Single-mode magnetic structures in a plasma with anisotropic pressure

The equations of vortex electron anisotropic hydrodynamics are used to show that, in a plasma with anisotropic pressure, the Weibel instability of short-wavelength perturbations gives rise to a large-amplitude quasi-harmonic magnetic field varying periodically as a function of time. The computed field parameters agree well with the proposed analytic estimates.     

A nonlinear anisotropic model for porcine aortic heart valves

The anisotropic property of porcine aortic valve leaflet has potentially significant effects on its mechanical behaviour and the failure mechanisms. However, due to its complex nature, testing and modelling the anisotropic porcine aortic valves remains a continuing challenge to date. This study has developed a nonlinear anisotropic finite element model for porcine heart valves. The model is based on the uniaxial experimental data of porcine aortic heart valve leaflet and the properties of nonlinear composite material. A finite element code is developed to solve this problem using the 8-node super-parameter nonlinear shells and the update Lagrangian method. The stress distribution and deformation of the porcine aortic valves with either uniform and non-uniform thicknesses in closed phase and loaded condition are calculated. The results showed significant changes in the stress distributions due to the anisotropic property of the leaflets. Compared with the isotropic valve at the same loading condition, it is found that the site of the peak stress of the anisotropic leaflet is different; the maximum longitudinal normal stress is increased, but the maximum transversal normal stress and in-plane shear stress are reduced. We conclude that it is very important to consider the anisotropic property of the porcine heart valves in order to understand the failure mechanism of such valves in vivo.     

MHD stability of a collisionless anisotropic plasma in a system with an internal conductor

A study is made of the MHD stability of a collisionless anisotropic-pressure plasma in a nonparaxial magnetic configuration with an internal conductor in cylindrical geometry. A stability criterion for flutelike modes is obtained, and the families of marginally stable profiles of the longitudinal and transverse plasma pressures are calculated by using the Chew-Goldberger-Low anisotropic MHD equations. Possible marginally stable plasma states are considered with allowance for the expected turbulent relaxation and self-organization processes, on the one hand, and isotropization processes, on the other. A stability criterion for Alfvén modes is also derived in the Chew-Goldberger-Low model.     

Redistribution of stress due to a circular hole in a nonlinear anisotropic membrane

Many clinical procedures introduce holes into thin tissues that are typically under multiaxial stresses and finite strains. Such incisions change the stresses and strains from their homeostatic values, which may induce cells to alter their orientation and cytoskeletal organization as well as to migrate, proliferate, change their synthesis of matrix, or even to enter the cell death cycle. To correlate such changes in cellular activity with changes in the mechanics, we need solutions for the native and the perturbed boundary value problems. Such problems will often be complex and require a finite element solution; weak solutions should be evaluated independently, however, at least for special cases. Herein, we present a numerical solution of the governing nonlinear ordinary differential equation for the special case of stress redistribution due to the introduction of a circular hole into a finitely deformed, Fung-type, circular membrane that exhibits a cylindrical orthotropy. Among other results, we show that the anisotropy plays an increasingly greater role as the size of the hole becomes smaller, which is of course a goal of minimally invasive procedures.     

Adiabatically reduced magnetohydrodynamic equations for a cylindrical plasma with an anisotropic pressure

A closed set of reduced equations describing low-frequency nonlinear flute magnetohydrodynamic (MHD) convection and the resulting nondiffusive processes of particle and energy transport in a weakly collisional cylindrical plasma with an anisotropic pressure is derived. The Chew-Goldberger-Low anisotropic magnetohydrodynamics is used as the basic dynamic model, because this model is applicable to describing flute convection in a cylindrical plasma column even in the low-frequency limit. The reduced set of equations was derived using the method of adiabatic separation of fast and slow motions. It is shown that the structure of the adiabatic transformation and the corresponding velocity field are identical to those obtained earlier in the isotropic MHD model. However, the derived heat transfer equations differ drastically from the isotropic pressure model. In particular, they indicate a tendency toward maintaining different radial profiles of the longitudinal and transverse pressures.     

Potential surface waves in anisotropic plasma

The dependences of the frequency and damping rate of a potential surface wave on the wavenumber and the degree of anisotropy of a bi-Maxwellian electron distribution characterized by different temperatures along and across the plasma surface are established. It is demonstrated that the influence of electron thermal motion along the plasma surface on the surface wave properties is similar to the influence of thermal motion on the properties of a bulk Langmuir wave. On the contrary, thermal motion across the surface qualitatively affects the dispersion relation and substantially increases the damping rate.     

Excitation of low-frequency electrostatic oscillations in a collisionless plasma with an anisotropic ion distribution

The stability of an anisotropic ion distribution with unoccupied regions (holes) in velocity space is studied. Such distributions are expected to form near the neutral plane of the Earth's magnetotail. It is shown that, in such systems, electrostatic waves can be excited. The growth rate and propagation direction of these oscillations are determined by the parameters characterizing the ion hole, as well as by the relation between the electron and ion temperatures. The solution to the quasilinear equation for the waves propagating perpendicular to the current sheet is found, and the energy of the excited oscillations as a function of the parameters of the ion hole is evaluated.     

Steady-state vortex structure in a plasma with a strong magnetic field

A study is made of nonquasineutral vortex structures in a plasma with a magnetic field B _z in which the charges separate on a spatial scale equal to the magnetic Debye radius r _B=B _z/4πen _e. The electric field arising due to charge separation leads to radial expansion of the ions, thereby destroying the initial electron vortex. It is shown that the ion pressure gradient stops ion expansion in a nonquasineutral electron vortex and gives rise to a steady structure with a characteristic scale on the order of r _B. With the electron inertia taken into account in the hydrodynamic approximation, the magnetic vortex structure in a hot plas mamanifests itself in the appearance of a “hole” in the plasma density.     

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the ‘computational dissection’ of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress–strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.     

Density measurements in a tenuous plasma by a high-frequency resonator with a periodic structure

It is proposed to measure plasma densities in the range of 10⁵–10⁹ cm^?3 by a high-frequency resonator with a periodic structure consisting of annual high-frequency electrodes mounted on oppositely directed racks. The method proposed substantially increases the proportionality factor between the electron density and the shift of the resonator eigenfrequency. This factor is determined by the calibration method using an electron beam with given parameters. The calibration ensures an accuracy of about 10% for density measurements in a plasma produced by a 5-MeV proton beam propagating in air at pressures of 10^?2–10^?5 torr.     

Kelvin-Helmholtz instability of a cylindrical plasma flow with an arbitrary temperature

The dispersion relation for Kelvin-Helmholtz magnetohydrodynamic instability of a cylindrical plasma flow in a longitudinal magnetic field is studied with allowance for plasma compressibility. Stability of the system in a wide range of plasma parameters is thoroughly analyzed in the incompressible plasma approximation. Using the results obtained, a diagram of the system stability is constructed in terms of the magnetic field and the ratio between the plasma densities in the flow and the ambient space. It is shown by numerically solving the dispersion relation for the case of a compressible plasma that perturbations with scale lengths on the order of the flow diameter and larger can develop even at a zero temperature. For low ion-sound velocities, c _S ²/U ₀² < 0.25, the growth rate of the axisymmetric mode with m = 0 is much smaller than that of non-axisymmetric modes. It is shown that, in an incompressible plasma, the eigenmodes are damped monotonically with distance from the flow. In plasma with a finite temperature, the character of damping is oscillatory; in this case, the lower the plasma temperature, the larger the distance at which the ambient plasma is perturbed.     

Reflection of electromagnetic radiation from plasma with an anisotropic electron velocity distribution

The reflection of a test electromagnetic pulse from the plasma formed as a result of tunnel ionization of atoms in the field of a circularly polarized high-power radiation pulse is analyzed using the kinetic approach to describe electron motion. It is shown that the reflected pulse is significantly amplified due to the development of Weibel instability. The amplification efficiency is determined by the maximum value of the instability growth rate, which depends on the degree of anisotropy of the photoelectron distribution function.     

On the nonlinear theory of collective Cherenkov interaction of a high-density relativistic beam with a plasma

The nonlinear dynamics of the instability of a straight high-density relativistic electron beam under the conditions of the stimulated Cherenkov effect in a plasma waveguide is studied both analytically and numerically. It is shown that, for a beam of sufficiently high density such that the stabilizing factors are nonlinear frequency shifts and for a plasma described in a linear approximation, the basic equations have soliton-like solutions and the electron beam after saturation of the instability relaxes to its initial, weakly perturbed state, provided that only one harmonic of the plasma and the beam density is taken into account. The analytical solutions obtained here for this case correlate well with the numerical ones. A more general model that accounts for the generation of higher harmonics of the plasma and the beam density does not yield soliton-like solutions for the time evolution of the amplitudes of the plasma and beam waves. In such a model, the instability will be collective again: it can be described analytically (at least, up to the time at which it saturates) by using equations with cubic nonlinearities and the method of expansion of the electron trajectories and momenta.     

Simulation of interstellar chemical evolution in a low temperature plasma

In order to simulate the interstellar chemical evolution, the chemical process was studied in a laboratory plasma flow. The apparatus was so designed as to establish the similarity between laboratory and cosmic conditions. The plasma temperature was found to be less than 100 K in the downstream region. HCN, HC₃N, H₂CO, and several kinds of hydrocarbons were produced from the plasma whose elementary composition was approximately same as the cosmic abundance. Based on the analysis by laser-induced-fluorescence method, HCN and HC₃N were concluded to be synthesized via CN loss reactions, while it was unlikely that the syntheses of C₂H₂ and H₂CO were related to the generation or depletion of C₂.     

Slow plasma waves in a fine-stratified periodic semiconductor structure

A study is made of the propagation of electromagnetic waves in an infinite fine-stratified periodic structure composed of alternating layers of two different semiconductors. Such a periodic structure, which can be treated as a uniform uniaxial semiconductor with two different values of the dielectric constant, has four characteristic frequencies: two plasma frequencies of the layers and two hybrid frequencies, which are determined by the parameters of the layers. These frequencies govern the dispersion properties of the eigenwaves of the semiconductor structure. The effect of the dissipative processes on the wave dispersion is considered, and the dependence of the minimum phase velocity on the thickness of the layers and on the collision frequency between charge carriers within them is determined.     

Stability of Alfvén modes in a collisionless anisotropic plasma confined by a highly curved magnetic field

The stability of Alfvén modes in a collisionless plasma with an anisotropic pressure in a highly curved magnetic field is studied. A linearized equation for describing longitudinally nonuniform MHD perturbations with frequencies below the bounce frequency is derived. In this equation, the perturbations of longitudinal and transverse pressures are calculated using a collisionless kinetic equation. It is shown that longitudinal fluxes of the transverse and longitudinal plasma energies give rise to pressure perturbations different from those in the Chew-Goldberger-Low collisionless hydrodynamics. The corresponding energy principle is constructed. A stability criterion for Alfvén modes is obtained and is found to be more stringent than that in the Chew-Gold-berger-Low model.     

A modified liquid-mosaic model of plasma membrane structure

A modified liquid-mosaic model of molecular organization of the plasma membrane is proposed, which allow one to interpret non-receptor effects of regulatory peptides and the efficiency of biologically active compounds in extra low concentrations. An evolutionarily earlier type of intercellular chemical signalling (without the participation of receptor structures) is suggested.     

Plant dispersal in the sub-Antarctic inferred from anisotropic genetic structure

Climatic conditions and landscape features often strongly affect species' local distribution patterns, dispersal, reproduction and survival and may therefore have considerable impacts on species' fine-scale spatial genetic structure (SGS). In this study, we demonstrate the efficacy of combining fine-scale SGS analyses with isotropic and anisotropic spatial autocorrelation techniques to infer the impact of wind patterns on plant dispersal processes. We genotyped 1304 Azorella selago (Apiaceae) specimens, a wind-pollinated and wind-dispersed plant, from four populations distributed across sub-Antarctic Marion Island. SGS was variable with Sp values ranging from 0.001 to 0.014, suggesting notable variability in dispersal distance and wind velocities between sites. Nonetheless, the data supported previous hypotheses of a strong NW-SE gradient in wind strength across the island. Anisotropic autocorrelation analyses further suggested that dispersal is strongly directional, but varying between sites depending on the local prevailing winds. Despite the high frequency of gale-force winds on Marion Island, gene dispersal distance estimates (σ) were surprisingly low (<10 m), most probably because of a low pollen dispersal efficiency. An SGS approach in association with isotropic and anisotropic analyses provides a powerful means to assess the relative influence of abiotic factors on dispersal and allow inferences that would not be possible without this combined approach.