Long-time translation and rotational Brownian motion in two dimensions

The long-time translational and rotational motion of a Brownian particle in two dimensions is studied on the basis of the fluctuation-dissipation theorem and linearized hydrodynamics. The long-time motion follows from the low frequency behavior of the mobility matrix. The coefficient of the long-time tail for the translational motion turns out to be independent of shape and size of the body, in agreement with mode-coupling theory. For rotational Brownian motion the coefficient of the long-time tail is found to depend on the shape of the body. This result is in conflict with a recent prediction from mode-coupling theory, and indicates that the mode-coupling calculation should be revised.This article is dedicated in friendship to Prof. Matthieu Ernst on the occasion of his 60th birthday.     

Modulation of structure and dynamics of water under alternating electric field and the role of hydrogen bonding

Using Molecular Dynamics simulations, we investigate the effect of alternating (AC) electric field on static and dynamic properties of water. The central question we address is how hydrogen bonds respond to perpetual field-induced dipole reorientations. We assess structural perturbations of water network and changes of hydrogen bond dynamics in a range of alternating electric field strengths and frequencies using a non-polarisable water model, SPC/E, and two distinct polarisable models: SWM4-NDP and BK3. We confirm that AC field causes only moderate structural perturbations. Dynamic properties, including the rates of bond breaking, switching of hydrogen-bonding partners, and diffusion, accelerate with the strength of AC fields. All models reveal a nonmonotonic frequency dependence with fastest dynamics at frequencies around 200?GHz where the period of the field oscillation is commensurate with the average time it takes a typical proton to switch from one acceptor to another. Higher frequencies result in smaller amplitudes of angle oscillations and in reduced probability to complete the switch to another acceptor before the field reversal restores the original configuration. As frequency increases, these effects gradually weaken the influence of the field on the kinetics of hydrogen bonding and the associated rates of translational and rotational diffusion in water.     

Ab initio molecular dynamics in a finite homogeneous electric field

We treat homogeneous electric fields within density functional calculations with periodic boundary conditions. A nonlocal energy functional depending on the applied field is used within an ab initio molecular dynamics scheme. The reliability of the method is demonstrated in the case of bulk MgO for the Born effective charges, and the high- and low-frequency dielectric constants. We evaluate the static dielectric constant by performing a damped molecular dynamics in an electric field and avoiding the calculation of the dynamical matrix. Application of this method to vitreous silica shows good agreement with experiment and illustrates its potential for systems of large size.     

导电炭黑／硅橡胶复合材料介电常数与压应力的关系

以填充了导电炭黑的导电硅橡胶和绝缘硅橡胶为主体材料,分别采用质量比1：9;3：7配比进行混炼、制备,研究了压力下复合材料的介电特性．实验结果表明：在恒压下样品介电常数实部ε’随外加电场频率的增加而减小;在恒压、同频率时导电硅胶含量大的样品介电常数大;在同频率时,增大压应力,样品介电常数实部ε’都会增加,导电硅胶含量大,增幅大．     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

FDTD analysis of 12-fold photonic quasi-crystal central pattern localized states

The TM bandgap features of the 2D 12-fold quasi-crystal are examined based on the width of the dielectric strip and pattern central symmetry location within the quasi-crystal. Results indicate that the bandgap properties observed for a particular fill factor is independent of the rotational symmetry center when the dielectric strip is wide, and still observable when the strip width is considerably reduced, confirming the general belief that the bandgap generating properties of the quasi-crystal are a local dielectric effect for the lower frequency band. Thin strips are shown to posses defect states in the bandgap region of the thicker equivalent strips, defect states analogous to intentionally introduced defect states of translational symmetric photonic crystals. We explore the mode profiles of the defect state when the defect is coincidental with the rotational symmetry central pivot point of the quasi-crystal pattern. In addition we show that the rotational center “defect” may be used to enhance the optical guidance of light around a 90° bend in a waveguide implanted in the quasi-crystal.     

Brownian dynamics simulation of electrostatically interacting proteins

Brownian dynamics simulation software has been developed to study the dynamics of proteins as a whole in solution. The proteins were modelled as spheres with point dipoles embedded in the centre of sphere. A set of Brownian dynamics simulations at different values of the dipole moments, protein concentration and translational diffusion coefficient was performed to investigate the influence of interprotein electrostatic interactions on dynamic protein behaviour in solution. It was shown that these interactions led to the slowing down of protein rotation and a complex non-exponential shape of the rotational correlation function. Analysis of the correlation functions was performed within the frame of the model of electrostatic interprotein interactions advanced earlier on the basis of NMR and dielectric spectroscopy data. This model assumes that, due to electrostatic interactions, protein Brownian rotation becomes anisotropic. The lifetime of this anisotropy is controlled mainly by translational diffusion of proteins. Thus, the correlation function can be decomposed into two components corresponding to anisotropic Brownian rotation and an isotropic motion of an external electric field vector produced by the surrounding proteins.     

Non-inertial electromagnetic effects in matter. Gyromagnetic effect

Non-inertial electromagnetic effects in matter, i.e. electromagnetic fields created by a non-inertial motion of material bodies, are discussed within the Drude–Lorentz (plasma) model of matter polarization. It is shown that an oscillatory motion of a point-like body, or wavelike motion in an extended body gives rise to electromagnetic fields with the same frequency as the frequency of the original motion, while shock-like movements of a point-like body generate electromagnetic fields with the characteristic (atomic scale) frequency of the bodies. The polarization of a rigid body induced by rotations is discussed in various circumstances. A uniform rotation produces a static electric field in a dielectric and a stationary current (and a static magnetic field) in a conductor. The latter corresponds to the gyromagnetic effect (while the former may be called the gyroelectric effect). Both fields are computed for a sphere and the gyromagnetic coefficient is derived. A non-uniform rotation induces emission of electromagnetic fields. The equations of motion for the polarization are linearized for slight non-uniformities of the angular velocity and solved both for a dielectric and a conducting sphere. The electromagnetic field emitted by a dielectric spherically shaped body in (a slightly) non-uniform rotation has the characteristic (atomic scale) frequency of the body (slightly shifted by the uniform part of the angular frequency). In the same conditions, a conducting sphere emits an electromagnetic field whose frequency is double the uniform part of the angular frequency.     

Electric-field-induced chirality flipping in smectic liquid crystals: the role of anisotropic viscosity

We demonstrate the homogeneous and permanent reversal of the chirality of a condensed phase by an applied electric field. Tilted chiral smectic layers exhibit a coupled polarization density and molecular orientation fields which reorient about the layer normal as couple of fixed handedness in response to small applied electric fields. Experiments on some bent-core smectics show that above a threshold field the induced rotation can occur instead about the molecular long axis and that, as a result, the handedness of the phase can be flipped. The effect is quantitatively described by a nonequilibrium dissipative model of chiral smectic dynamics with anisotropic rotational viscosities.     

Effective frequency-dependent anchoring coefficient and rotational viscosity of nematic liquid crystals

The effective rotational viscosity and polar anchoring coefficient of a nematic liquid crystal were determined using electro-optical response by changing the frequency of the electric field in the kilohertz range. Both quantities monotonically decreased with an increase in the frequency and converged to a certain value at several tens of kilohertz. The effective rotational viscosity changes more than the order of magnitude in experimental range. On the other hand, the effective value of anchoring coefficient changes several times. We tried to explain the trends with the effect of an electric field induced by the motion of ionic impurity in liquid crystal.     

Many-body hydrodynamic interactions in suspensions

We consider hydrodynamic interactions between N rigid bodies of arbitrary shape immersed in an incompressible fluid. We study the generalized mobility matrix relating the translational and rotational velocities and the symmetric force dipole moments to the forces, the torques and the strain of an incident flow field. We show that the elements of the mobility matrix may be obtained as matrix elements of an operator related to the friction kernel. This allows a multiple scattering expansion of the mobility matrix.     

Thermodielectric bistability in dual frequency nematic liquid crystal

We report on a thermodielectric bistability in dual frequency nematic liquid crystals (LCs) caused by the anisotropic nature of dielectric heating and director reorientation in an electric field. The bistability is a result of the positive feedback loop: director reorientation --> anisotropic dielectric heating --> dielectric anisotrophy --> director reorientation. We demonstrate both experimentally and theoretically that two states with different temperature and director orientation, namely, a cold planar state and a hot homeotropic state coexist in a LC cell for a certain frequency and amplitude range of the applied voltage.     

Debye's relaxation frequency: A poor man's approach

We present a simple approach to introduce Debye's relaxation frequency. Our model is based on a kinetic equation at the electrodes, describing the time variation of the ionic charge pushed at the limiting surfaces by the effective electric field. In a first approximation the surface region where the ions are confined is assumed of negligible thickness. We show that this approximation allows to define a frequency at which the effective resistance of the sample begins to decrease. This frequency coincides with Debye's relaxation frequency. An equivalent electric circuit describing the frequency dependence of the effective impedance of the cell, valid in this approximation, is presented. In a second approximation we discuss the influence of a perfectly dielectric surface layer on the relaxation frequency, where the electrolytic cell is described by means of a Maxwell-Wagner system. The equivalent electrical circuit is discussed.     

Force and torque on a sphere with electric dipole moment moving in a dielectric fluid in the presence of a uniform magnetic field

The torque exerted by a magnetic field on a sphere with permanent electric dipole moment moving steadily in a dielectric fluid is calculated to lowest order in the dipole moment. Hence the force exerted on a steadily rotating sphere with electric dipole moment is found by Onsager symmetry. The modification from the vacuum values of torque and force depends only on the slip parameter and the static dielectric constant of the fluid. It is suggested that for a macroscopic ferro electric sphere the calculated effects could be measured experimentally without great difficulty.     

Influence of the torsional vibration of the periodically attached perpendicular beam resonator on the flexural band of a Euler-Bernoulli beam

The bending and torsional vibration of the periodic perpendicular cantilever beam-mass resonators (PCBMR) is idealized as translational and rotational oscillators attached to the main beam. In this paper, the effect of that torsional vibration of the PCBMR on the dynamics of an infinitely long Euler-Bernoulli beam is evaluated. The band-structure is explored by implementing the transfer matrix method in conjunction with Bloch-Floquet's theorem. The combination of the translational and rotational oscillator modifies the relative position of the coupling coefficient in the transfer matrix, which plays a pivotal role in the band-gap formation. The flexural band-structure is highly sensitive to the torsional vibration while the radius of gyration of the tip mass is considerably higher than the length of the PCBMR. Ill-tuning leads to split and reduction of attenuation band to 50%; whereas, around 38% elongation of the attenuation band in the low frequency regime can be achieved by proper tuning.     

电介质表面纵向射频电场对次级电子倍增效应的影响

基于次级电子倍增动力学模型和次级电子发射曲线,运用蒙特卡罗方法模拟电介质表面具有纵向射频电场作用下的单边次级电子倍增现象,研究次级电子倍增的表面电场敏感曲线和时间演化图像. 以一个S波段射频介质窗为例,计算次级电子在其介质表面的沉积功率. 结果表明,纵向射频电场可能加剧电介质表面的次级电子倍增效应,易于导致介质片破裂,不利于高频能量传输. 关键词： 纵向射频场 次级电子倍增效应 蒙特卡罗方法 功率沉积     

Coupling of exciton states in superlattice and bulk GaAs optoelectronic modulators,studied by density matrix models and optical modulation spectroscopy

The dielectric function of GaAs/AlGaAs superlattices and bulk GaAs material are studied with density matrix models and modulation spectroscopy on optoelectronic modulator devices, showing the Coulomb enhanced Wannier–Stark effect and the Coulomb enhanced Franz–Keldysh effect, respectively. The models include the Coulomb interaction for the coupled excitonic states and an applied electric field. Transfer matrix models are used to calculate the reflection or transmission spectra of the devices. The dielectric function is modulated by the electric field over the active layer, by optical pumping of the p–i–n–i structure of the superlattice device and by electrical contacts for the bulk GaAs modulator device. In both material structures the exciton dissociates or polarizes due to the applied electric field, modulating the dielectric function and reflected or transmitted light.     

Influence of an external electric field on the motion of a ferroelectric domain wall

The study of the influence of an external electric field on the motion from rest of a domain wall in ferroelectric crystals is presented. The solution of the problem representing the translational and rotational motions of the chain is sought in terms of solitary waves. Both electric and mechanical state of the structure in domains can be determined. The evolution of the velocity of the wall altered by the applied field is determined by means of energy arguments accounting for electromechanical couplings. A numerical simulation is given which illustrates the transient motion from rest of a wall separating two ferroelectric domains.     

Theory of polar fluids. I

We examine a classical fluid composed of molecules which contain a polarizable electric dipole with finite permanent moment. The long-ranged dipolar and the short-ranged interactions are treated on a different footing by expanding relative to a reference system characterized by the absence of electrostatic interactions. Extensions of graph theoretical techniques developed in an earlier paper are used to analyse the pair distribution function and the dielectric constant. Reduction of the number of graphs and their complexity is effected by introducing renormalizations of the permanent moment and the polarizability. The analysis leads to the definition of a new function w(12), which is free of terms dependent on the shape of the sample. For polar, polarizable molecules the direct correlation function lacks translational invariance; its role as a basic quantity is ceded to w(12). The pair distribution function and the dielectric constant ε are expressed in terms of w(12) and two closely related functions. Attention is drawn to an unsolved problem in dielectric theory, and an alternative formula for ε is presented in the form of a conjecture. An approximation for ε is formulated for the case in which the short-ranged non-dipolar interactions are independent of the molecular orientations. A simplified version is solved analytically.