Nonhomogeneous Systems Research Articles

On the gas adsorption effect upon electronic structure of ferromagnetic Co(0 0 0 1)

Effect of C, N or O adsorption on ferromagnetic Co(0 0 0 1) surface on evolution of important electronic features is studied within the local-density functional scheme. At high oxygen or carbon coverage, the spin asymmetry of Co(3d) states at the Fermi level can be reversed; for oxygen, however, the effect is not stable with respect to geometry variation and might correspond to non-equilibrium adatom positions. The concept of exchange splitting for non-homogeneous systems is poorly defined and its presence for well distinguished peaks in the local density of adatom 2p states is expected especially for oxygen. The calculations find, nevertheless, a simple and accurate relation between the spin-splitting of the centre of gravity of 2p electronic sates and value of the magnetic moment induced on adatoms.

Anomalous Subdiffusion in Heterogeneous Lipid Bilayers

Fluorescence photobleaching recovery (FPR) is commonly used to measure lipid and protein diffusion in cellular membranes. Typically, a model wherein diffusion is constant with time and the mean-squared displacement is directly proportional to time is used to analyze the results; however, in nonhomogeneous systems such as cellular membranes, anomalous subdiffusion may occur. In anomalous subdiffusion, the diffusion coefficient, D, decreases with time and thus the mean-squared displacement is proportional to some power of time less than 1. Although theory predicts that diffusion can be anomalous through protein interactions or obstruction, the complex composition of cellular membranes has made the actual origin and consequences of anomalous diffusion in phospholipid bilayers unclear. In this study, we use atomic force microscopy to detect and measure the amount of the solid phase in supported bilayers that contain coexisting fluid- and solid-phase lipids. Solid-phase domains in bilayers have been shown to a...

Analytical solution of non-homogeneous anisotropic wave equations based on differential transfer matrices

We present a new analytical method for solution of non-homogeneous anisotropic optical systems, based on the extension of transfer matrices into differential form. This approach can be used for exact calculation of various functions including reflection and transmission coefficients, band structures and bound states. We discuss improvements of the method for infinite periodic structures and bounded modes. Then simplifications of the approach are considered for the TE and TM polarized isotropic structures, pseudo-isotropic and uniaxial non-magnetic media. Moreover a general variational representation of bound states is introduced. As application examples, we consider the reflection from inhomogeneous structures, the band structure of infinite periodic media and bounded modes in inhomogeneous anisotropic waveguides. Excellent agreement between the results from our differential transfer matrix method and other methods is observed where comparison is possible.

Chebyshev rational matrix approximation with a priori error bounds for linear and Riccati matrix equations

This paper deals with initial value problems for Lipschitz continuous coefficient matrix Riccati equations. Using Chebyshev polynomial matrix approximations the coefficients of the Riccati equation are approximated by matrix polynomials in a constructive way. Then using the Fröbenius method developed in [1], given an admissible error ϵ > 0 and the previously guaranteed existence domain, a rational matrix polynomial approximation is constructed so that the error is less than ϵ in all the existence domain. The approach is also considered for the construction of matrix polynomial approximations of nonhomogeneous linear differential systems avoiding the integration of the transition matrix of the associated homogeneous problem.

Hydrodynamic modelling of dense gas-fluidised beds: Comparison of the kinetic theory of granular flow with 3D hard-sphere discrete particle simulations

A novel technique to sample particle velocity distributions and collision characteristics from dynamic discrete particle simulations of intrinsically unsteady, non-homogeneous systems, such as those encountered in dense gas-fluidised beds, is presented. The results are compared to the isotropic Maxwellian particle velocity distribution and the impact velocity distribution that constitute the zeroth-order Enskog approximation for the kinetic theory of granular flow. Excellent agreement with the kinetic theory is obtained for elastic particles. The individual particle velocity distribution function is isotropic and Maxwellian. A good fit of the collision velocity distribution and frequency is obtained, using the radial distribution function proposed by Carnahan and Starling (J. Chem. Phys. 51 (1969) 635). However, for inelastic and rough particles an anisotropic Maxwellian velocity distribution is obtained. It is concluded that the formation of dense particle clusters disturbs spatial homogeneity and results in collisional anisotropy. Analysis of the impact velocity shows that, in dense gas-fluidised beds, not all impact angles are of equal likelihood. The observed anisotropy becomes more pronounced with increasing degree of inelasticity of the particles.

Average momentum equation for interdendritic flow in a solidifying columnar mushy zone

This paper deals with the derivation of the macroscopic momentum transport equation in a non-homogeneous solidifying columnar dendritic mushy zone using the method of volume averaging. One of the originalities of this study lies in the derivation of an associated closure problem for the determination of the spatial evolution of the effective transport properties in such a complex situation. In this analysis—where the phase change has been included at the different stages of the derivation—all the terms arising from the averaging procedure (geometrical moments, phase interactions, interfacial momentum transport due to phase change, porosity gradients, etc.) are systematically estimated and compared on the basis of the characteristic length-scale constraints associated with the porous structures presenting evolving heterogeneities. For dendritic structures with “moderate” (but not small) evolving heterogeneities, we show that phase change and non local effects could hardly affect the determination of the permeability and inertia tensors. Finally, a closed form of the macroscopic momentum equation is proposed and a discussion is presented about the need to consider inertia terms and the second Brinkman correction (explicitly involving gradients of the liquid volume fraction) in such non-homogeneous systems.

Estimates of Exponents of Linear Nonhomogeneous Systems via the Grobman Improperness Coefficient

Estimates of Exponents of Linear Nonhomogeneous Systems via the Grobman Improperness Coefficient

Precise Time-Integration Method with Dimensional Expanding for Structural Dynamic Equations

The precise time-integration method proposed for a linear time-invariant dynamic system can give precise numerical results approaching the exact solution at the integration points. However, dife culties arise when the algorithm is used for nonhomogeneous dynamic systems due to the inverse matrix calculation required. A new algorithm isproposedto convertnonhomogeneousdynamicequationsinto homogeneousequationsbymeansofthe dimensional expanding method. With this conversion, the inverse matrix calculation is not required in the precise time-integration method. The new algorithm has enhanced the precise time-integration method by benee ting the programming implementation and the numerical stability; it has improved the computational efe ciency as well. Numerical examples are given to demonstrate the validity and efe ciency of the algorithm. Nomenclature Ai = coefe cient of the solution of Fourier series ai = coefe cient vector Bi = coefe cient of the solution of Fourier series bi = coefe cient vector C = magnitude of the load on the nodes of the structure D = coefe cient matrix of ordinary differential equations satise ed by the nonhomogeneous vector d = number of terms of one series f = load vector G = damping matrix H = coefe cient matrix of structural dynamic system H ¤ = coefe cient matrix of expanding structural dynamic system I = identity matrix K = number of time steps K = stiffness matrix k = order of time step l = number of dynamic modes M = mass matrix m = number of 2 N N = algorithm parameter of precise time integration n = dimension of the structural dynamic system p = transformed system state variable q = displacement vector r = nonhomogeneous vector of structural dynamic system Ta = small part of the matrix exponential Tc = part of matrix exponential according to matrix C Td = part of matrix exponential according to matrix D t = time v = state variable of structure dynamic system v ¤ = state variable vector of expanding structural

Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems

<i>Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems</i>

On limit reliability functions of large multi-state systems with ageing components

In this paper after basic multi-state systems defining and their reliability functions fixing the classes of possible limit reliability functions for series, parallel, series–parallel and parallel–series non-homogeneous systems are given. Next, multi-state systems with components having exponential reliability functions with different transition rates between subsets of their states are completely considered and their asymptotic reliability functions are fixed. Some applications of the results to reliability and risk evaluation of real technical systems are presented as well.

Performance evaluation of unbalanced flow lines with general distributed processing times, failures and imperfect production

In this paper an analytical approximation for the performance of non-homogenous asynchronous Flow Production Systems (FPSs) with finite buffers is presented. Generally distributed stochastic processing times as well as breakdowns and imperfect production are considered. The procedure explicitly accounts for simultaneous blocking and starving. The approximation is based on the decomposition of an M-station-line into M — 1 two-station-lines which are analyzed with the help of a GI/G/I/Nmax queueing model. Numerical comparisons with exact and simulation results for hypothetical as well as for real-life flow-lines indicate that the procedure provides accurate results.

A Revised Stern Equation for Ion Exchange at Charged Membranes

We revised the classical Stern equation for ion exchange at charged membranes using the statistical mechanics concept of chemical potential and ion activity in nonhomogeneous systems. Our proposed equation does not require an iterative procedure to obtain the self-regulated surface charge at the membranes. We predict significant differences with the classical results. When compared with experimental results, our approach not only gives a better fit but also predicts dissociation constants that are physically more reasonable than those from the classical approach.

Performance evaluation of unbalanced flow lines with general distributed processing times, failures and imperfect production

In this paper an analytical approximation for the performance of non-homogenous asynchronous Flow Production Systems (FPSs) with finite buffers is presented. Generally distributed stochastic processing times as well as breakdowns and imperfect production are considered. The procedure explicitly accounts for simultaneous blocking and starving. The approximation is based on the decomposition of an M-station-line into M − 1 two-station-lines which are analyzed with the help of a GI/G/1/N max queueing model. Numerical comparisons with exact and simulation results for hypothetical as well as for real-life flow-lines indicate that the procedure provides accurate results.

Calculating the outage probability in a CDMA network with spatial Poisson traffic

In this paper, we provide a spatial Poisson point pattern model of traffic in a code division multiple access (CDMA) wireless network. We show how the theory of Poisson processes can be applied to provide statistical information about interference levels in the network. In particular, we calculate approximations and a bound on the outage probability at a designated cell site in the network, utilizing high-order cumulants, which have very simple analytical forms and can easily be computed once the mean measure of the spatial Poisson point pattern is known. We consider a Poisson-Gaussian approximation and an Edgeworth approximation in which the Gaussian distribution is twisted to satisfy the required cumulants, and we provide a Chernoff bound on performance that also utilizes the cumulant information. We show that the theory can be applied to nonstationary, time nonhomogeneous systems. We provide a particular example of a M/M//spl infin/, spatial queueing model of a CDMA wireless network.

Second order optimality conditions for differentiable multiobjective problems

A second order optimality condition for multiobjective optimization with a set constraint is developed; this condition is expressed as the impossibility of nonhomogeneous linear systems. When the constraint is given in terms of inequalities and equalities, it can be turned into a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced.

LOCADIS—a model and numerical code for simulating local aerosol dispersion

This paper describes the computer code LOCADIS which we developed to model local aerosol dispersion in the atmosphere. The code can simulate (1) the release of contaminants in aerosol form, (2) the interaction of aerosols with other particles in the atmosphere, (3) the atmospheric dispersion of released aerosols, and (4) the deposition of contaminants on the ground and surrounding infrastructure. The code is also linked with the RIVMORPH model, which describes transport in surface water and sedimentation. LOCADIS is based on an integrated model of transport processes in non-homogeneous systems. It includes unsteady-state conservation equations for separate phases in a two-dimensional space, equations of transport processes at interface boundaries, descriptions of geometrical characteristics of a source, and heat- and mass-exchange of the source with the surroundings. LOCADIS can be used as a stand-alone code model, or as part of an expert system supporting decision-making after an industrial accident. A case study involving atmospheric dispersion and deposition around a release source is also presented.

Weak centers and bifurcation of critical periods in reversible cubic systems

In this paper, we investigate nonhomogeneous cubic differential systems with reversibility, which guarantees that the systems have a center at the origin. We apply the Ritt-Wu method to process algebraic equations and inequalities using Maple V.3 on a computer. We give an inductive algorithm for computing the period coefficient polynomials, we find the structure of solutions of systems of algebraic equations corresponding to isochronous centers and weak centers of every finite order, and we derive conditions on the parameters under which the origin is an isochronous center or a weak center of finite order. We show that with appropriate perturbations local bifurcation of critical periods will occur from weak centers of finite order and isochronous centers.

Systems with exponential eigenfunctions and exponential-input/constant-output operators

Vaidyanathan (1999) and Ferreira (1999) reported on nonlinear systems with exponential eigenfunctions. In this letter, we introduce a larger class of such systems, generated from a special family of exponential-input/constant-output operators that capture exponential signals from general inputs. In particular, we extend the classes of systems with exponential eigenfunctions defined in Vaidyanathan and Ferreira to include causal nonhomogeneous time-varying systems.

Object-oriented hybrid systems of coalgebras plus monoid actions

Hybrid systems combine discrete and continuous dynamics. We introduce a semantics for such systems consisting of a coalgebra together with a monoid action. The coalgebra captures the (discrete) operations on a state space that can be used by a client (like in the semantics of ordinary (non-temporal) object-oriented systems). The monoid action captures the influence of time on the state space, where the monoids that we consider are the natural numbers monoid ( N,0,+) of discrete time, and the positive reals monoid ( R ⩾0,0,+) of real time. Based on this semantics we develop a hybrid specification formalism with timed method applications: it involves expressions like s. meth @α, with the following meaning: in state s let the state evolve for α units of time (according to the monoid action), and then apply the (coalgebraic) method meth. In this formalism we specify various (elementary) hybrid systems, investigate their correctness, and display their behaviour in simulations. We further define a suitable notion of homomorphism between our hybrid models (of coalgebras plus monoid actions), in such a way that minimal realizations (of the specified behaviour) appear as terminal models. We identify the terminal models of our example specifications, and give general constructions. This leads to an investigation of various topics related to terminality: bisimilarity, invariance, refinement and behaviour-realization adjunctions. In a final section we briefly discuss non-homogeneous hybrid systems (with continuous inputs).

Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems

In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type. In particular we obtain a complete theory for the 2×2 systems of genuinely nonlinear hyperbolic balance laws in 1≳D with a strong dissipative term. A different method, which combines the div–curl lemma with accretive operators, is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics. We also investigate relaxation results for some 2≳D cases, which include the Cattaneo model for nonlinear heat conduction and the compressible Euler flow. Moreover, convergence result is also obtained for general semilinear systems in 1≳D.