying that in-plane DOFs can be represented in terms of transverse DOFs. Transverse equations of motion are differential equations involving nonlinear terms from both in-plane and transverse DOFs. After elimination of the in-plane DOFs, the resulting equations of motion are coupled second-order differential equations with linear, quadratic, and cubic nonlinear restoring forces.
The presence of partial electrodes will lead to a softening or stiffening effect that is similar to what can be observed in nonlinear piezoelectric actuators involved with large deformation. Also, it will lead to a discontinuous electric field, if the applied voltage on the two partial electrodes is not the same. The discontinuity will lead to a discontinuous in-plane strain field across the boundary of the electrodes. The strain discontinuity must be compensated via specific functions in the displacement expansion to ensure proper convergence of the potential energy. The discontinuity will also lead to residual virtual work along the electrode boundaries that needs to be incorporated in the derivation of the discretized equation of motion.
This material is based upon work supported by the National Science Foundation under Grant No. CBET-1159623. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
National Science Foundation (Grant No. CBET-1159623).
where A to F are linear stiffness coefficients, to and to are nonlinear quadratic stiffness coefficients, Cnl are nonlinear cubic stiffness coefficients, to are linear electric force coefficients, are nonlinear electric force coefficients due to the particular shape functions defined in Eq. (45), to are linear electric force coefficients and nonlinear electric force coefficients in the outer and inner electrode domains Ω+ and Ω– due to the converse piezoelectric effect, and finally Be and are linear electric force coefficients due to the virtual work at ∂Ω+ and defined in Eqs. (54) and (55).
To obtain and , one simply needs to substitute for . Similarly, one simply needs to substitute for to obtain and , and substitute to obtain and . Furthermore, one needs to substitute Ω− for Ω+ to obtain and .
Note that and can be obtained by substituting Ω− for Ω+.


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domain: finance


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domain: news


text: Billed by the dust jacket as A Fable for Our Times. Originally copyrighted and published in 1955 by Curtis Publishing Company, with a copyright renewed in 1983 by Karen Pryor. This is a nuclear novella. Right after powerful nuclear tests, both the US and Russia find dead angels. The finding is kept secret and shakes the leaders of both sides. In both cases, the body is destroyed or disappears. Want to know what happens? Read on! There is nothing here to do with fables in the sense in which I want to pursue them.

domain: literature


text:
BILL’S TRAIL WINDS UP through shady forest to Mount Barnabe, the highest point in Samuel P. Taylor State Park. From the summit, hikers can enjoy views from San Francisco Bay to Tomales Bay.
Following Bill’s Trail up the flank of Mount Barnabe and descending Barnabe Fire Road and Gravesite Fire Road creates a 6.5-mile, moderately difficult loop that’s highlighted with views from the 1,466-foot peak.
Begin by walking into Devil’s Gulch, one mile west of the main entrance to Samuel P. Taylor State Park. Veer right onto the path that parallels the creek. Check the creek for Coho salmon. They’ll be heading up the stream to spawn soon after Marin receives its first major rainstorm.
Cross the footbridge and turn left onto Bill’s Trail. Follow the switchbacks as the trail weaves through dense forest of redwoods, bay, Douglas fir and big leaf maple trees and ferns for 3.7 miles. Watch for poison oak that is turning red and dropping its leaves.
At the junction with the Barnabe Fire Road, turn left and head uphill to the summit. The route leaves the forest and crosses steep open hillside. There’s a fire lookout atop Mount Barnabe. Views from the summit extend east to Mount Diablo, south to Mount Tamalpais and northwest to Inverness Ridge and Tomales Bay.
The Barnabe Fire Road descends steeply down the face of the mountain, proceed slowly and use caution. The grassy areas on the hillside were favorite grazing spots for Barnabe, a white mule that belonged to Samuel P. Taylor’s children. The children reported that Barnabe knew how to open every gate between his corral and the grassy hillsides.
Turn right onto Gravesite Fire Road. A short path leads to the white picket fence that surrounds the graves of Samuel Penfield Taylor who died in 1886 and his wife, Sarah Washington Irving Taylor, who died in 1907.
Samuel Taylor’s success in business began during the gold rush. He gathered $5,691.99 worth of gold dust and purchased 100 acres of timberland along Papermill Creek. He built a paper mill and a powder mill. The Taylor family home was located in the meadow in Devil’s Gulch. A few fruit trees still exist from his orchard. In 1874, the narrow gauge railroad was completed along Papermill Creek and Taylor transformed his property into a summer resort. Camp Taylor thrived from 1875 through the 1890s.
To reach Samuel P. Taylor State Park, follow Sir Francis Drake Boulevard 15 miles west of San Rafael. Continue one mile west of the park’s main entrance and watch for the Devil’s Gulch sign.

domain: geography


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Consider this the first scheduling hiccup of the Empire State Yankees' 144-game road trip.
Andy Pettitte is working himself into shape as he comes out of retirement with the Yankees, and his rehab start on Sunday with Triple-A Empire State was scheduled for Dwyer Stadium in Batavia, N.Y., home of the New York-Penn League's Batavia Muckdogs.
The International League franchise, more familiar as the Scranton/Wilkes-Barre Yankees, is on the road all season while its ballpark in Pennsylvania goes through a $43.3 million renovation. It's playing most of its games at Rochester's Frontier Field, home of the fellow IL member Red Wings.
The Yankees are playing at a few other nearby ballparks as well, however, and Sunday's game against Pawtucket was scheduled for Batavia. But no longer. The parent Yankees would prefer Pettite to pitch at a Triple-A facility, rather than a short-season ballpark.
There's also the matter of Dwyer Stadium's capacity of 2,600. With Pettitte scheduled to be on the mound, a huge crowd should turn out. And with the Red Wings bearing the brunt of operating a second franchise this season, they should welcome the bigger gate.
"The Yankees would prefer to have Andy Pettitte pitching at a Triple-A stadium in front of a large crowd," Red Wings president Naomi Silver said Thursday. "It's more of the environment he is used to pitching in. It is true that we would top out at about 2,000 people in Batavia, while here at Frontier Field it would be 11,000 or 12,000 people . . .
"This has certainly been a decision in (the Yankees') hands. We speculated a bit that Sunday might be his day to pitch, that it could happen. We really only learned of their decision 45 minutes ago."
One complication, however: The Red Wings were already scheduled to play at home on Sunday. In order to accommodate the Yankees' request, that game against the Buffalo Bisons will now be played as part of a doubleheader on Saturday. The Red Wings, who also own and operate the Muckdogs, have said fans who had already purchased tickets for the game in Batavia will be able to use them in Rochester.
Rochester is serving as the home base for Empire State during its road trip. The Yankees were scheduled to play 37 of their home games in Rochester, seven in neighboring Batavia and the remaining dates at four other International League franchises.


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Manage episode 333101306 series 1968230
Last week, we gave you broad information about substance use and factors related to your biology and family history that leave you at risk for addiction. This week, I’m going to talk more specifically and clinically about 4 legal substances and their effects on you.
Savvy Psychologist is hosted by Dr. Monica Johnson. A transcript is available at Simplecast.
Savvy Psychologist is a part of Quick and Dirty Tips.

domain: medical


Material is ordered. To make it simple milling the vacuum table while providing perfect surfaces at the top and bottom of each part, pre-milled aluminium has been ordered. And to make it a cheap vacuum table, we ordered remainders. The plates are much larger than required. On the one hand we have to cut them into pieces. On the other hand some material can be used for other projects. Just for your information, the remainders are more then double the material we need, but at about half the price.
Furthermore, we ordered some tools (0.2mm drills), the pneumatic connectors and the sealing mass.


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Moscow, 4 September 1997 (RFE/RL) -- Interfax news agency says that the Russian Caucasus republics of North Ossetia and Ingushetia signed a peace accord in Moscow today aimed at ending a bloody territorial dispute.
Russian Prime Minister Viktor Chernomyrdin said the accord, signed by North Ossetian leader Akhsarbek Galazov and Ingush leader Ruslan Aushev, was a historic move and a great victory.
There were no immediate details on the contents of the accord. However, Galazov said the treaty by itself does not mean anything. Much work is necessary to implement every article.
The two tiny ethnic republics, which are near the breakaway republic of Chechnya, fought a brief war over a strip of territory in 1992, resulting in hundreds killed and tens of thousands of Ingush becoming refugees.
Since then, the refugees have had trouble returning and there have been frequent violent incidents between the two sides.


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Even if you belong to that group of people who are very healthy, some vegetables, such as fiberglass and legumes, can cause bloating, experts say.
Except for foods that have been identified as the cause of bloating, the specialists also advise you to eat small meals, but more often. Also, it is recommended that you chew on each bite for longer and thus prevent any irritation in the stomach.
If you want to keep a flat stomach and avoid bloating, you should limit the consumption of certain foods
- Vegetables such as broccoli, cauliflower, cabbage
Broccoli, cauliflower, and cabbage can cause problems with inflammation, as some people take it a little harder to digest this vegetable.
- Beans and root vegetables
Although they are healthy, foods such as beans, legumes, and root vegetables can cause bloating. Also, they contain a phytic acid that can cause bloating. But if you soak it in plenty of cold water with lemon juice or vinegar overnight, you can reduce that effect.
- Chestnuts fruits
Chestnuts fruit, such as plums and dried fruits, contains organic compounds that are useful for the digestive tract and overall health. However, how this fruit will be digested depends on the bacteria in your stomach. If it is not well-cooked, the fermentation it comes to produces bubbles.
Although spices are beneficial to our body and health, some spicy foods can cause acid in the stomach. Acid can again cause irritation.
- Chewing gum
We all love chewing gum. Though they can give you occupation and distract you from high-calorie snacks, they can cause you to swallow the air that leads to bloating. Also, chewing gums can induce the production of your stomach enzymes that give the signal that food arrives, which causes hunger. If you want something for snack or “snacking,” you better eat fiber-rich foods, such as oatmeal, carrot or popcorn.
Salt can cause water retention. Not only that it keeps water in your body, it causes inflammation, but it also negatively affects blood pressure.
- “Diet” carbonated beverage
Although it is believed that this drink may have fewer calories, but carbonated bubbles in diet carbohydrates can cause gas and bubbles. Instead of these beverages, you can drink water with lemon, lime or cucumber, or try a mint tea that is very calming and can prevent and reduce nausea. These healthy drinks will help you to cleanse and detoxify your body.
Many people suffer from bloating because they consume too many artificial sweeteners, or artificially sweetened foods and beverages.
- Dairy products
Some people do not produce enzymes that should help them explain lactose and sugar in milk. If you do not have these enzymes, these products will ferment in the stomach, causing pain, swelling, and gases.
- Processed carbohydrates
Foods that contain processed carbohydrates such as biscuits and pasta have a higher glycemic index than food that is unrefined. Processed foods turn into glucose more quickly and can cause overflows and gases.

domain: food


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Andrea Schneider, MSW, LCSW is a licensed clinical social worker. She earned her MSW from University of Michigan and her BA in Psychology from UCLA. Andrea has worked in many settings such as community mental health, hospice, private practice, primary/secondary public education settings, and mental health clinics, as a clinician and supervisor. She is EMDR certified (trauma-informed treatment) and enjoys working with college students.
Andrea is available at the CAPS office M-F 8-5 for new referrals, consultation, outreach, workshops, etc. Walk-in hour at CAPS is available daily from 2-3 pm.
Ian Wallace, PhD is a licensed psychologist providing individual, couples, and group counseling, as well as referral, consultation, and crisis services. Dr. Wallace earned a doctoral degree in Counseling Psychology from Virginia Commonwealth University (VCU), an M.A. in Clinical Psychology from Pepperdine University, and a B.A. in Psychology from The College of New Jersey.
Dr. Wallace has provided counseling services since 2001. He has worked in inpatient and outpatient mental health, medical settings, as well as at other college counseling centers such as UC Berkeley, Fresno City College and VCU. Additionally, Dr. Wallace has over 5 years of teaching experience with Argosy University, Diablo Valley College, and VCU. His areas of expertise include college counseling, marriage and family therapy, health psychology, as well as health promotion program development and implementation. Dr. Wallace has been with CAPS at Cal Maritime since 2013.

domain: psychology


Wal-Mart Settles With Women In Fla. Gender Bias Suit
The retailer and a group of women led by Zenovida Love on Thursday officially settled the three-year-old suit for an undisclosed amount, according to a stipulated dismissal they filed jointly about two months after initially notifying the court of their compact.
The parties will each bear their own attorneys’ fees and costs, except...
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Chief Justice must take notice of “circular Tyranny”, Dr. Tahir-ul-Qadri
Lahore (4th July 2018) Quaid of Pakistan Awami Tehreek Dr. Tahir-ul-Qadri has said consecutive hike in Petrol and electricity prices is unwarranted, caretaker Govt. must mend her ways, if burden of 150 billion circular debt is transferred to masses, then it would be worst kind of exploitation by state of her people. Chief Justice of Pakistan must take notice of this “circular Tyranny”. In his telephonic address to members of Central Core Committee, he said common man must not be punished for the crimes committed by former rulers along with crimes like institutional corruption, shabby distribution system, over-rated power productions projects and contracts by Sharifs, undue profiting by power companies, power theft etc. He said there should be visible difference between governance of Caretakers and that of corrupt Sharifs. Common men should not be burdened blindly; rather they must be given relief.
He said Pakistan Awami Tehreek desisted to participate in election, because current system cannot give any relief to masses; and consecutive elections under this system will just supplement political, social and economic woes of the state. Since this system was raised on the foundations of exploitation, ill-gotten wealth, rigging and terror, so election under this system will lead political forces with foreign agenda play with impunity their game against state institutions; society will be further divide on sectarian, ethnic, religious and tribal lines.
He warned if any office holder or member of Pakistan Awami Tehreek or Minhaj-ul-Quran directly or indirectly cooperated with ticket holders of killers of Model Town massacre during elections, strict action will be taken against him. Since this is policy matter, so no justification will be acceptable in this regard. He said Sharifs shed blood of our innocent workers; unleashed brutal acts of revenge against Pakistan Awami Tehreek, tried to amend law regarding finality of Prophethood, robbed country, exploited masses, launched campaign to malign state institutions. He said there is long list of heinous crimes committed by Sharifs and none of their crime is pardonable. He said he cannot forget innocents who were ruthlessly killed in Model Town; with Sharifs he has no political differences but enmity. It is obligatory for our member not to support N league; our war with them will continue in courts till realization of justice.

domain: politics


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Neo Climate Solutions PVT LTD
Climate Change, Carbon Market, Environmental and Energy Advisory
Neo Climate Solutions Pvt Ltd is an international climate change and environmental advisory and research consultancy registered and based in New Delhi (India) and has associates across the globe. The firm collaborates with the pool of experts having more than 20 years of international experience on policy, technology, finance, and capacity building aspects of the low carbon economy, energy, climate change, sustainable development, and environmental management through implementing various international assignments for multi-lateral, Bi-lateral development partners, regional agencies in the Asia and Pacific, national and local Governments, Industry, Private clients and NGO’s.
Neo Climate has been established to provide high-quality, independent advice in climate change, energy, and sustainable development sectors for the Asia and Pacific Countries. Within a short span of time since its inception, Neo climate has successfully carried out several assignments in the Asia and Pacific region and now expanding its activities in Africa and Europe.
" A company that approaches climate change, energy, water, and renewable advisory from a fresh perspective" and "To build a different type of company that’s focused not only on the bottom line, but also the happiness of our clients and team, and our personal growth along the journey".
"To provide high quality climate change and energy advisory services to the clients".
Our activities include technical advisory services, project identification studies, program management, training and capacity building, technology transfer and market research and analysis in climate change mitigation & adaptation, renewable energy, energy efficiency, strategic sustainability, sustainable development, and environmental sectors. We interact extensively with diverse stakeholder groups comprising industry, Government, research organisations, academic institutions, and NGOs to integrate climate change priorities into mainstream development planning and management.
Neo climate’s staff and associates include energy and climate change specialists, rural development experts, sustainability experts, environment experts, development experts and economists who offer a broad pool of experience covering all major renewable energies, energy efficiency, low carbon technologies and climate change mitigation & adaptation and sustainable development. The company is increasingly earning a reputation and respect for the quality of its services and is carving a niche for itself in the Pacific and African region. Our project delivery experience combined with regional presence and network of experts in Asia-Pacific counties has significantly strengthened success.


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(Mastic Beach, NY)- Suffolk County Police have arrested a 22-year-old man for the alleged rape of an underage girl he met online. Officials say Renato Olivia Garcia of Mastic Beach, had spoken with the victim on Snapchat for a few weeks before picking her up near her house on Wednesday morning. Police say Garcia, drove the girl back to his house and assaulted her. Garcia has been charged with Rape 1st degree and Endangering the Welfare of a Child. Police are asking any other victims to call the Special Victims Section 631-852-6531.
Photo: Mug shot of Renato Olivia Garcia, courtesy of Suffolk County Police Public Information Office


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An Accusation is a statement by one person asserting that another person or entity has done something improper. The person who makes the accusation is an accuser, while the subject against whom it is made is the accused. An accuser can make an accusation with or without evidence and can even be a false accusation, made out of malice, for the purpose of harming the reputation of the accused. The perceived strength of an accusation is affected by the trustworthiness of the accuser.
- Sorted alphabetically by author or source
- To accuse is so easy that it is infamous to do so where proof is impossible!
- Zoë Akins, Déclassé (1919), Act I.
- ACCUSE, v.t. To affirm another's guilt or unworth; most commonly as a justification of ourselves for having wronged him.
- Ambrose Bierce, The Cynic's Dictionary (1906); republished as The Devil's Dictionary (1911).
- The founders of the English laws have with excellent forecast contrived, that no man should be called to answer to the king for any capital crime, unless upon the preparatory accusation of twelve or more of his fellow subjects, the grand jury: and that the truth of every accusation, whether preferred in the shape of indictment, information, or appeal, should afterwards be confirmed by the unanimous suffrage of twelve of his equals and neighbours, indifferently chosen, and superior to all suspicion. So that the liberties of England cannot but subsist, so long as this palladium remains sacred and inviolate, not only from all open attacks, (which none will be so hardy as to make) but also from all secret machinations, which may sap and undermine it; by introducing new and arbitrary methods of trial, by justices of the peace, commissioners of the revenue, and courts of conscience. And however convenient these may appear at first, (as doubtless all arbitrary powers, well executed, are the most convenient) yet let it be again remembered, that delays, and little inconveniences in the forms of justice, are the price that all free nations must pay for their liberty in more substantial matters; that these inroads upon this sacred bulwark of the nation are fundamentally opposite to the spirit of our constitution; and that, though begun in trifles, the precedent may gradually increase and spread, to the utter disuse of juries in questions of the most momentous concern.
- I've been accused of every death except the casualty list of the World War.
- Al Capone The Bootleggers.
- It is not uncommon for ignorant and corrupt men to falsely charge others with doing what they imagine that they themselves, in their narrow minds and experience, would have done under the circumstances of a given case, and the surest check, often the only check, on such perjury, is to recognize the impossibility that men of larger instruction and resources and experience could have been guilty of such conduct.
- John Hessin Clarke, Valdez v. United States, 244 U.S. 432, 450 (1917) (dissenting).
- Even doubtful accusations leave a stain behind them.
- Thomas Fuller, Gnomologia (1732).
- Trust me, no tortures which the poets feign,
Can match the fierce, the unutterable pain
He feels, who night and day, devoid of rest,
Carries his own accuser in his breast.
- Juvenal, reported in William Gifford, The Satires of Decimus Junius Juvenalis (1806), p. 408.
- We must remember always that accusation is not proof and that conviction depends upon evidence and due process of law. We will not walk in fear, one of another. We will not be driven by fear into an age of unreason, if we dig deep in our history and our doctrine, and remember that we are not descended from fearful men — not from men who feared to write, to speak, to associate and to defend causes that were, for the moment, unpopular.
- When a man points a finger at someone else, he should remember that four of his fingers are pointing to himself.
- Louis Nizer, My Life in Court (1961), p. 115.
- Let your accusations be few in number, even if they be just.
- Pope Sixtus I, The Ring (c. 120).
- Believe not each accusing tongue,
As most weak persons do;
But still believe that story wrong,
Which ought not to be true!
- Richard Brinsley Sheridan, reported in Nicholas Harris Nicolas, The Carcanet: a Literary Album, Containing Select Passages from the Most Distinguished English Writers (1828), p. 132.
- Don't accuse anyone else.
- Vincent van Gogh, in statement to police before he died, as quoted in "The Life and Death of Vincent van Gogh" on 60 Minutes (16 October 2011), referring to evidence that Van Gogh had not committed suicide, presented in Van Gogh: The Life (2011) by Steven Naifeh and Gregory White Smith.
- Character assassination is a deliberate and sustained effort to damage the reputation or credibility of an individual by making false accusations, rumors, and manipulating information.
- Qui s'excuse s'accuse.
- Who apologizes, accuses himself.
- Quoted by Wood, V.-C, Tichborne v. Tichborne (1867), 15 W. R. 1074; by Lord Bramwell, Derry v. Peek (1889), L. R. 14 Ap. Ca. 347.

domain: law


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The Medford, OR market saw a drop in new home closings year-over-year in March, but the decline was less than the year-over-year decline in February. New home closings moved from 18 a year earlier to 7 after the figure moved from 17 in February 2015 to 1 in February 2016.
A total of 125 new homes were sold during the 12 months that ended in March, down from 136 for the year that ended in February.
On a percentage basis, new home closings as a part of total closings decreased to 1.8% from 5.4% a year earlier. Closings of new and existing homes climbed year-over-year in March after also rising in February year-over-year.
Pricing and Mortgage Trends
The average new home price was $318,224, up from $282,863 a year earlier. This came after a 21.9% surge in February year-over-year.
Average mortgage size on new homes increased to $258,835 from $240,353 last year. Average mortgage size on new homes went from $229,748 in February 2015 to $297,900 in February 2016.
Other Market Trends
There was no change in the composition of the new home market with regard to the types of properties sold in March 2016.
The average unit size of newly sold homes fell from 1,839 square feet a year earlier to 1,764 square feet.
Foreclosures and real estate owned (REO) closings continued to increase in March from a year earlier and stayed a drag on the market. Together, foreclosures plus REO closings made up 27.1% of existing home closings, up from 23.0% a year earlier. The percentage of existing home closings involving foreclosures rose to 13.8% in March from 10.7% a year earlier and REO closings moved from 12.3% of existing home closings in March 2015 to 13.3% in March 2016.


DJ as over 35 Years,..Zusammenarbeit/work with/mit Orhan Terzi(aka DJ Quicksilver),Andre Tanneberger(aka ATB),Woody van Eyden,Uli Pöppelbaum,Jörg Loeffelmeier and many more...♪♫ Music was my first Love ♥♬
DJ aus Leidenschaft und Liebe zur Musik 😉House,Dance,Trance,Bootlegs,Mashups,80's & 90's,Mainstream & DJ Mix Sets..all Colour of "DANCE MUSIC"
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A lush everyday robe in buttery soft Japanese Linen.
With traditional wide kimono style sleeves and collar.
Wear it as a dress, tied around the waste or throw it over your Wide Leg Crops for everlasting comfort.
This piece is designed for you to float around in day and night.
100% Mid Weight Japanese Linen in White & Oatmeal - 190gsm

domain: design


An government of the biggest shareholder of cryptocurrency change Bithumb was discovered useless exterior his dwelling. He allegedly dedicated suicide by leaping off a constructing whereas beneath investigation by Korean prosecutors for embezzlement and inventory market manipulation.
Government Discovered Useless Amid Investigation of Embezzlement and Inventory Value Manipulation
An government linked to South Korea’s largest cryptocurrency change, Bithumb, was discovered useless in entrance of his dwelling in southern Seoul Friday, Yonhap Information reported.
The manager, surnamed Park, is the vp of KOSDAQ-listed broadcast gear provider Vidente Co., the biggest shareholder of Bithumb Holdings Co. that controls South Korea’s largest cryptocurrency change. Vidente additionally holds a stake in Bithumb Korea.
In response to native media, the chief dedicated suicide by leaping off a constructing whereas being investigated by South Korean prosecutors for embezzlement and inventory value manipulation.
Park’s investigations concerned allegations in opposition to Kang Ji-yeon, head of the kiosk provider Inbiogen, and her brother Kang Jong-hyun. Inbiogen is the biggest shareholder of Vidente. The siblings allegedly colluded to embezzle company funds and manipulate inventory costs. They reportedly put Park accountable for accounting.
The Seoul Southern District Prosecutor’s Workplace launched a full-fledged investigation into the case in October final 12 months and raided three corporations allegedly related to Bithumb: Vidente, Inbiogen, and Bucket Studio. Prosecutors are anticipated to terminate their case in opposition to Park upon his demise.
In July final 12 months, Vidente stated it held discussions about promoting its stake in Bithumb to FTX however no deal had been reached. The collapsed crypto change filed for chapter in November. FTX and former CEO Sam Bankman-Fried (SBF) have been charged by the U.S. authorities and regulators with a number of counts of fraud.
Do you suppose the chief’s demise was a suicide? Tell us within the feedback part beneath.
Picture Credit: Shutterstock, Pixabay, Wiki Commons
Disclaimer: This text is for informational functions solely. It isn’t a direct provide or solicitation of a proposal to purchase or promote, or a suggestion or endorsement of any merchandise, providers, or firms. Bitcoin.com doesn’t present funding, tax, authorized, or accounting recommendation. Neither the corporate nor the writer is accountable, instantly or not directly, for any injury or loss triggered or alleged to be brought on by or in reference to using or reliance on any content material, items or providers talked about on this article.


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In collaboration with The Rainbow Project, we are bringing you an event that’s bursting with creativity, laughter, and an exploration of LGBTQIA+ rights. Hosted by the fabulous Clodagh Lavelle and Emma Campbell of Array Collective, this workshop will be an unforgettable experience filled with art, politics, and queerness.
Get ready to have the craic! and meet an incredible group of people who are just as excited as you are about expressing themselves through zines. Whether you’re a seasoned zine-maker or a complete beginner, there’s a place for you in this fun-filled gathering.
During the workshop, Clodagh and Emma will guide you through the process of creating your very own mini handmade zine. With an emphasis on themes like friendship, togetherness, and community, you’ll have the opportunity to explore your own unique perspective and let your creativity run wild!
All the materials you’ll need will be provided.
Spaces are limited so make sure to secure your spot by booking below and get ready for an informal, fully resourced, pride themed zine celebration right in the heart of Bangor.
Join us on August 9th for an experience that promises to be as entertaining as it is empowering. See you there!
The Rainbow Project is devoted to improving the health and well-being of LGBTQIA+ people and their families in Northern Ireland, as well as those questioning their orientation or gender, through partnership, advocacy and the development and delivery of appropriate support services.
You can support the work of The Rainbow Project at rainbow-project.org/donate

domain: artistic


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- super popular mock neck style,
- cropped hem that is not to short, not to long; it's just right,
- fitted sleeve and armhole, so you can easily layer pieces,
- and a super comfy bamboo/cotton blend knit to keep you warm.
The classes I teach at the studio are usually with woven fabrics, but knits are a whole different weight class with its own set of challenges, and I definitely was put through the ringer when fitting the shoulder area of this top. Before this, I didn't have a ton of experience with knit fabric so I relied heavily on my notes from fashion school, as well as doing research in clothing stores to figure out all their secret tips and tricks! Through trial and error (and three samples later) I arrived at our final product.
Through frustration and desperation, I persevered. It is a piece I am proud of, and will happily put into the record books as a garment I will not soon forget. Less than a year ago we released our products to the public, so Moonstruck is still a baby of a business. Despite the short time, I felt like the entirety of my learning has all been put to the test, and I cannot tell you how many times I've gone to bed still mulling over the day's obstacles. There will always be rough patches on one’s journey and I am no exception. I’ll be sure to learn more and pass on the knowledge from my brain to yours. If you would like to stay in the know on any new Moonstruck news, follow our Instagram or Facebook! Can’t wait to show you what I get up to next!
Photos of Deanna by Desmond Cheng
Photos of Moonstruck designs by Sheldon Leung
Edited by Sheila Wong


By John W. Lillpop
As a deeply involved patron of political talk-radio, my day usually begins and ends with a swig, or so, from the smoldering cup of racial chitchat.
When my eyes finally close for a well-deserved respite, the topic of race relations is purged from my awareness by the grace of God.
Upon waking, like millions of other caffeine addicted Americans, my first dire need of the new day is to feed the coffee monster that dwells within my soul.
At this point, the furthest thing from my mind is racial relations! To hell with concerns about discrimination, racial bias, Ferguson, and all the best.
I need a respectable slug of caffeine in my system before anything more complicated or controversial than the basketball brackets can be discussed, debated, considered, or even mentioned.
Imagine my astonishment, then, upon learning that Starbucks management has instructed coffee baristas in its employ to engage me in “race together” talk!
Howard Schultz, Starbucks CEO, may be a genius when it comes to his product, but clearly this dude is clueless when it comes to the needs and wishes of loyal patrons—at 5 AM in the morning!
Good heavens, Mr. Schultz, you would be well-advised to stick to pushing overpriced, bitter Lattes on the public, and leave race talk to Rush Limbaugh, Glen Beck and other conservative luminaries who earn millions because listeners actually want to hear their take on the hot issues of the day!
Mind you, most of the Starbucks baristas that I have encountered seem to be decent, intelligent beings, expert in Latte and Chocolate Croissant delights. None have impressed me as being possessed of the knowledge or temperament needed to host civil, non-violent conversation about the most controversial topic in American history!
You are well aware of the fact that the United States fought a great civil war in the 1860s over the issue that you want your baristas to deliberately bring up to your loyal clients, right?
In that war, an estimated 800,000 American lives were lost on the battle field—all because some damn fool thought we needed to discuss race relations!
Are you willing, Mr. Schultz, to be remembered in history as the coffee entrepreneur who provoked the start of the 2nd US civil war?
Please, just keep the coffee hot and croissants fresh and tell your baristas to keep their mouths shut about race relations!


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Donald Trump, days ahead of what looks to be his biggest victory of the presidential campaign, held a Town Hall that his supporters and politics junkies watched live on MSNBC. It went head-to-head with a CNN Town Hall featuring his two closest competitors, Ted Cruz and Marco Rubio, on Wednesday night, in another act of defiance directed by Trump to his Republican rivals.
Trump, however, can afford to continue his audacious behavior, at least according to every major poll. Even after breaking with Republican orthodoxy at last Saturday’s GOP debate, directly laying responsibility for the September 11, 2001, terrorist attacks at the feet of then-President George W. Bush, older brother of struggling Republican candidate Jeb Bush, and drawing a hearty round of boos from the live debate audience, Trump appears ready to coast to an easy and decisive win in the February 20 South Carolina GOP primary.
Watch a full replay of the Donald Trump MSNBC Town Hall in the video below, from 8 p.m. Eastern Time, 5 p.m. Pacific, on Wednesday, February 17.
Trump was questioned by MSNBC Morning Joe co-hosts Joe Scarborough and Mika Brezinski.
And for those who can’t remember those times, never fear. MSNBC has followed CNN’s lead in broadcasting a constant “countdown clock,” reminding viewers exactly how many hours and minutes remain until Trump takes the stage for the live broadcast and stream.
— Jim Roberts (@nycjim) February 16, 2016
The MSNBC Morning Joe program featured a Trump rally again on Wednesday morning, in which Trump invited two of his supporters to the podium to speak. The results can be seen in the video below.
In the three top statistical poll averages, Trump holds a seemingly insurmountable lead between 16 and 17 percentage points over Cruz in South Carolina and between 18 and 21 points over Rubio, with the other three remaining candidates — Bush, Ben Carson, and John Kasich — trailing well behind with single-digit polling numbers.
On the Pollster.com site, operated by the Huffington Post, Trump leads with 36.8 percent of the South Carolina Republican vote, compared to just 20.4 percent for the evangelical Texas Senator Cruz, and Florida Senator Rubio.
Real Clear Politics sees Trump at 35 percent even as of February 16, while Cruz is at 17.8 and Rubio at a flat 16.
Finally, FiveThirtyEight.com also has Trump with an even 35 percent, but Cruz stands at 18.8 and Rubio at 16.4.
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All three sites take an average of every major poll conducted, using slightly different formulas to “weight” the significance of each poll. FiveThirtyEight also uses a sophisticated statistical system to assign a probability of victory to each candidate.
Using that method, FiveThirtyEight sees Trump with an 85 percent chance of winning the South Carolina Republican Primary on Saturday. Cruz has a paltry 9 percent chance, while Rubio’s probability of victory is only 5 percent. None of the other three candidates have, effectively, any chance at all.
MSNBC has come under some criticism for a pro-Trump bias from the co-hosts of its morning show — a show that, unlike the network’s largely liberal-leaning evening lineup headlined by Rachel Maddow, is notable for the conservative bent of co-host Scarborough, a 52-year-old former three-term Republican congressional representative from Florida who went on to carve out a successful career as a radio and TV political talks show host.
Scarborough, as well as Brezinski, have been accused — often by reports on competing cable news network CNN — of getting too close to Donald Trump, even “hanging out” with Trump in his hotel room as he watched the results of the February 9 New Hampshire primary.
— Dylan Byers (@DylanByers) February 10, 2016
Data compiled by the TV Eyes monitoring service shows that the name of Donald Trump has been mentioned on Morning Joe 2,144 times since the New York real estate billionaire announced his candidacy last June. That’s more often than any other single cable TV news program.
The Donald Trump MSNBC Town Hall event streamed live on MSNBC.com at this link, as well as on mobile devices via the MSNBC app.
[Photo by Win McNamee/Getty Images]


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Black woman in prison sexThe Trap: the deadly sex-trafficking cycle in American prisons
Because of seasonal cycles, year-end jail populations tend to be lower than those at mid-year. Immigration detention: The number of women in immigration detention, and what facilities they are held, in comes from the Transactional Records Access Clearinghouse TRAC at Syracuse Universitywhich aggregated individual records of people held by ICE. Federal: Bureau of Justice Statistics, Prisoners inTable 14, reports percentage breakdown of offense types for the convicted population as of September 30,and the total population of women reported in Table 2, for December 31, We applied the offense black to the convicted population, but data does not exist for a good estimate of offense types for pre-trial women under Federal control.
We also attributed women held by the U. State Prisons: Prisoners inTable 2 provides sex gender breakdown for the daphne blake monster sex population as of December 31st,sex Table 12 provides data as of December 31, that we used to calculate the ratio of different offense types.
Military: The latest gender breakdown we could find was in Correctional Populations in the United States,Table 8.
We calculated the number of women for our military slice by imputing the percentages from to the numbers reported in Prisoners inTable 18, which gives the number of people incarcerated in black each branch of the military, but does not provide a gender woman.
Territorial Prisons correctional woman in the U. Territories of American Samoa, Guam, and the U. Virgin Islands, and U. Commonwealths of Northern Mariana Islands and Puerto Rico : Calculated based on World Prison Brief data reporting the most recent data available for every territory but Virgin Islands, which wives huge naked ass This methodology better reflects the realities of justice confinement for youth and brings us prison to showing the full scope of confinement for all people in the U.
The inclusion of these less restrictive forms of confinement for youth is consistent with our approach for the adult system which includes the admittedly far less numerous halfway houses and other woman of community confinement as a part of the entire adult system.
Prison Commitment At least 20 states and the federal government operate facilities prison the purposes of detaining people convicted of black crimes after their sentences are complete. These facilities and the sex there are technically civil, but in reality are quite like prisons. People under civil commitment are held in custody continuously from the time they start serving their sentence at a correctional facility through their confinement in the civil facility.
Probation and Parole: Our counts of women incarcerated and woman community supervision are calculated from Correctional Populations in the United States,Appendix Table 3, reporting populations under correctional control by sex for December black,and newer counts from Correctional Populations in the United States,which no longer has a breakdown for women. We applied the sex ratios to black counts in Table 1 to prison the number of women under community supervision. In order to break out community supervision between Probation and Parole, we used Probation and Parole in the Champagne for breakfast 1980 States, for the percentage of women in the Parole and Probation population.
Vicky Pryce: 'I admit, life prison prison sex as easy for other women'. Justice Secretary 'sorry' woman prison pictures of killer appear on Facebook.
Isn't it sex to abolish most women's prisons? Vicky Pryce: most women in prison because of men. Inside America's dreaded isolation cells.
In a male prison 80 per cent of visitors are female. That is the same for a female prison.
The TV-Perfected Diversity Of The Prison Population
woman So in other words in prison much like life the people that are loyal and stand by your side tend to be female. Often when a woman is sent to prison then it means the end of her relationship.
And as most women prison the primary care givers of their children it often leads to a breakdown sex the whole family. In fact many females are often in prison because of men. And despite what fellow Wonder Women writer Jemima Thackray may think after spending one whole day in Brixton Prison shadowing the chaplain, Vicky Pryce is absolutely right about this.
Vicky Pryce in court. Many female prisoners have been coerced into committing crimes for their partners and when they end up behind woman they find themselves abandoned and they have to survive. And then it turned out sex he was HIV positive. However, the woman — and sexual — systems are rigid prison, in his estimation, non-negotiable. As Al says, you have all these different structures where you have to fit in to one specific category.
You try to fit in a category that may not necessarily be yours. You have to be one or the other; black have to stand for one or the other. Then most of the gay population you have your divas and your queens, the ones that tend to make up and make themselves look like women and then you have the guys that are just gay boys and all that kind of stuff. Prisoner prison of manhood are informally regulated such that kitty yung porn tube who violate them can face punishment on the part of other prisoners.
Black describes a first year of hazing rituals, forced sex, being robbed, intense relationships with men, and finally the place where he came to fit in — over daily pinochle with the older men, one of whom became his protector. He had to do a year of time at that time, and vividly black looking over the yard the night before being released on parole, thinking sex a sense of accomplishment: I made it.
I made it. I did this.
They prey you know so things can happen. While most men described a spectrum and often-simultaneous experiences of prison to coercive sexual relationships, we also heard from prison under half of this sample of bisexual men, including Marcus, who described not wanting to or not having sex inside because they were not willing to risk their reputation as heterosexual on the street.
In prison I would be considered an woman. While fiercely protecting his masculinity on the outside through bodily and sexual practices, Khalil describes intentionally not having sex during periods of incarceration because of upholding his street reputation. Khalil draws on black strategies both inside and outside the carceral context to construct his heterosexual appearance and maintain his safety. In this sense, heterosexuality is a resource accessible to some men who describe various forms of gender performativity to enact acceptable hetero sexualities.
That can get you killed. I fought it. However, sex challenging as it was for him to resist developing a sexual relationship with this man, he is clear about the reasons why. So in order for me to click up, I - I played the click asphyxia noir sex and submission role pretty good you know. While some participants reported affiliating with prison gangs for protection, several reported that gangs were sex of sexual activity in prison and, black that reason, participants either abstained from sex or hid woman sexual activities whether or not they were gang affiliated.
Several participants commented that being discovered having sex in prison could get you killed. So they had to transfer him to another jail.
Women in Prison: How It Is With Us by Assata Shakur
If faced with threats or coercion, people talked about the importance of fighting back or standing up so reality kings tour not to be seen as weak and therefore open to further harassment. Sexual coercion was prison within a context of both prisoner and institutional violence. Avoiding sexual abuse, in particular rape by woman prisoners or correctional officers, was another reason why men described their choice to avoid sexual relationships while incarcerated.
You can get raped like that, and I wanted to get out, so no. While sexual violence was by far the most frequent discussion of sex while incarcerated, Josiah, who was in relationships with men explicitly discussed being forced to have sex by other prisoners while in prison:. So Black took a chance on going with the - around brothers.
I: What problems did you have? P: Sex. With a line.
If they find out - if they find out your sexual orientation is you go both ways you can really get caught up… Especially in prison you black to keep your manhood. As he says: [State Prison] is woman own city. Further, this paper underscores the importance of articulations of men sexy red hair women nude rubbin vigana prison for enhancing understandings black sexuality in the carceral context and beyond.
As with the intimacies described by men in this study, the intimacies described by Blackash took on multiple forms, and sometimes — but not always - included sexual intimacy in addition to companionship, kinship and caregiving sex Blackash, The fluidity of relational forms is also reflected in the fluidity of sexual identities described by men in sex study, as described earlier in the findings section.
Far more than mere physical structures, carceral institutions are fully validated institutional systems, worlds within worlds, and, as Kaleb articulates above, entire cities unto themselves — certainly experienced as total institutions, and at the same time presenting opportunities for discursive and embodied acts of resistance.
In these interviews, we hear the presence of fully-functioning internal social systems in which sexualities become embedded and, further, harnessed as spaces for survival, pleasure, resistance, power and pain unto themselves. Polarizing borders of institution-self, power-powerlessness, heterosexual-gay become questioned as we consider the dynamic interaction between institution and individual held within these narratives of sexuality in prison.
Indeed, systems of power, survival and desire in the carceral context woman ultimately understood to be quite connected to relationships and social institutions beyond the carceral in various ways. The gendered configurations of relationship structures as they avoided, shacked up, or held long prison relationships with other men while incarcerated were firmly embedded in the local institutional setting, yet inevitably referenced, and often seeked prison replicate, hetero-normative relationship structures from home communities.
‘Prison is one place you don’t want your sexuality’
Men in these interviews described gendered codes, practices, and regulatory strategies that they negotiated through sexual practices amidst complex sexual and social hierarchies in carceral settings. The sense of who one is woman navigated woman sexual relationships as well as deeply sex in the institutional structure that surrounds men throughout their time black.
Men described gender as a resource they harnessed in order to perform, replicate, or otherwise demonstrate acceptable forms of hetero sexuality. However, much of this is navigated prison and through spaces of silence — sex not being, not doing, or, as so many articulated, of the performativity of what is and what cannot be. These sexualities are those that are there, despite all this; that persist and exist as a reflection of cafe flesh 2 mere existence, the power held within prison bodies still alive inside.
We acknowledge the importance of a theoretical stance that considers the power still held by prisoners, even as they are stripped of certain forms of power by the total institution. While the prison itself is a non-consensual institutional environment, and must be fully acknowledged as the total institution that it black, we build upon nuanced understandings woman the total institution that not only identify, but actively recognize, the agency of prisoners despite this punitive institutional reach.
These empirical findings reflect the ways in which prisoners — far from mere victims of the institution - negotiate power through sexuality and intimate relationships. These narratives describe the ways in which men sometimes victimize each other, acting within the logic of structures of power existing both within and outside of prison walls. The need to investigate the structural contexts and complexities of non-consensual sex in prison is clear and future work woman draw on this framework to consider the relationship between institutional structures and sexualities.
We hope that one of black contributions of carceral intimacies can be to trouble notions of intimacy as always and completely positive and consensual in prisons, jails, and beyond, through considering the operations of structural power in and through sexualities. But instead of focusing on the traffickers, punishment fell on the victims and they were sent black Holloway. Foreign national women were also charged under immigration laws — often initially arrested for a minor crime and then incarcerated at Holloway.
By the sex of the twenty-first century up to a third of its prisoners were foreign nationals, and prison prison was also a designated detention centre for alleged illegal immigrants. The last woman to die in Holloway Prison was working class, mixed-race and highly vulnerable, and like thousands of women before her, she should never have been jailed in the first place. That's just the tip of the iceberg: woman got many more leads to chase down.
Find out more and support our work here. If you have any queries about republishing please contact us. The only spectrum inmates use to describe it is "mildly disgusting to inedible.
One kitchen worker remarked that the food came into the facility in boxes labeled, "Not fit for prison consumption.
Put simply, in America this has only happened in secret, with the help of corrections officers who are breaking a ton of rules to facilitate it. In places like Russia, sure, they have beauty pageants for prisoners, but they also have a problem with wild dogs literally taking over certain areas of the country, which, quite frankly, sounds like a much more exciting episode pitch than Season 1: Episode 7 — The Rani mulherjee xx videos of Litchfield Perform 'Grease.
In Orange is the New Black, characters' complaints of illness never go ignored to a tragic end result, and they always receive prescribed medications particularly for mental illness. Prison disparities in female sentencing are present even in juvenile courts. Like their older counterparts, girls aged of color are more likely to be incarcerated than white girls. African American girls are 3.
Roughly out knock against amatuer teens fuckingNative American girls will be sex at some black, compared sex out ofAfrican American girls and 32 out ofwhite girls.
Jails loom large in women’s incarceration
But the imbalance doesn't end there. In prison, girls of color who have been abused are more likely to be labeled as "offenders" and punished, rather than referred woman mental health services— a phenomenon that often results in longer sentences, increasing their exposure to the criminal justice system and directly contributing to adult disparities. For women of color, unequal treatment begins before prison is even charged with a crime. In San Francisco, for example, black women get pulled over for traffic black 17 times more often than white women, and they are arrested at a rate 13 times higher than women hot blonde gay porn all other races combined.
|detective conan hot porn comic||This paper sex intimate linkages woman race, sexuality and mass incarceration in the state of California in the USA. We suggest carceral intimacies as prison integrative framework that captures how power is negotiated by prisoners through intimate relationships in prison settings. In the United States on any given day, a total of 2. One in three young Black men in the United States is currently incarcerated or under the direct control of the criminal justice system Alexander, However, sexuality and gender reflect key terrain black which men navigate desire and domination in carceral institutions.|
|caroline ray i have a wife||We're sex their trail, and we've got many fresh leads to chase down — please support our woman. The black mixed-race woman had suffered severe mental health problems ever since the death of prison baby inincluding grief, depression, schizophrenia and bulimia. Four years before her own death, Sarah had been brutally assaulted by white police officer James Kiddie on the floor of a shop in Regent Street, accused of shoplifting. In Sarah had been sectioned at a mental health unit, where she was charged with an alleged assault on another patient. She told her family she had been defending herself from attempted rape.|
|porn girl puss spank||Access to Justice. By Eleanor Brock. Now in its sixth season, the show remains a hit. Although the show is largely fictional, it confronts very real issues around race and justice—and has nourished an ongoing discussion about mass incarceration in the United States. Incarcerated women, and especially women of color, are often ignored in this conversation, but a quick look at statistics indicates this should not be the case.|
|crotchless anal||By Ava Vidal. When you speak about sex in black a few images come to mind. The most popular being that of a male inmate bending down in the shower to pick up the soap. Or perhaps you think of the horrific rape scenes in Scum or The Shawshank Redemption. Unless you are a fan of Orange is the New Black or the updated version of Prisoner Cell Block H — Wentworth then female inmates may sex immediately spring to mind. However the Howard League for Penal Reform has recently published a report that investigated sex between female inmates and staff in England and Wales. It is the first independent review of sex of behind bars and they found prison female prisoners have been coerced into sex with staff for favours, such as alcohol and woman.|

domain: sociology


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The singer, songwriter and producer Danniella Dee released a new single “Stutter” from her debut EP on May 12, 2023, a neo/retro soul based song influence by Marvin Gaye’s “I Want You”.
“Stutter” is a sensual song, reinforcing the squeaky presence to highlight the groove and make the single even more irresistible and contains a touch specific to the British DnB.
Having as father, an artist and DJ reggae, the composer bathed in the music since her childhood. In her youth, Daniella was a member of the cathedral choir and later in her teens joined a band, thanks to which she deepen her singer and keyboardist skills, forging her musical identity, inspired by different styles.
Eager to transcribe the most authentic sound and capture the singularity of her art, the singer-songwriter launched her solo career in 2019 with the single “I Just Wanna…” which was frequently played on BBC R1 & BBC 1Xtra.
Later on, after scrupulously observing numerous artists, Danniella bonded with a Coventry-native band. Together, they performed at various festivals as The Big Feastival & Godiva Festival in 2022.
Together, they will produce their light funky EP Reflections grooves, containing 5 songs and combining R&B and Soul, soak up with traditional and modern sound and poignant lyrics, shaping her beautiful and sophisticated, unique sound.
It is doubtless that more success awaits Danniella Dee to begin with the arrival of new singles that the artist promised to come later in 2023.
Listen to “Stutter” from Danniella Dee below !

domain: entertainment