Linear Transport Theory Research Articles

Electrochemical Study of the Cross Effect Between Ion and Electron Flows in Semiconducting CoO

According to the linear transport theory, the mobile cation flux, , in an electronic conductor oxide, e.g., , is given as , being the transport coefficient and the electrochemical potential gradient of charge carriers of type . It has, however, been normally presumed that without experimental verification. By an electrochemical means we have measured the “charge of transport” of the cation, , in the ranges of temperature and oxygen partial pressure, and , respectively, and found, contrary to the normal presumption, that takes a value in a range of 0.7 to 1.6. Furthermore, it tends to increase with decreasing temperature and increasing oxygen partial pressure. The principle and details of the electrochemical experiment employed are given and the compilation is made of all the data on of which have been made available via various means up until now.

Theory of magnetotransport in inhomogeneous magnetic structures

The origin of the giant magnetoresistance of magnetic multilayers and magnetic granular solids is investigated through a unified spin-dependent linear transport theory, in which the primary source of electrical resistivity is short-range scattering by impurities in the different magnetic or nonmagnetic regions and at the interfaces. Our theory predicts that magnetotransport in granular solids is similar to that for currents perpendicular to the plane of the layers in multilayers in that their magnetoresistance is independent of the average distance between adjacent magnetic regions.

Relation between scattering and albedo operators in linear transport theory

Abstract In spite of the fact that the scattering and albedo operators are defined in a different setting in the linear transport theory, there is a close resemblance between them. In this paper we try to explore this analogy. The scattering operator comes from the evolutionary linear transport system: and it involves a comparison of the dynamics U(t) of the above system with the dynamics U0(t) of the collisionless transport system, the so called advection system:

Experimental evidence of the interference between ionic and electronic flows in an oxide with prevailing electronic conduction

Linear transport theory prescribes that for, e.g. a binary oxide Co 1− δ O, a flow of cations ( J 1) may be induced not only by its direct cause which is a gradient of the cationic electrochemical potential (▿η 1), but also indirectly by a gradient of the electronic electrochemical potential (▿η 2), or J 1=− L 11▿ η 1− L 12▿ η 2, L ik being the transport coefficient. Routine practice, however, has been neglecting the cross coefficient, i.e. L 12=0. We have determined experimentally the charge of transport of the cation α ∗ 1 (≡ L 12 L 11 ) for Co 1-δO with three different and independent techniques, and concluded that the cross coefficient is not negligible by any means. All the numerical data on α ∗ 1 up to date are compiled. Consequences of the non-zero cross coefficient and the physico-chemical nature of the charge of transport are discussed.

Time and energy dependent recoil distributions in mixtures

An approach based on linear transport theory is described here to model the transport of incident ions and recoil particles in complex target materials. Using the time and energy dependent Boltzmann Fokker-Planck (BFP) equation, we have numerically computed particle densities for two incident ion (oxygen and barium) species as well as for all recoil particle species, self-consistently, in the superconducting material YBa 2Cu 3O 7. An advantage of our approach is that the scattering, recoil and energy deposition cross sections are computed once for each combination of incident ion and target material and a given (e.g., Universal) potential. These interaction cross sections are then used in the BFP code to study both time dependent (pulsed ion beam) and equilibrium (steady-state ion beam) scenarios. Pulsed mode results provide insight into the decay behavior of each recoil species and equilibrium spectra are obtained in steady state mode. Our numerical model also describes the partitioning of energy deposition amongst the atomic species as well as the fate of the incident ion and recoils in interstitial, substitution or replacement sites.

Nonlinear transport processes in disordered media

AbstractNonlinear transport processes in disordered systems such as porous media and heterogeneous solids are studied, which are represented by two‐ or three‐dimensional networks of interconnected bonds, by a Bethe network (a branching network with no closed loops) of a given coordination number, or by a continuum in which circular or spherical inclusions have been inserted at random. The bonds represent the pores of the pore space, or the conducting and insulating regions of a disordered solid, to which we assign effective properties (radii or conductances) selected at random from a probability density function. Three types of nonlinear transport processes are considered. (1) The relation between the current q and the potential gradient v is of power‐law type (as in, for example, flow of power‐law fluids or the electric current in doped polycrystalline semiconductors). (2) The relation between q and v is piecewise linear, characterized by a threshold (as in flow of Bingham fluids or in mechanical or dielectric breakdown of composite solids). (3) A large v is imposed on the system, so that a linear transport theory is not valid. The behavioral study of the effective transport and topological properties of the system, such as the permeability, conductivity, diffusivity, and the shape of the samplespanning cluster of conducting paths shows that in all cases the concepts of percolation theory play a prominent role, even if the system is well connected and percolation may seem not to play any role. For most cases, new effective‐medium approximations (EMAs) are derived for estimating effective transport properties. Compared to the case of linear transport, new EMAs are considerably more accurate in predicting the scaling properties of the transport coefficients near a critical point such as the percolation threshold. For a power‐law transport process, an exact solution is also derived for the Bethe networks. Using the concepts of percolation theory, scaling laws relating the effective properties to various regimes of transport and to topological properties of the system are also given. A relation between the volumetric flow rate of a power‐law fluid in porous media and the macroscopic pressure drop is derived, which contains no adjustable parameter and is valid at any porosity. To test the accuracy of our analytical predictions, Monte Carlo simulations are carried out for several cases. In most cases, good agreement is found between the simulation results and predictions. The extension of the results to other types of nonlinearities is also discussed.

Nonnegativity of the Anisotropic Scattering Source in Two-Angle (μ, φ) Transport

In this paper, the use of piecewise constant functions (PCFs) in two-angle linear transport theory to represent the scattering cross sections ([sigma]([nu]), [nu][element of][-1,1], and the angular scattering source density S[Omega], [Omega][equivalent to]([mu]pw)[element of]U, on a partition (S[sub N] or finite element discretization, for example) of the unit sphere U of directions is considered. Average oriented transition cross sections [sigma][sub tn]([plus minus], B[prime],B) describe scattering from [Omega][prime][equivalent to][mu][prime],pw [prime](equivalent of)B[prime][contained in]U to [Omega][equivalent to][mu], (pw)(equivalent of)B[contained in]U with the constraint 0<[plus minus](pw-pw[prime]) < [pi]. Unit steps [sigma][nu] = H[nu]-[gamma]) and [sigma][nu] = [delta][nu]-[gamma] are pretreated on an intrinsic [gamma] grid for the chosen partition. All [sigma][sub tn]([plus minus],B[prime]), B are derived by interpolation.

Diffusive Limits for Linear Transport Equations

The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion.

Hyperbolic models for linear transport theory

The linear transport equation and taking its moments are considered for seeking a second-order closure. It is found that all closures consistent with an entropy principle are elements of a one-parameter family. It is also shown that all the Eddington factors appearing in literature are all elements of the above family.

The Effect of Velocity-field Characteristics on the Modelling of A Sub-micron Channel MESFET

The modelling of sub-micron channel GaAs MESFET's, based on an electron velocity field characteristic derived from an asymmetric high-field distribution function is presented. Drift velocity, electric field, potential, and carrier density profiles along the MESFET channel are calculated. The channel pinch-off at the onset of saturation is explicitly lifted by the inclusion of high-mobility degradation, even in long channel MESFET's. MESFET I-V characteristics based on the given drift velocity expression are also computed. It is shown by comparison with experiment that the I-V model based on the correct velocity-field profile is superior to those models based on the linear transport theory of the Botzmann transport equation. A discussion of the difficulties in MESFET modelling which arise from intervalley electron transfer in GaAs is also presented.

Identification of Scattering Media from Reflected Flows

An inverse problem of linear transport theory is investigated. Using an approach closely related to the well-known invariant imbedding techniques, an equation is derived relating the time distribution of reflected flows at one end of a slab $[0,1]$ to the density distribution of the scattering medium in the interior. Criteria for the wellposedness of the inverse problem of identifying the medium from the reflected flow are formulated and a numerical scheme is proposed.

Transverse baryon flow as possible evidence for a quark-gluon-plasma phase.

In order to investigate the coupling between collective flow of nucleons and pions in hot pion-dominated hadronic matter, we calculate the pion-nucleon drag coefficient in linearized transport theory. We find that the characteristic time for flow equalization is longer than the time scale of the expansion of a hardonic fireball created in high-energy collisions. The analysis of transverse-momentum data from p+p\ifmmode\bar\else\textasciimacron\fi{} collisions at \ensuremath{\surd}s =1.8 TeV reveals the same flow velocity for mesons and antinucleons. We argue that this may be evidence for the formation of a quark-gluon plasma in these collisions.

The application of transport theory to visualization of 3-D scalar data fields

This paper describes a general visualization model for 3-D scalar data fields based on linear transport theory that contains common volume rendering models as special cases and/or approximations. The concept of ‘‘virtual’’ particles for the extraction of information from data fields is introduced. The role of different types of interaction of the data field with those particles such as absorption, scattering, source, and color shift are discussed and demonstrated. Special attention is given to possible tools for the enhancement of interesting data features. Random distortions or noise of the data field are mapped onto the image plane in a well-defined way such that picture processing methods can be used to reconstruct the appearance of the undistorted data set. Random texturing can provide visual insights as to the magnitude and distribution of deviations of related data fields, e.g., originating from analytic models and measurements, or in the noise content of a given data field. Hidden symmetries of a data set can often be identified visually by allowing it to interact with a preselected beam of ‘‘physical’’ particles with the attendant appearance of characteristic structural effects such as channeling.

Volume rendering and data feature enhancement

This paper describes a general visualization model for 3D scalar data fields based on linear transport theory which contains common volume rendering models as special cases and/or approximations. The concept of "virtual" particles for the extraction of information from data fields is introduced. The role of different types of interaction of the data field with those particles such as absorption, scattering, source and color shift are discussed and demonstrated.Special attention is given to possible tools for the enhancement of interesting data features. Random distortions or noise of the data field are mapped onto the image plane in a well-defined way such that picture processing methods can be used to reconstruct the appearance of the undistorted data set. Random texturing can provide visual insights as to the magnitude and distribution of deviations of related data fields, e.g., originating from analytic models and measurements, or in the noise content of a given data field. Hidden symmetries of a data set can often be identified visually by allowing it to interact with a preselected beam of "physical" particles with the attendant appearance of characteristic structural effects such as channeling.

Relativistic transport theory for a two-temperature magnetized plasma

The relativistic kinetic theory of linear transport is worked out within the framework of a new moment method. A complete analytical study of the transport in a two-temperature inhomogeneous magnetized fusion plasma is given. The transport relations and coefficients are derived from the kinetic equation with the full relativistic Beliaev–Budker collision operator and the impact of relativistic effects on the confinement are investigated.

Demixing of oxide solid solutions in oxygen potential gradients: Two-phase systems and the morphological stability of the interface

Demixing experiments have been done with two-phase oxide solid solutions. In the case of (Mn,Fe)O(wustite) and (Me,Fe) 3O 4(spinel), a remarkable band structure of these phases appeared at the high oxygen potential side. Large demixing was found in the two-phase region, where composition of each phase continuously changed. This unique behaviour was explained theoretically in the framework of linear transport theory.

Transfer by anisotropic scattering between subsets of the unit sphere of directions in linear transport theory

The exact kernel method for linear transport problems with azimuth-dependent angular fluxes is here based on the evaluation of average scattering densities (ASD's) that fully describe the neutron (or particle) transfer between subsets of the unit sphere of directions by anisotropic scattering. Reciprocity and other ASD functional properties are proved and combined with the symmetry properties of suitable SN quadrature sets. This greatly reduces the number of independent ASD's to be computed and stored. An approach to perform ASD computations with reciprocity checks is presented. The ASD expressions of the scattering source for the typical 2D geometries are explicitly given.

Demixing in oxygen potential gradients: Two‐phase systems and the morphological stability of the interface

AbstractIn order to complement previous investigations on the demixing of one‐phase oxide solid solutions on oxygen potential gradients, solid solutions in two‐phase regions were exposed in an analogous way. The demixing under (quasi‐) steady state conditions is basically the same as found in the one‐phase mixtures. However, in the case of (Mn,Fe)O (wustite)‐(Mn,Fe)3O4 (spinel) solid solutions, the phase boundary between the lower (w) and the higher (sp) oxidized solid solution was not stable morphologically. In fact, a zone of phase mixtures developed in which wustite and spinel with continuously changing composition coexisted locally. This unique behaviour can be explained theoretically in the framework of linear transport theory.

Noise-induced transitions: An example from linear transport theory

The statistics of the reflection and transmission coefficients of a two-state Markov medium is analysed using the rod model of the invariant imbedding approach in linear transport theory. The presence of a noise-induced transition in the reflectivity of a semi-infinite medium, as the mean size of the fluid packets is varied, is pointed out. Expressions for the moments of the transmission coefficient and the mean thickness of the medium, required to yield a specified transmission coefficient in the cases of a purely absorbing and purely scattering medium, are derived.

On a class of iteration methods in linear transport theory

A class of iteration methods for solving the transport equation is considered. The convergence and rate of convergence of methods from this class are investigated. Specific examples of iteration processes from the class under consideration and an analysis of their rates of convergence are presented.