Self-consistent System Research Articles

Spatial variation of the supersonic thermal plasma flow downstream of the termination shock

In this paper we start from the most recently observed fact that the solar wind plasma after passage over the termination shock is still supersonic with a Mach number of about 2. To explain this unexpected phenomenon and to predict the evolution of properties of the downstream plasma flow we here consider a two-fluid proton plasma with pick-up protons as a separate suprathermal, second proton fluid. We then formulate a self-consistent system of hydrodynamical conservation equations coupling the two fluids by dynamical and thermodynamical coupling terms and taking into account the effects of newly incorporated protons due to charge exchange with the H-atoms in the heliosheath. This then allows us to predict that in the most probable case the solar wind protons will become subsonic over a distance of about 30AU downstream of the shock. As we can also show, it may, however, happen that the plasma mixture later again reconverts to a supersonic signature and has to undergo a second shock before meeting the heliopause.

Endoscopic cross-polarization spectrometer as an instrument for puncture diagnostics

A modification of the polarization reflection spectroscopy method is proposed with the use of a polarization-maintaining single-mode fiber. The choice of the fiber made it possible to create an optimal self-consistent system for the illumination of a biological tissue and the reception of scattered radiation and to create a probe compatible with any endoscopic equipment. The first clinical results of diagnosing tumor diseases with the created instrument showed that it is possible to determine the tumor-norm boundary, which is very important for organ-preserving operations. All of the results obtained by this method agree well with the results obtained by the method of polarization-sensitive optical coherence tomography.

Description of magnetic moments of long isotopic chains within the FFS theory

Dipole magnetic moments of several long isotopic chains are analyzed within the self-consistent finite Fermi system theory with exact account for the pairing and quasiparticle continuum. The momentum dependence of the spin-isospin Landau-Migdal amplitude g′ is taken into account. This dependence was introduced previously to describe high-energy electron magnetic scattering. New moment data for nuclei far from the \( \beta\) -stability valley are included in the analysis. For a number of semi-magic isotopes of the tin and lead chains a good description of the data is obtained, with an accuracy of 0.1- 0.2\( \mu_{{N}}^{}\) . A chain of non-magic isotopes of copper is also analyzed in detail.

The statistical and numerical study of the global distribution of coronal plasma and magnetic field near 2.5 Rs over a 10-year period

The basic characteristics of the global distribution for the corona plasma and magnetic field near 2.5 Rs are analyzed with the statistical and numerical methods for 136 Carrington Rotations (CRs) covering four different phases of solar activity. By using the observational data and the velocity distribution model in the corona, the statistical average distribution of the magnetic field, density and the coronal mass outputs are analyzed for the four different phases. Then, a numerical study of the global distribution near 2.5 Rs has been made by solving a self-consistent MHD system. Finally, the solar wind speed at 1 AU is given by mapping the speed at 2.5 Rs to that near 1 AU, and the comparison of the numerical results with the observational measurements and the simulation result of the Wang–Sheeley–Arge (WSA) model are made during more than 5 years. The numerical results indicate that the global distributions on the source surface of 2.5 Rs at different phases of solar activity could be used to predict the change of the solar wind in interplanetary space.

Propagation of the ultrashort laser pulses through the quantum nonlinear medium with resonant properties

The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrodinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.

Dense Plasma Focus <formula formulatype="inline"><tex Notation="TeX">$Z$</tex></formula>-Pinches for High-Gradient Particle Acceleration

The final <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -pinch stage of a dense plasma focus (DPF) could be used as a simple, compact, and potentially rugged plasma-based high-gradient accelerator with fields at the 100-MV/m level. In this paper, we review previously published experimental beam data that indicate the feasibility of such a DPF-based accelerator, qualitatively discuss the physical acceleration processes in terms of the induced voltages, and as a starting point, examine the DPF acceleration potential by numerically applying a self-consistent DPF system model that includes the induced voltage from both macroscopic and instability-driven plasma dynamics. Applications to the remote detection of high explosives and a multistaged acceleration concept are briefly discussed.

Spinor field with induced nonlinearity in Bianchi VI cosmology: Exact and numerical solutions

A self-consistent system of interacting spinor and scalar fields in Bianchi type VI (B-VI) cosmology is studied in the presence of a cosmological constant. Exact solutions to the spinor, scalar and gravitational field equations are obtained for some special choice of the spinor field nonlinearity. It is shown that introduction of Λ > 0, which is often used to model dark energy, results in a rapid growth of the universe, while Λ < 0 gives rise to an oscillatory or non-periodic mode of expansion. If the metric functions a and b are taken to be inverse to each other (ab = 1), we have a singularity-free universe independently of the sign of Λ.

Non-minimal coupling of photons and axions

We establish a new self-consistent system of equations accounting for a non-minimal interaction of gravitational, electromagnetic and axion fields. The procedure is based on a non-minimal extension of the standard Einstein–Maxwell–axion action. The general properties of a ten-parameter family of non-minimal linear models are discussed. We apply this theory to the models with pp-wave symmetry and consider propagation of electromagnetic waves non-minimally coupled to the gravitational and axion fields. We focus on exact solutions of electrodynamic equations, which describe quasi-minimal and non-minimal optical activity induced by the axion field. We also discuss empirical constraints on coupling parameters from astrophysical birefringence and polarization rotation observations.

10.1007/s11443-008-3003-4

Based on an axisymmetric galactic disk model, we estimate the equilibrium gas pressure P/k in the disk plane as a function of the galactocentric distance R for several galaxies (MW, M33, M51, M81, M100, M101, M106, and the SMC). For this purpose, we solve a self-consistent system of equations by taking into account the gas self-gravity and the presence of a dark pseudo-isothermal halo. We assume that the turbulent velocity dispersions of the atomic and molecular gases are fixed and that the velocity dispersion of the old stellar disk corresponds to its marginal stability (except for the Galaxy and the SMC). We also consider a model with a constant disk thickness. Of the listed galaxies, the SMC and M51 have the highest pressure at a given relative radius R/R 25, while M81 and the Galaxy has the lowest pressure. The pressure dependence of the relative molecular gas fraction confirms the existence of a positive correlation between these quantities, but it is not so distinct as that obtained previously when the pressure was estimated very roughly. This dependence breaks down for the inner regions of M81 and M106, probably because the gas pressure has been underestimated in the bulge region. We discuss the possible effects of factors other than the pressure affecting the relative content of the molecular gas in the galaxies under consideration.

Interacting spinor and scalar fields in a bianchi type-I universe filled with viscous fluid: Exact and numerical solutions

We consider a self-consistent system of spinor and scalar fields in a Bianchi type I gravitational field filled with a viscous fluid in the presence of a cosmological constant. Exact solutions to the set of spinor, scalar and gravitational field equations are obtained in terms of v, the volume scale of Bianchi-I universe. A set of equations for v and ε, where ε is the energy of the viscous fluid, is deduced. Some special cases allowing exact solutions are thoroughly studied.

Nonlinear spinor fields in an anisotropic universe filled with viscous fluid: Exact solutions and qualitative analysis

A self-consistent system containing a nonlinear spinor field and a Bianchi type-I (BI) gravitational field is considered in the presence of a viscous fluid and the cosmological constant. Nonlinear terms in the Lagrangian spinor-field appear either due to a self-action, or as a result of interaction with a scalar field. They are given by power functions of the invariants I and J, constructed from the bilinear spinor forms S and P. As far as the viscosity is concerned, it is a function of the energy density ɛ exhibiting a power-law behavior. Self-consistent solutions of the spinor, scalar, and gravitational field equations are derived. The obtained solutions are expressed in terms of the function τ(t), where τ is the volume scale in the BI-type Universe. A system of equations for τ, H, and ɛ is derived, where H is the Hubble constant, and ɛ is the viscous-flow energy. Exact solutions of the system are found for some special choices of the nonlinearity and viscosity. A complete qualitative analysis of the evolution at the boundaries is performed, and numerical solutions are obtained in the most interesting cases. In particular, it is shown that the system has Big Rip type solutions, which is typical for systems containing a phantom matter.

Large-scale zonal flow and magnetic field generation due to drift-Alfven turbulence in ionosphere plasma

In the present work, the generation of large-scale zonal flows and magnetic field by short-scale collision-less electron skin depth order drift-Alfven turbulence in the ionosphere is investigated. The self-consistent system of two model nonlinear equations, describing the dynamics of wave structures with characteristic scales till to the skin value, is obtained. Evolution equations for the shear flows and the magnetic field is obtained by means of the averaging of model equations for the fast-high-frequency and small-scale fluctuations. It is shown that the large-scale disturbances of plasma motion and magnetic field are spontaneously generated by small-scale drift-Alfven wave turbulence through the nonlinear action of the stresses of Reynolds and Maxwell. Positive feedback in the system is achieved via modulation of the skin size drift-Alfven waves by the large-scale zonal flow and/or by the excited large-scale magnetic field. As a result, the propagation of small-scale wave packets in the ionospheric medium is accompanied by low-frequency, long-wave disturbances generated by parametric instability. Two regimes of this instability, resonance kinetic and hydrodynamic ones, are studied. The increments of the corresponding instabilities are also found. The conditions for the instability development and possibility of the generation of large-scale structures are determined. The nonlinear increment of this interaction substantially depends on the wave vector of Alfven pumping and on the characteristic scale of the generated zonal structures. This means that the instability pumps the energy of primarily small-scale Alfven waves into that of the large-scale zonal structures which is typical for an inverse turbulent cascade. The increment of energy pumping into the large-scale region noticeably depends also on the width of the pumping wave spectrum and with an increase of the width of the initial wave spectrum the instability can be suppressed. It is assumed that the investigated mechanism can refer directly to the generation of mean flow in the atmosphere of the rotating planets and the magnetized plasma.

Internal coarse-graining of molecular systems

Modelers of molecular signaling networks must cope with the combinatorial explosion of protein states generated by posttranslational modifications and complex formation. Rule-based models provide a powerful alternative to approaches that require explicit enumeration of all possible molecular species of a system. Such models consist of formal rules stipulating the (partial) contexts wherein specific protein–protein interactions occur. These contexts specify molecular patterns that are usually less detailed than molecular species. Yet, the execution of rule-based dynamics requires stochastic simulation, which can be very costly. It thus appears desirable to convert a rule-based model into a reduced system of differential equations by exploiting the granularity at which rules specify interactions. We present a formal (and automated) method for constructing a coarse-grained and self-consistent dynamical system aimed at molecular patterns that are distinguishable by the dynamics of the original system as posited by the rules. The method is formally sound and never requires the execution of the rule-based model. The coarse-grained variables do not depend on the values of the rate constants appearing in the rules, and typically form a system of greatly reduced dimension that can be amenable to numerical integration and further model reduction techniques.

Stable States of Biological Organisms

A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole. The organism is modeled by a five-dimensional dynamical system. The organism homeostasis is described by the evolution equations for five interacting components: healthy cells, ill cells, innate immune cells, specific immune cells, and pathogens. The stability analysis demonstrates that, in a wide domain of the parameter space, the system exhibits robust structural stability. There always exist four stable stationary solutions characterizing four qualitatively differing states of the organism: alive state, boundary state, critical state, and dead state.

Energetic variational approaches in modeling vesicle and fluid interactions

In this paper, we establish a hydrodynamic system to study vesicle deformations under external flow fields. The system is in the Eulerian formulation, involving the coupling of the incompressible flow system and a phase field equation. The phase field mixing energy can be viewed as a physical approximation/regularization of the Helfrich energy for an elastic membrane. We derive a self-consistent system of equations describing the dynamic evolution of vesicles immersed in an incompressible, Newtonian fluid, using an energetic variational approach. Numerical simulations of the membrane deformations in flow fields can be conducted based on the developed model.

Enhancement of the Thermoelectric Figure of Merit in Gated Bismuth Telluride Nanowires

AbstractWe theoretically studied how the electric filed effect can modify thermoelectric properties of intrinsic bismuth telluride nanowires, which are grown along [110] direction. The electronic structure and wave functions were calculated by solving the self-consistent system of the Schrodinger and Poisson equations by means of both the Thomas-Fermi approximation and the spectral element method. The thermoelectric parameters were determined using a constant relaxation-time approximation. The external electric field can increase the Seebeck coefficient of a nanowire with 7 - 15 nm lateral dimensions by nearly a factor of two, and enhance the figure of merit by an order of magnitude.

Damping of the free oscillations of a neutral buoyancy sphere in a viscous stratified fluid

A technique is developed for calculating the oscillations of balanced spheres at neutral buoyancy levels based on the linearization of the equations of the mechanics of a viscous, continuously stratified fluid. A self-consistent system of integro-differential equations is obtained and analysed using perturbation theory methods. The results of calculations of the displacements of the centres of the spheres are reduced to a form which a permits direct comparison with a laboratory experiment and they agree with the data of measurements. A comparison is made with calculations of the free oscillations of a sphere in an ideal fluid.

Molecular Single‐Bond Covalent Radii for Elements 1–118

A self-consistent system of additive covalent radii, R(AB)=r(A) + r(B), is set up for the entire periodic table, Groups 1-18, Z=1-118. The primary bond lengths, R, are taken from experimental or theoretical data corresponding to chosen group valencies. All r(E) values are obtained from the same fit. Both E-E, E-H, and E-CH(3) data are incorporated for most elements, E. Many E-E' data inside the same group are included. For the late main groups, the system is close to that of Pauling. For other elements it is close to the methyl-based one of Suresh and Koga [J. Phys. Chem. A 2001, 105, 5940] and its predecessors. For the diatomic alkalis MM' and halides XX', separate fits give a very high accuracy. These primary data are then absorbed with the rest. The most notable exclusion are the transition-metal halides and chalcogenides which are regarded as partial multiple bonds. Other anomalies include H(2) and F(2). The standard deviation for the 410 included data points is 2.8 pm.

Bianchi type-V cosmological models with perfect fluid and dark energy

We consider a self-consistent system of Bianchi type-V cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein equations are obtained as a quadrature. The cases of disordered radiation and models with power-law and exponential expansion have discussed in detail. For large t, the models tend to be isotropic.

Anisotropic cosmological models with spinor and scalar fields and viscous fluid in presence of a Λ term: Qualitative solutions

The study of a self-consistent system of interacting spinor and scalar fields within the scope of a Bianchi type I (BI) gravitational field in the presence of a viscous fluid and Λ term has been carried out. The system of equations defining the evolution of the volume scale of BI universe, energy density, and corresponding Hubble constant has been derived. The system in question has been thoroughly studied qualitatively. Corresponding solutions are graphically illustrated. The system in question is also studied from the view point of blow up. It has been shown that the blow up takes place only in the presence of viscosity.