Lorentzian framed structures in general relativity

We study a class of four-dimensional real Lorentzian manifolds generated by a global operator (satisfying a cubic equation). We characterize empty, Einstein, conformally flat spaces and construct mathematical models of two physical space-times. Locally, the solutions presented have been identified with known solutions. Kruskal space-time is generated by using the warped product technique [11].     

Influence of thermophoresis on heat and mass transfer under non-Darcy MHD mixed convection along a vertical flat plate embedded in a porous medium in the presence of radiation

The paper presents an investigation of the influence of thermophoresis on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid along a vertical flat plate with radiation effects. The plate is permeable and embedded in a porous medium. To describe the deviation from the Darcy model the Forchheimer flow model is used. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The nonlinear ordinary differential equations are linearized by using quasilinearization technique and then solved numerically by using implicit finite difference scheme. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, mixed convection parameter Ra _d /Pe _d , Reynolds number Red, radiation parameter R, thermophoretic parameter τ, Prandtl number Pr, and Schmidt number Sc. The heat transfer coefficient is also tabulated for different values of physical parameters.     

Magnetic Branes in Brans-Dicke-Maxwell Theory

We present a new class of magnetic brane solutions in (n+1)-dimensional Brans-Dicke-Maxwell theory in the presence of a quadratic potential for the scalar field. These solutions are neither asymptotically flat nor (anti)-de Sitter. Our strategy for constructing these solutions is applying a conformal transformation to the corresponding solutions in dilaton gravity. This class of solutions represents a spacetime with a longitudinal magnetic field generated by a static brane. They have no curvature singularity and no horizons but have a conic geometry with a deficit angle δ. We generalize this class of solutions to the case of spinning magnetic brane with all rotation parameters. We also use the counterterm method and calculate the conserved quantities of the solutions.     

Spherically symmetric space-times transparent to scalar multipole waves

Using nonscattering potentials of Chang and Janis, a large class of spherically symmetric space-times is constructed on which all multipole solutions to the minimally coupled scalar wave equation are expressible in terms of characteristic data functions in essentially as simple a fashion as for flat space-time. The space-times are transparent to multipole waves in the same sense that flat space-time is. Both conformally flat and not conformally flat space-times are obtained. Some examples are discussed which show that the variety of transparent space-times is large even within the class of Robertson-Walker spaces.     

Optical diffraction by two-dimensional photonic structures with hexagonal symmetry

Photonic structures with hexagonal symmetry have been prepared by the additive technology of two-photon laser lithography, and their optical properties have been investigated. The structure of the samples has been examined using scanning electron microscopy. The calculations have been performed for the optical diffraction in the Born approximation of the scattering theory for structures with a limited number of scatterers. The images formed in the monochromatic light on a flat screen located behind the sample have been calculated. The diffraction patterns on the screen have C_6v symmetry and consist of three straight lines intersecting at an angle of 120° and hyperbolas, the number of which is a multiple of six. An important feature of these diffraction patterns is the superstructure, i.e., the partition of straight lines and hyperbolas into individual diffraction reflections, the number of which is determined by the number of scatterers of a particular sample. The results of the experimental investigation of the diffraction patterns completely coincide with the calculated data, including the number and arrangement of the superstructure reflections.     

A new model for spherically symmetric charged compact stars of embedding class 1

In the present study we search for a new stellar model with spherically symmetric matter and a charged distribution in a general relativistic framework. The model represents a compact star of embedding class 1. The solutions obtained here are general in nature, having the following two features: first of all, the metric becomes flat and also the expressions for the pressure, energy density, and electric charge become zero in all the cases if we consider the constant \(A=0\), which shows that our solutions represent the so-called ‘electromagnetic mass model’ [17], and, secondly, the metric function \(\nu (r)\), for the limit n tending to infinity, converts to \(\nu (r)=C{r}^{2}+ ln~B\), which is the same as considered by Maurya et al. [11]. We have investigated several physical aspects of the model and find that all the features are acceptable within the requirements of contemporary theoretical studies and observational evidence.     

Detailed numerical simulation of laminar flames by a parallel multiblock algorithm using loosely coupled computers

A parallel algorithm for the detailed multidimensional numerical simulation of laminar flames able to work efficiently with loosely coupled computers is described. The governing equations have been discretized using the finite volume technique over staggered grids. A SIMPLE-like method has been employed to solve the velocity–pressure fields while the species equations have been calculated in a segregated manner using an operator-splitting technique. The domain decomposition method is used to optimize the domain's discretization and to parallelize the code. The main attributes and limitations, together with the computational features (computational effort, parallel performance, memory requirements, etc), are shown, taking into account different degrees of chemical modelling and two benchmark problems: a premixed methane/air laminar flat flame and a confined co-flow non-premixed methane/air laminar flame. In order to assess the validity of the numerical solutions, a post-processing procedure, based on the generalized Richardson extrapolation for h-refinement studies and on the grid convergence index, has been used.     

FRW in Cosmological Self-creation Theory

We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $[\frac{1}{\phi}T^{\mu \nu M}+T^{\mu \nu}(\phi)]_{;\nu}=0$ . We take as a first model the flat FRW metric and with the law of variation for Hubble’s parameter proposal by Berman and Gomide (Nuovo Cimento B 74: 182, 1983), we find solutions to the Einstein field equations by the cases: inflation (γ=?1), radiation ( $\gamma=\frac{1}{3}$ ), stiff matter (γ=1). For the Inflation case the scalar field grows fast and depends strongly of the constant M _γ=?1 that appears in the solution, for the Radiation case, the scalar stop its expansion and then decrease perhaps due to the presence of the first particles. In the Stiff Matter case, the scalar field is decreasing so for a large time, ?→0. In the same line of classical solutions, we find an exact solution to the Einstein field equations for the stiff matter (γ=1) and flat universe, using the Hamilton-Jacobi scheme.     

Light Trapping and Down‐Shifting Effect of Periodically Nanopatterned Si‐Quantum‐Dot‐Based Structures for Enhanced Photovoltaic Properties

Periodically nanopatterned Si structures have been prepared by using a nanosphere lithography technique. The formed nanopatterned structures exhibit good anti‐reflection and enhanced optical absorption characteristics. The mean surface reflectance weighted by AM1.5 solar spectrum (300–1200 nm) is as low as 5%. By depositing Si quantum dot/SiO₂ multilayers (MLs) on the nanopatterned Si substrate, the optical absorption is higher than 90%, which is significantly improved compared with the same multilayers deposited on flat Si substrate. Furthermore, the prototype n‐Si/Si quantum dot/SiO₂ MLs/p‐Si heterojunction solar cells has been fabricated, and it is found that the external quantum efficiency is obviously enhanced for nanopatterned cell in a wide spectral range compared with the flat cell. The corresponding short‐circuit current density is increased from 25.5 mA cm^?2 for flat cell to 29.0 mA cm^?2 for nano‐patterned one. The improvement of cell performance can be attributed both to the reduced light loss and the down‐shifting effect of Si quantum dots/SiO₂ MLs by forming periodically nanopatterned structures.     

Non-Vacuum Plane Symmetric Solutions and their Energy Contents in f (R) Gravity

The exact vacuum solutions of static plane symmetric spacetimes in four, five, six and n-dimensions in metric approach of f (R) theory of gravity have already been found and are available in literature. In this paper, we extend the work done by Sharif and Farasat for the case of vacuum static plane symmetric solutions in f (R) theory of gravity to non-vacuum case. Two non-vacuum solutions have been determined by using constant Ricci scalar assumption. Moreover, for some specific choices of f (R) models, the energy distribution of these solutions has been explored by applying the generalized Landau-Lifshitz energy-momentum complex in the context of f (R) theory of gravity. In addition, we discuss the stability conditions for these solutions.     

Rotating,Stationary, Axially Symmetric Spacetimes with Collisionless Matter

The existence of stationary solutions to the Einstein–Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat non-vacuum spacetimes. If angular momentum is allowed to be non-zero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on ${\mathbb{R}^5}$ .     

Exact Solutions for Shear-free Motion of Spherically Symmetric Charged Perfect Fluid Distributions in General Relativity

An in-depth study of various methods, and their correlations, of obtaining exact solutions of Einstein-Maxwell field equations representing shear free motion of spherically symmetric charged perfect fluid distributions has been made. It is shown that one can employ isotropic coordinate systems without any loss of generality. However the investigations have been carried out in an arbitrary coordinate system. The exact solutions relating to simple situations viz. (i) homogeneous density distribution, ϱ=ϱ(t), (ii) conformally flat solutions and (iii) distributions obeying an equation of state, p=p(ϱ) are briefly discussed. The methods due to MCVITTIE (1967), introduced initially for neutral fluids, and MASHHON and PARTOVI (1979) where one assumes the metric in a convenient form form one group and the methods due to SHAH and VAIDYA (1968), CHAKRAVARTY and CHATTERJEE (1978), CHATTERJEE (1984) and SUSSMAN (1987) where one chooses suitably two arbitrary functions of integration form the other group. This splitting of various methods into two is based on the earlier analogous work for the neutral fluids due to SRIVASTAVA (1987). Using McVittie's procedure we obtain a solution which in its uncharged limit reduces to Friedmann-Robertson-Walker solution whereas for non-vanishing charge is equivalent to the solution due to SHAH and VAIDYA (1967). This solution is termed as generalised Shah-Vaidya solution or charged Friedmann-Robertson-Walker solution. A suitable generalisation of Mashhoon and Partovi's procedure has been found to contain MASHHOON-PARTOVI solution (1979) and SHAH-VAIDYA solution (1967) as members of a class. The method employed by CHATTERJEE (1978), which does not yield the general solution of the problem, has been shown to lead to the procedure adopted by SUSSMAN (1987) after it is generalised suitably. The McVittie type and Wyman type solutions introduced by Sussman has been found to be contained in McV class of metries discussed here. It is also found that solutions obtained by CHAKRAVARTY and CHATTERJEE (1978) represent a class of charged Kustaanheimo-Qvist solution which are expressible as elementary functions. Finally, all known solutions have been derived introducing an adhoc assumption in the form of a mathematical relation and searching for the solutions free from movable critical points.     

有厚度平板尾缘可压缩剪切层中的涡结构数值模拟

采用一个新型Fu Ma高精度UCD5 SCD6紧致差分算法,通过直接求解二维Navier Stokes方程,成功实现了有厚度平板尾缘可压缩剪切层中涡结构的数值模拟,并考查了平板厚度对其的影响.计算对流马赫数M_c=0.3,平板厚度分别为1,2,3,4个参考长度.结果表明,增加平板厚度可促使平板尾缘可压缩剪切层中的涡提前卷起,有利于两股气流混合.     

Measurement of optical nonlinearity by antiresonant ring interferometric nonlinear spectroscopic (ARINS) technique

We have reported the measurement of third-order optical nonlinearity by antiresonant ring interferometric nonlinear spectroscopic (ARINS) technique and discussed its usefulness over other popular measuring techniques such as Z-scan, degenerate four wave mixing (DFWM) and third harmonic generation (THG). The measurement has been simulated theoretically by taking different numerical values as well as sign of δ, which is a key parameter of ARINS. The technique has been benchmarked using toluene and the theoretical simulation has been substantiated experimentally by measuring the nonlinear optical coefficients (n₂ and β) of two different samples. The disadvantages of the technique have also been discussed. However, a number of advantages of ARINS override its disadvantages and therefore, ARINS may be preferred over other measuring techniques for the measurement of nonlinear optical parameters.     

Particle creation in asymptotically Minkowskian spacetimes

Exact solutions of Klein–Gordon and Dirac equations are obtained for two classes of Robertson–Walker (RW) spacetimes with asymptotically Minkowskian regions. One class is Minkowskian in the remote past and future. In this class in$in$ and out$out$ vacua are well defined, because the scale factor reduces to a constant at the asymptotic regions. Another class is asymptotically flat only in the far past. Using the obtained exact solutions we calculate the density of scalar and Dirac particles created through the Bogolubov transformations technique. For Dirac field it is shown that the rates of creation of particles and antiparticles are equal.     

All static and electrically charged solutions with Einstein base manifold in the arbitrary-dimensional Einstein–Maxwell system with a massless scalar field

We present a simple and complete classification of static solutions in the Einstein–Maxwell system with a massless scalar field in arbitrary \(n(\ge 3)\) dimensions. We consider spacetimes which correspond to a warped product \(M^2 \times K^{n-2}\), where \(K^{n-2}\) is a \((n-2)\)-dimensional Einstein space. The scalar field is assumed to depend only on the radial coordinate and the electromagnetic field is purely electric. Suitable Ansätze enable us to integrate the field equations in a general form and express the solutions in terms of elementary functions. The classification with a non-constant real scalar field consists of nine solutions for \(n\ge 4\) and three solutions for \(n=3\). A complete geometric analysis of the solutions is presented and the global mass and electric charge are determined for asymptotically flat configurations. There are two remarkable features for the solutions with \(n\ge 4\): (i) Unlike the case with a vanishing electromagnetic field or constant scalar field, asymptotically flat solution is not unique, and (ii) The solutions can asymptotically approach the Bertotti–Robinson spacetime depending on the integrations constants. In accordance with the no-hair theorem, none of the solutions are endowed of a Killing horizon.     

Emergent Universe with Particle Production

The possibility of an emergent universe solution to Einstein’s field equations allowing for an irreversible creation of matter at the expense of the gravitational field is shown. With the universe being chosen as spatially flat FRW spacetime together with equation of state proposed in Mukherjee et al. (Class. Quant. Grav. 23, 6927, 2006), the solution exists when the ratio of the phenomenological matter creation rate to the number density times the Hubble parameter is a number β of the order of unity and independent of time. The thermodynamic behaviour is also determined for this solution. Interestingly, we also find that an emergent universe scenario is present with usual equation of state in cosmology when the matter creation rate is chosen to be a constant. More general class of emergent universe solutions are also discussed.     

A class of static coupled zero-mass and electromagnetic fields

A class of solutions, which may be called the Majumdar-Papapetrou (MP) class, has been derived for static coupled zero-mass and source-free electromagnetic fields. This has been done in two stages. First, it has been shown that the well-known MP relation between theg ₄₄ component of the metric tensor and the electrostatic potential, in certain physical situations, continues to remain the same without being affected by the presence of the zeromass field. Second, using the method of Majumdar, we have developed a theorem that enables one to generate solutions for the coupled field from Einstein's vacuum equations and the solution of a differential equation which, due to its resemblance, may be called a generalized Laplace equation.     

Uniqueness and nonuniqueness of static black holes in higher dimensions

We prove a uniqueness theorem for asymptotically flat static charged dilaton black-hole solutions in higher-dimensional space-times. We also construct infinitely many nonasymptotically flat regular static black holes on the same space-time manifold with the same spherical topology. An application to the uniqueness of a class of flat p-branes is also given.