Finite Total Energy Research Articles

IR-finite thermal acceleration radiation

A charge accelerating in a straight line following the Schwarzschild–Planck moving mirror motion emits thermal radiation for a finite period. Such a mirror motion demonstrates quantum purity and serves as a direct analogy of a black hole with unitary evolution and complete evaporation. Extending the analog to classical electron motion, we derive the emission spectrum, power radiated, and finite total energy and particle count, with particular attention to the thermal radiation limit. This potentially opens the possibility of a laboratory analog of black hole evaporation.

Axisymmetric, stationary collisionless gas clouds trapped in a Newtonian potential

The properties of an axisymmetric, stationary gas cloud surrounding a massive central object are discussed. It is assumed that the gravitational field is dominated by the central object which is modeled by a nonrelativistic rotationally-symmetric potential. Further, we assume that the gas consists of collisionless, identical massive particles that follow bound orbits in this potential. Several models for the one-particle distribution function are considered and the essential formulae that describe the relevant macroscopical observables, such as the particle and energy densities, pressure tensor, and the kinetic temperature are derived. The asymptotic decay of the solutions at infinity is discussed and we specify configurations with finite total mass, energy and (zero or non-zero) angular momentum. Finally, our configurations are compared to their hydrodynamic analogs. In an accompanying paper, the equivalent general relativistic problem is discussed, where the central object consists of a Schwarzschild black hole.

SOLITON OF SELF-CONSISTENT SYSTEM OF NONLINEAR SPINOR AND GRAVITATIONAL FIELDS WITH THE ARBI- TRARY FUNCTION DEPENDING ON THE BILINEAR PAULI- FIERZ INVARIANT IS = S2 IN GENERAL RELATIVITY

A self-consistent system of nonlinear spinor and gravitational fields, modeled by static spherical symmetric metric, is considered and studied. Exact spherical symmetric solutions of nonlinear spinor field equations in the Gravitational Theory are obtained. The nonlinearity in the spinor lagrangian is given by an arbitrary function which depends on the invariant generated from the Fierz-Pauli bilinear spinor form IS = S2. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Let us emphasize that the effect of gravitational field on the properties of regular localized solutions significantly depends on the symmetry of the system. The nonlin- ear terms, the gravitational field of elementary particles and the geometrical properties of the metric of the space-time play an important role in the obtaining of analytical solutions having the soliton-like configuration. Let us emphasize that the numerical solutions of the solutions obtained here are presented in graphical form.

Electron as a Tiny Mirror: Radiation from a Worldline with Asymptotic Inertia

We present a moving mirror analog of the electron, whose worldline possesses asymptotic constant velocity with corresponding Bogoliubov β coefficients that are consistent with finite total emitted energy. Furthermore, the quantum analog model is in agreement with the total energy obtained by integrating the classical Larmor power.

Nonlinear Spinor Field Equation of the Bilinear Pauli-Fierz Invariant Iv = S2 + P2: Exact Spherical Symmetric Soliton-Like Solutions in General Relativity

Taking into account the own gravitational field of elementary particles, we have obtained exact static spherical symmetric
 solutions to the spinor field equation. The nonlinear terms LN are arbitrary functions of bilinear Pauli-Fierz invariant
 Iv = S2 + P2. It characterizes the self-interaction of a spinor field. We have investigated in detail equations with power
 and polynomial nonlinearities. The spinor field equation with a power-law nonlinearity have regular solutions with a
 localized energy density and regular metric. In this case a soliton-like configuration has finite and negative total energy.
 As for equations with polynomial nonlinearity, the obtained solutions are regular with a localized energy density and
 regular metric but its total energy is finite and positive.

Heisenberg-Ivanenko Nonlinear Spinor Field Equation: Spherical Symmetric Soliton-Like Solutions in Gravitational Theory

This research work deals with the concept of soliton as regular localized stable solutions of nonlinear di erential equations. In this context, exact static, spherically symmetric solutions to Heisenberg-Ivanenko nonlinear spinor field equation have been obtained in General Relativity. We opted to the static spherical symmetric metric defined in the pseudoriemannian varieties. It has been shown that the obtained solutions are regular with localized energy density and a finite total energy. In addition, the total charge and the total spin are bounded. Therefore the obtained solutions of Heisenberg-Ivanenko nonlinear spinor field equation are soliton-like configurations. Note that the e ect of gravitational field on the properties of regular localized solutions significantly depends on the symmetry of the system.

Free Space Strange and Unipolar EM Pulses: Yes or No?

E.G. Bessonov suggested the time integrated strength of an electric field ∫−∞∞E(r,t)dt=SE(r) as a parameter to classify electromagnetic (EM) waves. Since then, this parameter has been studied and used in many works on microwave and laser physics, especially when it comes to unipolar, bipolar and few cycle EM pulses. In this paper, it is shown that SE(r)=0 is an identity for a wide class of free space pulses of finite total energy. This property can be useful in various applications of few cycle radiation and as a benchmark in EM and QED computations.

BASF drives innovation with new global Catalyst Development and Solids Processing Center

In this paper we study the well-posedness of the (1+1)-dimensional Maxwell-Chern-Simons gauged O(3)-sigma model with the Lorenz gauge condition. First, we provide the global well-posedness of a solution in a high regular space. We also prove the existence of a global solution with the finite total energy. Moreover, we consider local well-posedness below the energy regularity by exploiting null form and wave-Sobolev space.

Heat diffusion-related damping process in a highly precise coarse-grained model for nonlinear motion of SWCNT

Second sound and heat diffusion in single-walled carbon nanotubes (SWCNT) are well-known phenomena which is related to the high thermal conductivity of this material. In this paper, we have shown that the heat diffusion along the tube axis affects the macroscopic motion of SWCNT and adapting this phenomena to coarse-grained (CG) model can improve the precision of the coarse-grained molecular dynamics (CGMD) exceptionally. The nonlinear macroscopic motion of SWCNT in the free thermal vibration condition in adiabatic environment is demonstrated in the most simplified version of CG modeling as maintaining finite temperature and total energy with suggested dissipation process derived from internal heat diffusion. The internal heat diffusion related to the cross correlated momentum from different potential energy functions is considered, and it can reproduce the nonlinear dynamic nature of SWCNTs without external thermostatting in CG model. Memory effect and thermostat with random noise distribution are not included, and the effect of heat diffusion on memory effect is quantified through Mori–Zwanzig formalism. This diffusion shows perfect syncronization of the motion between that of CGMD and MD simulation, which is started with initial conditions from the molecular dynamics (MD) simulation. The heat diffusion related to this process has shown the same dispersive characteristics to second wave in SWCNT. This replication with good precision indicates that the internal heat diffusion process is the essential cause of the nonlinearity of the tube. The nonlinear dynamic characteristics from the various scale of simple beads systems are examined with expanding its time step and node length.

Compensated compactness and corrector stress tensor for the Einstein equations in $\mathbb T^2$ symmetry

We consider the Einstein equations in \mathbb T^2 symmetry, either for vacuum spacetimes or coupled to the Euler equations for a compressible fluid, and we introduce the notion of \mathbb T^2 areal flows on \mathbb T^3 with finite total energy. By uncovering a hidden structure of the Einstein equations, we establish a compensated compactness framework which allows us to solve the global evolution problem for vacuum spacetimes as well as for self-gravitating compressible fluids. We study the stability and instability of such flows and prove that, when the initial data are well-prepared, any family of \mathbb T^2 areal flows is sequentially compact in a natural topology. In order to handle general initial data we propose a ‘‘relaxed’’ notion of \mathbb T^2 areal flows endowed with a corrector stress tensor (as we call it) which is a bounded measure generated by geometric oscillations and concentrations propagating at the speed of light. This generalizes a result for vacuum spacetimes in: Le Floch B. and P. G. LeFloch, Arch. Rational Mech. Anal. 233 (2019), 45–86.

Spherical Symmetric Solitons of Interacting Spinor, Scalar and Gravitational Fields in General Relativity

The concept of soliton as regular localized stable solutions of nonlinear differential equations is being widely utilized in pure science for various aims. In present analysis, the soliton concept is used as a model in order to describe the configurations of elementary particles in general relativity. To this end, our study deals with the spherical symmetric solitons of interacting Spinor, Scalar and Gravitational Fields in General Relativity. Thus, exact spherical symmetric general solutions to the interaction of spinor, scalar and gravitational field equations have been obtained. The Einstein equations have been transformed into a Liouville equation type and solved. Let us emphasize that these solutions are regular with localized energy density and finite total energy. In addition, the total charge and spin are limited. Moreover, the obtained solutions are soliton-like solutions. These solutions can be used in order to describe the configurations of elementary particles.

Local and global solutions to the O(3)-sigma model with the Maxwell and the Chern-Simons gauges in [formula omitted

In this paper we study the well-posedness of the (1+1)-dimensional Maxwell-Chern-Simons gauged O(3)-sigma model with the Lorenz gauge condition. First, we provide the global well-posedness of a solution in a high regular space. We also prove the existence of a global solution with the finite total energy. Moreover, we consider local well-posedness below the energy regularity by exploiting null form and wave-Sobolev space.

Exact solutions to 2D isothermal Euler-Poisson equations with qualitative analysis

The family of exact solutions with parameter λ of the 2D isothermal Euler-Poisson equations, which can be used to model the evolution of self-gravitating galaxies or gaseous stars, is investigated. By solving the Liouville equation in Yuen’s analytical solutions, a family of exact solutions is obtained for λ=0. We show that although such solutions remain local with finite mass and finite potential energy for all time, they have unbounded kinetic energy for any given time. In physics terms, these (2+1)-dimensional solutions may correspond to a (3+1)-dimensional model of an infinite universe with finite mass and infinite kinetic energy. We also show that the mass and kinetic energy of the solutions are finite for λ < 0, thereby demonstrating in the (2+1)-dimensional case a universe model with finite total energy, provided that the finiteness of the potential energy is given.

Weak Solutions of Ideal MHD Which Do Not Conserve Magnetic Helicity

We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In view of Taylor’s conjecture, this proves that there exist finite energy weak solutions to ideal MHD which cannot be attained in the infinite conductivity and zero viscosity limit. Our proof is based on a Nash-type convex integration scheme with intermittent building blocks adapted to the geometry of the MHD system.

Exact Soliton-Like Spherical Symmetric Solutions of the Heisenberg-Ivanenko Type Nonlinear Spinor Field Equation in Gravitational Theory

In the present research work, we have obtained the exact spherical symmetric solutions of Heisenberg-Ivanenko nonlinear spinor field equations in the Gravitational Theory. The nonlinearity in the spinor Lagrangian is given by an arbitrary function which depends on the invariant generated from the bilinear spinor form Is = S2. We admit the static spherical symmetric metric. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Role of the metric i.e. the proper gravitational field of elementary particles in the formation of the field configurations with limited total energy, spin and charge has been examined by solving the field equations in flat space-time. It has been established that the obtained solutions are soliton-like configuration with bounded energy density and finite total energy. In order to clarify the role of the nonlinearity in this model, we have obtained exact statical symmetric solutions to the above spinor field equations in the linear case corresponding to Dirac’s linear equation. It is proved that soliton-like solutions are absent.

Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere

Abstract This study investigates strongly nonlinear gravity waves in the compressible atmosphere from the Earth’s surface to the deep atmosphere. These waves are effectively described by Grimshaw’s dissipative modulation equations which provide the basis for finding stationary solutions such as mountain lee waves and testing their stability in an analytic fashion. Assuming energetically consistent boundary and far-field conditions, that is no energy flux through the surface, free-slip boundary, and finite total energy, general wave solutions are derived and illustrated in terms of realistic background fields. These assumptions also imply that the wave-Reynolds number must become less than unity above a certain height. The modulational stability of admissible, both non-hydrostatic and hydrostatic, waves is examined. It turns out that, when accounting for the self-induced mean flow, the wave-Froude number has a resonance condition. If it becomes 1/ 1 / 2 1/\sqrt 2 , then the wave destabilizes due to perturbations from the essential spectrum of the linearized modulation equations. However, if the horizontal wavelength is large enough, waves overturn before they can reach the modulational stability condition.

Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields

The present research work deals with an extension of a previous work [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. We have obtained exact kink-like static spherical symmetric solutions to the self-consistent system of spinor and gravitational fields equations. The Einstein’s field equation shave been solved by the Liouville method. The principal difference between kink soliton with antikink soliton has been established. The nonlinear terms in the lagrangian are arbitrary functions F(IS) depending on the invariant IS = S2= ( )2. It is shown that the initial set of the Einstein and spinor field equations have regular solutions with a localized energy density of the spinor field only if m = 0 (m is the mass parameter in the spinor field equations). Equations with polynomial nonlinearities are thoroughly scrutinized. Let us emphasize that the spinor field with polynomial nonlinearities has a regular solutions with localized, positive and alternating energy density and finite total energy. In addition, the total charge and the total spin are also finte. We have also obtained exact solutions to the linear spinor field equations. We remarked that in this case soliton-like solutions are absent. Furthermore, we note that the properties of regular localized solutions depend on the symmetry and the nonlinear terms in the lagrangian of the self-consistent system of gravitational and spinor fields.

Uniqueness of the Boundary Value Problem of Harmonic Maps via Harmonic Boundary

We prove the uniqueness of solutions for the boundary value problem of harmonic maps in the setting: given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a regular geodesic ball, there exists a unique harmonic map, which is a limit of a sequence of harmonic maps with finite total energy in the sense of the supremum norm, from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.

Finite energy but infinite entropy production from moving mirrors

Accelerating mirrors provide a simple conceptual laboratory for studying particle production and the relation between trajectory and particle, energy, and entropy fluxes. We focus on the relation between energy and entropy, studying some special cases with finite total energy but infinite integrated entropy (though the entropy flux may be finite at any particular moment). We present a new asymptotically static moving mirror trajectory with solvable beta Bogolyubov coefficients, total energy and fully relativistic particle count. The integrated entropy diverges despite finite global radiative particle and energy emission. Another class of models includes exponentially accelerated mirrors in proper time; one of its unexpected behaviors is finite energy emission but divergent entropy. We compare mirrors exponentially accelerated in other coordinates as well, showing their close relation and an interesting duality property.

Quasimonochromatic exact solutions to Maxwell's equations with finite total energy and arbitrary frequencies in the vacuum.

We analyze a family of exact finite energy solutions to Maxwell's equations. These solutions are a subset of the modified-power-spectrum solutions found by Ziolkowski [Phys. Rev. A 39, 2005 (1989)10.1103/PhysRevA.39.2005]. There are three characteristic parameters in the solutions: q_{1},q_{2}, and k_{0}. q_{1} and q_{2} are related to the frequency bandwidth of the solution. In the parameter space of k_{0}q_{1}≫1 and k_{0}q_{2}≫1, they represent quasimonochromatic continuous wave fields with the main angular frequency k_{0}c and energy localized in the transverse directions. Under the restriction of q_{1}≪q_{2}, the beam propagates mainly in the +z direction with velocity c and limited diffraction.