Isotropic Conduction Research Articles

Relaxation procedures for an iterative MFS algorithm for two-dimensional steady-state isotropic heat conduction Cauchy problems

We investigate two algorithms involving the relaxation of either the given Dirichlet data (boundary temperatures) or the prescribed Neumann data (normal heat fluxes) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [26] applied to two-dimensional steady-state heat conduction Cauchy problems, i.e. Cauchy problems for the Laplace equation. The two mixed, well-posed and direct problems corresponding to each iteration of the numerical procedure are solved using a meshless method, namely the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. The iterative MFS algorithms with relaxation are tested for Cauchy problems associated with the Laplace operator in various two-dimensional geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the method.

Numerical simulation of hot accretion flows with thermal conduction

We report on the effects of isotropic thermal conduction in non-radiative collisionless accretion flows in two dimensions. In comparison to accretion flows without conduction, we find that the disk generally becomes cooler and thinner. Specifically, the magnitude of this effect depends on the kinetic viscosity coefficient. If it is proportional to density, the density profile of the accretion flow is flat, therefore the effect is not very obvious. But, if it is proportional to r1/2, as is usual for the “α” disk description, the density profile is steeper. Therefore, the effect will be much more obvious, with the temperature profile of the accretion flow becoming much flatter. This will have important observational consequences.

Higher‐order energy‐momentum consistent time‐stepping schemes for dynamic finite thermo‐viscoelasticity

AbstractThis paper is concerned with the energy consistent simulation of a finite thermo‐viscoelastic continuum body. The algorithm is based on a four‐field formulation in the Lagrangian description, in which the deformation field, the velocity field, the temperature field and a strain‐like viscous internal variable field are independent unknowns. The Lagrangian temperature field is determined by the entropy evolution equation associated with Fourier's law of isotropic heat conduction. The viscous evolution equation is derived from a nonlinear internal dissipation. The coupled nonlinear differential equations are discretised by a new space‐time finite element method, consisting of continuous as well as discontinuous finite element approximations in time. Owing to particular time approximations in the constitutive laws, the energy and momentum balances are exactly fulfilled in the fully discrete case. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulation of the Magnetothermal Instability

In many magnetized, dilute astrophysical plasmas, thermal conduction occurs almost exclusively parallel to magnetic field lines. In this case, the usual stability criterion for convective stability, the Schwarzschild criterion, which depends on entropy gradients, is modified. In the magnetized long mean free path regime, instability occurs for small wavenumbers when (dP/dz)(dln T/dz) > 0, which we refer to as the Balbus criterion. We refer to the convective-type instability that results as the magnetothermal instability (MTI). We use the equations of MHD with anisotropic electron heat conduction to numerically simulate the linear growth and nonlinear saturation of the MTI in plane-parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured from the simulations are in excellent agreement with the weak field dispersion relation. The addition of isotropic conduction, e.g. radiation, or strong magnetic fields can damp the growth of the MTI and affect the nonlinear regime. The instability saturates when the atmosphere becomes isothermal as the source of free energy is exhausted. By maintaining a fixed temperature difference between the top and bottom boundaries of the simulation domain, sustained convective turbulence can be driven. MTI-stable layers introduced by isotropic conduction are used to prevent the formation of unresolved, thermal boundary layers. We find that the largest component of the time-averaged heat flux is due to advective motions as opposed to the actual thermal conduction itself. Finally, we explore the implications of this instability for a variety of astrophysical systems, such as neutron stars, the hot intracluster medium of galaxy clusters, and the structure of radiatively inefficient accretion flows.

A method of fundamental solutions for inverse heat conduction problems in an anisotropic medium

Recently, Hon and Wei proposed a method of fundamental solutions for solving isotropic inverse heat conduction problems (IHCP). It provides an efficient global approximation scheme in both spatial and time domains. In this paper, we try to extend the inherently meshless and integration-free method to solve 2D IHCP in an anisotropic medium. First, we acquire the fundamental solution of the governing equation through variables transformation. Then the truncated singular value decomposition and the L-curve criterion are applied to solve the resulting matrix equation which is highly ill-conditioned. Results for several numerical examples are presented to demonstrate the efficiency of the method proposed. The relationship between the accuracy of the numerical solutions and the value of the parameter T is also investigated.

Separation of Orbital Contributions to the Optical Conductivity ofBaVS3

The correlation-driven metal-insulator transition (MIT) of BaVS(3) was studied by polarized infrared spectroscopy. In the metallic state two types of electrons coexist at the Fermi energy: the quasi-1D metallic transport of A(1g) electrons is superimposed on the isotropic hopping conduction of localized E(g) electrons. The "bad-metal" character and the weak anisotropy are the consequences of the large effective mass m(eff) approximately 7 m(e) and scattering rate Gamma > or = 160 meV of the quasiparticles in the A(1g) band. There is a pseudogap above T(MI) = 69 K, and in the insulating phase the gap follows the BCS-like temperature dependence of the structural order parameter with Delta(ch) approximately 42 meV in the ground state. The MIT is described in terms of a weakly coupled two-band model.

A meshless BEM for isotropic heat conduction problems with heat generation and spatially varying conductivity

In this paper, a new and simple boundary-domain integral equation is presented for heat conduction problems with heat generation and non-homogeneous thermal conductivity. Since a normalized temperature is introduced to formulate the integral equation, temperature gradients are not involved in the domain integrals. The Green's function for the Laplace equation is used and, therefore, the derived integral equation has a unified form for different heat generations and thermal conductivities. The arising domain integrals are converted into equivalent boundary integrals using the radial integration method (RIM) by expressing the normalized temperature using a series of basis functions and polynomials in global co-ordinates. Numerical examples are given to demonstrate the robustness of the presented method. Copyright © 2005 John Wiley & Sons, Ltd.

Nonlinear Evolution of the Magnetothermal Instability in Two Dimensions

In weakly magnetized, dilute plasmas in which thermal conduction along magnetic field lines is important, the usual convective stability criterion is modified. Instead of depending on entropy gradients, instability occurs for small wavenumbers when (∂P/∂z)(∂ ln T/∂z) > 0, which we refer to as the Balbus criterion. We refer to the convective instability that results in this regime as the magnetothermal instability (MTI). We use numerical MHD simulations that include anisotropic electron heat conduction to follow the growth and saturation of the MTI in two-dimensional, plane-parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured in the simulations agree with the weak-field dispersion relation. We investigate the effect of strong fields and isotropic conduction on the linear properties and nonlinear regime of the MTI. In the nonlinear regime, the instability saturates and convection decays away when the atmosphere becomes isothermal. Sustained convective turbulence can be driven if there is a fixed temperature difference between the top and bottom edges of the simulation domain, and if isotropic conduction is used to create convectively stable layers that prevent the formation of unresolved, thermal boundary layers. The largest component of the time-averaged heat flux is due to advective motions. These results have implications for a variety of astrophysical systems, such as the temperature profile of hot gas in galaxy clusters and the structure of radiatively inefficient accretion flows.

Three-dimensional MHD simulations of X-ray emitting subcluster plasmas in cluster of galaxies

Recent high resolution observations by the Chandra X-ray satellite revealed various substructures in hot X-ray emitting plasmas in cluster of galaxies. For example, Chandra revealed the existence of sharp discontinuities in the surface brightness at the leading edge of subclusters in merging clusters (e.g., Abell 3667), where the temperature drops sharply across the fronts. These sharp edges are called cold fronts. We present results of three-dimensional (3D) magnetohydrodynamic simulations of the interaction between a dense subcluster plasma and ambient magnetized intracluster medium. Anisotropic heat conduction along magnetic field lines is included. At the initial state, magnetic fields are assumed to be uniform and transverse to the motion of the dense subcluster. Since magnetic fields ahead of the subcluster slip toward the third direction in the 3D case, the strength of magnetic fields in this region can be reduced compared to that in the 2D case. Nevertheless, a cold front can be maintained because the magnetic field lines wrapping around the forehead of the subcluster suppress the heat conduction across them. On the other hand, when the magnetic field is absent, a cold front cannot be maintained because isotropic heat conduction from the hot ambient plasma rapidly heats the cold subcluster plasma.

MHD SIMULATIONS OF A MOVING SUB CLUMP WITH HEAT CONDUCTION

High resolution observations of cluster of galaxies by Chandra have revealed the existence of an X-ray emitting comet-like galaxy C153 in the core of cluster of galaxies A2125. The galaxy C153 moving fast in the cluster core has a distinct X-ray tail on one side, obviously due to ram pressure stripping, since the galaxy C153 crossed the central region of A2125. The X-ray emitting plasma in the tail is substantially cooler than the ambient plasma. We present results of two-dimensional magnetohydrodynamic simulations of the time evolution of a subclump like C153 moving in magnetized intergalactic matter. Anisotropic heat conduction is included. We found that the magnetic fields are essential for the existence of the cool X-ray tail, because in non-magnetized plasma the cooler subclump tail is heated up by isotropic heat conduction from the hot ambient plasma and does not form such a comet-like tail.

Thermal conduction in cosmological SPH simulations

Thermal conduction in the intracluster medium has been proposed as a possible heating mechanism for offsetting central cooling losses in rich clusters of galaxies. In this study, we introduce a new formalism to model conduction in a diffuse ionised plasma using smoothed particle hydrodynamics (SPH), and we implement it in the parallel TreePM/SPH-code GADGET-2. We consider only isotropic conduction and assume that magnetic suppression can be described in terms of an effective conductivity, taken as a fixed fraction of the temperature-dependent Spitzer rate. We also account for saturation effects in low-density gas. Our formulation manifestly conserves thermal energy even for individual and adaptive timesteps, and is stable in the presence of small-scale temperature noise. This allows us to evolve the thermal diffusion equation with an explicit time integration scheme along with the ordinary hydrodynamics. We use a series of simple test problems to demonstrate the robustness and accuracy of our method. We then apply our code to spherically symmetric realizations of clusters, constructed under the assumptions of hydrostatic equilibrium and a local balance between conduction and radiative cooling. While we confirm that conduction can efficiently suppress cooling flows for an extended period of time in these isolated systems, we do not find a similarly strong effect in a first set of clusters formed in self-consistent cosmological simulations. However, their temperature profiles are significantly altered by conduction, as is the X-ray luminosity.

A Green's function for steady‐state two‐dimensional isotropic heat conduction across a homogeneously imperfect interface

AbstractThe problem of calculating the steady‐state two‐dimensional temperature field in a thermally isotropic bimaterial which has a homogeneously imperfect interface is considered. There is a temperature jump across the imperfect interface. To devise a boundary element method, which does not require the imperfect interface to be discretized, for the numerical solution of the problem, a special Green's function satisfying the appropriate interface condition is derived. A specific test problem is solved numerically using the boundary element method. Copyright © 2004 John Wiley & Sons, Ltd.

Effects of Thermal Conduction on the X‐Ray and Synchrotron Emission from Supernova Remnants

Several physical mechanisms have been studied in order to explain why composite supernova remnants (SNRs) have shell-like morphologies in the radio continuum while their X-ray emission is centrally peaked. One of the proposed mechanisms has been the presence of thermal conduction, which can raise the density at the center of SNRs, increasing the X-ray emission from these regions. In this work, we have carried out axisymmetric numerical simulations with the adaptive grid Yguaz?-a code, which includes advection of the magnetic field and thermal conduction. We have considered cases with anisotropic and isotropic thermal conduction, as well as with no conduction. We have simulated X-ray (as well as radio synchrotron) emission maps from our numerical simulations, which can be directly compared with observations.

Characterization of the metallic phases in BaCo0.9Ni0.1S1.87

The temperature dependence of the resistivity along the c axis and in the a-b plane of layered ${\mathrm{BaCo}}_{0.9}{\mathrm{Ni}}_{0.1}{\mathrm{S}}_{1.87}$ has been measured on a single crystal under hydrostatic pressures. The monoclinic metallic (LTM) phase stable at $Tl~150\mathrm{K}$ is suppressed under a pressure $Pg1.5\mathrm{kbar};$ it has a nearly isotropic conductivity. Pressure induces an insulator-metal (IM) transition at $Pg10\mathrm{kbar}$ within the tetragonal phase. A change from a nearly isotropic conduction to a highly anisotropic conduction is associated with the IM transition. Isotropic conduction in the LTM phase is consistent with its crystallographic structure; the IM transition in the tetragonal phase has been interpreted to be due to a high-spin to low-spin transition of Co(II) ions. The resistivity and thermal conductivity of the LTM metallic phase are typical of those of a normal metal.

Computer simulation of intrinsic defects inPbWO4

A computer simulation study has been performed to investigate the intrinsic defects in ${\mathrm{PbWO}}_{4}$ (PWO). The interatomic potentials were empirically fit to the known crystal properties. Calculations reveal that PbO nonstoichiometry dominates the intrinsic defects in PWO, whereas the oxygen Frenkel defects will only be significant at high temperature. Through binding-energy calculations, defect clusters are predicated to actually exist in the material. An analysis of activation energy corroborates that oxygen vacancy migration is the mobile ionic defect in PWO, moreover, isotropic conduction is suggested despite the tetragonal symmetry of the crystal. The concentration dependence of electronic defects on the oxygen partial pressure is also studied.

Isotropic and anisotropic conduction patterns in the isolated feline duodenum

Isotropic and anisotropic conduction patterns in the isolated feline duodenum

Comments about the paper entitled “A generalized boundary integral equation for isotropic heat conduction with spatially varying thermal conductivity” by A. J. Kassab and E. Divo

An integral formulation for heat conduction problems in non-homogeneous media has recently been proposed by Kassab and Divo [Engineering Analysis with Boundary Elements 1996;18:273]. The goal of this communication is to revisit and clarify two key features of the formulation of Kassab and Divo. First, the contention that the integral equation formulation proposed by them does not possess the desired boundary-only character is made and substantiated; it is shown in particular that Eq. (10)therein does not hold owing to the fact that a crucial requirement for the fundamental solution, Eqs. (5c) and (5d) therein, is actually not met. Second, the limiting process associated with a vanishing neighbourhood in connection with the particular kernel function used therein is revisited.

On the existence of Kassab and Divo's generalized boundary integral equation formulation for isotropic heterogeneous steady state heat conduction problems

In this note, we prove that the boundary integral equation formulation for isotropic heterogeneous steady state conduction problems recently suggested Kassab and Divo is not general. We also obtain the complete integral representation for the new formulation which is of the boundary domain type instead of the boundary only type, as originally proposed by the above authors. The resulting integral equation representation possesess the same difficulty than previous BEM formulations of the problem, however the evaluation of the domain integral in the new formulations is simpler than those of previous formulations.

Biexciton-biexciton interaction in semiconductors

For a semiconductor with single isotropic conduction and valence bands, the effective biexciton-biexciton interaction is derived starting from the second-quantization representation for the Hamiltonian of the system of interacting excitons and for the biexciton wave function within the framework of the adiabatic approximation. The interaction is found to be an average of the sum of effective interactions between excitons forming interacting biexcitons over the envelope functions of these biexcitons. Depending on the momentum transfer and on the difference between the momenta of interacting biexcitons, the interaction admits an analytical study when the first vanishes. In this case, the interaction has in the r space the form of a function of the interbiexciton distance consisting of a strong repulsive and a weak attractive part. At low temperatures the function describes main features in the behavior of the interaction among biexcitons, in which repulsion predominates over attraction. It is shown that while biexcitons remain stable quasiparticles they weakly attract each other for any value of the distance. A quantitative analysis of obtained results for the CuCl crystal shows that the biexciton system in this model substance is a weakly nonideal Bose gas with positive scattering length ${\mathrm{a}}_{\mathrm{s}}$\ensuremath{\simeq}${3\mathrm{a}}_{\mathrm{x}}$, which closely approaches the ideal one at excitation densities n\ensuremath{\leqslant}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.

Thermal modelling of micropulsed diode laser retinal photocoagulation.

Recent studies have sought to utilize diode laser "micropulsing" in order to preserve therapeutic efficacy of retinal photocoagulation while minimizing pain and subjacent tissue injury. A model for the transient thermal tissue response to continuous and micropulsed diode laser output is presented in order to understand the laser-tissue interactions and to generate optimum parameters for exploiting potential advantages of micropulsed application. The tissue thermal response was calculated by convolving the analytical solution to the three-dimensional, isotropic heat conduction equation with a source term corresponding to the spot size of the laser incident on the absorbing retinal pigment epithelium (RPE) and choroid layers of the ocular fundus. Thermal localization is quantitated by comparing the temperature rise in the RPE (T(RPE) and deep choroid (T(Ch). A 1-watt (average power), 20-microns diameter, 100 ms pulse (continuous or micropulsed) of 810 nm radiation was modelled to be incident on a geometric idealization of the human retina and choroid. A temperature gradient is rapidly established with only modest temperature augmentation between 10 and 100 ms. At 100 ms T(RPE) and T(Ch) are 32 and 23 C, respectively, for continuous application, and 41 and 27 C for 2 ms on/off micropulsed application. For a duty factor (total laser "on" time divided by pulse length) of 50%, T(RPE)/T(Ch) is maximal for a micropulse on/off duration of 2 ms; however, the variation over micropulse durations from 200 microseconds to 50 ms is small. In addition, whereas end-pulse T(RPE)/T(Ch) is greater for 2 ms on/off application when compared with continuous delivery (1.53 vs. 1.39), thermal relaxation during pulse quiescence in the micropulsed mode allows for an early increase in deep choroidal temperature with respect to T(RPE). For ten 200 microseconds pulses equally separated over 100 ms (duty factor = 2%), T(RPE)/T(Ch) = 3.2. With more numerous, lower power micropulses, T(RPE)/T(Ch) decreases monotonically to 1.39 as the duty factor is increased to 100%. These modelling studies provide the first quantitative predictions of thermal localization achieved with diode laser micropulsing and demonstrate that short pulse lengths and low duty factors allow for maximum thermal localization. These studies will potentiate pulse-shape optimization strategies for diode laser retinal photocoagulation applications.