Effective dynamics of reduced models

2021 ◽  
pp. 87-106
Keyword(s):  
Reduced Models ◽  
Effective Dynamics

Hybrid Reduced Model of Rotor

2013 ◽  
Vol 60 (3) ◽  
pp. 319-333
Author(s):  
Rafał Hein ◽  
Cezary Orlikowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hybrid Model ◽  
Rotor System ◽  
Reduced Model ◽  
Order Model ◽  
Gyroscopic Effect ◽  
Reduced Models ◽  
Rigid Finite Element Method ◽  
Low Order

Abstract In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range

scholarly journals Perturbation Analysis of Quantum Reset Models

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Géraldine Haack ◽  
Alain Joye
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Coupling Constant ◽  
Coupling Term ◽  
Open Quantum ◽  
Effective Dynamics ◽  
A Chain

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

scholarly journals Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

1985 ◽  
Vol 40 (7) ◽  
pp. 752-773
Author(s):  
H. Stumpf
Keyword(s):  
Composite Particle ◽  
Particle Interaction ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Statistical Interpretation ◽  
Quantum Field ◽  
Mapping Procedure ◽  
Effective Dynamics ◽  
Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

scholarly journals Global and local reduced models for interacting, heterogeneous agents

2021 ◽  
Vol 31 (7) ◽  
pp. 073139
Author(s):  
Thomas N. Thiem ◽  
Felix P. Kemeth ◽  
Tom Bertalan ◽  
Carlo R. Laing ◽  
Ioannis G. Kevrekidis
Keyword(s):  
Heterogeneous Agents ◽  
Reduced Models ◽  
Global And Local

scholarly journals Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Andreas Bittracher ◽  
Stefan Klus ◽  
Boumediene Hamzi ◽  
Péter Koltai ◽  
Christof Schütte
Keyword(s):  
Stochastic Systems ◽  
Reproducing Kernel ◽  
Learning Algorithm ◽  
Reproducing Kernel Hilbert Space ◽  
Mathematical Framework ◽  
Reaction Coordinates ◽  
Effective Dynamics ◽  
Distortion Bounds ◽  
Low Dimensional ◽  
Metastable Systems

AbstractWe present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.

scholarly journals Effective dynamics of magnetic vortices

2006 ◽  
Vol 199 (2) ◽  
pp. 448-498 ◽  
Author(s):  
S. Gustafson ◽  
I.M. Sigal
Keyword(s):  
Magnetic Vortices ◽  
Effective Dynamics

Energy-Based Model Reduction Methodology for Automated Modeling

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Loucas S. Louca ◽  
Jeffrey L. Stein ◽  
Gregory M. Hulbert
Keyword(s):  
Model Reduction ◽  
Order Reduction ◽  
Process Models ◽  
Model Parameters ◽  
Automated Modeling ◽  
Reduced Models ◽  
System Models ◽  
Quarter Car Model ◽  
Reduction Techniques ◽  
Physical Phenomena

In recent years, algorithms have been developed to help automate the production of dynamic system models. Part of this effort has been the development of algorithms that use modeling metrics for generating minimum complexity models with realization preserving structure and parameters. Existing algorithms, add or remove ideal compliant elements from a model, and consequently do not equally emphasize the contribution of the other fundamental physical phenomena, i.e., ideal inertial or resistive elements, to the overall system behavior. Furthermore, these algorithms have only been developed for linear or linearized models, leaving the automated production of models of nonlinear systems unresolved. Other model reduction techniques suffer from similar limitations due to linearity or the requirement that the reduced models be realization preserving. This paper presents a new modeling metric, activity, which is based on energy. This metric is used to order the importance of all energy elements in a system model. The ranking of the energy elements provides the relative importance of the model parameters and this information is used as a basis to reduce the size of the model and as a type of parameter sensitivity information for system design. The metric is implemented in an automated modeling algorithm called model order reduction algorithm (MORA) that can automatically generate a hierarchical series of reduced models that are realization preserving based on choosing the energy threshold below which energy elements are not included in the model. Finally, MORA is applied to a nonlinear quarter car model to illustrate that energy elements with low activity can be eliminated from the model resulting in a reduced order model, with physically meaningful parameters, which also accurately predicts the behavior of the full model. The activity metric appears to be a valuable metric for automating the reduction of nonlinear system models—providing in the process models that provide better insight and may be more numerically efficient.

Sign in / Sign up

Export Citation Format

Share Document