State Of Physical System Research Articles

Adaptive control for nonlinear nonnegative dynamical systems

Nonnegative and compartmental models are widespread in engineering systems and life sciences and play a key role in the understanding of these systems. In this paper, we develop a direct adaptive control framework for nonlinear uncertain nonnegative and compartmental dynamical systems. The proposed framework is Lyapunov-based and guarantees partial asymptotic set-point regulation; that is, asymptotic set-point regulation with respect to part of the closed-loop system states associated with the plant. In addition, the adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space.

Chapter 3: Plasma Control in ASDEX Upgrade

In modern tokamak machines, exploration and successful development of improved plasma regimes is impossible without adequate control systems. In ASDEX Upgrade, the control tasks are performed by two systems, the continuously operating machine control and the plasma control active as long as a plasma discharge lasts. Machine control based on programmable logic controllers operates on a relatively slow timescale of τ = 100 ms to configure and monitor the machine’s technical systems. Real-time plasma controllers run on faster cycle times of a few milliseconds to feedback (FB) control plasma shape and performance quantities. During the burn of a discharge, a real-time supervisor monitors the full technical and physical system state τ = 10 ms) and applies alternate discharge program segments to optimize discharge performance or react to failures. The supervisor is fully integrated with a layered machine protection system.Plasma position and shape control in ASDEX Upgrade is particularly difficult: Since the poloidal magnetic field (PF) coils are located reactor relevant outside the toroidal magnetic field coil system and distant from the plasma, each PF coil has a global effect on all shape quantities. This makes simultaneous control of shape parameters a multivariable problem. The feedback control algorithm is based on a matrix proportional-integral-derivative method, adapted to handle saturation of coil currents, excess of coil forces, or to balance loads among coils. Control cycle time is ~3 ms.In parallel, the plasma performance control (sometimes called kinetic control) acts on particle fueling and auxiliary heating systems. It consists mainly of FB loops each controlling a single variable. These circuits can be freely combined to simultaneously control a number of different plasma quantities. A clear hierarchy in the control processes allows special real-time processes to override the programmed plasma discharge feedback action: The set of controlled quantities may be changed dynamically, depending on the plasma regime detected; stabilizing actions may be triggered when plasma instabilities grow; and discharge termination by means of impurity addition is initiated when a neural network indicates an imminent disruption. The computation of the needed plasma parameters and instability indicators requires signal inputs from many diagnostic systems during each controller cycle.Currently, a new plasma control system is being implemented as a distributed system of real-time controllers and diagnostic systems, which are connected via a deterministic communication network.

Adaptive control for non‐negative and compartmental dynamical systems with applications to general anesthesia

AbstractNon‐negative and compartmental dynamical system models are composed of homogeneous interconnected subsystems or compartments which exchange variable non‐negative quantities of material with conservation laws describing transfer, accumulation, and elimination between the compartments and the environment. These models are widespread in biological and physiological sciences and play a key role in understanding these processes. In this paper, we develop a direct adaptive control framework for linear uncertain non‐negative and compartmental systems. The proposed framework is Lyapunov‐based and guarantees partial asymptotic set‐point regulation; that is, asymptotic set‐point stability with respect to part of the closed‐loop system states associated with the plant. In addition, the adaptive controller guarantees that the physical system states remain in the non‐negative orthant of the state space. Finally, a numerical example involving the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for non‐cardiac surgery is provided to demonstrate the efficacy of the proposed approach. Copyright © 2003 John Wiley & Sons, Ltd.

Adaptive nudged elastic band approach for transition state calculation

We present a method for the location of transition states in complicated physical systems. Our algorithm is a variation of the well-established nudged elastic band method and leads to significant improvements in efficiency and accuracy. We assess the applicability of our method by testing it on several systems of practical interest representing a variety of physical situations. At the molecular level, we apply the method to tautomerization processes in nucleic acid bases and the double proton transfer in nucleic acid base pairs. For bulk systems, we considered the concerted exchange mechanism in Si, which is a complicated pathway for defect-free diffusion in the diamond lattice. For surface systems, we considered ad-dimer diffusion mechanisms on Si(100). We incorporated the climbing image extension of the nudged elastic band method and compared it against the original approach on two-dimensional model potential energy surfaces. Based on favorable comparisons with related methods and the general implementation of our method, we believe that this is well suited for efficient estimates of activation barriers with sophisticated electronic structure codes.

Cloning of symmetricd-level photonic states in physical systems

Optimal procedures play an important role in quantum information. It turns out that some naturally occurring processes like emission of light from an atom can realize optimal transformations. Here we study how arbitrary symmetric states of a number of d-level systems can be cloned using a multilevel atomic system. It is shown that optimality is always ensured even though the output number of systems is probabilistic.

Towards a coherent theory of physics and mathematics.

As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and sufficient strength may be useful to reject candidate coherent theories for which the description is less than maximal. Other aspects of a coherent theory discussed include universal applicability, the relation to the anthropic principle, and possible uniqueness. It is suggested that the basic properties of the physical and mathematical universes are entwined with and emerge with a coherent theory. Support for this includes the indirect reality status of properties of very small or very large far away systems compared to moderate sized nearby systems. Discussion of the necessary physical nature of language includes physical models of language and a proof that the meaning content of expressions of any axiomatizable theory seems to be independent of the algorithmic complexity of the theory. Godel maps seem to be less useful for a coherent theory than for purely mathematical theories because all symbols and words of any language must have representations as states of physical systems already in the domain of a coherent theory.

Inverted spectroscopy and interferometry for quantum-state reconstruction of systems withSU(2) symmetry

We consider how the conventional spectroscopic and interferometric schemes can be rearranged to serve for reconstructing quantum states of physical systems possessing SU(2) symmetry. The discussed systems include a collection of two-level atoms, a two-mode quantized radiation field with a fixed total number of photons, and a single laser-cooled ion in a two-dimensional harmonic trap with a fixed total number of vibrational quanta. In the proposed rearrangement, the standard spectroscopic and interferometric experiments are inverted. Usually one measures an unknown frequency or phase shift using a system prepared in a known quantum state. Our aim is just the inverse one, i.e., to use a well-calibrated apparatus with known transformation parameters to measure unknown quantum states.

Nonlinearly saturated dynamical state of a three-wave mode-coupled dissipative system with linear instability

Linearly unstable dissipative systems with quadratic nonlinearity occurring in plasma physics, optics, fluid mechanics, etc. are often modeled by a general set of three-wave mode-coupled ordinary differential equations for complex variables. Bounded attractors of the set approximate nonlinearly saturated turbulent states of real physical systems. Exact criteria for boundedness of the attractors are found. Fundamentally different kinds of asymptotic behavior of the wave triad are classified in the parameter space and quantitatively assessed.

Individualism and the Nature of Syntactic States

It is widely assumed that the explanatory states of scientific psychology are type-individuated by their semantic or intentional properties. First, I argue that this assumption is implausible for theories like David Marr's [1982] that seek to provide computational or syntactic explanations of psychological processes. Second, I examine the implications of this conclusion for the debate over psychological individualism. While most philosophers suppose that syntactic states supervene on the intrinsic physical states of information-processing systems, I contend they may not. Syntatic descriptions must be adequately constrained, and the most plausible such constraints appeal to a system's teleological function or design and hence to its history. As a result, physical twins may not realize the same syntactic states.

Dynamic Risk Management Systems: Hybrid Architecture and Offshore Platform Illustration

This paper describes and illustrates the architecture of computer‐based Dynamic Risk Management Systems (DRMS) designed to assist real‐time risk management decisions for complex physical systems, for example, engineered systems such as offshore platforms or medical systems such as patient treatment in Intensive Care Units. A key characteristic of the DRMSs that we describe is that they are hybrid, combining the powers of Probabilistic Risk Analysis methods and heuristic Artificial Intelligence techniques. A control module determines whether the situation corresponds to a specific rule or regulation, and is clear enough or urgent enough for an expert system to make an immediate recommendation without further analysis of the risks involved. Alternatively, if time permits and if the uncertainties justify it, a risk and decision analysis module formulates and evaluates options, including that of gathering further information. This feature is particularly critical since, most of the time, the physical system is only partially observable, i.e., the signals observed may not permit unambiguous characterization of its state. The DRMS structure is also dynamic in that, for a given time window (e.g., 1 day or 1 hour), it anticipates the physical system's state (and, when appropriate, performs a risk analysis) accounting for its evolution, its mode of operations, the predicted external loads and problems, and the possible changes in the set of available options. Therefore, we specifically address the issue of dynamic information gathering for decision‐making purposes. The concepts are illustrated focusing on the risk and decision analysis modules for a particular case of real‐time risk management on board offshore oil platforms, namely of two types of gas compressor leaks, one progressive and one catastrophic. We describe briefly the DRMS proof‐of‐concept produced at Stanford, and the prototype (ARMS) that is being constructed by Bureau Veritas (Paris) based on these concepts.

LABORATORY STUDY OF REAL-TIME OPTICAL MICROSCOPE TRACKING OF THERMAL REACTION PROGRESS OF VACUUM RESIDUA II: CHEMICAL RELEVANCE OF PHYSICAL PROCESSES IN THERMAL REACTION SYSTEMS OF VACUUM RESIDUA

ABSTRACT It has been indicated from analyses of the vicissitude of chemical states and their comparisons with the occurring physical processes in the thermal reaction systems of vacuum residua that the first characteristic state point coincides with the induction period of coke formation, and the third characteristic state point, immediately after which a large amount of coke is yielded, manifests the critical point at which concentration of the neo-asphaltenes generated in-situ by the fast-reaction resins is high enough to approach its phase separation. The industrial implication of the second characteristic state point is not clear enough. It is accordingly pointed out, in combination with the conclusions drawn in the first part of the serial, that the real-time optical microscope tracking of the thermal reaction progress of vacuum residua based on the first and third characteristic state points is feasible on the laboratory scale for forecasting the sudden changes of the physical and/or chemical states of the thermal reaction systems of vacuum residua, and is expected to find applications in the industrial visbreaking process.

Questionable predictions

Examples of inaccurate or questionable predictions exist in the economic, political, social and scientific fields. Predictions about the future states of dynamic physical systems fare somewhat better if the model is accurately known, and if the future inputs are known, at least in an accurate statistical sense. Some procedures, parameters and assumptions that go into prediction have been discussed. Some of the pitfalls and potential problems have been demonstrated by examples.

Fundamental manifestations of symmetry in physics

Five fundamental manifestations of symmetry in physics—reproducibility as symmetry, predictability as symmetry, symmetry of evolution of isolated physical systems, symmetry of states of physical systems, and gauge symmetry—are investigated for their essential meaning and physical significance. The approach is conceptual, to the complete exclusion of mathematical formalism.

Complexity as thermodynamic depth

A measure of complexity for the macroscopic states of physical systems is defined. Called depth, the measure is universal: it applies to all physical systems. The form of the measure is uniquely fixed by the requirement that it be a continuous, additive function of the processes that can result in a state. Applied to a Hamiltonian system, the measure is equal to the difference between the system's coarse- and fine-grained entropy, a quantity that we call thermodynamic depth. The measure satisfies the intuitive requirements that wholly ordered and wholly random systems are not thermodynamically deep and that a complex object together with a copy is not much deeper than the object alone. Applied to systems capable of computation, the measure yields a conventional computational measure of complexity as a special case. The relation of depth and thermodynamic depth to previously proposed definitions of complexity is discussed, and applications to physical, chemical, and mathematical problems are proposed.

On-line estimation of nonlinear physical systems

Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared.

A simple approach to nonlinear estimation of physical systems

Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared.

Spatial Transient Analysis of Inertia-Variant Flexible Mechanical Systems

An analytical method for transient dynamic simulation of large-scale inertia-variant spatial mechanical and structural systems is presented. Multibody systems consisting of interconnected rigid and flexible substructures which may undergo large angular rotations are analyzed. A finite element technique is used to characterize the elastic properties of deformable substructures. A component mode technique is then employed to eliminate insignificant substructure modes. Nonlinear holonomic constraint equations are used to define joints between different substructures. The system equations of motion are written in terms of a mixed set of modal and physical coordinates. A generalized coordinate partitioning technique is then employed to eliminate redundant differential equations. An implicit-explicit numerical integration algorithm solves the remaining set of differential equations and the approximate physical system state is recovered. The transient analysis of a spatial vehicle with flexible chassis is presented to demonstrate the method.

Environment-induced superselection rules

We show how the correlations of a quantum system with other quantum systems may cause one of its observables to behave in a classical manner. In particular, reduction of the wave packet, postulated by von Neumann to explain definiteness of an outcome of an individual observation, can be explained when a realistic model of an apparatus is adopted. Instead of an isolated quantum apparatus with a number of states equal to the number of possible distinct outcomes of the measurement, discussed by von Neumann, we consider an apparatus interacting with other physical systems, described here summarily as The interaction of the quantum apparatus with the environment results in correlations. Correlations impose effective superselection rules which prevent apparatus from appearing in a superposition of states corresponding to different eigenvalues of the privileged pointer observable. It is the propagation of the correlations with the pointer basis states which is ultimately responsible for the choice of the pointer observable. It can be thought of as a process of in which the state of many distinct physical systems becomes correlated with the pointer basis state. Whether these environment systems are regarded as a part of the apparatus setup, or as a part of its environment is irrelevant. What is crucial is the redundancy of the record concerning the pointer observable which is imprinted into the correlations. Eigenspaces of the pointer observable provide a natural basis for the pointer of the quantum apparatus and determine the to-be-measured observable of the quantum system. Decay of those elements of the apparatus-system density matrix, which are off-diagonal in the pointer observable, is caused by the natural evolution of the combined system-apparatus-environment object. For a hypothetical finite environment with $N$ distinct eigenvalues of the apparatus-environment interaction Hamiltonian, off-diagonal terms will decay to become of the order of ${N}^{\ensuremath{-}\frac{1}{2}}$, and will recur only on a Poincar\'e time scale. No recurrences will be observed in realistic circumstances. As the correlations spread through the environment on a time scale typically much shorter than the recurrence time scale calculated for the environment already correlated with the pointer observable, the measurement becomes effectively irreversible. Relevance of this model of the measurement process for the understanding of the second law of thermodynamics and its relation to Bohr's irreversible act of amplification is briefly discussed. The emergence of the pointer observable can be interpreted as a clue about the resolution of the measurement problem in case of no environment. It points towards the possibility that properties of quantum systems have no absolute meaning. Rather, they must be always characterized with respect to other physical systems.

The eigenvalue density of rational Jacobi matrices

The calculation of the density of states of certain physical systems (e.g. the electronic state density of some disordered materials, the nuclear level density, etc.) often reduces to the determination of the density of eigenvalues of a rational Jacobi matrix (i.e. a Jacobi matrix whose elements are rational functions of the suffix) when its dimension N to infinity . Here the asymptotical (N to I) density of eigenvalues of such a matrix is investigated.

The law of perceptual stability: Abstract foundations

Confronted with an object of perception, an individual will spontaneously try to identify unambiguously and consistently all its parts; except in rare instances of "illusory phenomena," he will immediately succeed. This elementary fact is formalized in a law of visual perception. It is used to define sets of stable states for a sensory mode of a biological system. As characterized, stable states are to perception as quantum states are to atomic structure: they represent natural states of physical systems. They are shown to be observable and to have an exact mathematical representation.A class of bounded open subsets of a two-dimensional Euclidean space, whose boundaries are piecewise compact analytic arcs, is used to construct a nontrivial mathematical model for stable states. The finitely many components of this mathematical model of a stable state (image) are mapped onto an object of perception (icon) by perceptual judgments. These judgments, which include the judgment of stability, have an exact interpretation in this model. They unify and make precise such traditional notions of psychology as "Gestalt," "figureground," and "(visual) boundary."Postulates for a general theory of perception are given. They are used to establish a formal relationship between biological and subjective studies of sensory phenomena and so provide a framework in which subjective studies can be used to analyze (their associated) biological processes. In applying these methods to cases, all icons are divided into two classes (the static and dynamic cases). The static case is treated.