Energy-Momentum and Equivalence Principle in Non-Riemannian Geometries

We introduce an energy-momentum density vector which is independent of the affine structure of the manifold and whose conservation is linked to observers. Integrating this quantity over time-like surfaces we can define Hamiltonian and momentum for the system which coincide with the corresponding ADM definitions for the case of irrotational Riemannian manifolds. As a consequence of our formalism, a Weak Equivalence Principle version for manifolds with torsion appears as the natural extension to non-Riemannian geometries from the Equivalence Principle of General Relativity.     

Conservation Laws and Symmetry Properties of a Class of Higher Order Theories of Gravity

We consider a class of fourth order theories of gravity with arbitrary matter fields arising from a diffeomorphism invariant Lagrangian density , with and the phenomenological representation of the nongravitational fields. We derive first the generalization of the Einstein pseudotensor and the von Freud superpotential. We then show, using the arbitrariness that is always present in the choice of pseudotensor and superpotential, that we can choose these superpotentials to have the same form as those for the Hilbert Lagrangian of general relativity (GR). In particular we may introduce the Moller superpotential of GR as associated with a double-index differential conservation law. Similarly, using the Moller superpotential we prove that we can choose the Komar vector of GR to construct a conserved quantity for isolated asymptotically flat systems. For the example R + R²theory we prove then, that the active mass is equal to the total energy (or inertial mass) of the system.     

A Self-Similar Dynamics in Viscous Spheres

We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically symmetric space-time. We match a very simple solution to the symmetry equations with the exterior one (Vaidya). We then obtain a system of two ordinary differential equations which rule the dynamics, and find a self-similar collapse which is shear-free and with a barotropic equation of state. Considering a huge set of initial self-similar dynamics states, we work out a model with an acceptable physical behavior.     

Inheriting Conformal and Special Conformal Killing Vectors in String Cosmology

In this paper we study the consequences of the existence of conformal and special conformal Killing vectors (CKV, SCKV) for string cloud and string fluid in the context of general relativity. The inheritance symmetries of the string cloud and string fluid are discussed. Einstein's field equations have been solved for static spherically symmetric space-time with cloud and fluid of strings source via CKV.     

The Relation of Generalized Scalar-Tensor Theory with the 5D Space-Time-Matter Theory

The relationship between cosmological solutionsof five-dimensional Space-Time-Matter (STM) theory anda Generalized Scalar-Tensor (GST) theory is investigatedin which the cosmological term Lambda depends not only on a scalar field but also onits time derivative .Identification of these solutions allows us to solve forthe functional form of the cosmological term, and mayhave relevance for the early Universe.     

Third Rank Killing Tensors in General Relativity. The (1 + 1)-dimensional Case

Third rank Killing tensors in (1 +1)-dimensional geometries are investigated andclassified. It is found that a necessary and sufficientcondition for such a geometry to admit a third rankKilling tensor can always be formulated as a quadratic PDE, oforder three or lower, in a Kahler type potential for themetric. This is in contrast to the case of first andsecond rank Killing tensors for which the integrability condition is a linear PDE. The motivation for studying higher rank Killing tensors in (1 +1)-geometries, is the fact that exact solutions of theEinstein equations are often associated with a first orsecond rank Killing tensor symmetry in the geodesicflow formulation of the dynamics. This is in particulartrue for the many models of interest for which thisformulation is (1 + 1)-dimensional, where just one additional constant of motion suffices forcomplete integrability. We show that new exact solutionscan be found by classifying geometries admitting higherrank Killing tensors.     

Solution Generating with Perfect Fluids

We apply a technique, due to Stephani, for generating solutions of the Einstein-perfect-fluid equations. This technique is similar to the vacuum solution generating techniques of Ehlers, Harrison, Geroch and others. We start with a seed solution of the Einstein-perfect-fluid equations with a Killing vector. The seed solution must either have (i) a spacelike Killing vector and equation of state P = or (ii) a timelike Killing vector and equation of state + 3P = 0. The new solution generated by this technique then has the same Killing vector and the same equation of state. We choose several simple seed solutions with these equations of state and where the Killing vector has no twist. The new solutions are twisting versions of the seed solutions.     

In situ polymer nanocomposites: Effect of nanoparticles on the interfacial region

Composites based on the blends of polyurethane and poly(methyl methacrylate) of various composition were synthesized in situ in the presence of various amounts of nanoparticles (fumed silica). From thermophysical measurements it was found that, during reaction, phase separation and evolution of two phases occur. The temperature transitions in the systems and their positions depend on the blend composition and on various amounts of nanoparticles. Using scanning differential calorimetry from the changing of heat capacity increments the fraction of an intermediate region between two main phases has been estimated. For the first time it was observed that in nanocomposites in the temperature region between two main relaxation transitions, there appears a third transition, which was related to the adsorption layers formed by both components at the interface of the nanoparticles. The appearance of such intermediate regions increases essentially the fraction of an interfacial region in the system.     

Killing Magnetic Curves in Sol Space

We determine magnetic curves corresponding to the Killing magnetic fields in the 3-dimensional homogenous Riemannian space Sol₃.     

Application of Halpin–Tsai equation to microfibril reinforced polypropylene/poly(ethylene terephthalate) composites

While the main goal of the first part of this study was to check the applicability of the Tsai–Hill equation to a polymer-polymer microfibril reinforced composite (MFC), in which the reinforcing elements represented microfibrils with a diameter around 1–3 μm and aspect ratio of about 100, in the present paper a similar goal involves the Halpin–Tsai equation. In addition, using compatibilised blends an attempt is made to shed light on the mechanism of the microfibril formation during drawing of isotropic polymer blends. For this purpose, injection moulded dog-bone test samples of blends of polypropylene/poly(ethylene terephthalate) (PP/PET) (60/40 wt%) have been prepared starting from highly drawn bristles, also from blends containing 0–9 wt% compatibiliser (ethylene-glycidyl methacrylate). The MFC structure of the test sample is established by X-ray and scanning electron microscope (SEM) analyses. The tensile data are compared with those predicted according to the Halpin–Tsai equation. It is shown that the predicted values are slightly higher than the measured ones and this finding is explained by the presence of a compatibiliser resulting in much lower aspect ratios of the microfibrils. The suggested mechanism of the microfibril formation is based on the coalescence of the individual elongated spheres during drawing. The SEM observations also show that the compatibilised blends contain much shorter microfibrils because the compatibiliser prevents the coalescence process.     

Research of Gravitation in Flat Minkowski Space

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor φ, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the n-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order c ⁻².     

反导火力单元空间杀伤区内拦截概率研究

拦截概率是评价反导作战效能的重要指标,对交战前任务规划至关重要。选取某一拦截弹建立其在空间的可达集区域,针对中段反导逆轨拦截情况,确立其在空间中的杀伤区。针对杀伤区内任一点可能为拦截点的情况,对某一来袭导弹的弹道轨迹,选取可拦截弧段上的理论拦截点,通过在选取不同高度上的理论拦截点上,调整拦截弹的发射位置,从而得到拦截点在杀伤区内不同高度,不同距离以及在不同的交汇角时对拦截概率的影响。为反导作战的阵地部署研究和交战策略提供了一定的参考。     

String Thermalization in Static Spacetimes

We study the evolution, the transverse spreadingand the subsequent thermalization of string states inthe Weyl static axisymmetric spacetime. This possessesa singular event horizon on the symmetry axis and a naked singularity along the otherdirections. The branching diffusion process of stringbits approaching the singular black-hole horizonprovides the notion of the temperature that iscalculated for this process. We find that the solution of theFokker-Planck equation in the phase space of thetransverse variables of the string, can be factored asa product of two thermal distributions, provided that the classical conjugate variables satisfy theuncertainty principle. We comment on the possiblephysical significance of this result.     

Some Remarks on Symmetries and Transformation Groups in General Relativity

The motivation for this paper is the recent interest in the study of symme tries in general relativity and its purpose is to discuss the mathematical foundations required for such a study. The general (formal and informal) ideas of what constitutes a symmetry of space-time are discussed and developed and the idea of a Lie algebra of symmetry vector fields is studied in detail. The relationship between such Lie algebras and the ideas of Lie transformation group theory (Palais' theorems) is stated and a general theorem regarding the orbits of such symmetries is given. Finally some specific symmetries in general relativity are explored and some of their similarities and differences noted.     

Noncommutative Integration of the Dirac Equation in a Flat Space and in the de Sitter Space

Noncommutative integration of the Dirac massive and massless equations is performed in a four-dimensional flat space and in the de Sitter space of arbitrary signature. A new class of rigorous solutions of the Dirac equation is constructed in these spaces. The properties of the solutions obtained are examined.     

Creation of Unstable Particles and Decoherence in Semiclassical Cosmology

We consider a simple cosmological model in orderto show the importance of unstable particle creation forthe validity of the semiclassical approximation. Usingthe mathematical structure of rigged Hilbert spaces we show that particle creation is theseed of decoherence which enables the quantum toclassical transition.     

On the Algebra of Symmetry of the Dirac Equation in Flat Space and De Sitter Space

The structure of the quadratic algebras of spinor symmetry operators for the Dirac equation is studied in a four-dimensional flat space and in the de Sitter space of arbitrary signature. The algebras are shown to be standard equivalent. Linear noncommutative subalgebras meeting the conditions of the noncommutative integrability theorem are found in these algebras.     

Thermodynamic Equilibrium in the Expanding Universe

We show that a relativistic gas may be at"global" equilibrium in the expanding universe for anyequation of state 0 < p /3, provided thatthe gas particles move under the influence of aself-interacting, efiective one-particle force in between elasticbinary collisions. In the force-free limit we recoverthe equilibrium conditions for ultrarelativistic matterwhich imply the existence of a conformal timelike Killing vector.