Symmetry group analysis and similarity solutions for the (2+1)‐dimensional coupled Burger's system

Symmetry group analysis and similarity reduction of nonlinear system of coupled Burger equations in the form of nonlinear partial differential equation are analyzed via symmetry method. The symmetry method has led to similarity reductions of this equation to solvable form to third‐order partial differential equation. The infinitesimal, similarity variables, dependent variables, and reduction have been tabulated. The search for solutions of these systems by using the improved tanh method has yielded certain exact solutions expressed by rational functions. Some figures are given to show the properties of the solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment

In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the proposed method for chaotic signal cryptography. The results show the effectiveness of the proposed method.     

Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory

Graphene-polymer nano-composites are one of the most applicable engineering nanostructures with superior mechanical properties. In the present study, a finite element (FE) approach based on the size dependent nonlocal elasticity theory is developed for buckling analysis of nano-scaled multi-layered graphene sheets (MLGSs) embedded in polymer matrix. The van der Waals (vdW) interactions between the graphene layers and graphene-polymer are simulated as a set of linear springs using the Lennard-Jones potential model. The governing stability equations for nonlocal classical orthotropic plates together with the weighted residual formulation are employed to explicitly obtain stiffness and buckling matrices for a multi-layered super element of MLGS. The accuracy of the current finite element analysis (FEA) is approved through a comparison with molecular dynamics (MD) and analytical solutions available in the literature. Effects of nonlocal parameter, dimensions, vdW interactions, elastic foundation, mode numbers and boundary conditions on critical in-plane loads are investigated for different types of MLGS. It is found that buckling loads of MLGS are generally of two types namely In-Phase (INPH) and Out-of-Phase (OPH) loads. The INPH loads are independent of interlayer vdW interactions while the OPH loads depend on vdW interactions. It is seen that the decreasing effect of nonlocal parameter on the OPH buckling loads dwindles as the interlayer vdW interactions become stronger. Also, it is found that the small scale and polymer substrate have noticeable effects on the buckling loads of embedded MLGS.     

Reserve stock models: Deterioration and preventive replenishment

Reserve stocks are needed in a wide spectrum of industries from strategic oil reserves to tactical (machine buffer) reserves in manufacturing. One important aspect under-looked in research is the effect of deterioration, where a reserve stock, held for a long time, may be depleted gradually due to factors such as spoilage, evaporation, and leakage. We consider the common framework of a reserve stock that is utilized only when a supply interruption occurs. Supply outage occurs randomly and infrequently, and its duration is random. During the down time the reserve is depleted by demand, diverted from its main supply. We develop optimal stocking policies, for a reserve stock which deteriorates exponentially. These policies balance typical economic costs of ordering, holding, and shortage, as well as additional costs of deterioration and preventive measures. Our main results are showing that (i) deterioration significantly increases cost (up to 5%) and (ii) a preventive replenishment policy, with periodic restocking, can offset some of these additional costs. One side contribution is refining a classical reserve stock model (Hansmann, 1962).     

On Finite Groups with a Given Number of Centralizers

For a finite group G, let Cent(G) denote the set of centralizers of single elements of G and #Cent(G) = |Cent(G)|. G is called an n-centralizer group if #Cent(G) = n, and a primitive n-centralizer group if #Cent(G) = #Cent(G/Z(G)) = n. In this paper, we compute #Cent(G) for some finite groups G and prove that, for any positive integer n 2, 3, there exists a finite group G with #Cent(G) = n, which is a question raised by Belcastro and Sherman [2]. We investigate the structure of finite groups G with #Cent(G) = 6 and prove that, if G is a primitive 6-centralizer group, then G/Z(G) A₄, the alternating group on four letters. Also, we prove that, if G/Z(G) A₄, then #Cent(G) = 6 or 8, and construct a group G with G/Z(G) A₄ and #Cent(G) = 8.This research was in part supported by a grant from IPM.2000 Mathematics Subject Classification: 20D99, 20E07     

Numerical Simulation of a Turbulent FSI Benchmark Case

In an effort to expand the capabilities of a validated simulation environment for fluid-structure interaction to turbulent flows, we present the simulation of a turbulent FSI benchmark case with large displacements in a simplified two-dimensional unsteady RANS setup. We find a fair agreement to experimental data that encourages further refinement of our approach and future three-dimensional simulations with eddy-resolving schemes. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Remarks on Generalized GCD Domains

An integral domain R is a generalized GCD (GGCD) domain if the semigroup of invertible ideals of R is closed under intersection. In this article we extend the definition of PF-prime ideals to GGCD domains and develop a theory of these ideals which allows us to characterize Prüfer and π -domains among GGCD domains. We also introduce the concept of generalized GCD modules as a natural generalization of GGCD domains to the module case. An R-module M is a GGCD module if the set of invertible submodules of M is closed under intersection. We show that an integral domain R is a GGCD domain if and only if a faithful multiplication R-module M is a GGCD module. Various properties and characterizations of faithful multiplication GGCD modules over integral domains are considered and consequently, necessary and sufficient conditions for a ring R(M), the idealization of M, to be a GGCD ring are given.     

Measurement of the thermoelectric power of lead sulphide

The thermoelectric power of natural specimens of lead sulphide crystals has been measured between room temperature and 700° K. Specimens which are of then-type remain as such throughout the temperature range. Thep-type specimens, however, show an initial small rise followed by a gradual decrease and a subsequent change of sign ata temperature which, in some specimens, is well defined. Further increase of temperature results in a negative extremum. From this stage onwards there seems to develop a common behaviour for both types of specimens. Some crystals which were initially of thep-type changed over to then-type and remained as such throughout subsequent investigation. Among the crystals one showed a metallic conduction and an extraordinary large thermoelectric power.