A novel architecture of ultracompact pulse position modulator in photonic crystals

We propose and analyze a novel photonic crystal pulse position modulator utilizing a coupled cavity waveguide delay line. Also, a nonlinear photonic crystal directional coupler is used as an all-optical switch in the proposed structure. The input data acts as the control signal of the switch and activates the switching operation. We show that the device size can be reduced significantly by designing the delay line to achieve a reduced group velocity and a quasi-flat impurity band. The size of the designed modulator is 32a × 16a, where a represents the lattice constant of the photonic crystal. The characteristics of the device are investigated by finite-difference time-domain (FDTD) and plane wave expansion (PWE) methods.     

MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method

The performance of a two-auxiliary-parameter homotopy analysis method (HAM) is investigated in solving laminar MHD flow of an upper-convected Maxwell fluid (UCM) above a porous isothermal stretching sheet. The analysis is carried out up to the 20th-order of approximation, and the effect of parameters such as elasticity number, suction/injection velocity, and magnetic number are studied on the velocity field above the sheet. The results will be contrasted with those reported recently by Hayat et al. [Hayat T, Abbas Z, Sajid M. Series solution for the upper-convected Maxwell fluid over a porous stretching plate. Phys Lett A 358;2006:396–403] obtained using a third-order one-auxiliary-parameter homotopy analysis method. It is concluded that the flow reversal phenomenon as predicted by Hayat et al. (2006) may have arisen because of the inadequacies of using just one-auxiliary-parameter in their analysis. That is, no flow reversal is predicted to occur if instead of using one-auxiliary-parameter use is made of two auxiliary parameters together with a more convenient set of base functions to assure the convergence of the series used to solve the highly nonlinear ODE governing the flow.     

Monitoring the accumulation of lipofuscin in aging murine eyes by fluorescence spectroscopy

The integrated fluorescence of murine eyes is collected as a function of age. This fluorescence is attributed to pigments generally referred to as lipofuscin and is observed to increase with age. No difference in fluorescence intensity is observed between the eyes of males or females. This work provides a benchmark for further studies that are planned in order to use such signatures as markers of central nervous system (CNS) tissue or even of diseased CNS tissue and provides a basis for determining the age of a healthy animal.     

Temporal discretization choices for stable boundary element methods in electromagnetic scattering problems

Diverse alternative temporal discretization schemes are analyzed for stable numerical solution of the surface integral equations in obtaining the transient scattering response of arbitrarily shaped conducting bodies. Streamlined formulations for three main categories including using either the conventional time integrators or the subdomain temporal basis functions, or the entire-domain time bases are presented in conceptually similar frameworks for solving types of the electric, magnetic, and combined field integral equations. To this end, first compatible temporal interpolations with conveniently usable time integrators are introduced based on stability analysis of the delay differential equations (DDE). Detailed guidelines for effective implementation of appropriate subdomain time basis functions are then studied. It is demonstrated that since in the latter approach the time derivatives are handled analytically, the extension of the stable region tremendously enhances while approaching small time step sizes. Eventually, the orthogonal weighted Laguerre polynomials are set forth to provide unconditionally stable schemes. Besides, adaptive partitioning of triangular patches is proposed to efficiently control the precision of numerical quadratures over the surface of source distribution. Numerical results are verified through comparison with the results obtained using the finite integration technique (FIT). Convergence behaviour of the widely used schemes is also investigated.     

An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks

Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to mass-balance constraints. A variety of cell functions in response to environmental stimuli can be quantified using flux balance analysis by parameterizing the linear program with respect to extracellular conditions. However, for most large, genome-scale metabolic networks of practical interest, the resulting parametric problem has multiple and highly degenerate optimal solutions, which are computationally challenging to handle. An improved multi-parametric programming algorithm based on active-set methods is introduced in this paper to overcome these computational difficulties. Degeneracy and multiplicity are handled, respectively, by introducing generalized inverses and auxiliary objective functions into the formulation of the optimality conditions. These improvements are especially effective for metabolic networks because their stoichiometry matrices are generally sparse; thus, fast and efficient algorithms from sparse linear algebra can be leveraged to compute generalized inverses and null-space bases. We illustrate the application of our algorithm to flux balance analysis of metabolic networks by studying a reduced metabolic model of Corynebacterium glutamicum and a genome-scale model of Escherichia coli. We then demonstrate how the critical regions resulting from these studies can be associated with optimal metabolic modes and discuss the physical relevance of optimal pathways arising from various auxiliary objective functions. Achieving more than fivefold improvement in computational speed over existing multi-parametric programming tools, the proposed algorithm proves promising in handling genome-scale metabolic models.     

Commutative rings whose proper ideals are direct sums of uniform modules

An interesting result, obtaining by some theorems of Asano, Köthe and Warfield, states that: “for a commutative ring R, every module is a direct sum of uniform modules if and only if R is an Artinian principal ideal ring.” Moreover, it is observed that: “every ideal of a commutative ring R is a direct sum of uniform modules if and only if R is a finite direct product of uniform rings.” These results raise a natural question: “What is the structure of commutative rings whose all proper ideals are direct sums of uniform modules?” The goal of this paper is to answer this question. We prove that for a commutative ring R, every proper ideal is a direct sum of uniform modules, if and only if, R is a finite direct product of uniform rings or R is a local ring with the unique maximal ideal ? of the form ? = U⊕S, where U is a uniform module and S is a semisimple module. Furthermore, we determine the structure of commutative rings R for which every proper ideal is a direct sum of cyclic uniform modules (resp., cocyclic modules). Examples which delineate the structures are provided.     

Symmetry and uniqueness of solutions to some Liouville-type equations and systems

We prove symmetry and uniqueness results for three classes of Liouville-type problems arising in geometry and mathematical physics: asymmetric Sinh-Gordon equation, cosmic string equation and Toda system, under certain assumptions on the mass associated to these problems. The argument is in the spirit of the sphere covering inequality which for the first time is used in treating different exponential nonlinearities and systems.