Charged D stars

We describe charged soliton stars with a solid angular deficit (charged boson D stars), and find the approximate solution in the external space. Besides, we discuss the stability of charged D stars and find when the number of bosons is less than certain value, charged D stars are quantum mechanically stable.     

Charged D stars

We describe charged soliton stars with a solid angular deficit (charged boson D stars), and find the approximate solution in the external space. Besides, we discuss the stability of charged D stars and find when the number of bosons is less than certain value, charged D stars are quantum mechanically stable.     

Thermodynamics of the model of equal spin-spin interactions

We consider the thermodynamics of the model of equal spin-spin interactions. We obtain exact expressions for the correlation functions and heat capacity of finite clusters applicable in the entire range of temperature and external fields. We analyze the obtained thermodynamic characteristics depending on the interaction parameters, the external magnetic field, and the number of particles in the cluster. We find an anomalous behavior of the heat capacity and other thermodynamic quantities due to elementary spin gap excitations occurring in the spectrum. The absence of a long-range order in the system is ensured by the presence of topological excitations (solitons). We study the effect of an anisotropic interaction parameter on the soliton structure.     

Effects of slip on steady Bödewadt flow and heat transfer of an electrically conducting non-Newtonian fluid

The steady flow and heat transfer arising due to the rotation of a non-Newtonian fluid at a larger distance from a stationary disk is extended to the case where the disk surface admits partial slip. The constitutive equation of the non-Newtonian fluid is modeled by that for a Reiner–Rivlin fluid. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The momentum equation gives rise to a highly nonlinear boundary value problem. Numerical solution of the governing nonlinear equations are obtained over the entire range of the physical parameters. The effects of slip, non-Newtonian fluid characteristics and the magnetic interaction parameter on the momentum boundary layer and thermal boundary layer are discussed in detail and shown graphically. It is observed that slip has prominent effects on the velocity and temperature fields.     

Numerical solutions of general-relativistic field equations for rapidly rotating neutron stars

Stationary axial symmetric equilibrium configurations rapidly rotating with uniform angular velocity in the framework of general relativity are considered. Sequences of models are numerically computed by means of a computer code that solves the full Einstein equations exactly. This code employs Neugebauer’s minimal surface formalism, where the field equations are equivalent to two-dimensional minimal surface equations for 4 metric potentials. The calculations are based upon 10 different equations of state. Results of various structures of neutron stars and the rotational effects on stellar structures and properties are reported. Finally some limits to equations of state of neutron stars and the stability for rapidly rotating relativistic neutron stars are discussed.     

Stability characteristics of periodic streaming fluids in porous media

We study the linear stability of a three-layer flow of immiscible liquids located in a periodic normal electric field. We consider certain porous media assumed to be uniform, homogeneous, and isotropic. We analytically and numerically simulate the system of linear evolution equations of such a medium. The linearized problem leads to a system of two Mathieu equations with complex coefficients of the damping terms. We study the effects of the streaming velocity, permeability of the porous medium, and the electrical properties of the flow of a thin layer (film) of liquid on the flow instability. We consider several special cases of such systems. As a special case, we consider a uniform electric field and solve the transition curve equations up to the second order in a small dimensionless parameter. We show that the dielectric constant ratio and also the electric field play a destabilizing role in the stability criteria, while the porosity has a dual effect on the wave motion. In the case of an alternating electric field and a periodic velocity, we use the method of multiple time scales to calculate approximate solutions and analyze the stability criteria in the nonresonance and resonance cases; we also obtain transition curves in these cases. We show that an increase in the velocity and the electric field promote oscillations and hence have a destabilizing effect.     

Semi-Classical Dirac Vacuum Polarisation in a Scalar Field

We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regularised vacuum energy. The leading order of this expansion is given by a classical formula due to Chin, Lee-Wick and Walecka, for which our result provides the first rigorous proof. We then discuss applications to the non-relativistic large-coupling limit of an interacting system, and to the stability of homogeneous systems.     

A three-dimensional phase transition model in ferromagnetism: Existence and uniqueness

We scrutinize both from the physical and the analytical viewpoint the equations ruling the paramagnetic-ferromagnetic phase transition in a rigid three-dimensional body. Starting from the order structure balance, we propose a non-isothermal phase-field model which is thermodynamically consistent and accounts for variations in space and time of all fields (the temperature θ, the magnetic field vector H and the magnetization vector M). In particular, we are able to establish a well-posedness result for the resulting coupled system.     

Thermally Stressed State of Bodies with Two Ellipsoidal Inclusions

Solutions are obtained for the interaction of two ellipsoidal inclusions in an elastic isotropic matrix with polynomial external athermal and temperature fields. Perfect mechanical and temperature contact is assumed at the phase interface. A solution to the problem is constructed. When the perturbations in the temperature field and stresses in the matrix owing to one inclusion are re-expanded in a Taylor series about the center of the second inclusion, and vice versa, and a finite number of expansion terms is retained, one obtains a finite system of linear algebraic equations in the unknown constants. The effect of a force free boundary of the half space on the stressed state of a material with a triaxial ellipsoidal inhomogeneity (inclusion) is investigated for uniform heating. Here it was assumed that the elastic properties of the inclusions and matrix are the same, but the coefficients of thermal expansion of the phases differ. Studies are made of the way the stress perturbations in the matrix increase and the of the deviation from a uniform stressed state inside an inclusion as it approaches the force free boundary.     

Effect of rotation on plane waves of generalized electro-magneto-thermoviscoelasticity with two relaxation times

A new model of the equations of generalized thermovisco-elasticity for a thermally, isotropic and electrically conducting half-space solid whose surface is subjected to a thermal shock is given. The formulation is applied to the generalized thermoelasticity based on the Green and Lindsay (GL) theory under the effect of rotation, where there is an initial magnetic field parallel to the plane boundary of the half-space. The medium is deformed because of thermal shock and due to the application of the magnetic field, it results an induced magnetic and electric fields in the medium. The normal mode analysis is used to obtain the expressions for the variables considered. The distributions of temperature, displacement, stress, induced magnetic and electric fields are represented graphically. Comparisons are made with the results predicted by the coupled theory (CD) in the presence and absence of rotation.     

Global solution for a one-dimensional model problem in thermally radiative magnetohydrodynamics

The dynamics of gaseous stars is often described by magnetic fields coupled to self-gravitation and radiation effects. In this paper we consider an initial-boundary value problem for nonlinear planar magnetohydrodynamics (MHD) in the case that the effect of self-gravitation as well as the influence of radiation on the dynamics at high temperature regimes are taken into account. Based on the fundamental local existence results and global-in-time a priori estimates, we establish the global existence of a unique classical solution with large initial data to the initial-boundary value problem under quite general assumptions on the heat conductivity.     

Γ-Convergence of 2D Ginzburg-Landau functionals with vortex concentration along curves

We study the variational convergence of a family of twodimensional Ginzburg-Landau functionals arising in the study of superfluidity or thin-film superconductivity as the Ginzburg-Landau parameter ε tends to 0. In this regime and for large enough applied rotations (for superfluids) or magnetic fields (for superconductors), the minimizers acquire quantized point singularities (vortices). We focus on situations in which an unbounded number of vortices accumulate along a prescribed Jordan curve or a simple arc in the domain. This is known to occur in a circular annulus under uniform rotation, or in a simply connected domain with an appropriately chosen rotational vector field. We prove that if suitably normalized, the energy functionals Γ-converge to a classical energy from potential theory. Applied to global minimizers, our results describe the limiting distribution of vortices along the curve in terms of Green equilibrium measures.     

An extended thermal-medium crack model

It is important to investigate the effects of heat conduction of crack interior on thermoelastic fields of a cracked material. In this paper, an extended thermal-medium crack model is proposed to address the influences of the thermal conductivity inside an opening crack on the induced thermoelastic fields. Then the problem of a penny-shaped crack in a transversely isotropic material is investigated under applied mechanical and uniform heat flow loadings. Based on the Hankel transform technique, the governing partial differential equations are transformed to ordinary differential equations, then to a system of coupled dual integral equations. The thermoelastic fields around the penny-shaped crack are obtained explicitly by solving the derived dual integral equations. Numerical results are reported to show the influences of the thermal conductivity of crack interior on partial insulation coefficient, temperature change across crack and thermal stress intensity factor. As compared to the known thermal-medium crack model, the proposed one exhibits more applicability.     

Decay to bound states of a soliton in a well

The decay of a soliton in a trapped state inside a well is shown numerically. Bound states of a kink in an attractive well, both centered and off centered are found. Their stability is studied. Unstable soliton solutions inside a repulsive barrier are also found.     

Darboux Transformation for a Semidiscrete Short-Pulse Equation

We define a Darboux transformation in terms of a quasideterminant Darboux matrix on the solutions of a semidiscrete short-pulse equation. We also give a quasideterminant formula for N-loop soliton solutions and obtain a general expression for the multiloop solution expressed in terms of quasideterminants. Using quasideterminants properties, we find explicit solutions and as an example compute one- and two-loop soliton solutions in explicit form.     

Induction heating of cylindrical nonmagnetic ingots by rotation in static magnetic field generated by permanent magnets

Induction heating of cylindrical nonmagnetic billets by their rotation in static magnetic field is modeled. The magnetic field is produced by a system of appropriately arranged permanent magnets. The numerical model is solved by our own full adaptive higher-order finite element method in a monolithic formulation, i.e., both magnetic and temperature fields are solved simultaneously, respecting their mutual interaction. All principal nonlinearities are included in the model (permeability of ferromagnetic parts of the system as well as temperature dependences of physical parameters of the heated metal). The methodology is illustrated by two examples whose results are discussed.     

The Effect of an Axial Magnetic Field at the Interface of a Crystal Grown by the Czochralski Method

A mathematical model has been developed which aims to give insightinto the transport phenomena in the vicinity of the interfaceof a crystal grown by the Czochralski method in the presenceof an axial magnetic field. The fluid flow, temperature andconcentration fields in this region have a strong effect onthe distribution of impurities and the occurrence of cracks,dislocations and other physical defects in the crystal and soknowledge and ultimately control of these factors is of greatpractical importance. The model incorporates rotation of both the crystal and crucibleby considering the crystal to be an infinite disc rotating ina semi-infinite fluid which may be rotating at infinity. Axialsymmetry is assumed and the magnetic Prandtl number is consideredto be very much less than unity. This means that induced currentscan be neglected and allows a similarity solution to be developed.The system of partial differential equations can then be replacedby an ordinary differential boundary-value problem which issolved numerically.     

Exponential Decay Rates for Structural Acoustic Model with an Overdamping on the Interface and Boundary Layer Dissipation

We study uniform stability properties of a strongly coupled system of Partial Differential Equations of hyperbolic/parabolic type, which arises from the analysis and control of acoustic models with structural damping on an interface. A challenging feature of the present model is the presence of additional strong boundary damping which is responsible for lack of uniform stability of the free system ( overdamping phenomenon). It has been shown recently that by applying full viscous damping in the interior of the domain and suitable static damping on the interface, then the corresponding feedback system is uniformly stable. In this article we prove that uniform decay rates of solutions to the system can be achieved even if viscous damping is active just in an arbitrary thin layer near the interface.     

On the dissipative effect of a magnetic field in a Mindlin-Timoshenko plate model

In this paper we are concerned with a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. The magnetic field that permeates the plate consists of a non-stationary part and a uniform (constant) part. When the uniform magnetic field is aligned with the mid-plane of the plate, a strongly interactive system emerges with direct coupling between the elastic field and the magnetic field occurring in all the equations of the system. The unique solvability of the model is established within the framework of semigroup theory. Spectral analysis methods are used to show strong asymptotic stability and determine the polynomial decay rate of weak solutions.     

Quantum Macroscopic Effects in a Degenerate Strongly Magnetized Nucleon Gas

A model of a degenerate gas consisting of neutrons that are in chemical equilibrium with degenerate protons and electrons in a stationary and homogeneous superstrong magnetic field is used to describe the state of the matter in central regions of strongly magnetized neutron stars. Expressions for thermodynamic quantities (such as energy density, particle density, pressure, and magnetization) characterizing a degenerate gas of neutrons, protons, and electrons are obtained. In these expressions, the contributions determined by the interaction between anomalous magnetic moments of fermions and the magnetic field are taken into account. Macroscopic effects that may occur in strongly magnetized neutron stars are discussed. We show that all thermodynamic quantities characterizing electrically charged fermions in a strong magnetic field are subject to nonperiodic oscillations caused by the interaction of the anomalous magnetic moments of protons and electrons with the magnetic field. We also show that if the nucleon density and the electron density exceed threshold values that are relatively small and depend on the magnetic field strength, all fermions are fully polarized with respect to the spin. The full spin polarization effect in neutrons is caused by the interaction between the anomalous magnetic moment and the magnetic field. The obtained results may prove useful in understanding processes that occur in the nucleus of a neutron star with a magnetic field frozen into the star.