scholarly journals On the physical nudging equations

2021 ◽  
Author(s):  
Giovanni Conti ◽  
Ali Aydoğdu ◽  
Silvio Gualdi ◽  
Antonio Navarra ◽  
Joe Tribbia
Keyword(s):  
Data Assimilation ◽  
Conjugate Gradient ◽  
Finite Time ◽  
Statistical Physics ◽  
Ad Hoc ◽  
Gaussian White Noise ◽  
Bohmian Mechanics ◽  
Langevin Equations ◽  
Noise Limit ◽  
Dynamical Information

AbstractIn this work we show how it is possible to derive a new set of nudging equations, a tool still used in many data assimilation problems, starting from statistical physics considerations and availing ourselves of stochastic parameterizations that take into account unresolved interactions. The fluctuations used are thought of as Gaussian white noise with zero mean. The derivation is based on the conditioned Langevin dynamics technique. Exploiting the relation between the Fokker–Planck and the Langevin equations, the nudging equations are derived for a maximally observed system that converges towards the observations in finite time. The new nudging term found is the analog of the so called quantum potential of the Bohmian mechanics. In order to make the new nudging equations feasible for practical computations, two approximations are developed and used as bases from which extending this tool to non-perfectly observed systems. By means of a physical framework, in the zero noise limit, all the physical nudging parameters are fixed by the model under study and there is no need to tune other free ad-hoc variables. The limit of zero noise shows that also for the classical nudging equations it is necessary to use dynamical information to correct the typical relaxation term. A comparison of these approximations with a 3DVar scheme, that use a conjugate gradient minimization, is then shown in a series of four twin experiments that exploit low order chaotic models.

scholarly journals Synchronicity in predictive modelling: a new view of data assimilation

2006 ◽  
Vol 13 (6) ◽  
pp. 601-612 ◽  
Author(s):  
G. S. Duane ◽  
J. J. Tribbia ◽  
J. B. Weiss
Keyword(s):  
Dynamical Systems ◽  
Data Assimilation ◽  
Ad Hoc ◽  
Predictive Modelling ◽  
Dimensional System ◽  
General View ◽  
Machine Perception ◽  
Loosely Coupled ◽  
Unidirectional Flow ◽  
Observational Noise

Abstract. The problem of data assimilation can be viewed as one of synchronizing two dynamical systems, one representing "truth" and the other representing "model", with a unidirectional flow of information between the two. Synchronization of truth and model defines a general view of data assimilation, as machine perception, that is reminiscent of the Jung-Pauli notion of synchronicity between matter and mind. The dynamical systems paradigm of the synchronization of a pair of loosely coupled chaotic systems is expected to be useful because quasi-2D geophysical fluid models have been shown to synchronize when only medium-scale modes are coupled. The synchronization approach is equivalent to standard approaches based on least-squares optimization, including Kalman filtering, except in highly non-linear regions of state space where observational noise links regimes with qualitatively different dynamics. The synchronization approach is used to calculate covariance inflation factors from parameters describing the bimodality of a one-dimensional system. The factors agree in overall magnitude with those used in operational practice on an ad hoc basis. The calculation is robust against the introduction of stochastic model error arising from unresolved scales.

Analysis of the interaction between particles in non-ideal quasi-equilibrium extended systems

2010 ◽  
Vol 76 (3-4) ◽  
pp. 593-602
Author(s):  
O. S. VAULINA ◽  
E. A. LISIN ◽  
A. V. GAVRIKOV ◽  
O. F. PETROV ◽  
V. E. FORTOV
Keyword(s):  
Inverse Problem ◽  
Radio Frequency ◽  
Dusty Plasma ◽  
Statistical Physics ◽  
Dust Particles ◽  
Langevin Equations ◽  
Quasi Equilibrium ◽  
Experimental Application ◽  
Extended Systems ◽  
Radio Frequency Discharge

AbstractTwo techniques for the analysis of the interaction between particles in non-ideal quasi-equilibrium extended systems are considered. The first technique is based on a solution of the inverse problem describing the movement of dust particles by a system of Langevin equations. The second technique proceeds from the basic integral approaches of statistical physics. The conditions for the correct use of these techniques are presented, together with the results of their experimental application for the analysis of inter-grain interactions in the dusty plasma of radio frequency discharge.

scholarly journals The Problem of Engines in Statistical Physics

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1095
Author(s):  
Robert Alicki ◽  
David Gelbwaser-Klimovsky ◽  
Alejandro Jenkins
Keyword(s):  
Statistical Physics ◽  
Degrees Of Freedom ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Equations Of Motion ◽  
Blind Spot ◽  
Langevin Equations ◽  
External Loading ◽  
Realistic Description ◽  
Irreversible Dynamics

Engines are open systems that can generate work cyclically at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their dynamics in time a theoretical blind spot. This has hampered the usefulness of statistical mechanics applied to active systems, including living matter. We argue that recent advances in the theory of open quantum systems, coupled with renewed interest in understanding how active forces result from positive feedback between different macroscopic degrees of freedom in the presence of dissipation, point to a more realistic description of autonomous engines. We propose a general conceptualization of an engine that helps clarify the distinction between its heat and work outputs. Based on this, we show how the external loading force and the thermal noise may be incorporated into the relevant equations of motion. This modifies the usual Fokker–Planck and Langevin equations, offering a thermodynamically complete formulation of the irreversible dynamics of simple oscillating and rotating engines.

Statistical Physics and Thermodynamics

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Statistical Physics ◽  
Ad Hoc ◽  
Macroscopic Scale ◽  
Classical Probability ◽  
Heat Engines ◽  
Statistical Framework ◽  
Wide Range ◽  
Key Concepts ◽  
Laws Of Thermodynamics ◽  
Macroscopic Domain

Statistical physics and thermodynamics describe the behaviour of systems on the macroscopic scale. Their methods are applicable to a wide range of phenomena: from heat engines to chemical reactions, from the interior of stars to the melting of ice. Indeed, the laws of thermodynamics are among the most universal ones of all laws of physics. Yet this subject can prove difficult to grasp. Many view thermodynamics as merely a collection of ad hoc recipes, or are confused by unfamiliar novel concepts, such as the entropy, which have little in common with the theories to which students have got accustomed in other areas of physics. This text provides a concise yet thorough introduction to the key concepts which underlie statistical physics and thermodynamics. It begins with a review of classical probability theory and quantum theory, as well as a careful discussion of the notions of information and entropy, prior to embarking on the development of statistical physics proper. The crucial steps leading from the microscopic to the macroscopic domain are rendered transparent. In particular, the laws of thermodynamics are shown to emerge as natural consequences of the statistical framework. While the emphasis is on clarifying the basic concepts, the text also contains many applications and classroom-tested exercises, covering all major topics of a standard course on statistical physics and thermodynamics. The text is suited both for a one-semester course at the advanced undergraduate or beginning graduate level and as a self-contained tutorial guide for students in physics, chemistry, and engineering.

scholarly journals Controlling Noise in Ensemble Data Assimilation Schemes

2010 ◽  
Vol 138 (5) ◽  
pp. 1502-1512 ◽  
Author(s):  
Malaquias Peña ◽  
Zoltan Toth ◽  
Mozheng Wei
Keyword(s):  
Data Assimilation ◽  
Ad Hoc ◽  
Forecast Accuracy ◽  
Covariance Structure ◽  
Sampling Errors ◽  
Background Error ◽  
Forecast Performance ◽  
Error Covariance ◽  
Additional Noise ◽  
Filter Divergence

Abstract A variety of ad hoc procedures have been developed to prevent filter divergence in ensemble-based data assimilation schemes. These procedures are necessary to reduce the impacts of sampling errors in the background error covariance matrix derived from a limited-size ensemble. The procedures amount to the introduction of additional noise into the assimilation process, possibly reducing the accuracy of the resulting analyses. The effects of this noise on analysis and forecast performance are investigated in a perfect model scenario. Alternative schemes aimed at controlling the unintended injection of noise are proposed and compared. Improved analysis and forecast accuracy is observed in schemes with minimal alteration to the evolving ensemble-based covariance structure.

scholarly journals Single-Precision in the Tangent-Linear and Adjoint Models of Incremental 4D-Var

2020 ◽  
Vol 148 (4) ◽  
pp. 1541-1552 ◽  
Author(s):  
Sam Hatfield ◽  
Andrew McRae ◽  
Tim Palmer ◽  
Peter Düben
Keyword(s):  
Data Assimilation ◽  
Conjugate Gradient ◽  
Standard Technique ◽  
Gradient Algorithm ◽  
Double Precision ◽  
Single Precision ◽  
Minimization Procedure ◽  
Quasigeostrophic Model ◽  
Numerical Precision ◽  
Assimilation Scheme

Abstract The use of single-precision arithmetic in ECMWF’s forecasting model gave a 40% reduction in wall-clock time over double-precision, with no decrease in forecast quality. However, using reduced-precision in 4D-Var data assimilation is relatively unexplored and there are potential issues with using single-precision in the tangent-linear and adjoint models. Here, we present the results of reducing numerical precision in an incremental 4D-Var data assimilation scheme, with an underlying two-layer quasigeostrophic model. The minimizer used is the conjugate gradient method. We show how reducing precision increases the asymmetry between the tangent-linear and adjoint models. For ill-conditioned problems, this leads to a loss of orthogonality among the residuals of the conjugate gradient algorithm, which slows the convergence of the minimization procedure. However, we also show that a standard technique, reorthogonalization, eliminates these issues and therefore could allow the use of single-precision arithmetic. This work is carried out within ECMWF’s data assimilation framework, the Object Oriented Prediction System.

scholarly journals FITS: A Finite-Time Reputation System for Cooperation in Wireless Ad Hoc Networks

2011 ◽  
Vol 60 (7) ◽  
pp. 1045-1056 ◽  
Author(s):  
Tingting Chen ◽  
Fan Wu ◽  
Sheng Zhong
Keyword(s):  
Ad Hoc Networks ◽  
Wireless Ad Hoc Networks ◽  
Finite Time ◽  
Ad Hoc ◽  
Reputation System ◽  
Hoc Networks

scholarly journals Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

2012 ◽  
Vol 19 (1) ◽  
pp. 9-22 ◽  
Author(s):  
V. Lucarini ◽  
D. Faranda ◽  
M. Willeit
Keyword(s):  
Stochastic Resonance ◽  
Ad Hoc ◽  
Thermohaline Circulation ◽  
Statistical Properties ◽  
Langevin Equations ◽  
Oceanic Circulation ◽  
One Dimensional ◽  
Bistable Systems ◽  
Box Models ◽  
Multistable Systems

Abstract. The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

Preconditioning of variational data assimilation and the use of a bi-conjugate gradient method

2012 ◽  
Vol 139 (672) ◽  
pp. 731-741 ◽  
Author(s):  
Amal El Akkraoui ◽  
Yannick Trémolet ◽  
Ricardo Todling
Keyword(s):  
Data Assimilation ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Variational Data Assimilation

scholarly journals About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Manuel De la Sen ◽  
Asier Ibeas ◽  
Raul Nistal
Keyword(s):  
Epidemic Model ◽  
Finite Time ◽  
Adaptive Sampling ◽  
Ad Hoc ◽  
The State ◽  
Time Interval ◽  
Control Effort ◽  
Control Objective ◽  
Output Controllability ◽  
Point To Point

This paper studies some basic properties of an SEIR (Susceptible-Exposed-Infectious-Recovered) epidemic model subject to vaccination and treatment controls. Firstly, the basic stability, boundedness, and nonnegativity of the state trajectory solution are investigated. Then, the problem of partial state reachability from a certain state value to a targeted one in finite time is focused on since it turns out that epidemic models are, because of their nature, neither (state) controllable from a given state to the origin nor reachable from a given initial condition. The particular formal statement of the partial reachability is focused on as a problem of output-reachability by defining a measurable output or lower dimension than that of the state. A special case of interest is that when the output is defined as the infectious subpopulation to be step-to-step tracked under suitable amounts being compatible with the required constraints. As a result, and provided that the output-controllability Gramian is nonsingular on a certain time interval of interest, a feedback control effort might be designed so that a prescribed value of the output can be approximately tracked. A linearization approximation is performed to simplify and facilitate the above task which is based on a point-to-point linearization of the solution trajectory. To this end, an “ad hoc” sampled approximate output trajectory is defined as control objective to be targeted through a point-wise calculated Jacobian matrix. A supervised appropriate restatement of the targeted suited sampled output values is redefined, if necessary, to make the initial proposed sampled trajectory compatible with the various needed constraints on nonnegativity and control boundedness. The design can be optionally performed under constant or adaptive sampling rates. Finally, some numerical examples are given to test the theoretical aspects and the design efficiency of the model.

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