Discrete-state Systems Research Articles

Analytic continuation for quantum nonadiabatic rate constants

We develop a method for calculating nonadiabatic rate constants in condensed phases. The method is based on a novel path integral representation of the imaginary time flux–flux correlation function combined with an analytic continuation technique. The method is general, and may be applied to systems with arbitrarily strong coupling parameters, arbitrary anharmonic environments and any number of discrete system states. The method is applied to a nontrivial benchmark system with encouraging results.

Using neural network function approximation for optimal design of continuous-state parallel–series systems

This paper presents a novel continuous-state system model for optimal design of parallel–series systems when both cost and reliability are considered. The advantage of a continuous-state system model is that it represents realities more accurately than discrete-state system models. However, using conventional optimization algorithms to solve the optimal design problem for continuous-state systems becomes very complex. Under general cases, it is impossible to obtain an explicit expression of the objective function to be optimized. In this paper, we propose a neural network (NN) approach to approximate the objective function. Once the approximate optimization model is obtained with the NN approach, the subsequent optimization methods and procedures are the same and straightforward. A 2-stage example is given to compare the analytical approach with the proposed NN approach. A complicated 4-stage example is given to illustrate that it is easy to use the NN approach while it is too difficult to solve the problem analytically. Scope and purpose The classical reliability theory assumes that the system and each component may only be in one of two possible states: working or failed. Thus, it is also referred to as binary reliability theory. A well-known reliability design problem under the binary reliability theory involves the determination of the number of redundancies in a parallel–series system which consists of N subsystems connected in series whereas each subsystem consists of a few components connected in parallel. In this paper, we consider the optimal design problem of a multi-state parallel–series system wherein both the system and its components may assume more than two levels of performance. Specifically, we assume that the state of each component and the system may be represented by a continuous random variable that may take values in the closed interval [0,1]. An optimization model is formulated for the determination of the number of redundancies in order to maximize the system's expected utility function. Because of the complexity of the optimization problem, we propose a neural network (NN) approach to approximate the objective function. The resulting optimization model is much easier to solve. Examples are given to illustrate the proposed approach.

An analytical methodology for the dependability evaluation of non-Markovian systems with multiple components

Very often, in dependability evaluation, the systems under study are assumed to have a Markovian behavior. This assumption highly simplifies the calculations, but introduces significant errors when the systems contain deterministic or quasi-deterministic processes, as it often happens with industrial systems. Existing methodologies for non-Markovian systems, such as device stage method [1] , the supplementary variables method or the imbedded Markov chain method [2] do not provide an effective solution to deal with this class of systems, since their usage is restricted to relatively simple and small systems. This paper presents an analytical methodology for the dependability evaluation of non-Markovian discrete state systems, containing both stochastic and deterministic processes, along with an associated systematic resolution procedure suitable for numerical processing. The methodology was initially developed in the context of a research work [3] addressing the dependability modeling, analysis and evaluation of large industrial information systems. This paper, extends the application domain to the evaluation of reliability oriented indexes and to the assessment of multiple components systems. Examples will be provided throughout the paper, in order to illustrate the fundamental concepts of the methodology, and to demonstrate its practical usefulness.

High Speed Indoor Navigation of Mobile Robots Using Hybrid Dynamic Control Approach

In this paper, we propose a new approach to the high-speed navigation of the indoor environments for wheeled mobile robots using hybrid dynamic control approach. The proposed hybrid system consists of the discrete state system as the high-level process and the continuous state system as the low-level process. In discrete state system, the di crete states are defined by the user-defined constraints and the abstracted motions specify the reference motion commands of mobile robots. The experimental results show that hybrid system approach is an effective method for the autonomous navigation and highspeed maneuvering.

The behavior of a finite difference approximation to a singular initial boundary value problem

We develop difference approximations to a singular parabolic initial-boundary value problem and its corresponding steady-state problem. A critical value for the existence of nonnegative solutions to the discrete steady state system is established. Convergence of the computed critical values is obtained. The long time behavior for the approximated solution of the parabolic problem is investigated. It is shown that the behavior of the discrete system is consistent with that of the continuous one

Some results for the comparative statics of steady states of higher-order discrete dynamic systems

Abstract Higher-order discrete dynamic systems arise naturally in many economic models in which the problem at hand requires an explicit treatment of dynamics involving lags of more than one period. In studying such models, one type of analysis that economists are often interested in is the assessment of the signs and the magnitudes of the effects of a change in the parameters of the dynamic system on the stable steady states of the system. This paper presents some results for such comparative statics analysis. Brief remarks explain the results and illustrate their potential economic usefulness.

Development and Analysis of Robust Algorithms for Guaranteed Ellipsoidal Estimation of the State of Multidimensional Linear Discrete Dynamic Systems. Part 1

Development and Analysis of Robust Algorithms for Guaranteed Ellipsoidal Estimation of the State of Multidimensional Linear Discrete Dynamic Systems. Part 1

Semiclassical dynamics of nonadiabatic transitions in discrete-state systems using spin coherent-state path integrals

We present a semiclassical method for simulating the dynamics of nonadiabatic transitions in a discrete-state quantum system coupled to a bath of explicit continuous coordinates. This method employs a coherent-state formulation of the path integrals for the discrete system whose dynamics is described by spin operators. This spin coherent-state formulation allows the discrete system to be mapped onto a continuous coordinate. Stationary approximations of the resulting coherent-state path integrals of the system plus bath lead to quasiclassical equations of motion which can be solved numerically by direct integration. This algorithm reduces the problem to a number of simple classical trajectory calculations and does not require calculating any fluctuation determinants.

Crossovers in the thermal decay of metastable states in discrete systems

The thermal decay of linear chains from a metastable state is investigated. A crossover from rigid to elastic decay occurs when the number of particles, the single-particle energy barrier, or the coupling strength between the particles is varied. In the rigid regime, the single-particle energy barrier is small compared to the coupling strength, and the decay occurs via a uniform saddle-point solution, with all degrees of freedom decaying instantly. Increasing the barrier one enters the elastic regime, where the decay is due to bent saddle-point configurations using the elasticity of the chain to lower their activation energy. Close to the rigid-to-elastic crossover, nucleation occurs at the boundaries of the system. However, in large systems, a second crossover from boundary to bulk nucleation can be found within the elastic regime, when the single-particle energy barrier is further increased. We compute the decay rate in the rigid and elastic regimes within the Gaussian approximation. Around the rigid-to-elastic crossover, the calculations are performed beyond the steepest-descent approximation. In this region, the prefactor exhibits a scaling property. The theoretical results are discussed in the context of discrete Josephson transmission lines and pancake vortex stacks that are pinned by columnar defects.

Anomalous redistribution of the intensity in the absorption spectra of a Pr3+ : LaF3 crystal

An experimental investigation was made of the optical absorption spectra corresponding to transitions in the Pr3+ ion in crystalline LaF3 and Y2SiO5 matrices. The investigation was carried out in the temperature range 5 — 80 K. An anomalous redistribution of the intensity was observed in the absorption spectrum of a Pr3+ :LaF3 crystal. This redistribution did not agree with the hypothesis of the Boltzmann population of the states in discrete multilevel systems.

Discrete and Hybrid State System Modeling and Analysis

Classical modeling of physical systems relies on differential-difference type equations. However many systems todey cnotain logical quantities and discrete decision makers. For example, a robot can be modeled by differential equations but the task of the robot or how to accomplish that task requires dealing with logic (discrete) variables. We develop a discrete and hybrid state system formulation to study systems with both discrete and continuous quantities. We provide some analysis methods for hybrid state systems. We investigate classical Lyapunov stability of a continuous state in a hybrid state system configuration. Furthermore, we consider two examples of hybrid state systems.

Sliding-mode control in discrete-state and hybrid systems

The sliding-mode control approach is developed for a class of discrete-state systems in a metric space. A concept of trajectory continuity is introduced which allows the use of sliding-mode design techniques similar to that in continuous state systems. This approach is then applied to a class of hybrid systems which consists of a continuous plant, an interface, and a discrete-state controller. The introduction of the sliding-mode concept leads to a design which is invariant to disturbances and also the solution of the stabilization problem.

Effects of nonlinearity on the time evolution of single-site localized states in periodic and aperiodic discrete systems.

We perform numerical investigations of the dynamical localization properties of the discrete nonlinear Schr\"odinger equation with periodic and deterministic aperiodic on-site potentials. The time evolution of an initially single-site localized state is studied, and quantities describing different aspects of the localization are calculated. We find that for a large enough nonlinearity, the probability of finding the quasiparticle at the initial site will always be nonzero and the participation number finite for all systems under study (self-trapping). For the system with zero on-site potential, we find that the velocity of the created solitons will approach zero and their width diverge as the self-trapping transition point is approached from below. A similar transition, but for smaller nonlinearities, is found also for periodic on-site potentials and for the incommensurate Aubry-Andr\'e potential in the regime of extended states. For potentials yielding a singular continuous energy spectrum in the linear limit, self-trapping seems to appear for arbitrarily small nonlinearities. We also find that the root-mean-square width of the wave packet will increase infinitely with time for those of the studied systems which have a continuous part in their linear energy spectra, even when self-trapping has occurred.

Instability of Discrete Pseudo-Conservative Structural Systems

Critical and postcritical states of pseudo-conservative discrete structural systems are studied by means of a new formulation leading to a classification of critical states and to an approximate form of the postcritical equilibrium path. The nonlinear equilibrium equations are derived from the total potential energy function of a classical system, but with the addition of at least one control parameter. The follower force effect is thus included by nonlinear constraints to the equilibrium equation. The nonlinear equations are solved by perturbation techniques. Finally the theory is applied to investigate the instability of some simple mechanical models.

Petri net tools for the specification and analysis of discrete controllers

An approach is presented for the specification, modeling, and analysis of discrete-state systems and controllers. The approach features a rule-based state-variable-specification formalism that is translated into Petri net models composed of interconnected state machines. The concept of reduced reachability graphs is introduced as a means of reducing the computational effort required to isolate and analyze subcomponent behavior within the system. The target application is discrete manufacturing systems where the costs involved in writing, debugging, and maintaining of code for online process control can be significantly reduced through the use of automated modeling and analysis techniques. The approach is illustrated by an example of a simple discrete-state system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Approach to the simulation of various LAN topologies

An approach to the simulation of various Local Area Network topologies is discussed, and a set of indices for evaluating their performance characteristics is examined. The LAN is defined in terms of a queuing network, and network topology is defined through its connectivity. Routing of data around this network is represented by a Markov process having N + 1 states (for an N node LAN), with each node being associated with one discrete system state. This approach provides flexibility in defining network topology, and makes it simple to modify. The coding used to define these network features is discussed, and an indication of its application to various network topologies is given.

Development and Comparison of Two Hierarchical Structures for On-Line Control of a Water System—A Case Study

In the paper two control structures for on-line control of a real water system are developed and comparative simulation study is performed. The system considered is a retention part of the Kamienna river catchment area. The basic physical components of the water system are: two water retention reservoirs, main river and its tributaries and two towns being the water users. The control goal consists in supplying desired daily quantities of water to users in towns and keeping a physical state of the system inside given constraints. Unknown system inflows are the source of uncertainty, but rich enough set of historical data enables to built the inflows prognosis. Due to the uncertainty timing and the reservoirs sizes the control problem time horizon has to be of one year lenght. To overcome the dimensionality problem a time aggregation concept is imployed. The result is a hierarchical control structure composed of three layers acting repeatedly with different frequency of intervention, based on the discrete system state measurements. The tasks of the upper layers are to generate the reservoirs targets for the third layer by solving long-term and mid-term optimization problems with different degree of time aggregation respectively. The third layer operation products obtained by solving short-term optimization problems are directly applied to the system. The inflows prognosis used in the optimization tasks for every layer are broght up to date in every moment of the layer intervention. Two versions of the short-term problems are proposed and investigated. The first version consists in direct determining daily releases of water from the reservoirs and daily quantities of water assigned to the towns. The second version is based on a decision rules concept. In the paper those two versions are compared by performing the exhaustive simulations of their operation.

A new method for the partition function of discrete systems with application to the 3D Ising model

We describe a new method to find numerically the density of states of discrete statistical systems. We apply the method to the zero-field, three-dimensional Ising model on a 5 3 lattice. Our method yields an excellent approximation to the partition function and can accurately predict its zeros near the critical points. We argue that our method can be used very effectively even on much larger systems.

Synthesis of digital control systems using discrete Walsh polynomials

The use of discrete Walsh polynomials to synthesize a digital control system and determine suitable internal system structure from its prescribed external (input/output) behaviour is studied in this paper. Algorithms for the synthesis of discrete system transfer functions and state equations are presented. The discrete Walsh approach method transforms the original model difference equations into computationally convenient algebraic forms. Two examples in which a transfer function and a state equation are synthesized illustrate the discrete Walsh technique.

Optimal estimation of state of linear discrete systems in the presence of pulsed perturbations

Optimal estimation of state of linear discrete systems in the presence of pulsed perturbations