Bloch function in an external electric field and Berry-Buslaev phase

To investigate the dielectrophoretic motions of multiple particles, we have performed the so-called direct numerical simulations on two-dimensional flows involving inertialess dielectric particles of two to five suspended in a viscous fluid under a uniform external electric field and then compared the results with those of the corresponding magnetophoretic counterparts. For the simulations, the electric field (or the force acting on each particle) is described by the numerical solution of the Maxwell equation (or Gauss’s law), where the smoothed representation technique is employed to tackle the jump of electric conductivity across the particle-fluid interface. The flow field, on the other hand, is described by the solution of the continuity and momentum equations, where one-stage smoothed profile method is employed to satisfy the no-slip condition at the interface. In all the simulations, the particles are initially equi-spaced on a circle with an origin at the center while a uniform electric field is externally imposed. Results show that all particles move with repelling or attracting one another depending on the locally nonuniform electric field formed due to the presence of multiple particles. Consequently, they become clustered largely into two groups, then revolve in the clockwise or counterclockwise direction, and finally get aligned in a line with the field direction. One exception is their initial configuration which is symmetric with respect to the axis perpendicular to the electric-field direction, where all the particles move eternally far away from one another with keeping the symmetry. In addition, it is found that the two-dimensional relative motions of dielectric particles under a uniform external electric field are qualitatively in fairly exact agreement with those of paramagnetic particles suspended in a nonmagnetic fluid under a uniform external magnetic field.

The collisions of electrons with atoms and ions in an external uniform quasi-steady electric field can differ significantly from collisions with an isolated atom even when the external electric field is far below the atomic field. This is explained by the interference and the change in the time the electrons stay in the vicinity of the scattering atom while they are reflected from the potential barrier of the external electric field. In this paper, the differential cross section for excitation of the atom by fast electrons in a electric field of a crystal surface or in the external electric field was calculated using the asymptotes of the wave functions of the final electron states were taken in the form of standing waves (along the external electric field) in the region between the atom nucleus and the reflection point of the electrons and in the form of progressive waves in the region where reflection points were absent. Quantitative study of this cross section was caried out using numerical methods. The differential cross section was calucated using the nonralativistic Born approximation.

The transport properties of water through a nanochannel influenced by the direction of an external electric field has been investigated by using molecular dynamics simulations. Water molecules flow unidirectionally across the nanochannel under a uniform external electric field without an osmotic pressure. It is found that the direction of the external field plays an important role in the interactions and dipole orientations of water molecules in the nanochannel, accordingly changing the net water flux dramatically. Most importantly, a critical angle (θC) between the external field and the nanochannel axis is found. The average net water flux increases as θ increases for θ≤θC but decreases sharply to a near-zero value for a further increase of θ. The maximum value of the average net water flux is 7.33 times as high as the value when the electric field is along the nanochannel axis. Our findings are of great practical importance for nanomolecular engineering, which provide a possible strategy for designing novel controllable water nanopumps.

The charging of a metal sphere in a weakly ionized collisional plasma in a uniform external electric field is investigated with allowance for the effect of the space charge field and ionization-recombination processes. The sphere charge and the spatial distributions of charged plasma particles are calculated both numerically and analytically (for some particular cases) for the case of a strong external field. It is found that the size of the perturbed plasma region is determined by the external field and the intensity of recombination processes. It is shown that the total electric charge (the sphere charge plus the plasma space charge) is zero in accordance with predictions of the theory of static currents in a conducting medium.

The deformation of polydimethylsiloxane (PDMS) spheres under uniform external electric field was studied experimentally and analytically. In the experiments, ∼1 mm diameter PDMS spheres with base-to-curing-agent mixing ratios of 10:1 and 60:1 were exposed to uniform external electric field with varying magnitudes and poling durations. The spheres elongate along the electric field direction. For a given electric field strength, the sphere deformation is initially a time function but reaches a terminal strain value over a certain time period. This terminal strain value is larger for stronger external electric fields and larger PDMS mixing ratio spheres. At this state, the material is no longer poled and the surface charge distribution remains constant. In the analysis, an expression for the sphere deformation is obtained by modeling the PDMS as a linear elastic solid and solving the Navier equation along with Maxwell’s equations for boundary conditions. The analysis takes into account the surface charge distribution and predicts well the experimental trends.

Recent laboratory and epidemiological results have stimulated interest in the hypothesis that human beings may exhibit biological responses to magnetic and/or electric field transients with frequencies in the range between 100 Hz and 100 kHz. Much can be learned about the response of a system to a transient stimulation by understanding its response to sinusoidal disturbances over the entire frequency range of interest. Thus, the main effort of this paper was to compare the strengths of the electric fields induced in homogeneous ellipsoidal models by uniform 100 Hz through 100 kHz electric and magnetic fields. Over this frequency range, external electric fields of about 25-2000 V/m (depending primarily on the orientation of the body relative to the field) are required to induce electric fields inside models of adults and children that are similar in strength to those induced by an external 1 microT magnetic field. Additional analysis indicates that electric fields induced by uniform external electric and magnetic fields and by the nonuniform electric and magnetic fields produced by idealized point sources will not differ by more than a factor of two until the sources are brought close to the body. Published data on electric and magnetic field transients in residential environments indicate that, for most field orientations, the magnetic component will induce stronger electric fields inside adults and children than the electric component. This conclusion is also true for the currents induced in humans by typical levels of 60 Hz electric and magnetic fields in U.S. residences.

The behavior of the free surface of a perfectly conducting liquid in an external uniform electric field is considered in the framework of the Hamiltonian formalism for the case of bounded axisymmetric geometry of the system (the fluid is bounded by a cylindrical rigid wall). Taking into account the influence of quadratic nonlinearities, we derive an amplitude equation which describes the evolution of the boundary. Using this equation, we find the condition for the hard excitation of boundary instability that leads to an explosive growth of surface perturbations. The differences in the description of the dynamics of axisymmetric perturbations of the boundary from the cases of plane, square, and hexagonal symmetries of the problem are discussed.

In this paper, we study the energy levels of an electron moving in a thin film. This film is considered as a two-dimensional electron gas which is under the influence of a uniform external magnetic field B and a uniform external electric field E. Here, the magnetic field is perpendicular to the film. Also, in this paper, we have selected the Landau gauge, because this gauge is useful for working in rectangular geometries.

The recent discovery of borospherene B40 marks the onset of a new class of all-boron fullerenes. External electric field can influence the structure and property of molecule. It is necessary to understand the electrostatic field effect in the borospherene B40. In this work, density functional theory method at the PBE0 level with the 6-31G* basis set is used to investigate the ground state structures, mulliken atomic charges, the highest occupied molecular orbital (HOMO) energy levels, the lowest unoccupied molecular orbital (LUMO) energy levels, energy gaps, electric dipole moments, infrared spectra and Raman spectra of borospherene B40 under the external electric field within the range of values F=0-0.06 a.u.. The electronic spectra (the first 18 excited states contain excited energies, excited wavelengths and oscillator strengths) of borospherene B40 are calculated by the time-dependent density functional theory method (TD-PBE0) with the 6-31G* basis set under the same external electric field. The results show that borospherene B40 can be elongated in the direction of electric field and B40 molecule is polarized under the external electric field. Meanwhile, the addition of external electric field results in lower symmetry (C2v), however, electronic state of borospherene B40 is not changed under the external electric field. Moreover, the calculated results show that the electric dipole moment is proved to be increasing with the increase of the external field intensity, but the total energy and energy gap are proved to decrease with the increase of external field intensity. The addition of external electric field can modify the infrared and Raman spectra, such as the shift of vibrational frequency and the strengthening of infrared and Raman peaks. Furthermore, the calculated results indicate that the external electric field has a significant effect on the electronic spectrum of borospherene B40. The increase of the electric field intensity can lead to the redshift of electronic spectrum. With the change of the electric field intensity, the strongest excited state (with the biggest oscillator strength) can become very weak (with the small oscillator strength) or optically inactive (with the oscillator strength of zero). Meanwhile, the weak excited state can become the strongest excited state by the external field. The ground state properties and spectral properties of borospherene B40 can be modified by the external electric field. Our findings can provide theoretical guidance for the application of borospherene B40 in the future.

By coupling the phase field model with the continuity equation of incompressible fluid, Navier–Stokes equation, electric field equation, and other governing equations, a multi-field coupling model for multi-bubble coalescence in a viscous fluids is established. The phase field method is used to capture the two-phase interface. The motion and coalescence of a pair of coaxial bubbles under an external uniform electric field and the effects of different electric field strengths on the interaction and coalescence of rising bubbles are studied. The results show that the uniform electric field accelerates the collision and coalescence process of double bubbles in the fluid, and increases the rising velocity of the coalesced bubble. The electric field with an intensity of E = 2 kV/mm is reduced about 2 times compared with that without electric field in coalescence time. When the electric field strength is strong (E ≥ 1 kV/mm), the coalesced bubble will rupture before it rises to the top of the calculation area, and the time of the bubble rupturing also decreases with the increase of the electric field strength. The phase field method is compared with the simulation results of Lattice Boltzmann Method (LBM), and the shape of bubble obtained by the two methods is in good agreement, which verifies the correctness of the calculation model.

Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.

Using the density functional B3P86/cc-PV5Z method, the geometric struc- ture of AlH molecule under different external electric fields are optimized, and the bond lengths, dipole moments, vibration frequencies and other physical properties parameters are obtained. The potential energy curves under different external fields are also obtained by CCSD(T) method with the same basis set. These results show that the properties parameters and potential energy curves may change with different external electric field, especially in the reverse electric fields. The potential energy function without external electric field is fitted by Morse potential, and the poten- tial energy curves under different external fields are fitted using constructed potential model, which adopted the dipole approximation theory. It is found that the fitting parameters are good agreement with experimental values and the critical dissociation electric parameter is consistent with numerical calculation. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics and molecular cooling with Stark effect.

The Rayleigh theory of oscillation of liquid drops is extended to include the effects of viscosity and a uniform external electric field. The resonant frequencies of the modes of the drop are shown to be shifted by the electric field. The magnitude and sign of the frequency shift depends on the dielectric constant of the drop. The condition for instability of drops in large electric fields is given and found to differ from that given by previous workers. This difference is attributed to the assumption by previous workers that the drops, under the influence of an electric field, distort into ellipsoids of revolution about the field direction. The dynamical equations are derived and the solution for small oscillations is given in an oscillating field and in an amplitude-modulated optical field.

Complementary to the semiclassical method developed in the preceding paper, here we develop a quantum-mechanical approach to characterize propagation of electron waves to large distances in photoionization microscopy of hydrogen atoms in uniform external electric fields. A formula for outgoing electron waves from the atomic source produced in photoionization has been derived. Spatial distributions of electron probability densities can be determined using the obtained formula. The electron waves that propagate to a large distance due to photoionization from the $n=2$ initial state of hydrogen atoms in electric fields has been calculated and the resulting probability densities are presented. Comparison with semiclassical results is made, and they are found to be in good agreement. A detailed analysis is given of strong quantum tunneling effects found in our calculations.

Effective properties of graded elliptical cylindrical composites