Stability of time-delay systems via Lyapunov functions

In this paper, a Lyapunov function candidate is introduced for multivariable systems with inner delays, without assuming a priori stability for the nondelayed subsystem. By using this Lyapunov function, a controller is deduced. Such a controller utilizes an input-output description of the original system, a circumstance that facilitates practical applications of the proposed approach.

Coupled 3-D finite difference time domain and finite volume methods for solving microwave heating in porous media

Computational results for the microwave heating of a porous material are presented in this paper. Combined finite difference time domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent both on temperature and moisture content. The model was able to reflect the evolution of temperature and moisture fields as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

On information rates of time-varying fading channels modeled as finite-state Markov channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.

Finite-Element Time-Step Coupled Generator, Load, AVR and Brushless Exciter Modelling

This paper presented results from a details and comprehensive simulation using finite element method of the practical operation of an electrical machine. The results it displayed have been used in practice to design more efficient equipment.

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Finite ion temperature effects on oblique modulational stability and envelope excitations of dust-ion acoustic waves

Theoretical and numerical investigations are carried out for the amplitude modulation of dust-ion acoustic waves (DIAW) propagating in an unmagnetized weakly coupled collisionless fully ionized plasma consisting of isothermal electrons, warm ions and charged dust grains. Modulation oblique (by an angle theta) to the carrier wave propagation direction is considered. The stability analysis, based on a nonlinear Schrodinger-type equation (NLSE), exhibits a sensitivity of the instability region to the modulation angle theta, the dust concentration and the ion temperature. It is found that the ion temperature may strongly modify the wave's stability profile, in qualitative agreement with previous results, obtained for an electron-ion plasma. The effect of the ion temperature on the formation of DIAW envelope excitations (envelope solitons) is also discussed.

Finite difference time domain modeling of phase grating diffusion

In this paper, a method for modeling diffusion caused by non-smooth boundary surfaces in simulations of room acoustics using finite difference time domain (FDTD) technique is investigated. The proposed approach adopts the well-known theory of phase grating diffusers to efficiently model sound scattering from rough surfaces. The variation of diffuser well-depths is attained by nesting allpass filters within the reflection filters from which the digital impedance filters used in the boundary implementation are obtained. The presented technique is appropriate for modeling diffusion at high frequencies caused by small surface roughness and generally diffusers that have narrow wells and infinitely thin separators. The diffusion coefficient was measured with numerical experiments for a range of fractional Brownian diffusers.

A Spherical Array Approach for Simulation of Binaural Impulse Responses using the Finite Difference Time Domain Method

The finite difference time domain (FDTD) method has direct applications in musical instrument modeling, simulation of environmental acoustics, room acoustics and sound reproduction paradigms, all of which benefit from auralization. However, rendering binaural impulse responses from simulated
data is not straightforward to accomplish as the calculated pressure at FDTD grid nodes does not contain any directional information. This paper addresses this issue by introducing a spherical array to capture sound pressure on a finite difference grid, and decomposing it into a plane-wave density
function. Binaural impulse responses are then constructed in the spherical harmonics domain by combining the decomposed grid data with free field head-related transfer functions. The effects of designing a spherical array in a Cartesian grid are studied, and emphasis is given to the relationships
between array sampling and the spatial and spectral design parameters of several finite-difference
schemes.

Discrete-Time Conserved Quantities for Damped Oscillators

Numerical sound synthesis is often carried out using the finite difference time domain method. In order to analyse the stability of the derived models, energy methods can be used for both linear and nonlinear settings. For Hamiltonian systems the existence of a conserved numerical energy-like quantity can be used to guarantee the stability of the simulations. In this paper it is shown how to derive similar discrete conservation laws in cases where energy is dissipated due to friction or in the presence of an energy source due to an external force. A damped harmonic oscillator (for which an analytic solution is available) is used to present the proposed methodology. After showing how to arrive at a conserved quantity, the simulation of a nonlinear single reed shows an example of an application in the context of musical acoustics.

Time Reversibility of Stationary Regular Finite State Markov Chains

We propose an alternate parameterization of stationary regular finite-state Markov chains, and a decomposition of the parameter into time reversible and time irreversible parts. We demonstrate some useful properties of the decomposition, and propose an index for a certain type of time irreversibility. Two empirical examples illustrate the use of the proposed parameter, decomposition and index. One involves observed states; the other, latent states.

On Space-Time Trade-Off for Montgomery Multipliers over Finite Fields

La multiplication dans le corps de Galois à 2^m éléments (i.e. GF(2^m)) est une opérations très importante pour les applications de la théorie des correcteurs et de la cryptographie. Dans ce mémoire, nous nous intéressons aux réalisations parallèles de multiplicateurs dans GF(2^m) lorsque ce dernier est généré par des trinômes irréductibles. Notre point de départ est le multiplicateur de Montgomery qui calcule A(x)B(x)x^(-u) efficacement, étant donné A(x), B(x) in GF(2^m) pour u choisi judicieusement. Nous étudions ensuite l'algorithme diviser pour régner PCHS qui permet de partitionner les multiplicandes d'un produit dans GF(2^m) lorsque m est impair. Nous l'appliquons pour la partitionnement de A(x) et de B(x) dans la multiplication de Montgomery A(x)B(x)x^(-u) pour GF(2^m) même si m est pair. Basé sur cette nouvelle approche, nous construisons un multiplicateur dans GF(2^m) généré par des trinôme irréductibles. Une nouvelle astuce de réutilisation des résultats intermédiaires nous permet d'éliminer plusieurs portes XOR redondantes. Les complexités de temps (i.e. le délais) et d'espace (i.e. le nombre de portes logiques) du nouveau multiplicateur sont ensuite analysées: 1. Le nouveau multiplicateur demande environ 25% moins de portes logiques que les multiplicateurs de Montgomery et de Mastrovito lorsque GF(2^m) est généré par des trinômes irréductible et m est suffisamment grand. Le nombre de portes du nouveau multiplicateur est presque identique à celui du multiplicateur de Karatsuba proposé par Elia. 2. Le délai de calcul du nouveau multiplicateur excède celui des meilleurs multiplicateurs d'au plus deux évaluations de portes XOR. 3. Nous determinons le délai et le nombre de portes logiques du nouveau multiplicateur sur les deux corps de Galois recommandés par le National Institute of Standards and Technology (NIST). Nous montrons que notre multiplicateurs contient 15% moins de portes logiques que les multiplicateurs de Montgomery et de Mastrovito au coût d'un délai d'au plus une porte XOR supplémentaire. De plus, notre multiplicateur a un délai d'une porte XOR moindre que celui du multiplicateur d'Elia au coût d'une augmentation de moins de 1% du nombre total de portes logiques.

Effect of the Vulcanization Time and Storage on the Stability and Physical Properties of Sulfur-Prevulcanized Natural Rubber Latex

Prevulcanized natural rubber latex was prepared by the heating of the latex compound at 55°C for different periods of time (2, 4, 6, 8, and 10 h). The changes in the colloidal stability and physical properties were evaluated during the course of prevulcanization. The prevulcanized latex compounds were stored for 300 days, and the properties were monitored at different storage intervals (0, 20, 40, 60, 120, 180, 240, and 300 days). During prevulcanization, the mechanical stability time increased, and the viscosity remained almost constant. The tensile strength increased during storage for a period of 20 days. The degree of crosslinking, modulus, elongation at break, and chloroform number were varied with the time of storage.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.