A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.

An object-orient designed FDTD simulator: Applications to high field systems

An object-oriented finite-difference time-domain (FDTD) simulator has been developed for electromagnetic study and design applications in Magnetic Resonance Imaging. It is aimed to be a complete FDTD model of an MRI system including all high and low-frequency field generating units and electrical models of the patient. The design method is described and MRI-based numerical examples are presented to illustrate the function of the numerical solver, particular emphasis is placed on high field studies.

Towards a Modeling Environment for Earth Systems Simulations

The developments of models in Earth Sciences, e.g. for earthquake prediction and for the simulation of mantel convection, are fare from being finalized. Therefore there is a need for a modelling environment that allows scientist to implement and test new models in an easy but flexible way. After been verified, the models should be easy to apply within its scope, typically by setting input parameters through a GUI or web services. It should be possible to link certain parameters to external data sources, such as databases and other simulation codes. Moreover, as typically large-scale meshes have to be used to achieve appropriate resolutions, the computational efficiency of the underlying numerical methods is important. Conceptional this leads to a software system with three major layers: the application layer, the mathematical layer, and the numerical algorithm layer. The latter is implemented as a C/C++ library to solve a basic, computational intensive linear problem, such as a linear partial differential equation. The mathematical layer allows the model developer to define his model and to implement high level solution algorithms (e.g. Newton-Raphson scheme, Crank-Nicholson scheme) or choose these algorithms form an algorithm library. The kernels of the model are generic, typically linear, solvers provided through the numerical algorithm layer. Finally, to provide an easy-to-use application environment, a web interface is (semi-automatically) built to edit the XML input file for the modelling code. In the talk, we will discuss the advantages and disadvantages of this concept in more details. We will also present the modelling environment escript which is a prototype implementation toward such a software system in Python (see www.python.org). Key components of escript are the Data class and the PDE class. Objects of the Data class allow generating, holding, accessing, and manipulating data, in such a way that the actual, in the particular context best, representation is transparent to the user. They are also the key to establish connections with external data sources. PDE class objects are describing (linear) partial differential equation objects to be solved by a numerical library. The current implementation of escript has been linked to the finite element code Finley to solve general linear partial differential equations. We will give a few simple examples which will illustrate the usage escript. Moreover, we show the usage of escript together with Finley for the modelling of interacting fault systems and for the simulation of mantel convection.

Hydrostability and Scaling Up Molecular Sieve Silica (MSS) Membranes for H2/CO Separation in Fuel Cell Systems

MSS membranes are a good candidate for CO cleanup in fuel cell fuel processing systems due to their ability to selectively permeate H2 over CO via molecular sieving. Successfully scaled up tubular membranes were stable under dry conditions to 400°C with H2 permeance as high as 2 x 10-6 mol.m-2.s^-1.Pa^-1 at 200 degrees C and H2/CO selectivity up to 6.4, indicating molecular sieving was the dominant mechanism. A novel carbonised template molecular sieve silica (CTMSS) technology gave the scaled up membranes resilience in hydrothermal conditions up to 400 degrees C in 34% steam and synthetic reformate, which is required for use in fuel cell CO cleanup systems.

Simulations of Bose fields at finite temperature

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomized initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

Interaction between Normative Systems and Cognitive Agents in Temporal Modal Defeasible Logic

While some recent frameworks on cognitive agents addressed the combination of mental attitudes with deontic concepts, they commonly ignore the representation of time. An exception is [1]that manages also some temporal aspects both with respect to cognition and normative provisions. We propose in this paper an extension of the logic presented in [1]with temporal intervals.

Entangled States and Collective Nonclassical Effects in Two-Atom Systems

We propose a review of recent developments on entanglement and nonclassical effects in collective two-atom systems and present a uniform physical picture of the many predicted phenomena. The collective effects have brought into sharp focus some of the most basic features of quantum theory, such as nonclassical states of light and entangled states of multiatom systems. The entangled states are linear superpositions of the internal states of the system which cannot be separated into product states of the individual atoms. This property is recognized as entirely quantum-mechanical effect and have played a crucial role in many discussions of the nature of quantum measurements and, in particular, in the developments of quantum communications. Much of the fundamental interest in entangled states is connected with its practical application ranging from quantum computation, information processing, cryptography, and interferometry to atomic spectroscopy.

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

A minimal defining set of a Steiner triple system on a points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v + 1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on, 3" points; we construct minimal defining sets of volumes varying by as much as 7(n-/-).

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

Increased apoptosis of T lymphocytes and macrophages in the central and peripheral nervous systems of Lewis rats with experimental autoimmune encephalomyelitis treated with dexamethasone

Using light and electron microscopic histological and immunocytochemical techniques, we investigated the effects of the glucocorticoid dexamethasone on T cell and macrophage apoptosis in the central nervous system (CNS) and peripheral nervous system (PNS) of Lewis rats with acute experimental autoimmune encephalomyelitis (EAE) induced with myelin basic protein (MBP). A single subcutaneous injection of dexamethasone markedly augmented T cell and macrophage apoptosis in the CNS and PNS and microglial apoptosis in the CNS within 6 hours (h). Pre-embedding immunolabeling revealed that dexamethasone increased the number of apoptotic CD5+ cells (T cells or activated B cells), αβ T cells, and CD11b+ cells (macrophages/microglia) in the meninges, perivascular spaces, and CNS parenchyma. The induction of increased apoptosis was dose-dependent. Daily dexamethasone treatment suppressed the neurological signs of EAE. However, the daily injection of a dose of dexamethasone (0.25 mg/kg). which, after a single dose, did not induce increased apoptosis in the CNS or PNS, was as effective in inhibiting the neurological signs of EAE as the high dose (4 mg/kg), which induced a marked increase in apoptosis. This indicates that the beneficial clinical effect of glucocorticoid therapy in EAE does not depend on the induction of increased apoptosis. The daily administration of dexamethasone for 5 days induced a relapse that commenced 5 days after cessation of treatment, with the severity of the relapse tending to increase with dexamethasone dosage.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

On the applicability of the Aris' equivalent sphere in multicomponent reacting systems

The validity of the concept of equivalent sphere introduced by Aris in 1957 to multicomponent reacting systems is investigated in this paper. A network of C6 hydrocarbon reforming reaction and a fixed bed reactor are taken as the model reaction network and the reactor configuration, respectively.

A demonstration of artificial dissipation effects in some finite volume solution methods for the Navier-Stokes equations

The artificial dissipation effects in some solutions obtained with a Navier-Stokes flow solver are demonstrated. The solvers were used to calculate the flow of an artificially dissipative fluid, which is a fluid having dissipative properties which arise entirely from the solution method itself. This was done by setting the viscosity and heat conduction coefficients in the Navier-Stokes solvers to zero everywhere inside the flow, while at the same time applying the usual no-slip and thermal conducting boundary conditions at solid boundaries. An artificially dissipative flow solution is found where the dissipation depends entirely on the solver itself. If the difference between the solutions obtained with the viscosity and thermal conductivity set to zero and their correct values is small, it is clear that the artificial dissipation is dominating and the solutions are unreliable.