Cylindrical Space–Time Model and Mirror Symmetry Violations

The symmetrical character of empty space–time is proposed as a putative reason for mirror symmetry violations in the bioorganic world and in the world of elementary particles, and a new geometrical model for the empty space–time is put forward. In contrast to flat four-dimensional Minkowski space, this model is described by a cylindrical four-dimensional space metrics. The geodesic lines of this space are helical. The helical structure of the model proposed shows that distortion of mirror symmetry may be a consequence of geometrical structure of the empty space rather than a characteristic of any specific interaction.     

Quantum Vacuum and the Structure of Empty Space–Time

We have considered the possibility of formation of a massless particles with spin 1 in the region of negative energies, within the framework of the Weyl-type equation for neutrinos. It is proved that the represented approach allows to get a stable structural formation in the ground state, which can be interpreted as a fundamental massless particle. The structure and properties of this vector boson are studied in detail. The problem of entangling two vector bosons with projections of spins +1 and −1 and, accordingly, the formation of a zero-spin boson is studied within the framework of a complex stochastic matrix equations of the Langevin type. The paper discusses the structure of the Bose particle of a scalar field and the space–time properties of an empty space (quantum vacuum).

     

Virtual Black Holes and Space–Time Structure

In the standard formalism of quantum gravity, black holes appear to form statistical distributions of quantum states. Now, however, we can present a theory that yields pure quantum states. It shows how particles entering a black hole can generate firewalls, which however can be removed, replacing them by the ‘footprints’ they produce in the out-going particles. This procedure can preserve the quantum information stored inside and around the black hole. We then focus on a subtle but unavoidable modification of the topology of the Schwarzschild metric: antipodal identification of points on the horizon. If it is true that vacuum fluctuations include virtual black holes, then the structure of space-time is radically different from what is usually thought.     

Spinning Particles in NUT–Reissner–Nordstrom Space–Time

We study the geodesic motion of pseudo-classical spinning particles in the NUT–Reissner–Nordstrom space–time. We investigate the generalized Killing equations for spinning space and derive the constants of the motion in terms of the solutions of these equations. We give an analysis of the motion on a cone and on a plane.     

Synthesis and Structure of Magnetic Core-shell Ni–Ce Nanocomposite Particles

A new type of magnetic core-shell Ni–Ce nanocomposite particles (15–50 nm) is presented. SEM observations suggest the particles are strongly ferromagnetic, interacting with ordered chain-like features. Typical HR-TEM images demonstrate that many planar defects (nanotwins and stacking faults) exist in the surface shell and large Ni core zone (10–40 nm) of the particles; the inner shell layers (4–6 nm) consist of NiCe alloy and the outermost shell is NiO. Nano-diffraction patterns show an indication of well-defined spots characteristic of nanocomposite materials, of which certain crystal facet orientation relationships between orthorhombic [111] of NiCe and cubic [311] of Ni₂Ce, face-center crystal [222] of NiO, cubic [111] of nickel have been identified. This confirms the nature of this core-shell nanocomposite particle.     

A Note on the Problem of Proper Time in Weyl Space–Time

We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space–time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space–time is investigated. Our starting point is the well known axiomatic approach to space–time given by Elhers, Pirani and Schild (EPS). In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called “second clock effect”. We take the view that if, based on experience, we were to reject space–time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable space–time as the most general structure that would be suitable to model space–time.     

Klein–Gordon and Dirac Equations in de Sitter Space–Time

We present and discuss the Klein–Gordonand Dirac wave equations in the de Sitter universe. Toobtain the Dirac wave equation we use the factorizationof the second-order invariant Casimir operatorassociated to the Fantappie–de Sitter group. Boththe Klein–Gordon and Dirac wave equations arediscussed in terms of the spherical harmonics with spinweight. A particular case of Dirac wave equation issolved in terms of a new class of polynomials.     

Symmetry Classification of the One–Dimensional Second Order Equation of a Hydrodynamic Type

Abstract

The paper contains a symmetry classification of the one–dimensional second order equation of a hydrodynamical type L(Lu)+λLu=F (u), where L ≡ ? _t+u? _x. Some classes of exact solutions of this equation are given.     

Black Hole and Cosmic Entropy for Schwarzschild–de Sitter Space–Time

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method in the background of the Schwarzschild–de Sitter space–time. We obtain the entropy of a black hole and the cosmic entropy at nonasymptotic flat space. When the cut-off satisfies the proper condition, the entropy of a black hole is proportional to the area of a black hole horizon, and the cosmic entropy is proportional to the cosmic horizon area.     

The Phase Structure of a Generalized Gross–Neveu Model in (2+1)-Dimensional Space–Time

The phase structure of a (2+1)-dimensional Gross–Neveu model with four different channels of fermion–antifermion interaction, and, correspondingly, four different coupling constants, is studied. It is shown that the model describes five different phases of the interaction of planar fermions in which either spatial parity or chiral symmetry can be broken. The existence of a phase that is characterized by simultaneous spontaneous breaking of both these symmetries that was not observed earlier in such models is demonstrated.     

Nonlocal Symmetry,CTE Solvability and Interaction Solutions of Whitham–Broer–Kaup Equations

Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.     

Comment on Fractional Fokker–Planck Equation with Space and Time Dependent Drift and Diffusion

The purpose of this paper is to correct errors presented recently in the paper [Lv et al. J Stat Phys 149:619–628 (2012)], where the authors analyzed Fractional Fokker–Planck equation (FFPE) with space–time dependent drift $F(x,t)=F(x)f(t)$ and diffusion $D(x,t)=D(x)\tilde{d}(t)$ coefficients in the factorized form. We show an important drawback in the derivation of the stochastic representation of FFPE presented in the aforementioned paper, which makes the whole proof wrong. Moreover, we present a correct proof of their result in even more general case, when both drift and diffusion can have any, not necessarily factorized, form.     

Structure,thermal behavior,and chemical durability of lead–calcium–phosphate glasses

ABSTRACT

Structure and physical properties of 25CaO–xPbO–(75–x)P₂O₅ (0≤x≤35) glasses are investigated in this paper. Substitution of PbO for P₂O₅ in the binary 25CaO–75P₂O₅ glass was found to increase the density and to decrease the molar volume. Fourier transform infrared (FTIR) and Raman spectroscopies show the evolution of the phosphate skeleton when the PbO content increases: Q³ to Q² species (0<x≤25) and Q² phosphate network (x = 25) to short phosphate groups (x > 25) such as (P₄O₁₃^6?) (x = 35). The glass transition temperature first decreases with x, then increases for x values larger than 10%. The evolution of the glass transition temperatures is interpreted from the structural data: the minimum point observed in T_g is attributed to the transition of the ultraphosphate network from the network containing the modifying cations at isolated sites to a network with modifier sub-structure sharing terminal oxygens. At higher PbO content, the large increase in T_g is due to the reticulation of the phosphate network by PbO₄ groups.     

Structure,stability and energetics of ionic arsenic–water complexes

The structure, stability and energetics of ionic arsenic–water complexes [As³⁺–nH₂O (n?=?1–5) and As⁵⁺–nH₂O (n?=?3–5)] have been studied in detail using the MP2 method. Both the trivalent and pentavalent ionic states of arsenic were considered. The change in binding energy of the complexes with increasing number of water molecules was investigated. For both complexes involving trivalent and pentavalent arsenic, highly intense modes are observed in the high-frequency region. The structure and symmetry of the complexes with increasing number of water molecules is discussed. The charge transfer in these complexes is illustrated with the help of the natural electron configuration. Both donation and back-donation processes involving the orbitals of oxygen and arsenic are analysed to explain the charge transfer.     

Mesoscopic Persistent Currents,Aharonov—Bohm Magnetic Flux and Time Reversal Symmetry

We discuss the effect of Aharonov-Bohm magnetic flux on the time reversal symmetric properties of mesoscopic metallic ring systems.It is usually believed that AB flux causes time reversal symmetry breaking.We analyse the case of mesoscopic persistent currents and find out that AB flux does not break time reversal symmetry.our arguments are supported by the general theory of mesoscopic persistent currents.     

Symmetry Reduction and Exact Solutions of the Euler–Lagrange–Born–Infeld,Multidimensional Monge–Ampere and Eikonal Equations

Abstract

Using the subgroup structure of the generalized Poincaré group P (1, 4), ansatzes which reduce the Euler–Lagrange–Born–Infeld, multidimensional Monge–Ampere and eikonal equations to differential equations with fewer independent variables have been constructed. Among these ansatzes there are ones which reduce the considered equations to linear ordinary differential equations. The corresponding symmetry reduction has been done. Using the solutions of the reduced equations, some classes of exact solutions of the investigated equation have been presented.     

Space–time inhomogeneity, anisotropy and gravitational collapse

We investigate the evolution of non-adiabatic collapse of a shear-free spherically symmetric stellar configuration with anisotropic stresses accompanied with radial heat flux. The collapse begins from a curvature singularity with infinite mass and size on an inhomogeneous space–time background. The collapse is found to proceed without formation of an even horizon to singularity when the collapsing configuration radiates all its mass energy. The impact of inhomogeneity on various parameters of the collapsing stellar configuration is examined in some specific space–time backgrounds.     

Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's

We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.