Determination of scalar meson masses in QCD-inspired quark models

We compare two QCD-inspired quark models with four-fermion interaction (with and without the remnant coupling to low-energy gluons) in the regime of dynamical chiral symmetry breaking (DCSB). The first one, the Nambu-Jona-Lasinio (NJL) model, ensures the factorization of scalar and pseudoscalar meson poles in correlators, the well-known Nambu relation between the scalar meson mass and the dynamical quark mass, m_σ=2m_dyn, and the residual chiral symmetry in coupling constants characteristic for the linear σ-model. The second one, the gauge NJL model (GNJL), happens to be qualitatively different from the NJL model, namely, the Nambu relation is not valid, and the factorization of light meson poles does not entail the residual chiral symmetry, i.e., it does not result in a linear σ-model. The more complicated DCSB pattern in the GNJL model is fully explained in terms of excited meson states with the same quantum numbers. The asymptotic restrictions on parameters of scalar and pseudoscalar meson states are derived from the requirement of chiral symmetry restoration at high energies. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 245, 1997, pp. 5–21.     

Numerical modeling of pollution transport in flexible vegetation

In this study, we present a large eddy simulation model of the flow and scalar transport in an open channel with flexible vegetation. We propose a model for recognizing flexible vegetation to simulate the deflected height of vegetation with flexibility. A mixed scale model is modified for canopy turbulence modeling. A random walk model is used to calculate the mechanical dispersion during the scalar transport process within the canopy. A two-stage second-order nonlinear strong stability-preserving Runge–Kutta scheme is combined with the operator splitting algorithm to solve the governing equations. We verified the numerical model based on previously reported experimental data and the comparisons between the simulations and measurements were favorable. The model was then applied to simulate scalar transport within flexible vegetation, where the simulations showed that the recognition of flexible vegetation could enhance the vertical mixing and diffusion of the scalar concentration.     

On NP-Completeness for Linear Machines

We consider linear and scalar versions of the Blum–Shub–Smale model of computation over the reals. The permitted computing operations of linear machines are addition and multiplication by constants. The scalar machines can only multiply by constants. The size of an input is its dimension, and the cost of any instruction is one. For each of these structures we consider DNP and NP, the corresponding complexity classes with respect to digital nondeterminism and standard real nondeterminism, respectively. We give DNP- and NP-complete problems for linear and real scalar machines. On the other hand, we show that the NP-class restricted to scalar machines over the integers with equality-tests does not own a complete problem.     

Instability of spikes in the presence of conservation laws

We show that spikes are unstable in a class of scalar reaction–diffusion equations coupled to a general conservation law. Our class includes the Keller–Segel model for chemotaxis, phase-field models and models for chemical reactions in closed chemical reactors.     

Two-Point Correlators of Composite Higgs Fields and Chiral Symmetry Restoration

We consider the effective quasilocal quark model with two composite Higgs doublets in strong coupling (polycritical) regime below the chiral symmetry breaking energy scale _CSB. The two-point correlators of scalar and pseudoscalar Higgs fields are calculated. The adjustment of their asymptotics at high energies allows one to implement the chiral symmetry restoration in correspondence to the operator product expansion in QCD-like (technicolor, topcolor) models. The requirement of chiral symmetry restoration (CSR) at high energies above the _CSB yields some bounds on parameters of (composite) Higgs particles and underlying effective quasilocal quark models. Bibliography: 26 titles.     

Integrable Models of (1+1)-Dimensional Dilaton Gravity Coupled to Scalar Matter

We describe a class of explicitly integrable models of (1+1)-dimensional dilaton gravity coupled to scalar fields in sufficient detail. The equations of motion of these models reduce to systems of Liouville equations with energy and momentum constraints. We construct the general solution of the equations and constraints in terms of chiral moduli fields explicitly and briefly discuss some extensions of the basic integrable model. These models can be related to higher-dimensional supergravity theories, but we mostly consider them independently of such interpretations. We also briefly review other integrable models of two-dimensional dilaton gravity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 115–131, January, 2006.     

The <Emphasis Type="Italic">k</Emphasis>-Essence in the Relativistic Theory of Gravitation and General Relativity

We consider a model of a scalar field with a nontrivial kinetic part (k-essence) on the background of a flat homogeneous isotropic universe in the framework of the relativistic theory of gravitation and general relativity. Such a scalar field simulates the substance of an ideal fluid and serves as a model of dark energy because it leads to cosmological acceleration at later times. For finding a suitable cosmological scenario, it is more convenient to determine the dependence of the energy density of such a field on the scale factor and only then find the corresponding Lagrangian. Based on the solution of such an inverse problem, we show that in the relativistic theory of gravitation, either any scalar field of this type leads to instabilities, or the compression stage ends at an unacceptably early stage. We note that a consistent model of dark energy in the relativistic theory of gravitation can be a scalar field with a negative potential (ekpyrosis) of Steinhardt–Turok. In general relativity, the k-essence model is viable and can represent both dark energy and dark matter. We consider several specific k-essence models.     

Solution of an integro-differential equation describing the electromagnetic field distribution in a magnetic compressor

We construct a mathematical model of electromagnetic processes in a magnetic accelerator. In the two-dimensional approximation, the Maxwell equations are reduced to a system of scalar integro-differential equations in the conductors and to the Laplace equation in the dielectric subdomains. We obtain a numerical model on the basis of the Galerkin–Petrovmethod with piecewise constant and piecewise linear basis functions. The results of computations are represented.     

The scalar Zeldovich–von Neumann–Döring combustion model (I) interactions of shock and detonation

In this paper, the interactions of shock and detonation for the scalar Zeldovich–von Neumann–Do¨ring combustion model are considered. The solutions of the problem are constructed by analyzing characteristics in the reaction zone. The shock speeds up the reaction front in some cases. By studying the limits of the solutions as the reaction rate goes to infinity, we obtain that the limits are the solutions of the corresponding initial value problem for the scalar Chapman–Jouguet combustion model.     

Chiral bosonization ofU A (1)-currents and the energy-momentum tensor in quantum chromodynamics

A generalization of the chiral lagrangian is obtained by extended low-temperature bosonization of vector, axial vector, scalar, and pseudoscalar U(3) quark currents. Estimates for its structural constants are given in accordance with the developed AANN model of QCD-bosonization. Following the ideology of chiral perturbation theory, we transform the bosonized chiral Lagrangian into the phenomenological form. Relations of Zweig-rule type are established. This enables us to express the new structural constants in terms of the given constants. The correspondence between the predictions obtained by the low-temperature bosonozation method and available phenomenological estimates are discussed. Bibliography: 9 titles. In memory of V. N. Popov Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 224, 1995, pp. 55–67. Translated by V. A. Andrianov.     

Solvability of the fractional hyperbolic Keller–Segel system

We study a new nonlocal approach to the mathematical modelling of the chemotaxis problem, which describes the random motion of a certain population due to a substance concentration. Considering the initial–boundary value problem for the fractional hyperbolic Keller–Segel model, we prove the solvability of the problem. The solvability result relies mostly on fractional calculus and kinetic formulation of scalar conservation laws.     

The scalar Zeldovich–von Neumann–Döring combustion model (II) interactions of shock and deflagration

In this paper, the interactions of shock and deflagration for the scalar Zeldovich–von Neumann–Döring combustion model are considered. The solutions of the problem are constructed by analysing characteristics in the reaction zone. Some burning gas in the zone will be extinguished at a finite time in some cases. By studying the limits of the solutions as the reaction rate goes to infinity, we obtain that the limits are the solutions of the corresponding initial value problem for the scalar Chapman–Jouguet combustion model.     

On scalar curvature rigidity of vacuum static spaces

In this paper we extend the local scalar curvature rigidity result in Brendle and Marques (J Differ Geom 88:379–394, 2011) to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in general in the light of the paper (Corvino, Commun Math Phys 214:137–189, 2000). We obtain the local scalar curvature rigidity of bounded domains in hyperbolic spaces. We also obtain the global scalar curvature rigidity for conformal deformations of metrics in the domains, where the lapse functions are positive, on vacuum static spaces with positive scalar curvature, and show such domains are maximal, which generalizes the work in Hang and Wang (Commun Anal Geom 14:91–106, 2006).     

Un modèle scalaire analogue aux équations de Navier–Stokes

We discuss on a new scalar model whose properties are similar to the NS equations (it preserves scaling, the antisymmetry of the bilinear term and is invariant by translations and dilations) but contains a singular integral operator. We construct a global-in-time weak solution when initial data is in a critical Morrey–Campanato space and show that it also satisfies a local energy inequality comparable to Scheffer?s one.     

Traveling wave solutions of the n-dimensional coupled Yukawa equations

We discuss traveling wave solutions to the Yukawa equations, a system of nonlinear partial differential equations which has applications to meson–nucleon interactions. The Yukawa equations are converted to a six-dimensional dynamical system, which is then studied for various values of the wave speed and mass parameter. The stability of the solutions is discussed, and the methods of competitive modes is used to describe parameter regimes for which chaotic behaviors may appear. Numerical solutions are employed to better demonstrate the dependence of traveling wave solutions on the physical parameters in the Yukawa model. We find a variety of interesting behaviors in the system, a few of which we demonstrate graphically, which depend upon the relative strength of the mass parameter to the wave speed as well as the initial data.     

Entropy Boundary Conditions in the Theory of Sedimentation of Ideal Suspensions

We study a non-linear generalized initial–boundary value problem of a scalar conservation law which models the sedimentation of an ideal suspension.     

Partial data inverse problems for Maxwell equations via Carleman estimates

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim–Uhlmann and Kenig–Sjöstrand–Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.     

A Galerkin approximation for integro-differential equations in electromagnetic scattering from a chiral medium

We consider the scattering of time-harmonic electromagnetic waves from a chiral medium. It is known for the Drude–Born–Fedorov model that the forward scattering problem can be described by an integro-differential equation. In this paper we study a Galerkin finite element approximation for this integro-differential equation. Our Galerkin scheme, which relies on a suitable periodization of the integral equation, enables the use of the fast Fourier transform and a simple numerical implementation. We establish a quasi-optimal convergence analysis for the Galerkin method. Explicit formulas for the discrete scheme are also provided.     

Quantum mechanics of stationary states of particles in a space–time of classical black holes

Theoretical and Mathematical Physics - We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner–Nordström, Kerr, and Kerr–Newman gravitational...