Finite Electrical Conductivity Research Articles

Effects of finite Larmor radius corrections and finite electron inertia on transverse Jean’s gravitational instability of radiative plasma with Hall current for star formation in ISM

We learn the consequences of finite ion Larmor radius (FLR) corrections, finite electron inertia, Hall current and radiative heat-loss function on the Jean’s-gravitational instability of an infinite homogeneous, viscous plasma integrating the impacts of finite electrical resistivity, thermal conductivity and permeability. A general dispersion relation is derived by means of the normal mode analysis method with the assistance of linearized perturbation equations of the problem. We find that the original Jeans criterion of gravitational instability is modified into the radiative instability criterion by the inclusion of thermal conductivity and radiative heat-loss function. The finite electrical resistivity eliminates the impact of the magnetic field and the viscosity of the medium eliminates the impact of FLR from radiative instability. The Hall parameter has no impact on the transverse mode of propagation. Numerical calculations demonstrate the stabilizing impact of temperature-dependent heat-loss function, FLR corrections and the destabilizing impact of density-dependent heat-loss function, finite electron inertia on the Jean’s-gravitational instability.

Relativistic shocks in conductive media

Context. Relativistic shocks are present in all high-energy astrophysical processes involving relativistic plasma outflows interacting with their ambient medium. While they are well understood in the context of relativistic hydrodynamics and ideal magnetohydrodynamics (MHD), there is a limited understanding of the properties related to their propagation in media characterized by finite electrical conductivity. Aims. This work presents a systematic method for the derivation and solution of the jump conditions for relativistic shocks propagating in MHD media with finite electrical conductivity. This method is applied to the numerical solution of the Riemann problem and the determination of the conditions inside the blastwave that is formed when ultrarelativistic magnetized ejecta interact with the circumburst medium during a gamma-ray burst. Methods. We derived the covariant relations expressing the jump conditions in a frame-independent manner. The resulting algebraic equations expressing the Rankine-Hugoniot conditions in the propagation medium’s frame were then solved numerically. A variable adiabatic index equation of state was used in order to obtain a realistic description of the post-shock fluid’s thermodynamics. This method was then employed for the solution of the Riemann problem for the case of a forward and a reverse shock, both of which form during the interaction of a gamma-ray burst ejecta with the circumburst medium. This allowed us to determine the kinematics of the resulting blastwave and the dynamical conditions in its interior. Results. Our solutions clearly depict the impact of the plasma’s electrical conductivity in the properties of the post-shock medium. Two characteristic regimes are identified with respect to the value of a dimensionless parameter that has a linear dependence on the conductivity. For small values of this parameter, the shock affects only the hydrodynamic properties of the propagation medium and leaves its electromagnetic field unaffected. No current layer forms in the shock front; thus, we refer to this as the current-free regime. For large values of this parameter, the ideal MHD regime has been retrieved. We also show that the assumption of a finite electrical conductivity can lead to higher efficiencies in the conversion of the ejecta energy into thermal energy of the blastwave through the reverse shock. The theory developed in this work can be applied to the construction of Riemann solvers for resistive relativistic MHD (RR4MHD).

Generalized cross-helicity in non-ideal magnetohydrodynamics

The objective of the present paper is to investigate the constancy of the topological invariant, denoted the non-barotropic generalized cross-helicity in the case of non-ideal magnetohydrodynamics (MHD). Existing work considers only ideal barotropic MHD and ideal non-barotropic MHD. Here, we consider dissipative processes in the form of thermal conduction, finite electrical conductivity and viscosity and the effect of these processes on the cross-helicity conservation. An analytical approach has been adopted to obtain the mathematical expressions for the time derivative of the cross-helicity. Obtained results show that the generalized cross-helicity is not conserved in the non-ideal MHD limit and indicate which processes affect the helicity and which do not. Furthermore, we indicate the configurations in which this topological constant is conserved despite the dissipative processes. Some examples and applications are also given.

Electrodynamic suspension of particles with finite electrical conductivity

The electrodynamic suspension of micrometric inertialess particles with finite electrical conductivity in the gap between two parallel horizontal electrodes subjected to a DC potential difference is analyzed in a collision-dominated regime in which the mean free path between particle collisions is small compared with the interelectrode distance. Operation with a constant number of suspended particles and with an excess of particles deposited on the lower electrode are modelled. Stationary solutions in a laterally unbounded gap are computed and their linear stability is analyzed. In both cases, these solutions become unstable when the number of suspended particles increases, and they transition to time dependent solutions. Numerical computations show that particle and charge accumulations develop at the lower electrode and eventually become electrohydrodynamic plumes rising across the gap. The electric current carried by the suspended particles from the lower to the upper electrode is a rapidly increasing function of the particle conductivity.

НИЗКОТЕМПЕРАТУРНЫЙ ЭЛЕКТРОННЫЙ ТРАНСПОРТ В ГИБРИДНЫХ ТОНКОПЛЕНОЧНЫХ НАНОСТРУКТУРАХ НА БАЗЕ ЭЛЕКТРОПРОВОДЯЩЕГО ПОЛИМЕРА

Most polymers are usually poor conductors of electric current and, accordingly, they can be classified as organic dielectrics. However, there is a special class of polymers, usually characterized by presence of conjugated pbonds, which provide electron delocalization, leading to electrical conductivity in the ground state of the system. In addition to such materials, there have been found polymers that are insulators in the ground state, but under the influence of external factors demonstrate a finite electrical conductivity. Polydiphenylenephthalide (PDP) belongs to the class of carbocyclic organic electroactive polymers that exhibit electrically conductive properties when an external electric field and/or mechanical stress is applied. The effect is explained by the nonzero density of electronic states inside the band gap. The depth of such states increases if the system accepts an additional electron, which indirectly provides electrical conductivity along the polymer chain. Accordingly, the presence of free electrons in contact region with a metal is an important condition for the appearance of final electrical conductivity in PDP. The working hypothesis that stimulates the proposed study is the assumption that superconducting correlations may arise in the electrically conductive state of an electroactive polymer. In the present work, the transport properties of thin-film lead-PDP-lead structures in two configurations are experimentally studied in a wide temperature range: a layered “sandwich” type and a quasi-planar “field-effect transistor” type. At temperatures below ~8 K, in layered samples, features of the PDP electron transport are observed, which can be explained by the effect of induced superconductivity in a thin film of a conducting polymer enclosed between two massive superconductors (lead). In the planar configuration, the electrical conductivity of the polymer in the plane of the structure does not appear. The reason for this observation may be related to the mechanism of the electrically conductive state of the PDP, characterized by formation of quasi-one-dimensional channels of electric current in the direction perpendicular to the plane of contact with the "donor" of electrons: metal in the normal or superconducting state. The effect of appearance of superconductivity in PDP requires further stidies and is potentially of significant interest for various applications in the field of practical microand nanoelectronics.

Directed flow in relativistic resistive magneto-hydrodynamic expansion for symmetric and asymmetric collision systems

We construct a dynamical model for high-energy heavy-ion collisions based on the relativistic resistive magneto-hydrodynamic framework. Using our newly developed ($3+1$)-dimensional relativistic resistive magneto-hydrodynamics code, we investigate magneto-hydrodynamic expansion in symmetric and asymmetric collision systems as the first application to high-energy heavy-ion collisions. As a realistic initial condition for electromagnetic fields, we consider the solutions of the Maxwell equations with the source term of point charged particles moving in the direction of the beam axis, including finite constant electrical conductivity of the medium. We evaluate the directed flow in the symmetric and asymmetric collisions at BNL Relativistic Heavy Ion Collider energy. We find a significant effect of finite electrical conductivity on the directed flow in the asymmetric collision system. We confirm that a certain amount of energy transfer by dissipation associated with Ohmic conduction occurs in the asymmetric collision system because of the asymmetry of the electric field produced by two different colliding nuclei. Because this energy transfer makes the pressure gradient of the medium flatter, the growth of directed flow decreases.

АНАЛИЗ И ОБРАБОТКА ИНФОРМАЦИИ ДЛЯ ОДНОЙ СТОХАСТИЧЕСКОЙ СИСТЕМЫ СОБОЛЕВСКОГО ТИПА

This article is devoted to the analysis and processing of information for a stochastic model based on the equation of potential distribution in a crystalline semiconductor with the Nelson–Glicklich derivative and the Showalter–Sidorov initial condition. By semiconductors, we mean substances that have a finite electrical conductivity that rapidly increases with increasing temperature. It is assumed that the initial experimental data may be affected by random noise, which leads to the study of the stochastic model. An analysis of the stochastic model of the potential distribution in a crystalline semiconductor is given. Conditions under which there are step-by-step solutions of the model under study with the Showalter–Sidorov initial condition are found. Further, on the basis of the theoretical results, an algorithm for the numerical analysis of the system is given. Its implementation is presented in the form of a computational experiment, which is necessary for the further processing of information.

Transverse thermal instability of partially ionized radiative plasma with impact of neutral collisions and finite electron inertia effect in ISM

The impact of neutral friction, finite electron inertia and radiative heat-loss function on the thermal instability of viscous, partially-ionized plasma has been explored integrating the impacts of finite electrical resistivity and thermal conductivity. Normal mode analysis scheme is used to derive universal dispersion relation by means of the related linearized perturbation equations of the difficulty and a tailored thermal situation of instability is explored. It is finding that the thermal condition of instability is modified owing the occurrence of radiative heat-loss function, thermal conductivity, finite electron inertia and neutral particle. For transverse mode of propagation, we discover that the condition of thermal instability depends on the finite electron inertia, magnetic field strength, radiative heat-loss function, thermal conductivity, neutral particle and finite electrical resistivity, but independent viscosity of two-components. From the graphs, we explored that the temperature dependent heat-loss function, thermal conductivity, neutral collision frequency and viscosity of two-components demonstrates stabilizing effect, while finite electron inertia and finite electrical resistivity demonstrates destabilizing effect. Our results help’s to understand the process of molecular cloud formation in ISM.

One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws

A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyzes the one-dimensional magnetohydrodynamics flows with cylindrical symmetry in the mass Lagrangian coordinates. The medium is assumed inviscid and thermally non-conducting. It is modeled by a polytropic gas. Symmetries and conservation laws are found. The cases of finite and infinite electric conductivity need to be analyzed separately. For finite electric conductivity σ(ρ,p) we perform Lie group classification, which identifies σ(ρ,p) cases with additional symmetries. The conservation laws are found by direct computation. For cases with infinite electric conductivity variational formulations of the equations are considered. Lie group classifications are obtained with the entropy treated as an arbitrary element. A variational formulation allows to use the Noether theorem for computation of conservation laws. The conservation laws obtained for the variational equations are also presented in the original (physical) variables.

Performance Limits of 433 MHz Quarter-wave Monopole Antennas due to Grounding Dimension and Conductivity

Among antennas for Industrial, Scientific and Medical (ISM band) applications at 433 MHz, quarter-wave monopole is a reasonably good trade-off between size, gain, and cost. The electrical performance of the monopole is largely dependent on the quality of the ground plane (size and conductivity), which exhibits a practical limit on the achievable gain as most industrial user environments can provide only a finite ground plane of finite electrical conductivity. Establishing traceability in understanding the performance degradation due to such limits due to the grounding dimension and conductivity is becoming mandatory. To this end, this work leverages universal MATLAB in place of off-the-shelf software (HFSS or CST) for the quarter-wave monopole antenna simulation at 433 MHz parametrised with the ground plane’s dimension with respect to the wavelength (λ). Results indicate that by enlarging the ground plane’s size from 0.14 λ to 14 λ, the gain (directivity for PEC) from the 3D radiation pattern rises from 1.79 dBi, then starts levelling off at 6.7 dBi (5.78 λ), until saturating at 7.49 dBi (13 λ). The radiation efficiency and gain of various grounding conductivity scenarios (e.g., gold, aluminium, steel) are also quantified to inform antenna designers and engineers for commercial, industrial, defence and space applications.

Effects of electrically conductive walls on turbulent magnetohydrodynamic flow in a continuous casting mold

In the present study, we have performed a series of numerical simulations of the turbulent liquid metal flow in a laboratory-scale setup of the continuous casting. The liquid metal flow was subjected to an external non-uniform magnetic field reproducing a realistic electromagnetic brake (EMBr) effect. The focus of this research was on the effects of the finite electrical conductivity of Hartmann walls on the flow and turbulence in the mold. To be able to simulate distributions of the electric potential and current in both the fluid and solid wall domains, we applied our recently developed and validated in-house conjugate MHD solver based on the open-source code OpenFOAM. The dynamic Large Eddy Simulation (LES) method was used to simulate the turbulent flow. The results obtained for the neutral (non-MHD) and MHD cases over a range of the imposed EMBr strengths – all for the perfectly electrically insulated walls – were compared with the available Ultrasound Doppler Velocimetry (UDV) measurements. A good agreement between simulations and experiments was obtained for all simulated cases. Next, we completed a series of simulations including a wide range of the finite electric conductivities (ranging from a weakly to perfectly conducting wall conditions) of the Hartmann walls for a fixed value of the imposed EMBr. The obtained results demonstrated a significant influence of the electric wall conductivities on the flow and turbulence reorganization. It is expected that here provided insights can be applicable for the new generation of the laboratory- and real-scale continuous casting setups.

Plane one-dimensional MHD flows: Symmetries and conservation laws

The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas. The equations are examined for symmetries and conservation laws. For the case of finite electric conductivity we establish Lie group classification, i.e. we describe all cases of the conductivity σ(ρ,p) for which there are symmetry extensions. The conservation laws are derived by direct computation. For the case of infinite electrical conductivity the equations can be brought into a variational form in the Lagrangian coordinates. Lie group classification is performed for the entropy function as an arbitrary element. Using the variational structure, we employ the Noether theorem for obtaining conservation laws. The conservation laws are also given in the physical variables.

Phase field model for electrically induced damage using microforce theory

In this paper, we present a consistent derivation of the phase field model for electrically induced damage. The derivation is based on Gurtin’s microstress and microforce theory and the Coleman–Noll procedure. The resulting model accounts for Ohmic currents, includes charge conservation law and allows for finite electric permittivity and conductivity distribution in the medium. Special attention is devoted to the case when the damaged region is a codimension-two object, i.e., a curve in three dimensions. It is shown that in this case the free energy of the model necessarily includes a high-order term, which ensures the well-posedness of the problem. A special problem setting is proposed to account for the prescribed charge distribution. Local features of the phase field distribution are illustrated with one-dimensional axisymmetric numerical experiments.

General theory of electroadhesion

We present a general theory of electroadhesion assuming layered materials with finite electric conductivity and an air gap resulting from interfacial surface roughness. The theory reduces to the results derived in Persson (2018 J. Chem. Phys. 148 144701) in the appropriate limits. We present numerical results to illustrate the theory.

Rayleigh–Bénard and Bénard–Marangoni magnetoconvection in variable viscosity finitely conducting liquids

AbstractThe thermorheological effect on magneto‐Bénard‐convection is studied numerically in fluids with finite electrical conductivity. A nonlinear thermorheological equation is considered in the problem. The results are compared with the classical approach of constant viscosity, which depicts the fact that the effect of increasing the strength of the magnetic field is to delay the onset of convection. The magnetic field is shown to have a rheostatic influence on convective instabilities. The results obtained by the study have possible applications in the field of astrophysics, sunspots, and in space applications under microgravity.

A new efficient fourth order collocation scheme for solving Burgers’ equation

In present work a new fourth order modified cubic B-spline (mCB) based upon collocation technique (mCBCT4) has been developed to evaluate new numeric results of the nonlinear Burgers’ equation, appear in rigorous real-world physical phenomena like - sound & shock waves in viscous medium, waves in fluid filled viscous elastic tubes, magneto-hydrodynamic-waves in medium with finite electrical-conductivity, in modeling of turbulent fluid, and in continuous stochastic processes. At first, the Burgers’ equation is remodeled into a set of 1st order ordinary differential equations (ODE), in which fourth order accurate approximation of the unknown functions, and its spatial derivatives obtained via mCBCT4. In this way a set of first-order ODE is obtained, which we solve via SSP-RK(ℓ+1,ℓ) scheme (ℓ=3,4). The accuracy, efficiency and effectiveness of the developed technique mCBCT4 is demonstrated in terms of six different test examples of nonlinear Burgers’ equation by computing the error norms: L2 and L∞ errors. The proposed mCBCT4 scheme is also tested for nonlinear Burger’s equation with very small kinematic viscosities. The proposed mCBCT4 is shown unconditionally stable scheme. The numerical findings demonstrate that the developed mCBCT4 performs better than some recently developed good techniques and enables to produces comparably more accurate solutions than some recently developed reliable techniques.

Semi-analytical solutions of seismo-electromagnetic signals arising from the motional induction in 3-D multi-layered media: part I\u2014theoretical formulations

Taking into account the motional induction effect, in which the Earth crust that has finite electrical conductivity vibrates in the ambient geomagnetic field resulting in motionally induced electric current, we derive semi-analytical solutions of seismo-electromagnetic signals generated by an earthquake source in 3-D multi-layered media, which consists of an air half-space and multiple solid layers. First, both the elastic and electromagnetic (EM) wave-fields involved in the governing equations, which have the form of Maxwell’s equations coupled with elastodynamic equations, are expanded by a set of vector basis functions in cylindrical coordinate system. Then, we reorganize the transformed governing equations expressed by expansion coefficients and obtain corresponding first-order ordinary differential equations for the wave-fields in air and solid media. The expansion of the motionally induced electric current and the reorganization of Maxwell’s equations are the most important part, and also the most complicated and tedious part of this work. Thereafter, we solve the first-order ordinary differential equations through the Luco–Apsel–Chen generalized reflection and transmission method gaining solutions of the expansion coefficients. Finally, we obtain the frequency–space-domain semi-analytical solutions written as integrations of corresponding expansion coefficients over wavenumber domain, which can be numerically calculated by the discrete wavenumber method. The time-domain solutions can be achieved by further applying the discrete inverse Fourier transform. To have a numerical stability at any high frequency, we adopt the analytical regularization approach in the derivation process by introducing two artificial interfaces with infinitely small distance from the source. On the basis of the semi-analytical solutions, we can tell that only EM fields of TM mode (in which magnetic fields are transversely polarized) will be induced by SH waves, whereas EM fields of both TE mode (in which magnetic fields are transversely polarized) and TM mode will be induced by P and SV waves. The derived semi-analytical solutions can be used to calculate seismo-electromagnetic signals either below or above the free surface.

Analytical RF Pulse Heating Analysis for High Gradient Accelerating Structures

The main aim of this work is to present a simple method, based on analytical expressions, for obtaining the temperature increase due to the Joule effect inside the metallic walls of an RF accelerating component. This technique relies on solving the 1-D heat-transfer equation for a thick wall, considering that the heat sources inside the wall are the ohmic losses produced by the RF electromagnetic fields penetrating the metal with finite electrical conductivity. Furthermore, it is discussed how the theoretical expressions of this method can be applied to obtain an approximation to the temperature increase in realistic 3-D RF accelerating structures, taking as an example the cavity of an RF electron photoinjector and a traveling wave linac cavity. These theoretical results have been benchmarked with numerical simulations carried out with commercial finite-element method (FEM) software, finding good agreement among them. Besides, the advantage of the analytical method with respect to the numerical simulations is evidenced. In particular, the model could be very useful during the design and optimization phase of RF accelerating structures, where many different combinations of parameters must be analyzed in order to obtain the proper working point of the device, allowing to save time and speed up the process. However, it must be mentioned that the method described in this article is intended to provide a quick approximation to the temperature increase in the device, which of course is not as accurate as the proper 3-D numerical simulations of the component.

Electrocapillary effect in liquid films with an electrically charged interface

Abstract The electrocapillary effect is the change in interfacial tension between two immiscible liquids when subjected to an electric field across the interface. The change in interfacial tension occurs due to variations in the surface charge density of adsorbed ions or polar species at the interface. In the present work, we provide fluid mechanical insights into electrocapillarity-based dynamics of an interface between a passive air layer and a thin liquid film that has small, but finite electrical conductivity. We formulate and solve mathematical equations that model the situation in which a liquid film bounded by an air layer of controllable thickness is sandwiched between two electrode plates, and an electric field is applied across the layers. As the liquid and air have different conductivities, free charges would accumulate at the liquid–air interface to ensure that current is conserved across the layers. In our model, the interfacial tension is assumed to vary as per the classical Lippmann’s equation. The present mathematical model describes spatiotemporal variation of the film height and interfacial charge density as a function of the applied potential, air layer width, and the sensitivity of interfacial tension to the electric potential. Our results show that ultrathin liquid films (

A Material Selection Criterion for Electrostatic Switches Based on Stability Considerations

Recent impressive advances of MEMS technology thanks to integration of emerging materials exhibiting exclusive properties, has led to fabrication of numerous high performance devices. Further development of the field necessitates more accurate analytical models capable of precisely accounting for all existing physical phenomena affected by new materials properties. In this regard, the present paper investigates how finite electrical conductivity of the composing materials may affect the pull-in instability of an electrostatically actuated cantilever MEMS switch. The governing coupled nonlinear equations of an equivalent lumped parameter model are derived by introducing an assumed mode solution to the extended Hamilton’s principle. A Lyapunov-based method is then employed to derive an estimation for the basin of attraction of the stable equilibrium and determine the minimum voltage needed for the cantilever to escape the attractor and touch the contact. Results indicate the substantial effect of electrical resistivity on both instability range and maximum switching frequency of the device. As evidenced by the presented findings the material selection for this type of switches should be made with a broader view bringing into focus the effect of electrical conductivity of the material on stability characteristics of the device.