Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman?Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron?electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron?electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.     

Nonlinear inverse bremsstrahlung absorption in a photoionized plasma

Nonlinear inverse bremsstrahlung absorption is investigated for a plasma photoionized in the Bethe regime of suppression of the ionization barrier, in which case the electron velocity distribution coincides with the distribution of atomic electrons. A comparison is made between the characteristic features of absorption in the cases where atomic electrons before ionization are in the ns and np states. It is established that, in the case of np states, the effective high-frequency conductivity is always nonlinear; in particular, for weak pump fields, it is proportional to the square of the pump field strength. The maximum plasma conductivity associated with p electrons is one order of magnitude lower than the maximum effective conductivity associated with s electrons, which creates conditions for less efficient plasma heating through inverse bremsstrahlung absorption.     

Anistropically varying conductivity in irreversible electroporation simulations

Background

One recent area of cancer research is irreversible electroporation (IRE). Irreversible electroporation is a minimally invasive procedure where needle electrodes are inserted into the body to ablate tumor cells with electricity. The aim of this paper is to propose a mathematical model that incorporates a tissue’s conductivity increasing more in the direction of the electrical field as this has been shown to occur in experiments.

Method

It was necessary to mathematically derive a valid form of the conductivity tensor such that it is dependent on the electrical field direction and can be easily implemented into numerical software. The derivation of a conductivity tensor that can take arbitrary functions for the conductivity in the directions tangent and normal to the electrical field is the main contribution of this paper. Numerical simulations were performed for isotropic-varying and anisotropic-varying conductivities to evaluate the importance of including the electrical field’s direction in the formulation for conductivity.

Results

By starting from previously published experimental results, this paper derived a general formulation for an anistropic-varying tensor for implementation into irreversible electroporation modeling software. The anistropic-varying tensor formulation allows the conductivity to take into consideration both electrical field direction and magnitude, as opposed to previous published works that only took into account electrical field magnitude.The anisotropic formulation predicts roughly a five percent decrease in ablation size for the monopolar simulation and approximately a ten percent decrease in ablation size for the bipolar simulations. This is a positive result as previously reported results found the isotropic formulation to overpredict ablation size for both monopolar and bipolar simulations. Furthermore, it was also reported that the isotropic formulation overpredicts the ablation size more for the bipolar case than the monopolar case. Thus, our results are following the experimental trend by having a larger percentage change in volume for the bipolar case than the monopolar case.

Conclusions

The predicted volume of ablated cells decreased, and could be a possible explanation for the slight over-prediction seen by isotropic-varying formulations.

     

Electron distribution and harmonic generation during plasma heating by high-power radiation

Anisotropic electron heating during the absorption of a strong high-frequency field due to electronion collisions is studied numerically by a Monte Carlo method. The electron distribution that forms in a strong high-frequency field under the action of electron-electron and electron-ion collisions is shown to be close to a bi-Maxwellian anisotropic velocity distribution. The extent to which the electron heating lowers the generation efficiency of the higher harmonics is determined.     

基于扩散张量成像的脑组织各向异性电导率计算模型的研究综述

脑组织电导率不仅对脑电源分析起着至关重要的作用,而且也是及时发现脑组织发生功能性病变的重要依据之一.扩散张量成像是一种无损伤功能性成像新技术,具有很高的空间分辨率.基于扩散张量成像的脑组织电导率计算是近年来的一项重要研究课题.本文综述了已有脑组织各向异性电导率的计算模型,主要包括张量特征值线性模型、电场力-粘力平衡模型...     

The Polarization of Light in a Tropical Rain Forest1

The light environment within forests presents complex patterns of brightness and spectral distribution of light. The polarized light field is no less complex. Using an imaging polarized light analyzer, we examined the natural fields of linearly polarized light in the tropical rain forest of Guatopo National Park, Venezuela. We found that the celestial polarization pattern remains visible underneath the forest canopy, although cloud and fog coverage may diffuse the light and reduce the polarization signal. We characterized several distinct light environments, each having a characteristic polarized light field. Furthermore, objects throughout the forest reflect light that is polarized in a predictable fashion depending upon the material, structure, and orientation of the reflecting surface. As a consequence of these patterns in the distribution of polarized light, some functions of polarization vision, such as navigation, must be limited to the spaces exposed to several extended portions of the sky, while others, such as remote sensing of surface orientation, object detection, and breaking of camouflage would be useful throughout the forest. The polarization of light adds another dimension to the complexity of the rain forest photic environment.     

Effect of counterion concentration on the dielectric behavior of a polypeptidic chain in the helix–coil transition

On the basis of the two-state model of a polyelectrolyte solution, the ion concentration in the polymer domain has been calculated by using the spherical Poisson–Boltzmann equation. The ion accumulation in the neighboring of the polyion influences, on different time scales, various electrical properties of the solution, in particular the low-frequency electrical conductivity and the high-frequency dielectric dispersion. These predictions have been compared with recent dielectric measurements on poly (L -glutamic acid) aqueous solutions during the conformational transition from the α-helix to random coil, and a satisfactory agreement has been found. This finding suggests that counterion distribution plays a different role in determining the electrical properties of charged polymer solutions, causing a electrophoretic contribution of the polymer domain to the electrical conductivity and influencing the high-frequency dielectric dispersion. © 1993 John Wiley & Sons, Inc.     

Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of ??slow?? equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period, is used to describe steady-state nonlinear oscillations in plasma.     

Low‐frequency conductivity tensor of rat brain tissues inferred from diffusion MRI

Conductivity tensor maps of the rat brain were obtained using diffusion magnetic resonance imaging (MRI). Signal attenuations in the cortex and the corpus callosum were measured using the stimulated echo acquisition mode (STEAM) sequence with b factors up to 6000 s/mm². Our previously published method was improved to infer 3 × 3 conductivity tensor at the low‐frequency limit. The conductivity tensor of the tissue was inferred from the fast component of the diffusion tensor and a fraction of the fast component. The mean conductivity (MC) of the cortex and the corpus callosum was 0.52 and 0.62 S/m, respectively. Diffusion‐weighted images were obtained with b factors up to 4500 s/mm². Conductivity tensor images were calculated from the fast diffusion tensor images. Tissues with highly anisotropic cellular structures, such as the corpus callosum, the internal capsule, and the trigeminal nerve, exhibited high anisotropy in conductivity. The resulting values corresponded to conductivities at the low‐frequency limit because our method assumed electric currents flowing only through extracellular fluid. Bioelectromagnetics 30:489–499, 2009. © 2009 Wiley‐Liss, Inc.     

Excitation of azimuthal surface modes by relativistic flows of electrons in the high-frequency range

Excitation of extraordinarily polarized azimuthal surface eigenwaves is shown to be possible in the frequency range above the upper hybrid resonance in waveguides with metal walls which are partially filled by cold magnetoactive plasma. Interaction of these waves with flows of electrons which rotate around the plasma column in the narrow gap separating the plasma from the wall of the waveguide is studied. Conditions of resonant interaction of the beam with the mentioned high-frequency azimuthal surface waves are shown by numerical methods to be reachable ones in the case of enough strong external magnetic fields without passing to the field of ultra-relativistic velocities of the beam.     

Configuration of an inviscid plasma in the field of a rotating magnetized central body

The problem is considered of configurations of a strongly magnetized inviscid plasma around a rotating magnetized central body. Strong plasma magnetization implies that the Hall conductivity is much lower than the transverse conductivity, which in turn is much lower than the longitudinal conductivity. For such conditions, a self-consistent set of equations is derived that describes the conduction current density, the magnetic and electric fields, and the angular frequency of the plasma rotation under the assumptions that the components of the dielectric tensor of the plasma envelope are known functions of height and that the plasma mass velocity has only the azimuthal component. Under the assumption that the transverse conductivity is constant over a magnetic surface, the nonlinear equations derived are solved in quadratures within the class of angular frequency distributions that are symmetric about the equatorial plane. A particular solution for the plasma configurations in a dipole magnetic field is considered that corresponds to a model exponential dependence of the transverse conductivity on the number of the L-envelope (or, equivalently, on the number of the unperturbed magnetic surface).     

Orientations of Cells on Compliant Substrates under Biaxial Stretches: A Theoretical Study

Mechanical cues from the microenvironments play a regulating role in many physiological and pathological processes, such as stem cell differentiation and cancer cell metastasis. Experiments showed that cells adhered on a compliant substrate may change orientation with an externally applied strain in the substrate. By accounting for actin polymerization, actin retrograde flow, and integrin binding dynamics, here we develop a mechanism-based tensegrity model to study the orientations of polarized cells on a compliant substrate under biaxial stretches. We show that the cell can actively regulate its mechanical state by generating different traction force levels along its polarized direction. Under static or ultralow-frequency cyclic stretches, stretching a softer substrate leads to a higher increase in the traction force and induces a narrower distribution of cell alignment. Compared to static loadings, high-frequency cyclic loadings have a more significant influence on cell reorientation on a stiff substrate. In addition, the width of the cellular angular distribution scales inversely with the stretch amplitude under both static and cyclic stretches. Our results are in agreement with a wide range of experimental observations, and provide fundamental insights into the functioning of cellular mechanosensing systems.     

A theoretical model to predict distribution of the fabric tensor and apparent density in cancellous bone

 The adaptation of cancellous bone to mechanical forces is well recognized. Theoretical models for predicting cancellous bone architecture have been developed and have mainly focused on the distribution of trabecular mass or the apparent density. The purpose of this study was to develop a theoretical model which can simultaneously predict the distribution of trabecular orthotropy/orientation, as represented by the fabric tensor, along with apparent density. Two sets of equations were derived under the assumption that cancellous bone is a biological self-optimizing material which tends to minimize strain energy. The first set of equations provide the relationship between the fabric tensor and stress tensor, and have been verified to be consistent with Wolff’s law of trabecular architecture, that is, the principal directions of the fabric tensor coincide with the principal stress trajectories. The second set of equations yield the apparent density from the stress tensor, which was shown to be identical to those obtained based on local optimization with strain energy density of true bone tissue as the objective function. These two sets of equations, together with elasticity field equations, provide a complete mathematical formulation for the adaptation of cancellous bone. Received: 25 February 1997/Revised version: 23 September 1997     

Kinetics of channelized membrane ions in magnetic fields

The cyclotron resonance model for channel ion transport in weak magnetic fields is extended to include damping losses. The conductivity tensor is obtained for different electric field configurations, including the circuital field E phi normal to the channel axis. The conductivity behavior close to the cyclotron resonance frequency omega c is compared to existing Ca2+-efflux data in the literature. A collision time of .023 s results from this comparison under the assumption that K+ ions are transiting in a 0.35 G field. We estimate a mean kinetic energy of 3.5 eV for this ion at resonance. This model leads to discrete modes of vibration (eigenfrequencies) in the ion-lattice interaction, such that omega n = n omega c. The presence of such harmonics is compatible with recent results by Blackman et al. [1985b] and McLeod et al. [1986] with the interesting exception that even modes do not appear in their observations, whereas the present model has no restriction on n. This harmonic formalism is also consistent with another reported phenomenon, that of quantized multiple conductances in single patch-clamped channels.     

Study of the near-electrode processes in quasi-steady plasma accelerators with impenetrable electrodes

Near-electrode processes in a coaxial plasma accelerator with equipotential impenetrable electrodes are simulated using a two-dimensional (generally, time-dependent) two-fluid MHD model with allowance for the Hall effect and the plasma conductivity tensor. The simulations confirm the theoretically predicted mechanism of the so-called “crisis of current” caused by the Hall effect. The simulation results are compared with available experimental data. The influence of both the method of plasma supply to the channel and an additional longitudinal magnetic field on the development of near-electrode instabilities preceding the crisis of current is studied.     

Keratin orientation in wool and feathers by polarized raman spectroscopy

Good quality polarized Raman spectra of a single wool fiber and an intact feather barbule are presented. The intensity ratio of the alpha-helix component of the amide I band measured parallel and perpendicular to the wool fiber axis was 0.39 +/- 0.05. This is consistent with theoretical predictions based on orientational calculations using the normal Raman polarizability tensor for an alpha-helical amide I band where the protein strands are aligned roughly parallel with the fiber axis. However, the depolarized spectral intensity of the alpha-helix mode was greater than expected. For the feather barbule, despite high quality spectra, a unique orientation of the beta-sheet structure could not be determined using the Raman intensity ratios of the amide I band alone. Using previously developed methods, the protein chains were found to be oriented between 60 and 90 degrees from the long axis of the barbule compared to an angle of 51 degrees calculated from polarized IR spectra of the same barbule. The Raman tensor methods for the determination of protein orientation in these fibers was found to be constrained by the complexity of the materials and the limitations of the band fitting methods used to apportion the intensity among the various vibrational modes of their spectra. Other advantages and limitations of polarized Raman microscopic methods of structural determination are discussed.     

Application of a changing field of growth rates to a description of root apex formation

Based on the growth tensor method an unsteady field of growth rates for developing root apex is presented. Maps of growth rates distribution as well as simulations in which the field was applied to initially uniform grid of points are presented. In the simulations, the grid undergoes deformation that resembles new root formation in its axial plane. Four variants of field operation on the grid are shown.     

Numerical simulations of plasma equilibrium in a one-dimensional current sheet with a nonzero normal magnetic field component

The force balance in a thin collisionless current sheet in the Earth’s magnetotail with a given constant magnetic field component B _z across the sheet is numerically studied for the first time in a self-consistent formulation of the problem. The current sheet is produced by oppositely directed plasma flows propagating from the periphery of the sheet toward the neutral plane. A substantially improved version of a macroparticle numerical model is used that makes it possible to simulate on the order of 10⁷ macroparticles even with a personal computer and to calculate equilibrium configurations with a sufficiently low discrete noise level in the first-and second-order moments of the distribution function, which determine the stress tensor elements. Quasisteady configurations were calculated numerically for several sets of plasma parameters in some parts of the magnetotail. The force balance in the sheet was checked by calculating the longitudinal and transverse pressures as well as the elements of the full stress tensor. The stress tensor in the current sheet is found to be nondiagonal and to differ appreciably from the gyrotropic stress tensor in the Chew-Goldberger-Low model, although the Chew-Goldberger-Low theory and numerical calculations yield close results for large distances from the region of reversed magnetic field.     

Kerr effect of charged dipolar macromolecules without condensed counterions in conducting solution.

The theoretical treatment of the Kerr constant of rigid, dipolar, conducting ellipsoidal macromolecules of O'Konski and Krause (1970. J. Phys. Chem. 74:3243) has been extended to very low ionic strength solutions for charged macromolecules. The O'Konski and Krause theoretical treatment postulated a surface conductivity directly on the surface of each macromolecule. For charged macromolecules, this surface conductivity was generally assumed to be caused by movement of condensed counterions on the macromolecules. In the present work, it has been assumed that, at very low ionic strength, the average counterion is at the Debye characteristic distance from the surface of each charged macromolecule and contributes to surface conductivity at that distance, with no additional surface conductivity on the true surface of the macromolecule. Essentially, these considerations change the calculated interaction energy of the macromolecule with an externally applied electric field via a change in both the internal field components and in the reaction field of the macromolecular dipole. The new interaction energy is used to calculate the orientation distribution function of the macromolecules in solution and this distribution function can, in principle, be used to calculate the steady state electric linear or circular dichroism, electric light scattering, anisotropy of conductivity, etc., using the appropriate theoretical treatment for each of these quantities.     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. II. Effects of osmotic perturbation

The effects of osmotic perturbation on the dielectric behavior of cultured rat basophilic leukemia (RBL-1) cells were examined. Cells exposed to osmolalities (pi) of 145-650 mosmolal showed dielectric dispersions of the following characteristics: Permittivity increment delta epsilon(= epsilon l - epsilon h where epsilon l and epsilon h refer to the low- and high-frequency limit values) for a fixed volume concentration increased with pi; gross permittivity behavior was apparently of a typical Cole-Cole type; however, frequency dependence of conductivity was undulant and could be simulated by a superposition of two separate Cole-Cole type dispersions; separation of these subdispersions along the frequency axis was an increasing function of pi, and so was conductivity increment in the high-frequency region. As examined by light microscopy, the cells were spherical in spite of imposed anisotonic stresses and behaved as osmometers at 200-410 mosmolal. When normalized by dividing by number (not volume) concentration, delta epsilon remained relatively constant irrespective of pi. Apparent membrane capacities (Cm), analyzed by applying a single-shell model, increased systematically from a hypotonic value of approx. 1 microF/cm2 up to 5 microF/cm2 at 650 mosmolal. This increase was interpreted as due to increased cellular 'surface/volume' ratios that were confirmed by scanning electron microscopy. Cole-Cole's beta parameter, which culminated around 0.9 for isotonic cells and declined to approx. 0.8 for anisotonic cells, did not parallel the broadening of cell volume distribution but appeared to reflect changes in the intracellular conductivity caused by the anisotonic challenge. The results indicate that the dispersion method can probe changes in surface morphology as well as subcellular organelles' constitution of living cells.