Higher Dimensional Unified Description of Early Universe with Variable <Emphasis Type="Italic">G</Emphasis> and Λ

A homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model with varying gravitational and cosmological constant is studied in the context of higher dimensional space time. Exact solution of the field equations are obtained by using the “gamma law” equation of state p=(γ−1)ρ, where γ is adiabatic parameter varies continuously as the universe expands. The functional form γ which is assumed to be the function of scale factor R as proposed by Carvalho (1996) is used to analyse the behavior of scale factor R, cosmological constant Λ and the gravitational constant G for two different phases: inflation and radiation. The various physical aspects of the early cosmological models has also been discussed in the framework of higher dimensional space time.     

Dispersive shock waves in three dimensional Benjamin–Ono equation

Dispersive shock waves (DSWs) in the three dimensional Benjamin–Ono (3DBO) equation are studied with step-like initial condition along a paraboloid front. By using a similarity reduction, the problem of studying DSWs in three space one time (3+1) dimensions reduces to finding DSW solution of a (1+1) dimensional equation. By using a special ansatz, the 3DBO equation exactly reduces to the spherical Benjamin–Ono (sBO) equation. Whitham modulation equations are derived which describes DSW evolution in the sBO equation by using a perturbation method. These equations are written in terms of appropriate Riemann type variables to obtain the sBO-Whitham system. DSW solution which is obtained from the numerical solutions of the Whitham system and the direct numerical solution of the sBO equation are compared. In this comparison, a good agreement is found between these solutions. Also, some physical qualitative results about DSWs in sBO equation are presented. It is concluded that DSW solutions in the reduced sBO equation provide some information about DSW behavior along the paraboloid fronts in the 3DBO equation.     

Extended Fisher-Kolmogorov系统的渐近吸引子

考虑了ExtendedFisher-Kolmogorov系统的解的长时间行为,构造了一个有限维解序列即该系统的渐近吸引子,证明了它在长时间后无限趋于方程的整体吸引子,并给出了渐近吸引子的维数估计.     

New (3+1)‐dimensional nonlinear equations with KdV equation constituting its main part: multiple soliton solutions

In thiswork,we present two new(3+1)‐dimensional nonlinear equationswith Korteweg‐de Vries equation constituting its main part. We show that the dispersive relation is distinct for each model, whereas the phase shift remains the same. We determine multiple solitons solutions, with distinct physical structures, for each established equation. The architectures of the simplified Hirota's method is implemented in this paper. The constraint conditions that fall out which must remain valid in order for themultiple solitons to exist are derived.Copyright © 2015 John Wiley & Sons, Ltd.     

Symmetry Reductions,Group‐Invariant Solutions,and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

Nonlinear spin excitations in ferromagnetic spin chains are studied for spintronic and magnetic devices including magnetic‐field sensors and for high‐density data storage. Here, (2+1)‐dimensional nonlinear Schrödinger equation is investigated, which describes the nonlinear spin dynamics for a Heisenberg ferromagnetic spin chain. Lie point symmetry generators and Lie symmetry groups of that equation are derived. Lie symmetry groups are related to the time, space, scale, rotation transformations, and Galilean boosts of that equation. Certain solutions, which are associated with the known solutions, are constructed. Based on the Lie symmetry generators, the reduced systems of such an equation are obtained. Based on the polynomial expansion and through one of the reduced systems, group‐invariant solutions are constructed. Soliton‐type group‐invariant solutions are graphically investigated and effects of the magnetic coupling coefficients, that is, α₁, α₂, α₃, and α₄, on the soliton's amplitude, width, and velocity are discussed. It is seen that α₁, α₂, α₃, and α₄ have no influence on the soliton's amplitude, but can affect the soliton's velocity and width. Lax pair and conservation laws of such an equation are derived.     

Anomalously high heat capacity of liquids: relation to structural properties

ABSTRACT

Heat capacity of several liquids which demonstrate anomalous behaviour is studied. It is shown that isochoric heat capacity of these liquids shows anomalously high values which is related to smooth structural crossover in these liquids. This phenomenon can be used for qualitative explanation of high heat capacity of water and some other substances.     

The analysis of a finite element method for the three-species Lotka–Volterra competition-diffusion with Dirichlet boundary conditions

A Galerkin finite element method is developed for the two dimensional/three dimensional nonlinear time-dependent three-species Lotka–Volterra competition-diffusion equations on a bounded domain. The existence and uniqueness of the solution to the numerical formulation are proved. An error estimate for the numerical solution is obtained. Numerical computations are carried out to examine the expected orders of accuracy in the error estimates.     

一种基于空间一致性降元的高光谱图像非监督分类

为了提高分类精度和边缘辨识性,该文引入图像空间一致性降元(pixels reduction with spatial coherence property, PRSCP)及线性回归分析,提出了一种基于空间一致性降元的非监督分类。该方法从像元光谱相似性出发,利用像元最小关联窗口合并相邻相似像元为像块完成降元。使用线性关系建模像块内像元的光谱向量,并利用F检验判断像块数据的线性显著性。利用一元线性回归(one dimensional linear regression, ODLR)估计出像块的基准向量,根据基准向量合并相似(同类)像块完成分类。利用AVIRIS数据评估了该方法性能,实验结果表明：与K-MEANS和ISODATA方法相比,该方法精度高、边缘辨识度好及鲁棒性强。     

N‐dimensional switch function for energy conservation in multiprocess reaction dynamics

The MReaDy program was designed for studying Multiprocess Reactive Dynamic systems, that is, complex chemical systems involving different and concurrent reactions. It builds a global potential energy surface integrating a variety of potential energy surfaces, each one of them representing an elementary reaction expected to play a role in the chemical process. For each elementary reaction, energy continuity problems may happen in the transition between potential energy surfaces due to differences in the functional form for each of the fragments, especially if built by different authors. A N‐dimensional switch function is introduced in MReaDy in order to overcome such a problem. As an example, results of a collision trajectory calculation for H₂ + OH → H₃O are presented, showing smooth transition in the potential energy, leading to conservation in the total energy. Calculations for a hydrogen combustion system from 1000 K up to 4000 K shows a variation of 0.012% when compared to the total energy of the system. © 2016 Wiley Periodicals, Inc.     

Fabrication of Boron Nitride Nanosheets by Exfoliation

Nanomaterials with layered structures, with their intriguing properties, are of great research interest nowadays. As one of the primary two‐dimensional nanomaterials, the hexagonal boron nitride nanosheet (BNNS, also called white graphene), which is an analogue of graphene, possesses various attractive properties, such as high intrinsic thermal conductivity, excellent chemical and thermal stability, and electrical insulation properties. After being discovered, it has been one of the most intensively studied two‐dimensional non‐carbon nanomaterials and has been applied in a wide range of applications. To support the exploration of applications of BNNSs, exfoliation, as one of the most promising approaches to realize large‐scale production of BNNSs, has been intensively investigated. In this review, methods to yield BNNSs by exfoliation will be summarized and compared with other potential fabrication methods of BNNSs. In addition, the future prospects of the exfoliation of h‐BN will also be discussed.