Journal articles on the topic 'Uniform-electric-field-approximation'
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1
BISWAS, S., A. SHAW, and B. MODAK. "SCHWINGER'S RESULT ON PARTICLE PRODUCTION FROM COMPLEX PATHS WKB APPROXIMATION." International Journal of Modern Physics A 15, no. 23 (September 20, 2000): 3717–31. http://dx.doi.org/10.1142/s0217751x00001221.
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This paper presents the derivation of Schwinger's gauge-invariant result of Im ℒ eff up to one loop approximation, for particle production in an uniform electric field through the method of complex trajectory WKB approximation (CWKB). The CWKB proposed by one of the authors1 looks upon particle production as being due to the motion of a particle in complex space–time plane, thereby requiring tunneling paths both in space and time. Recently2,3 there have been some efforts to calculate the reflection and the transmission coefficients for particle production in an uniform electric field that differ from our expressions for the same. In this paper we clarify the confusion in this regard and establish the correctness of CWKB.
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Bakke, Knut, and Claudio Furtado. "Analysis of the interaction of an electron with radial electric fields in the presence of a disclination." International Journal of Geometric Methods in Modern Physics 16, no. 11 (November 2019): 1950172. http://dx.doi.org/10.1142/s021988781950172x.
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We consider an elastic medium with a disclination and investigate the topological effects on the interaction of a spinless electron with radial electric fields through the WKB (Wentzel, Kramers, Brillouin) approximation. We show how the centrifugal term of the radial equation must be modified due to the influence of the topological defect in order that the WKB approximation can be valid. Then, we search for bound states solutions from the interaction of a spinless electron with the electric field produced by this linear distribution of electric charges. In addition, we search for bound states solutions from the interaction of a spinless electron with radial electric field produced by uniform electric charge distribution inside a long non-conductor cylinder.
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Kichigin, Gennadiy. "Acceleration of particles in a constant magnetic field and an electric field perpendicular to it, increasing with time." Solar-Terrestrial Physics 7, no. 2 (June 30, 2021): 22–27. http://dx.doi.org/10.12737/stp-72202103.
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The paper addresses the problem of acceleration of particles in a constant, uniform magnetic field of magnitude B and a uniform electric field perpendicular to it, which slowly increases with time. Assuming that the electric field grows linearly up to the maximum value Em=B, approximate analytical relations have been found which determine the particle velocity dependence on the acceleration time. The particles are shown to accelerate for the entire time of the increase in the electric field to a certain final energy, whose value depends on the acceleration rate. It has been established that the lower the acceleration rate, the greater the limiting energy. In the case when the ratio Em/B <0.9, using the solution method proposed by Alfvén in the drift approximation, an analytical solution of the relativistic equation of particle motion has been obtained. The results can be used to find the energy of particles in various pulsed processes in space plasma.
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Kichigin, Gennadiy. "Acceleration of particles in a constant magnetic field and an electric field perpendicular to it, increasing with time." Solnechno-Zemnaya Fizika 7, no. 2 (June 30, 2021): 24–29. http://dx.doi.org/10.12737/szf-72202103.
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The paper addresses the problem of acceleration of particles in a constant, uniform magnetic field of magnitude B and a uniform electric field perpendicular to it, which slowly increases with time. Assuming that the electric field grows linearly up to the maximum value Em=B, approximate analytical relations have been found which determine the particle velocity dependence on the acceleration time. The particles are shown to accelerate for the entire time of the increase in the electric field to a certain final energy, whose value depends on the acceleration rate. It has been established that the lower the acceleration rate, the greater the limiting energy. In the case when the ratio Em/B <0.9, using the solution method proposed by Alfvén in the drift approximation, an analytical solution of the relativistic equation of particle motion has been obtained. The results can be used to find the energy of particles in various pulsed processes in space plasma.
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Gavin, H. P., R. D. Hanson, and F. E. Filisko. "Electrorheological Dampers, Part I: Analysis and Design." Journal of Applied Mechanics 63, no. 3 (September 1, 1996): 669–75. http://dx.doi.org/10.1115/1.2823348.
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Electrorheological (ER) materials are suspensions of specialized, micron-sized particles in nonconducting oils. When electric fields are applied to ER materials, they exhibit dramatic changes (within milli-seconds) in material properties. Pre-yield, yielding, and post-yield mechanisms are all influenced by the electric field. Namely, an applied electric field dramatically increases the stiffness and energy dissipation properties of these materials. A previously known cubic equation which describes the flow of fluids with a yield stress through a rectangular duct can be applied to annular flow, provided that certain conditions on the material properties are satisfied. An analytic solution and a uniform approximation to the solution, for the rectangular duct Poiseuille flow case is presented. A numerical method is required to solve the flow in annular geometries. The approximation for rectangular ducts is extended to deal with the annular duct case.
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BALANTEKIN, A. B., J. E. SEGER, and S. H. FRICKE. "DYNAMICAL EFFECTS IN PAIR PRODUCTION BY ELECTRIC FIELDS." International Journal of Modern Physics A 06, no. 05 (February 20, 1991): 695–725. http://dx.doi.org/10.1142/s0217751x91000393.
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Nonperturbative dynamical effects in fermion-antifermion pair production by classical electric fields are investigated. Following a summary of the results previously given in the literature, a formal connection between fermion pair production in an external field and supersymmetric quantum mechanics is pointed out. Pair production probabilities are calculated in a uniform semiclassical approximation, which yields the Schwinger result in the constant field limit. The multiplicity distributions of the created pairs are shown to be related to the elementary symmetric functions.
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Udalov, Artur, Denis Alikin, and Andrei Kholkin. "Piezoresponse in Ferroelectric Materials under Uniform Electric Field of Electrodes." Sensors 21, no. 11 (May 26, 2021): 3707. http://dx.doi.org/10.3390/s21113707.
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The analytical solution for the displacements of an anisotropic piezoelectric material in the uniform electric field is presented for practical use in the “global excitation mode” of piezoresponse force microscopy. The solution is given in the Wolfram Mathematica interactive program code, allowing the derivation of the expression of the piezoresponse both in cases of the anisotropic and isotropic elastic properties. The piezoresponse’s angular dependencies are analyzed using model lithium niobate and barium titanate single crystals as examples. The validity of the isotropic approximation is verified in comparison to the fully anisotropic solution. The approach developed in the paper is important for the quantitative measurements of the piezoelectric response in nanomaterials as well as for the development of novel piezoelectric materials for the sensors/actuators applications.
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Krasnitsky, Y. A., A. E. Popov, and A. Kalnacs. "Evaluation of the Uniform Field Distortions Produced by a Toroidal Dielectric Body / Novērtējums Viendabīga Elektriskā Lauka Izkropļojumiem, Kurus Rada Toroīda Formas Dielektrisks Ķermenis." Latvian Journal of Physics and Technical Sciences 52, no. 4 (August 1, 2015): 57–68. http://dx.doi.org/10.1515/lpts-2015-0023.
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Abstract Distortions of the structure of a uniform electric field when a dielectric body with a toroidal shape is placed in it are considered in the quasi-static approximation. The rate of distortion is proposed to estimate through the effective permittivity of toroid determined by solving the corresponding boundary value problem. Some numerical estimates obtained using specially developed software in the language of Matlab are given.
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Abu Hamed, Mohammad, and Ehud Yariv. "Boundary-induced electrophoresis of uncharged conducting particles: near-contact approximation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2106 (April 2009): 1939–48. http://dx.doi.org/10.1098/rspa.2008.0533.
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A zero net charge ideally polarizable particle is suspended within an electrolyte solution, nearly in contact with an uncharged non-polarizable wall. This system is exposed to a uniform electric field that is applied parallel to the wall. Assuming a thin Debye thickness, the induced-charge electro-osmotic flow is investigated with the goal of obtaining an approximation for the force experienced by the particle. Singular perturbations in terms of the dimensionless gap width δ are used to represent the small-gap singular limit δ ≪1. The fluid is decomposed into two asymptotic regions: an inner gap region, where the electric field and strain rate are large, and an outer region, where they are moderate. The leading contribution to the force arises from hydrodynamic stresses in the inner region, while contributions from both hydrodynamic stresses at the outer region and Maxwell stresses in both regions appear in higher order correction terms.
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Yariv, Ehud. "Boundary-induced electrophoresis of uncharged conducting particles: remote wall approximations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2103 (November 18, 2008): 709–23. http://dx.doi.org/10.1098/rspa.2008.0322.
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An initially uncharged ideally polarizable particle is freely suspended in an electrolyte solution in the vicinity of an uncharged dielectric wall. A uniform electric field is externally applied parallel to the wall, inflicting particle drift perpendicular to it. Assuming a thin Debye thickness, the electrokinetic flow is analysed for large particle–wall separations using reflection methods, thereby yielding an asymptotic approximation for the particle velocity. The leading-order correction term in that approximations stems from wall polarization.
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Deshmukh, Snehal D., Pierre-Michel Déjardin, and Yuri P. Kalmykov. "Dynamic Kerr effect in a strong uniform AC electric field for interacting polar and polarizable molecules in the mean field approximation." Journal of Chemical Physics 147, no. 9 (September 7, 2017): 094501. http://dx.doi.org/10.1063/1.4995021.
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Li, Xiao-Xue, and Gang Chen. "Effect of electron–electron interaction on polarization and dissociation of the charged oligomer after single-photon absorption." International Journal of Modern Physics B 31, no. 32 (December 18, 2017): 1750256. http://dx.doi.org/10.1142/s0217979217502563.
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By using the extended Hubbard model under the Hartree–Fock approximation, we theoretically investigate the effect of electron–electron interaction on the polarization of the single-photon excited state of the charged [Formula: see text]-conjugated oligomer. In the framework of one-dimensional tight-binding model, a uniform weak electric field is applied for polarization. The results show that the polarization property will vary with the electron–electron interaction. For example, with the increase of on-site Coulomb interaction strength, the value of the induced dipole moment is decreased. Its physical origin is revealed by analyzing the wavefunction of the localized energy level. In addition, the relation between the critical electric field for the dissociation of the single-photon excited state of the charged oligomer and the electron–electron interaction strength is also discussed.
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Biswas, Dipankar, and Bimalendu B. Bhattacharya. "2-D Electrical Modeling over Undulated Topography." GEOPHYSICS 63, no. 3 (May 1998): 898–907. http://dx.doi.org/10.1190/1.1444400.
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The electrical response of a cylindrical inclusion in topographic relief has been treated analytically for a uniform electric field. The undulated topography has been conveniently defined by a smoothly connected mathematical surface defining a hump or bump. A Born approximation of Laplace’s equation in a bipolar coordinate system has been derived by solving for the mixed‐boundary conditions, namely Neumann and Dirichlet conditions, respectively. The topographic relief causes focusing and defocusing at the transition zones of flat and topographic relief and the central zone of the hump. Consequently, the electric field is weakly linear within the flat zone and entirely nonlinear within the hump. The inclusion of a cylindrical target aggravates the field nonlinearity. The electric field and induced polarization (IP) response over the cylindrical target embedded in topographic relief are strongly dependent on the width and height of the hump and a steady function of increase in resistivity ([Formula: see text]) as well as chargeability ([Formula: see text]) contrasts. The electrical field and IP response over the cylindrical target embedded in the topographic relief, after correcting for topographic effect, resembles most closely the field measured on an equivalent flat half‐space of a particular elevation. The areas of the topographic surface above and below this unique datum bisecting the topographic relief are exactly equal.
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Yariv, Ehud, and Yaniv Almog. "The effect of surface-charge convection on the settling velocity of spherical drops in a uniform electric field." Journal of Fluid Mechanics 797 (May 24, 2016): 536–48. http://dx.doi.org/10.1017/jfm.2016.286.
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The mechanism of surface-charge convection, quantified by the electric Reynolds number $Re$, renders the Melcher–Taylor electrohydrodynamic model inherently nonlinear, with the electrostatic problem coupled to the flow. Because of this nonlinear coupling, the settling speed of a drop under a uniform electric field differs from that in its absence. This difference was calculated by Xu & Homsy (J. Fluid Mech., vol. 564, 2006, pp. 395–414) assuming small $Re$. We here address the same problem using a different route, considering the case where the applied electric field is weak in the sense that the magnitude of the associated electrohydrodynamic velocity is small compared with the settling velocity. As convection is determined at leading order by the well-known flow associated with pure settling, the electrostatic problem becomes linear for arbitrary value of $Re$. The electrohydrodynamic correction to the settling speed is then provided as a linear functional of the electric-stress distribution associated with that problem. Calculation of the settling speed eventually amounts to the solution of a difference equation governing the respective coefficients in a spherical harmonics expansion of the electric potential. It is shown that, despite the present weak-field assumption, our model reproduces the small-$Re$ approximation of Xu and Homsy as a particular case. For finite $Re$, inspection of the difference equation reveals a singularity at the critical $Re$-value $4S(1+R)(1+M)/(1+S)M$, wherein $R$, $S$ and $M$ respectively denote the ratios of resistivity, permittivity and viscosity values in the suspending and drop phases, as defined by Melcher & Taylor (Annu. Rev. Fluid Mech., vol. 1, 1969, pp. 111–146). Straightforward numerical solutions of this equation for electric Reynolds numbers smaller than the critical value reveal a non-monotonic dependence of the settling speed upon the electric field magnitude, including a transition from velocity enhancement to velocity decrement.
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Wang, Guang Xin, and Xiu Zhi Duan. "Influence of Al Composition on Donor Impurity States in Self-Formed GaAs-AlxGa1-xAs Quantum Rings." Applied Mechanics and Materials 380-384 (August 2013): 4284–89. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.4284.
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Based on the the effective mass approximation and variational approach, the donor impurity states confined in self-formed GaAs/AlxGa1-xAs quantum rings (QRs) are investigated theoretically. A uniform electric field is applied along the growth direction of the QR. The different effective masses in the different regions of the GaAs/AlxGa1-xAs QR are taken into consideration. Numerical results show that the binding energy of a donor impurity increases gradually, reaches a maximum value, and then decreases quickly to the special value as the QR height decreases. Given a fixed QR size, the binding energy increases for the impurity located at the center of the QR when the Al composition increases. In addition, it can also be found that when the applied electric field strength increases, the donor binding energy increases for impurities localized at the negative z axis of the QR; however, the donor binding energy decreases slightly for impurities located at the center and positive z axis of the QR.
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Tzoulis, A., and T. F. Eibert. "Combining the multilevel fast multipole method with the uniform geometrical theory of diffraction." Advances in Radio Science 3 (May 12, 2005): 183–88. http://dx.doi.org/10.5194/ars-3-183-2005.
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Abstract. The presence of arbitrarily shaped and electrically large objects in the same environment leads to hybridization of the Method of Moments (MoM) with the Uniform Geometrical Theory of Diffraction (UTD). The computation and memory complexity of the MoM solution is improved with the Multilevel Fast Multipole Method (MLFMM). By expanding the k-space integrals in spherical harmonics, further considerable amount of memory can be saved without compromising accuracy and numerical speed. However, until now MoM-UTD hybrid methods are restricted to conventional MoM formulations only with Electric Field Integral Equation (EFIE). In this contribution, a MLFMM-UTD hybridization for Combined Field Integral Equation (CFIE) is proposed and applied within a hybrid Finite Element - Boundary Integral (FEBI) technique. The MLFMM-UTD hybridization is performed at the translation procedure on the various levels of the MLFMM, using a far-field approximation of the corresponding translation operator. The formulation of this new hybrid technique is presented, as well as numerical results.
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Riccio, Giovanni, Gianluca Gennarelli, Flaminio Ferrara, Claudio Gennarelli, and Rocco Guerriero. "Scattering from a Truncated Metamaterial Layer Hosted by a Planar PEC Structure: Uniform Asymptotic Solution and Validation Tests." Applied Sciences 12, no. 14 (July 20, 2022): 7302. http://dx.doi.org/10.3390/app12147302.
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This research paper proposes an analytical approach for evaluating electromagnetic scattering from a planar complex object made of a perfect electric conductor, which hosts a double negative metamaterial half-layer on the lit face. The method is based on the physical optics approximation of equivalent sources and works in the framework of the uniform geometrical theory of diffracion, so that the scattered field in the surrounding free space is obtained by adding the reflected contribution and the diffracted one, which is originated by the surface break. The effectiveness of the proposed approach is tested and proved by using a full-wave numerical tool to generate reference values.
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CHEN, TAIRONG, WENFANG XIE, and SHIJUN LIANG. "NONLINEAR OPTICAL PROPERTIES OF THE WURTZITE InGaN/AlGaN PARABOLIC QUANTUM DOT." Nano 08, no. 02 (April 2013): 1350019. http://dx.doi.org/10.1142/s1793292013500197.
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The linear and nonlinear optical properties in a wurtzite In x Ga 1-x N / Al y Ga 1-y N strained spherical quantum dot (QD) subjected to a uniform external electric field with a direction opposite to that of the built-in electric (BEF) within the framework of effective-mass approximation have been investigated. The results show that the BEF has great effects on the linear and nonlinear optical absorption coefficients (ACs) and refractive index (RI) changes. Moreover, the dependence of the linear and nonlinear optical properties on the In composition, on the Al composition and on the inner sphere radius has been studied in detail. It is indicated that the ACs and RI changes of the Wurtzite spherical QD have strongly affected by these factors. The results may make a significant contribution to designing some important photodetectors and photonic crystal devices.
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Metwaly, T. M. N., and N. M. Hafez. "Electroviscoelstic Stability Analysis of Cylindrical Structures in Walters B Conducting Fluids Streaming through Porous Medium." Fluids 7, no. 7 (July 1, 2022): 224. http://dx.doi.org/10.3390/fluids7070224.
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In this research, the linear stability of a cylindrical interface between two viscoelstic Walters B conducting fluids moving through a porous medium is investigated theoretically and numerically. The fluids are influenced by a uniform axial electric field. The cylindrical structure preserves heat and mass transfer across the interface. The governing equations of motion and continuity are linearized, as are Maxwell’s equations in quasi-static approximation and the suitable boundary conditions at the interface. The method of normal modes has been used to obtain a quadratic characteristic equation in frequency with complex coefficients describing the interaction between viscoelstic Walters B conducting fluids and the electric field. In light of linear stability theory, the Routh–Hurwitz criteria are used to govern the structure’s stability. Several special cases are recoverd under suitable data choices. The stability analysis is conferred in detail via the behaviors of the applied electric field and the imaginary growth rate part with the wavenumbers. The effects of various parameters on the interfacial stability are theoretically presented and illustrated graphically through two sets of figures. Our results demonstrate that kinematic viscosities, kinematic viscoelasticities, and medium porosity improve stability, whereas medium permeability, heat and mass transfer coefficients, and fluid velocities decrease it. Finally, electrical conductivity has a critical influence on the structure’s stability.
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RHODES, DOV, and EHUD YARIV. "The elongated shape of a dielectric drop deformed by a strong electric field." Journal of Fluid Mechanics 664 (November 29, 2010): 286–96. http://dx.doi.org/10.1017/s0022112010004581.
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A dielectric drop is suspended within a dielectric liquid and is exposed to a uniform electric field. Due to polarization forces, the drop deforms from its initial spherical shape, becoming prolate in the field direction. At strong electric fields, the drop elongates significantly, becoming long and slender. For moderate ratios of the permittivities of the drop and surrounding liquid, the drop ends remain rounded. The slender limit was originally analysed by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047) using a singularity representation of the electric field. Here, we revisit it using matched asymptotic expansions. The electric field within the drop is continued into a comparable solution in the ‘inner’ region, at the drop cross-sectional scale, which is itself matched into the singularity representation in the ‘outer’ region, at the drop longitudinal scale. The expansion parameter of the problem is the elongated drop slenderness. In contrast to familiar slender-body analysis, this parameter is not provided by the problem formulation, and must be found throughout the course of the solution. The drop aspect-ratio scaling, with the 6/7-power of the electric field, is identical to that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047). The predicted drop shape is compared with the boundary-integral solutions of Sherwood (J. Fluid Mech., vol. 188, 1988, p. 133). While the agreement is better than that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047), the weak logarithmic decay of the error terms still hinders an accurate calculation. We obtain the leading-order correction to the drop shape, improving the asymptotic approximation.
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Архипов, Дмитрий Александрович, and Элла Петровна Шурина. "Analysis of the toroidal coil approximation technique for the electromagnetic simulations." Вычислительные технологии, no. 4 (October 6, 2022): 63–76. http://dx.doi.org/10.25743/ict.2022.27.4.005.
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Предложены два метода аппроксимации тороидального источника электромагнитного поля для решения системы уравнений Максвелла в естественных переменных векторным методом конечных элементов: электрическая постановка (плотность электрического тока вдоль обмотки катушки); магнитная постановка (эффективная плотность магнитного тока в сердечнике катушки). Выполнен сравнительный анализ методов в зависимости от электрофизических и геометрических характеристик источника и свойств среды. Численные эксперименты демонстрируют преимущество аппроксимации тороидальной генераторной катушки плотностью магнитного тока. Objective. In well-logging applications, the electromagnetic field is generated by the toroidal or solenoidal coils. The physically correct and efficient approximation of these coils is of utmost importance. In this paper, we propose two techniques to approximate the toroidal coil: the electric source and the magnetic source. Methods. In the frequency domain the electromagnetic field is governed by the second-order partial differential equation for the electric or magnetic fields. The computational scheme is based on the vector finite element method with a hierarchical basis of the complete second order. The tetrahedral discretization of the computational domain is non-uniform. When approximating the toroidal coil as an electric current density in the coil winding, the finite element mesh must capture the geometry of the winding. For a coil with multiple winding turns, it results in an extremely fine mesh, which leads to large linear systems, hence, poor solver performance. To overcome this, we develop a new technique for approximating a toroidal coil as a magnetic current density in the core of the coil. This approach does not require including the winding into the finite element mesh. Therefore, the size of the resulting linear system is independent of the number of turns in the coil winding. Results. The article shows that the magnetic current density in the generator coil does not depend on the host medium, but is determined only by the geometric (core size and number of turns) and electrophysical characteristics of the toroidal source core. The paper presents the distribution of the electromagnetic field strength for both formulations in a homogeneous medium. Conclusion. The behavior of the electromagnetic field is the same for both methods of source approximation, but the magnetic formulation does not depend on the geometry of the toroidal coil therefore the computational mesh does no.
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Siddiqui, Abuzar A., and Akhlesh Lakhtakia. "Steady electro-osmotic flow of a micropolar fluid in a microchannel." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2102 (October 28, 2008): 501–22. http://dx.doi.org/10.1098/rspa.2008.0354.
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We have formulated and solved the boundary-value problem of steady, symmetric and one-dimensional electro-osmotic flow of a micropolar fluid in a uniform rectangular microchannel, under the action of a uniform applied electric field. The Helmholtz–Smoluchowski equation and velocity for micropolar fluids have also been formulated. Numerical solutions turn out to be virtually identical to the analytic solutions obtained after using the Debye–Hückel approximation, when the microchannel height exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. For a fixed Debye length, the mid-channel fluid speed is linearly proportional to the microchannel height when the fluid is micropolar, but not when the fluid is simple Newtonian. The stress and the microrotation are dominant at and in the vicinity of the microchannel walls, regardless of the microchannel height. The mid-channel couple stress decreases, but the couple stress at the walls intensifies, as the microchannel height increases and the flow tends towards turbulence.
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Staňák, Peter, Ján Sládek, Vladimír Sládek, and Slavomír Krahulec. "Numerical MLPG Analysis of Piezoelectric Sensor in Structures." Slovak Journal of Civil Engineering 22, no. 2 (July 15, 2014): 15–20. http://dx.doi.org/10.2478/sjce-2014-0009.
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AbstractThe paper deals with a numerical analysis of the electro-mechanical response of piezoelectric sensors subjected to an external non-uniform displacement field. The meshless method based on the local Petrov-Galerkin (MLPG) approach is utilized for the numerical solution of a boundary value problem for the coupled electro-mechanical fields that characterize the piezoelectric material. The sensor is modeled as a 3-D piezoelectric solid. The transient effects are not considered. Using the present MLPG approach, the assumed solid of the cylindrical shape is discretized with nodal points only, and a small spherical subdomain is introduced around each nodal point. Local integral equations constructed from the weak form of governing PDEs are defined over these local subdomains. A moving least-squares (MLS) approximation scheme is used to approximate the spatial variations of the unknown field variables, and the Heaviside unit step function is used as a test function. The electric field induced on the sensor is studied in a numerical example for two loading scenarios.
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Reity, O. K., V. K. Reity, and V. Yu Lazur. "Quasiclassical Approximation in the Non-Relativistic and Relativistic Problems of Tunneling Ionization of a Hydrogen-Like Atom in a Uniform Electric Field." EPJ Web of Conferences 108 (2016): 02039. http://dx.doi.org/10.1051/epjconf/201610802039.
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Smith, J. Torquil. "Conservative modeling of 3-D electromagnetic fields, Part I: Properties and error analysis." GEOPHYSICS 61, no. 5 (September 1996): 1308–18. http://dx.doi.org/10.1190/1.1444054.
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Conservation of electric current and magnetic flux can be explicitly enforced by modeling Maxwell’s equations on a staggered grid, where the different field components are sampled at points offset relative to each other. A staggered finite‐difference (SFD) approximation gives divergence‐free magnetic fields and electric currents ensuring good behavior at all periods. Comparisons of SFD solutions with 2-D quasi‐analytic solutions are very good (∼1% rms error). When a modeled region can be subdivided into uniform subdomains, comparison of analytic solutions and SFD approximations show that the greatest differences occur near the Nyquist wavenumbers; the SFD solutions do not attenuate in space as rapidly as the analytic solutions. The accuracy of a computed SFD solution can be estimated from its wavenumber content. For test cases the accuracy estimates are surprisingly close to the actual accuracies. Grid requirements for modeling short horizontal wavelength components of a solution seem more demanding than for modeling the infinite wavelength (plane‐wave) component: for 2% accuracy 4π samples are required per horizontal wavelength compared to two samples per skin depth for the plane‐wave component.
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Геворкян, В. Е., and V. E. Gevorkyan. "Computer modeling and molecular dynamics of polarization switching in the ferroelectric films PVDF and P(VDF-TrFE) on nanoscale." Mathematical Biology and Bioinformatics 10, no. 1 (April 9, 2015): 131–53. http://dx.doi.org/10.17537/2015.10.131.
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In this paper, molecular models are used to investigate and analyze the structure and polarization of polyvinylidene fluoride (PVDF) and poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) Langmuir-Blodgett (LB) nanofilms, depending on the structure and composition of the monomers of their polymer and copolymer chains. Quantum-mechanical calculations and modeling, as well as molecular dynamics (MD) simulations based on semi-empirical quantum-chemical methods (such as PM3), show that the energy of the studied PVDF and P (VDF-TrFE) molecular structures, and their polarization switching proceed by homogeneous switching mechanism in the framework of the phenomenological theory of Landau-Ginzburg-Devonshire (LGD) in the linear approximation of low values of the electric field. The magnitude of the resulting critical coercive field is within the EC ~ 0.5 ... 2.0 GV/m, which is consistent with experimental data. It is also found that the uniform polarization switching mechanism of the polymer chains PVDF and P (VDF-TrFE) is due to the quantum properties of the molecular orbitals of the electron subsystem: the applied electric field induces a gradual shift of the electron "clouds" density (electron polarizability), which in turn causes a gradual shift of the nuclear cores, in accordance with the principle of minimum total energy of the system, and this leads eventually, when it reaches a critical point (bifurcation) - to overturn of the entire chain and a sharp decrease in the total energy of the total system to its energetically more favorable state. This is clearly seen in both the polarization hysteresis loops, and the total energy changes. In this case, the turnover chain time, obtained by molecular dynamics within semi-empirical quantum-chemical PM3 approach in a limited Hartree-Fock approximation, when approaching this critical point, increases sharply, tending to infinity, which corresponds to the theory of LGD.
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Быстров, В. С., and V. S. Bystrov. "Анализ вычислительных и экспериментальных исследований переключения поляризации в ПВДФ и П (ВДФ-ТрФЭ) сегнетоэлектрических пленках на наноуровне." Mathematical Biology and Bioinformatics 10, no. 2 (September 27, 2015): 372–86. http://dx.doi.org/10.17537/2015.10.372.
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In this paper, molecular models are used to investigate and analyze the polarization switching in the polyvinylidene fluoride (PVDF) and poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) Langmuir-Blodgett (LB) nanofilms, in comparison with the experimental data at the nanoscale. Quantum-mechanical calculations and modeling, as well as molecular dynamics (MD) simulations based on semi-empirical quantum-chemical methods (such as PM3), show that the energy of the studied PVDF and P (VDF-TrFE) molecular structures, and their polarization switching proceed by the intrinsic homogeneous switching mechanism in the framework of the phenomenological theory of Landau-Ginzburg-Devonshire (LGD) in the linear approximation at low values of the electric field. The magnitude of the resulting critical coercive field is within the EC ~ 0.5 ... 2.5 GV/m, which is consistent with experimental data. It is also found that the uniform polarization switching mechanism of the polymer chains PVDF and P (VDF-TrFE) is due to the quantum properties of the molecular orbitals of the electron subsystem. This is clearly seen in both the polarization hysteresis loops, and the total energy changes. In this case, the turnover chain time, obtained by molecular dynamics within semi-empirical quantum-chemical PM3 approach in a limited Hartree-Fock approximation, when approaching this critical point, increases sharply, tending to infinity, which corresponds to the theory of LGD. Otherwise, at the high values of the applied electric field the polarization switching correspond to the extrinsic domain mechanism in the frame of the microscopic Kolmogorov–Avrami–Ishibashi (KAI) theory, describing bulk ferroelectric crystals and thick films. The performed analysis of computational and experimental data allows us to estimate the critical sizes of the possible transition region approximately on the order of 10 nm between intrinsic homogeneous and extrinsic domain switching mechanisms.
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Gavrilik, A. M., and A. V. Nazarenko. "Statistics effects in extremal black holes ensemble." International Journal of Modern Physics A 34, no. 32 (November 20, 2019): 1950215. http://dx.doi.org/10.1142/s0217751x19502154.
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We consider the grand canonical ensemble of the static and extremal black holes, when the equivalence of the electric charge and mass of individual black hole is postulated. Assuming uniform distribution of black holes in space, we are finding the effective mass of test particle and mean time dilation at the admissible points of space, taking into account the gravitational action of surrounding black holes. Having specified the statistics that governs extremal black holes, we study its effect on those quantities. Here, the role of statistics is to assign a statistical weight to the configurations of certain fixed number of black holes. We borrow these weights from Bose–Einstein, Fermi–Dirac, classical and infinite statistics. Using mean field approximation, the aforementioned characteristics are calculated and visualized, which permits us to draw the conclusions on visible effect of each statistics.
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Summa, Francesco Ferdinando, Guglielmo Monaco, Riccardo Zanasi, and Paolo Lazzeretti. "Origin independent current density vector fields induced by time-dependent magnetic field. I. The LiH molecule." Journal of Chemical Physics 156, no. 15 (April 21, 2022): 154105. http://dx.doi.org/10.1063/5.0089605.
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The electronic current density, induced in a molecule by the optical magnetic field associated with a frequency-dependent monochromatic plane wave, assumed to be spatially uniform within the electric quadrupole approximation, has been studied by using a theoretical method based on a continuous translation of its origin. The induced electronic current density vector field designated by this procedure, invariant of the origin for any point of the molecular domain, is obtained via a computational scheme, formally annihilating the diamagnetic contribution of the conventional common-origin approach based on perturbation theory. In a preliminary application of the theoretical methods outlined in the present work, the simple molecule of lithium hydride has been investigated. Particular attention has been paid to the structure of induced electronic current density for several values of the magnetic field frequency by investigating equilibrium points of four different types, organized in stagnation lines, which constitute its stagnation graph, i.e., a topological fingerprint of the vector field conveying complete information in the condensed form, to verify the fulfillment of fundamental requirements, e.g., the continuity equation and the Poincaré–Hopf theorem on spherical and toroidal surfaces.
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García Rodríguez, Alexis O., and Alain Destexhe. "A reformulation of the brain’s magneto-quasistatic approximation and a formalism for the long-distance magnetic field generated by populations of neurons." Journal of Applied Physics 132, no. 17 (November 7, 2022): 174701. http://dx.doi.org/10.1063/5.0094862.
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To evaluate the long-distance magnetic field generated by neurons, we propose a reformulation of the brain’s magneto-quasistatic approximation based on the Jefimenko’s time-dependent generalization of the Biot–Savart law. This differs from the traditional approach relying on Maxwell’s equations and not on their general solution. Instead of a typical length of the medium in the conventional approach, we use the signal traveling distance [Formula: see text], from the farthest source point [Formula: see text] to the field point [Formula: see text], as the proper length to define the quasistatic dynamics. We consider relatively low frequencies below a typical value [Formula: see text]. The quasistatic approximation is justified since [Formula: see text]. We take [Formula: see text], with the gray matter permittivity, previously underestimated, to be [Formula: see text]. A formalism for the long-distance magnetic field generated by neuronal populations is then developed. Each population is described as a region of small dimensions compared to the average distance from the field point. We split the impressed current density into synaptic and action potential contributions and study their magnetic field. Assuming a small contribution of the impressed currents at the region boundary surface, we obtain two equivalent expressions of the synaptic current dipole moment in terms of the scalar potential and/or its spatial derivatives. Using Maxwell–Wagner’s time, the synaptic current dipole moment of a region is also shown to be related to the electric dipole moment of each part with uniform conductivity and permittivity. Finally, the long-distance magnetic field of action potential currents is expressed in terms of the magnetic dipole moment for these currents.
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Nikodijevic, Dragisa, Zivojin Stamenkovic, Dragan Zivkovic, Aleksandar Boricic, and Milos Kocic. "Active control of flow and heat transfer in boundary layer on the porous body of arbitrary shape." Thermal Science 16, suppl. 2 (2012): 295–309. http://dx.doi.org/10.2298/tsci120427170n.
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The paper discusses the possibility of active control of flow and heat transfer using a magnetic field and suction in a generalized form. The unsteady temperature two-dimensional laminar magnetohydrodynamic boundary layer of incompressible fluid on a porous body of arbitrary shape is analyzed. Outer electric filed is neglected, magnetic Reynolds number is significantly lower than one i. e. the considered problem is in inductionless approximation. Characteristic properties of fluid are constant and it is assumed that a uniform suction or injection of a fluid, same as the fluid in primary flow, can take place through the body surface. The boundary-layer equations are generalized such that the equations and the boundary conditions are independent of the particular conditions of the problem, and this form is considered as universal. Obtained universal equations are numerically solved using the ?progonka? method. Numerical results for the dimensionless velocity, temperature, shear stress and heat transfer as functions of introduced sets of parameters are obtained, displayed graphically and used to carry out general conclusions about the development of temperature magnetohydrodynamic boundary layer.
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Yin, Changchun. "MMT forward modeling for a layered earth with arbitrary anisotropy." GEOPHYSICS 71, no. 3 (May 2006): G115—G128. http://dx.doi.org/10.1190/1.2197492.
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The standard model of a layered isotropic earth is a good approximation to geophysical reality in geoelectromagnetic mapping. In regions with distinct dipping stratification, however, it is difficult to model these fine structures because of large storage and time requirements. In this case, we may approximately replace the isotropic conductors with a preferential electrical direction by macro-scale anisotropy. The marine-magnetotelluric (MMT) forward problem is formulated for a layered earth with arbitrary anisotropy. For a given layer beneath the ocean, the two horizontal components of the electric field are projected onto the principal anisotropic directions and continued from layer to layer using continuity conditions. The formulation is used to derive the impedance tensor and apparent resistivities for a uniform anisotropic half-space, which clearly distinguish the effect of electrical anisotropy on MMT responses. The principal anisotropic orientations are clearly identified in the polar plots, which show the azimuthal variation of the apparent resistivity. The resolvability analysis of a resistive intermediate layer indicates that the depth of exploration for the MMT method depends strongly on the anomaly threshold associated with system sensitivity and environmental noise level but less on the resistivity contrast between the target and surrounding media. For an anisotropic target, to obtain a larger depth of exploration the electric field should be measured in the direction of higher target-host resistivity contrast. The simulation of reservoir characterization using marine MT shows that the current MMT technique cannot be an effective tool yet for direct offshore reservoir characterization, but it can be a good complementary tool for controlled-source electromagnetic (EM) technologies emerging for offshore hydrocarbon exploration.
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BüHler, L. "Instabilities in quasi-two-dimensional magnetohydrodynamic flows." Journal of Fluid Mechanics 326 (November 10, 1996): 125–50. http://dx.doi.org/10.1017/s0022112096008269.
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The improvement of heat transfer conditions in liquid-metal magnetohydrodynamic (MHD) flows is of prime importance for self-cooled fusion blanket design concepts. For many years the research was based on stationary inertialess assumptions since it was expected that time-dependent inertial flows would be suppressed by strong electromagnetic damping, especially in the extreme range of fusion relevant parameters. In the present analysis the stationary inertialess assumptions are abandoned. Nevertheless, the classical ideas usually used to obtain inertialess asymptotic solutions are drawn on. The basic inertial equations are reduced to a coupled two-dimensional problem by analytical integration along magnetic field lines. The magnetic field is responsible for a quasi-two-dimensional flow; the non-uniform distribution of the wall conductivity creates a wake-type profile, the MHD effect reducing to a particular forcing and friction. The solution for the two-dimensional variables, the field aligned component of vorticity, the stream function, and the electric potential are obtained by numerical methods. In a flat channel with non-uniform electrical wall conductivity, time-dependent solutions similar to the Kármán vortex street behind bluff bodies are possible. The onset of the vortex motion, i.e. the critical Reynolds number depends strongly on the strength of the magnetic field expressed by the Hartmann number. Stability analyses in viscous hydrodynamic wakes often use the approximation of a unidirectional flow which does not take into account the spatial evolution of the wake. The present problem exhibits a wake-type basic flow, which does not change along the flow path. It represents, therefore, an excellent example to which the simple linear analysis on the basis of Orr-Sommerfeld-type equations applies exactly. Once unstable, the flow first exhibits a regular time periodic vortex pattern which is rearranged further downstream. One can observe an elongation, pairing, or sometimes more complex merging of vortices. All these effects lead to larger flow structures with lower frequencies. The possibility for a creation and maintenance of time-dependent vortex-type flow pattern in MHD flows is demonstrated.
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Prigoda, Kristina, Anna Ermina, Vladimir Bolshakov, Denis Nazarov, Ilya Ezhov, Oleksiy Lutakov, Maxim Maximov, Vladimir Tolmachev, and Yuliya Zharova. "The Array of Si Nanowires Covered with Ag Nanoparticles by ALD: Fabrication Process and Optical Properties." Coatings 12, no. 11 (November 15, 2022): 1748. http://dx.doi.org/10.3390/coatings12111748.
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In this work, we proposed a method for creating an Ag/Si composite structure consisting of an array of vertical silicon nanowires (SiNWs) decorated with silver nanoparticles (AgNPs). A two-stage metal-assisted chemical etching of Si was used to obtain the SiNW array, and atomic layer deposition was used to fabricate the AgNPs. A uniform distribution of AgNPs along the SiNW height was achieved. The measured characteristics by spectroscopic ellipsometry directly established the presence of AgNPs deposited on the SiNWs. The height of the sublayers and the fractions of Si and Ag in them were determined using the multilayer model and the effective Bruggeman medium approximation in the interpretation of the experimental data. For AgNP layers deposited on an Si wafer surface, the thickness (from 2.3 to 7.8 nm) and complex dielectric functions were verified within the framework of the Drude–Lorentz model. The optical properties of Ag/SiNW structures with complex spatial geometry were simulated in the COMSOL Multiphysics software. The expected localization of the electric field on the surface and near the AgNP was observed as a result of the plasmon resonance excitation. The calculated enhancement factor reached 1010, which indicates the possibility of using such structures as substrates for surface-enhanced Raman scattering.
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Pigeonneau, Franck, Alexandre Cornet, and Fredéric Lopépé. "Thermoconvective instabilities of a non-uniform Joule-heated liquid enclosed in a rectangular cavity." Journal of Fluid Mechanics 843 (March 23, 2018): 601–36. http://dx.doi.org/10.1017/jfm.2018.168.
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Natural convection produced by a non-uniform internal heat source is studied numerically. Our investigation is limited to a two-dimensional enclosure with an aspect ratio equal to two. The energy source is Joule dissipation produced by an electric potential applied through two electrodes corresponding to a fraction of the vertical walls. The system of conservative equations of mass, momentum, energy and electric potential is solved assuming the Boussinesq approximation with a discontinuous Galerkin finite element method integrated over time. Three parameters are involved in the problem: the Rayleigh number $Ra$, the Prandtl number $Pr$ and the electrode length $L_{e}$ normalized by the enclosure height. The numerical method has been validated in a case where electrodes have the same length as the vertical walls, leading to a uniform source term. The threshold of convection is established above a critical Rayleigh number, $Ra_{cr}=1702$. Due to asymmetric boundary conditions on thermal field, the onset of convection is characterized by a transcritical bifurcation. Reduction of the size of the electrodes (from bottom up) leads to disappearance of the convection threshold. As soon as the electrode length is smaller than the cavity height, convection occurs even for small Rayleigh numbers below the critical value determined previously. At moderate Rayleigh number, the flow structure is mainly composed of a left clockwise rotation cell and a right anticlockwise rotation cell symmetrically spreading around the vertical middle axis of the enclosure. Numerical simulations have been performed for a specific $L_{e}=2/3$ with $Ra\in [1;10^{5}]$ and $Pr\in [1;10^{3}]$. Four kinds of flow solutions are established, characterized by a two-cell symmetric steady-state structure with down-flow in the middle of the cavity for the first one. A first instability occurs for which a critical Rayleigh number depends strongly on the Prandtl number when $Pr<3$. The flow structure becomes asymmetric with only one steady-state cell. A second instability occurs above a second critical Rayleigh number that is quasiconstant when $Pr>10$. The flow above the second critical Rayleigh number becomes periodic in time, showing that the onset of unsteadiness is similar to the Hopf bifurcation. When $Pr<3$, a fourth steady-state solution is established when the Rayleigh number is larger than the second critical value, characterized by a steady-state structure with up-flow in the middle of the cavity.
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Zhang, Ya, Duc Duy Nguyen, Kewei Du, Jin Xu, and Shan Zhao. "Time-Domain Numerical Solutions of Maxwell Interface Problems with Discontinuous Electromagnetic Waves." Advances in Applied Mathematics and Mechanics 8, no. 3 (January 27, 2016): 353–85. http://dx.doi.org/10.4208/aamm.2014.m811.
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Abstract.This paper is devoted to time domain numerical solutions of two-dimensional (2D) material interface problems governed by the transverse magnetic (TM) and transverse electric (TE) Maxwell's equations with discontinuous electromagnetic solutions. Due to the discontinuity in wave solutions across the interface, the usual numerical methods will converge slowly or even fail to converge. This calls for the development of advanced interface treatments for popular Maxwell solvers. We will investigate such interface treatments by considering two typical Maxwell solvers – one based on collocation formulation and another based on Galerkin formulation. To restore the accuracy reduction of the collocation finite-difference time-domain (FDTD) algorithm near an interface, the physical jump conditions relating discontinuous wave solutions on both sides of the interface must be rigorously enforced. For this purpose, a novel matched interface and boundary (MIB) scheme is proposed in this work, in which new jump conditions are derived so that the discontinuous and staggered features of electric and magnetic field components can be accommodated. The resulting MIB time-domain (MIBTD) scheme satisfies the jump conditions locally and suppresses the staircase approximation errors completely over the Yee lattices. In the discontinuous Galerkin time-domain (DGTD) algorithm – a popular GalerkinMaxwell solver, a proper numerical flux can be designed to accurately capture the jumps in the electromagnetic waves across the interface and automatically preserves the discontinuity in the explicit time integration. The DGTD solution to Maxwell interface problems is explored in this work, by considering a nodal based high order discontinuous Galerkin method. In benchmark TM and TE tests with analytical solutions, both MIBTD and DGTD schemes achieve the second order of accuracy in solving circular interfaces. In comparison, the numerical convergence of the MIBTD method is slightly more uniform, while the DGTD method is more flexible and robust.
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Penskikh, Yury, Sergey Lunyushkin, and Vyacheslav Kapustin. "Geomagnetic method for automatic diagnostics of auroral oval boundaries in two hemispheres of Earth." Solnechno-Zemnaya Fizika 7, no. 2 (June 30, 2021): 63–76. http://dx.doi.org/10.12737/szf-72202106.
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The ground-based automatic method for determining auroral oval (AO) boundaries developed by the authors [Lunyushkin, Penskikh, 2019] has been modified and expanded to the Southern Hemisphere. Input data of the method contains large-scale distributions of the equivalent current function and field-aligned current density calculated in the polar ionospheres of two hemispheres in a uniform ionospheric conductance approximation based on the magnetogram inversion technique and the geomagnetic database of the world network of stations of the SuperMAG project. The software implementation of the method processes large volumes of time series of input data and produces coordinates of the main boundaries of AO in both hemi- spheres: the boundaries of the ionospheric convection reversal, the AO polar and equatorial boundaries, the lines of maximum density of field-aligned currents and auroral electrojets. The automatic method reduces the processing time for a given amount of data by 2–3 orders of magnitude (up to minutes and hours) compared to the manual method, which requires weeks and months of laborious operator work on the same task, while both methods are comparable in accuracy. The automatic geomagnetic method has been tested for diagnostics of AO boundaries during the isolated substorm of August 27, 2001, for which the expected synchronous dynamics of polar caps in two hemispheres has been confirmed. We also show the AO boundaries identified are in qualitative agreement with simultaneous AO images from the IMAGE satellite, as well as with the results of the OVATION and APM models; the boundary of ionospheric convection reversal, determined by the geomagnetic method in two hemispheres, is consistent with the maps of the electric potential of the ionosphere according to the SuperDARN-RG96 model.
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Penskikh, Yury, Sergey Lunyushkin, and Vyacheslav Kapustin. "Geomagnetic method for automatic diagnostics of auroral oval boundaries in two hemispheres of Earth." Solar-Terrestrial Physics 7, no. 2 (June 30, 2021): 57–69. http://dx.doi.org/10.12737/stp-72202106.
Full textAbstract:
The ground-based automatic method for determining auroral oval (AO) boundaries developed by the authors [Lunyushkin, Penskikh, 2019] has been modified and expanded to the Southern Hemisphere. Input data of the method contains large-scale distributions of the equivalent current function and field-aligned current density calculated in the polar ionospheres of two hemispheres in a uniform ionospheric conductance approximation based on the magnetogram inversion technique and the geomagnetic database of the world network of stations of the SuperMAG project. The software implementation of the method processes large volumes of time series of input data and produces coordinates of the main boundaries of AO in both hemi- spheres: the boundaries of the ionospheric convection reversal, the AO polar and equatorial boundaries, the lines of maximum density of field-aligned currents and auroral electrojets. The automatic method reduces the processing time for a given amount of data by 2–3 orders of magnitude (up to minutes and hours) compared to the manual method, which requires weeks and months of laborious operator work on the same task, while both methods are comparable in accuracy. The automatic geomagnetic method has been tested for diagnostics of AO boundaries during the isolated substorm of August 27, 2001, for which the expected synchronous dynamics of polar caps in two hemispheres has been confirmed. We also show the AO boundaries identified are in qualitative agreement with simultaneous AO images from the IMAGE satellite, as well as with the results of the OVATION and APM models; the boundary of ionospheric convection reversal, determined by the geomagnetic method in two hemispheres, is consistent with the maps of the electric potential of the ionosphere according to the SuperDARN-RG96 model.
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Лунюшкин, Сергей, Sergey Lunyushkin, Владимир Мишин, Vladimir Mishin, Юрий Караваев, Yuriy Karavaev, Юрий Пенских, Yury Penskikh, Вячеслав Капустин, and Vyacheslav Kapustin. "Studying the dynamics of electric currents and polar caps in ionospheres of two hemispheres during the August 17, 2001 geomagnetic storm." Solar-Terrestrial Physics 5, no. 2 (June 28, 2019): 15–27. http://dx.doi.org/10.12737/stp-52201903.
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The magnetogram inversion technique (MIT), developed at ISTP SB RAS more than forty years ago, has been used until recently only in the Northern Hemisphere. In recent years, MIT has been improved and extended to make instantaneous calculations of 2D distributions of electric fields, horizontal and field-aligned currents in two polar ionospheres. The calculations were carried out based on one-minute ground-based geomagnetic measurements from the worldwide network of stations in both hemispheres (SuperMAG). In this paper, this extended technique is used in the approximation of uniform ionospheric conductance and is applied for the first time to calculations of equivalent and field-aligned currents in two hemispheres through the example of the August 17, 2001 geomagnetic storm. We have obtained the main and essential result: the advanced MIT-ISTP can calculate large-scale distributions of ionospheric convection and FACs in the Northern (N) and Southern (S) polar ionospheres with a high degree of expected hemispheric similarity between these distributions. Using the said event as an example, we have established that the equivalent and field-aligned currents obtained with the advanced technique exhibit the expected dynamics of auroral electrojets and polar caps in two hemispheres. Hall current intensities in polar caps and auroral electrojets, calculated from the equivalent current function, change fairly synchronously in the N and S hemispheres throughout the magnetic storm. Both (westward and eastward) electrojets of the N hemisphere are markedly more intense than respective electrojets of the S hemisphere, and the Hall current in the north polar cap is almost twice as intense as that in the south one. This interhemispheric asymmetry is likely to be due to seasonal conductance variations, which is implicitly contained in the current function. From FAC distributions we determine auroral oval boundaries and calculate magnetic fluxes through the polar caps in the N and S hemispheres. These magnetic fluxes coincide with an accuracy of about 5 % and change almost synchronously during the magnetic storm. In the N hemisphere, the magnetic flux in the dawn polar cap is more intense that that in the dusk one, and vice versa in the S hemisphere. These asymmetries (dawn–dusk and interhemispheric) in the polar caps are consistent with the theory of reconnection for IMF By>0 and with satellite images of auroral ovals; both of these asymmetries decrease during the substorm expansion phase.
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Лунюшкин, Сергей, Sergey Lunyushkin, Владимир Мишин, Vladimir Mishin, Юрий Караваев, Yuriy Karavaev, Юрий Пенских, Yury Penskikh, Вячеслав Капустин, and Vyacheslav Kapustin. "Studying the dynamics of electric currents and polar caps in ionospheres of two hemispheres during the August 17, 2001 geomagnetic storm." Solnechno-Zemnaya Fizika 5, no. 2 (June 28, 2019): 17–29. http://dx.doi.org/10.12737/szf-52201903.
Full textAbstract:
The magnetogram inversion technique (MIT), developed at ISTP SB RAS more than forty years ago, has been used until recently only in the Northern Hemisphere. In recent years, MIT has been improved and extended to make instantaneous calculations of 2D distributions of electric fields, horizontal and field-aligned currents in two polar ionospheres. The calculations were carried out based on one-minute ground-based geomagnetic measurements from the worldwide network of stations in both hemispheres (SuperMAG). In this paper, this extended technique is used in the approximation of uniform ionospheric conductance and is applied for the first time to calculations of equivalent and field-aligned currents in two hemispheres through the example of the August 17, 2001 geomagnetic storm. We have obtained the main and essential result: the advanced MIT-ISTP can calculate large-scale distributions of ionospheric convection and FACs in the Northern (N) and Southern (S) polar ionospheres with a high degree of expected hemispheric similarity between these distributions. Using the said event as an example, we have established that the equivalent and field-aligned currents obtained with the advanced technique exhibit the expected dynamics of auroral electrojets and polar caps in two hemispheres. Hall current intensities in polar caps and auroral electrojets, calculated from the equivalent current function, change fairly synchronously in the N and S hemispheres throughout the magnetic storm. Both (westward and eastward) electrojets of the N hemisphere are markedly more intense than respective electrojets of the S hemisphere, and the Hall current in the north polar cap is almost twice as intense as that in the south one. This interhemispheric asymmetry is likely to be due to seasonal conductance variations, which is implicitly contained in the current function. From FAC distributions we determine auroral oval boundaries and calculate magnetic fluxes through the polar caps in the N and S hemispheres. These magnetic fluxes coincide with an accuracy of about 5 % and change almost synchronously during the magnetic storm. In the N hemisphere, the magnetic flux in the dawn polar cap is more intense that that in the dusk one, and vice versa in the S hemisphere. These asymmetries (dawn–dusk and interhemispheric) in the polar caps are consistent with the theory of reconnection for IMF By>0 and with satellite images of auroral ovals; both of these asymmetries decrease during the substorm expansion phase.
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Bologna, Mauro. "Exact Approach to Uniform Time-Varying Magnetic Field." Mathematical Problems in Engineering 2018 (October 16, 2018): 1–8. http://dx.doi.org/10.1155/2018/9521975.
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In this paper, we will find in terms of Fourier integrals an exact expression for the magnetic and electric fields generated by an infinite solenoid where an arbitrary current density J(t) flows. Considering the central region of an infinite solenoid, we will obtain an exact expression relating the flowing current and the magnetic and electric fields as functions of the time. Being an exact expression, it will allow us to go beyond the quasistatic approximation. The result can apply in theoretical problems and experimental setups where the flowing current may change abruptly in time, such as pulsed or stochastic currents.
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Muñoz-Enano, Jonathan, Jesús Martel, Paris Vélez, Francisco Medina, Lijuan Su, and Ferran Martín. "Parametric Analysis of the Edge Capacitance of Uniform Slots and Application to Frequency-Variation Permittivity Sensors." Applied Sciences 11, no. 15 (July 29, 2021): 7000. http://dx.doi.org/10.3390/app11157000.
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This paper presents a parametric analysis relative to the effects of the dielectric constant of the substrate, substrate thickness and slot width on the edge capacitance of a slot-based resonator. The interest is to find the conditions (ranges of the previously cited parameters) compatible with the presence of a quasi-magnetic wall in the plane of the slot (or plane of the metallization). If such magnetic wall is present (or roughly present), the electric field in the plane of the slot is tangential (or quasi-tangential) to it and the edge capacitance can be considered to be the parallel combination of the capacitances at both sides of the slot. Moreover, variations in one of such capacitances, e.g., caused by a change in the material on top of the slot, or by a modification of the dielectric constant of the substrate do not affect the opposite capacitance. Under the magnetic wall approximation, the capacitance of certain electrically small slot-based resonators can be easily linked to the dielectric constant of the material present on top of it. The consequence is that such resonators can be used as sensing elements in a permittivity sensor and the dielectric constant of the so-called material under test (MUT) can be determined from the measured resonance frequency and a simple analytical expression. In this paper, the results of this parametric analysis are validated by considering several sensing structures based on dumbbell defect ground structure (DB-DGS) resonators of different dimensions.
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Siu, Zhuo Bin, Mansoor B. A. Jalil, and Seng Ghee Tan. "Hamiltonian term for a uniform dc electric field under the adiabatic approximation." Physical Review A 97, no. 2 (February 1, 2018). http://dx.doi.org/10.1103/physreva.97.022101.
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Panda, S., B. K. Panda, S. Fung, and C. D. Beling. "Stark Shift and Field Induced Tunneling in Doped Quantum Wells with Arbitrary Potential Profiles." MRS Proceedings 450 (1996). http://dx.doi.org/10.1557/proc-450-165.
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ABSTRACTThe energies and resonance widths of single doped quantum wells consisting of Al-GaAs/GaAs with rectangular and annealing induced diffusion modified shapes are calculated under an uniform electric field using the stabilization method. The electronic structure is calculated without an electric field in the finite temperature density functional theory with exchange-correlation potential treated in the local density approximation. Our scheme for solving the Schrödinger and Poisson equations is based on the Fourier series method. The electric field is added to the self-consistent potential and energies are obtained as a function of the combined width of the well and barriers. This yields us the stabilization graph from which the energies and resonance widths at different field strengths are extracted using the Fermi Golden rule.
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Trukhanova, Mariya Iv, and Pavel Andreev. "A quantum hydrodynamical model of skyrmions with electrical dipole moments and novel magneto-electric skyrmion Hall effect." Progress of Theoretical and Experimental Physics 2020, no. 4 (April 1, 2020). http://dx.doi.org/10.1093/ptep/ptaa036.
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Abstract To introduce novel ways of manipulating the skyrmion dynamics we need to develop new fundamental models. Many-particle quantum hydrodynamics allows us to study inter-skyrmion interactions in the approximation of point-particle skyrmions, which were discovered in multiferroic insulators, where the spiral magnetic structure is accompanied by a finite electric dipole moment. We propose a new model of many-particle quantum hydrodynamics for dipolar skyrmions with dipole–dipole interaction, in the presence of electric and magnetic field gradients. Based on the developed model we find a new way to control the positions of skyrmions, using the crossed gradients of magnetic and electric fields or a novel magneto-electric Hall effect. We have shown that the influence of non-uniform magnetic field provides circular motion of the dipolar skyrmion in the plane with the frequency determined by the derivative of the external magnetic field and the amplitude of the dipole moment. We study the wave processes in the system of skyrmions. We investigate hydrodynamic waves in a skyrmion gas in crossed non-uniform electric and magnetic fields, and predict the generation of a new type of hydrodynamic waves and instabilities. Also, we predict a new type of polarization waves in a rigid skyrmion gas with the dipole–dipole interaction.
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Brevik, Iver H., and Moshe M. Chaichian. "Electric current and heat production by a neutral carrier: an effect of the axion." European Physical Journal C 82, no. 3 (March 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10150-1.
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AbstractA general axion-electrodynamic formalism is presented on the phenomenological level when the environment is dielectric (permittivity and permeability assumed to be constants). Thereafter, a strong and uniform magnetic field is considered in the z direction, the field region having the form of a long material cylinder (which corresponds to the haloscope setup). If the axion amplitude depends on time only, the axions give rise to an oscillating electric current in the z direction. We estimate the magnitudes of the azimuthal magnetic fields and the accompanying Joule heating in the cylinder, taking the cylinder to have ordinary dissipative properties. We evaluate and calculate the electric current and the heat production separately, without using the effective approximation, both when there is a strong magnetic field and when there is a strong electric one, showing that with the magnetic field there is a heat production, while with the electric field there is not. The heat generation that we consider, is a nontrivial effect as it is generated by the electrically neutral axions, and has obvious consequences for axion thermodynamics. The heat production can moreover have an additional advantage, since the effect is accumulative and so grows with time. The boundary conditions (in a classical sense) are explained and the use of them in a quantum mechanical context is discussed. This point is nontrivial, accentuated in particular in connection with the Casimir effect. For comparison purposes, we present finally some results for heat dissipation taken from the theory of viscous cosmology.
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"On relaxation processes in a completely ionized plasma." 3, 2020, no. 3 (2020). http://dx.doi.org/10.26565/2312-4334-2020-3-03.
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Relaxation of the electron energy and momentum densities is investigated in spatially uniform states of completely ionized plasma in the presence of small constant and spatially homogeneous external electric field. The plasma is considered in a generalized Lorentz model which contrary to standard one assumes that ions form an equilibrium system. Following to Lorentz it is neglected by electron-electron and ion-ion interactions. The investigation is based on linear kinetic equation obtained by us early from the Landau kinetic equation. Therefore long-range electron-ion Coulomb interaction is consequentially described. The research of the model is based on spectral theory of the collision integral operator. This operator is symmetric and positively defined one. Its eigenvectors are chosen in the form of symmetric irreducible tensors which describe kinetic modes of the system. The corresponding eigenvalues are relaxation coefficients and define the relaxation times of the system. It is established that scalar and vector eigenfunctions describe evolution of electron energy and momentum densities (vector and scalar system modes). By this way in the present paper exact close set of equations for the densities valid for all times is obtained. Further, it is assumed that their relaxation times are much more than relaxation times of all other modes. In this case there exists a characteristic time such that at corresponding larger times the evolution of the system is reduced described by asymptotic values of the densities. At the reduced description electron distribution function depends on time only through asymptotic densities and they satisfy a closed set of equations. In our previous paper this result was proved in the absence of an external electric field and exact nonequilibrium distribution function was found. Here it is proved that this reduced description takes also place for small homogeneous external electric field. This can be considered as a justification of the Bogolyubov idea of the functional hypothesis for the relaxation processes in the plasma. The proof is done in the first approximation of the perturbation theory in the field. However, its idea is true in all orders in the field. Electron mobility in the plasma, its conductivity and phenomenon of equilibrium temperature difference of electrons and ions are discussed in exact theory and approximately analyzed. With this end in view, following our previous paper, approximate solution of the spectral problem is discussed by the method of truncated expansion of the eigenfunctions in series of the Sonine polynomials. In one-polynomial approximation it is shown that nonequilibrium electron distribution function at the end of relaxation processes can be approximated by the Maxwell distribution function. This result is a justification of Lorentz–Landau assumption in their theory of nonequilibrium processes in plasma. The temperature and velocity relaxation coefficients were calculated by us early in one- and two-polynomial approximation.
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Belardinelli, Pierpaolo, Stefano Lenci, and Maurizio Brocchini. "Modeling and Analysis of an Electrically Actuated Microbeam Based on Nonclassical Beam Theory." Journal of Computational and Nonlinear Dynamics 9, no. 3 (February 14, 2014). http://dx.doi.org/10.1115/1.4026223.
Full textAbstract:
This work investigates the mechanical behavior of a clamped-clamped microbeam modeled within the framework of the strain-gradient elasticity theory. The governing equation of motion gives proper account of both the effect of the nonlinear midplane stretching and of an applied axial load. An electric-voltage difference, introducing into the model a further source of nonlinearity, is considered, including also a correction term for fringing field effects. The electric force acting on the microbeam is rearranged by means of the Chebyshev method, verifying the accuracy of the proposed approximation. The results show that a uniform error on the whole domain can be achieved. The static solution is obtained by a numerical differential quadrature method. The paper looks into the variation of the maximal deflection of the microbeam with respect to several parameters. Study of the pull-in limit on the high-order material parameters introduced by the nonclassical approach and a comparison with respect to the classical beam theory are also carried out. The numerical simulation indicates that the static response is larger, affected by the use of a nonclassical theory near the pull-in instability regime. The dynamical problem is, finally, analyzed, deriving the multi degree-of-freedom problem through a Galerkin-based approach. The study on the single degree-of-freedom model enables us to note the large influence of the nonlinear terms.
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Avital, E. J., and T. Miloh. "Self-thermophoresis of laser-heated spherical Janus particles." European Physical Journal E 44, no. 11 (November 2021). http://dx.doi.org/10.1140/epje/s10189-021-00128-4.
Full textAbstract:
Abstract An analytic framework is presented for calculating the self-induced thermophoretic velocity of a laser-heated Janus metamaterial micro-particle, consisting of two conducting hemispheres of different thermal and electric conductivities. The spherical Janus is embedded in a quiescent fluid of infinite expanse and is exposed to a continuous light irradiation by a defocused laser beam. The analysis is carried under the electrostatic (Rayleigh) approximation (radius small compared to wavelength). The linear scheme for evaluating the temperature field in the three phases is based on employing a Fourier–Legendre approach, which renders rather simple semi-analytic expressions in terms of the relevant physical parameters of the titled symmetry-breaking problem. In addition to an explicit solution for the self-thermophoretic mobility of the heated Janus, we also provide analytic expressions for the slip-induced Joule heating streamlines and vorticity field in the surrounding fluid, for a non-uniform (surface dependent) Soret coefficient. For a ‘symmetric’ (homogeneous) spherical particle, the surface temperature gradient vanishes and thus there is no self-induced thermophoretic velocity field. The ‘inner’ temperature field in this case reduces to the well-known solution for a laser-heated spherical conducting colloid. In the case of a constant Soret phoretic mobility, the analysis is compared against numerical simulations, based on a tailored collocation method for some selected values of the physical parameters. Also presented are some typical temperature field contours and heat flux vectors prevailing in the two-phase Janus as well as light-induced velocity and vorticity fields in the ambient solute and a new practical estimate for the self-propelling velocity. Graphic abstract
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Wang, Boshuo, Aman S. Aberra, Warren M. Grill, and Angel V. Peterchev. "Responses of model cortical neurons to temporal interference stimulation and related transcranial alternating current stimulation modalities." Journal of Neural Engineering, December 13, 2022. http://dx.doi.org/10.1088/1741-2552/acab30.
Full textAbstract:
Abstract Objective. Temporal interference stimulation (TIS) was proposed for non-invasive, focal, and steerable deep brain stimulation. However, the mechanisms underlying experimentally-observed suprathreshold TIS effects are unknown, and prior simulation studies had limitations in the representations of the TIS electric field (E-field) and cerebral neurons. We examined the E-field and neural response characteristics for TIS and related transcranial alternating current stimulation modalities. Approach. Using uniform-field approximation, we simulated a range of stimulation parameters in biophysically-realistic model cortical neurons, including different orientations, frequencies, amplitude ratios, amplitude modulation, and phase difference of the E-fields, and obtained thresholds for both activation and conduction block. Results. For two E-fields with similar amplitudes (representative of E-field distributions at the target region), TIS generated an amplitude-modulated total E-field. Due to the phase difference of the individual E-fields, the total TIS E-field vector also exhibited rotation where the orientations of the two E-fields were not aligned (generally also at the target region). TIS activation thresholds (75–230 V/m) were similar to those of high-frequency stimulation with or without modulation and/or rotation. For E-field dominated by the high-frequency carrier and with minimal amplitude modulation and/or rotation (typically outside the target region), TIS was less effective at activation and more effective at block. Unlike amplitude-modulated high-frequency stimulation, TIS generated conduction block with some orientations and amplitude ratios of individual E-field at very high amplitudes of the total E-field (>1700 V/m). Significance. The complex 3D properties of the TIS E-fields should be accounted for in computational and experimental studies. The mechanisms of suprathreshold cortical TIS appear to involve neural activity block and periodic activation or onset response, consistent with computational studies of peripheral axons. These phenomena occur at E-field strengths too high to be delivered tolerably through scalp electrodes and may inhibit endogenous activity in off-target regions, suggesting limited significance of suprathreshold TIS.