Modeling of Dynamic Systems with Interval Parameters in the Presence of Singularities

The paper is concerned with the issues of modeling dynamic systems with interval parameters. In previous works, the authors proposed an adaptive interpolation algorithm for solving interval problems; the essence of the algorithm is the dynamic construction of a piecewise polynomial function that interpolates the solution of the problem with a given accuracy. The main problem of applying the algorithm is related to the curse of dimension, i.e., exponential complexity relative to the number of interval uncertainties in parameters. The main objective of this work is to apply the previously proposed adaptive interpolation algorithm to dynamic systems with a large number of interval parameters. In order to reduce the computational complexity of the algorithm, the authors propose using adaptive sparse grids. This article introduces a novelty approach of applying sparse grids to problems with interval uncertainties. The efficiency of the proposed approach has been demonstrated on representative interval problems of nonlinear dynamics and computational materials science.

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Parallel Adaptive Interpolation Algorithm based on Sparse Grids for Modeling Dynamic Systems with Interval Parameters

PROGRAMMNAYA INGENERIA ◽

10.17587/prin.12.395-403 ◽

2021 ◽

Vol 12 (8) ◽

pp. 395-403

Author(s):

A. Yu. Morozov ◽

Keyword(s):

Dynamic Systems ◽

Polynomial Interpolation ◽

Parallel Implementation ◽

Sparse Grids ◽

Piecewise Polynomial Function ◽

Call Graph ◽

Interval Parameters ◽

Computational Costs ◽

Adaptive Interpolation ◽

Grid Nodes

The paper presents a parallel algorithm for adaptive interpolation based on sparse grids for modeling dynamic systems with interval parameters. The idea of the algorithm is to construct a piecewise polynomial function that interpolates the dependence of the solution to the problem on the point values of the interval parameters. In the classical version of the algorithm, polynomial interpolation on complete grids is used, and with a large number of uncertainties, the algorithm becomes difficult to apply due to the exponential growth of computational costs. The use of sparse grids can significantly reduce the computational costs, but nevertheless the complexity of the algorithm in the general case remains exponential with respect to the number of interval parameters. In this regard, the issue of accelerating the algorithm is relevant. The algorithm can be divided into several sets of independent subtasks: updating the values corresponding to the grid nodes; calculation of weighting factors; interpolation of values at new nodes. The last two sets imply parallelization of recursion, so here the techniques for traversing the width of the call graph are mainly used. The parallel implementation of the algorithm was tested on two ODE systems containing two and six interval parameters, respectively, using a different number of computing cores. The results obtained demonstrate the effectiveness of the approaches used.

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Uncertain reduced-order modeling via balanced truncation for structural dynamic systems with interval parameters

2018 AIAA Non-Deterministic Approaches Conference ◽

10.2514/6.2018-2167 ◽

2018 ◽

Author(s):

Xianjia Chen ◽

Zhiping Qiu ◽

Yunlong Li ◽

Nan Jiang

Keyword(s):

Dynamic Systems ◽

Reduced Order Modeling ◽

Balanced Truncation ◽

Structural Dynamic ◽

Reduced Order ◽

Interval Parameters

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Modeling of Dynamic Systems With Interval Parameters

Modelling and Data Analysis ◽

10.17759/mda.2019090401 ◽

2019 ◽

Vol 09 (4) ◽

pp. 5-31

Author(s):

A.Y. Morozov ◽

D.L. Reviznikov

Keyword(s):

Dynamic Systems ◽

Interval Analysis ◽

Interpolation Algorithm ◽

Interval Parameters ◽

Estimates Of Solutions ◽

Software Libraries ◽

Adaptive Interpolation ◽

Over Time

The paper provides a review of existing libraries and methods of modeling dynamic systems with interval parameters. Available software libraries AWA, VNODELP, COZY Infinity, RiOT, FlowStar, as well as the author’s adaptive interpolation algorithm are considered. The traditional software for interval analysis gives guaranteed estimates of solutions, however, over time, these estimates become extremely significantly overstated. Due to the use of a fundamentally different approach to constructing solutions, the adaptive interpolation algorithm is not subject to the accumulation of errors, determines the boundaries of solutions with controlled accuracy, and works much faster than analogues.

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Phase behavior of cationic and anionic surfactants at low concentrations

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100123878 ◽

1992 ◽

Vol 50 (1) ◽

pp. 694-695

Author(s):

E. Naranjo

Keyword(s):

Phase Behavior ◽

Structural Characterization ◽

Dynamic Systems ◽

Anionic Surfactants ◽

Intermolecular Forces ◽

Stable Form ◽

Surfactant Mixtures ◽

Low Concentrations ◽

Cationic And Anionic Surfactants ◽

General Method

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.

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Improving Feeding Outcomes in the NICU: Moving From Volume-Driven to Infant-Driven Feeding

Perspectives on Swallowing and Swallowing Disorders (Dysphagia) ◽

10.1044/sasd19.3.68 ◽

2010 ◽

Vol 19 (3) ◽

pp. 68-74 ◽

Cited By ~ 9

Author(s):

Catherine S. Shaker

Keyword(s):

Intensive Care Unit ◽

Dynamic Systems ◽

Neonatal Intensive Care ◽

Well Being ◽

Dynamic Systems Theory ◽

Feeding Problems ◽

Care Giving ◽

Extremely Preterm ◽

Extremely Preterm Infants

Current research on feeding outcomes after discharge from the neonatal intensive care unit (NICU) suggests a need to critically look at the early underpinnings of persistent feeding problems in extremely preterm infants. Concepts of dynamic systems theory and sensitive care-giving are used to describe the specialized needs of this fragile population related to the emergence of safe and successful feeding and swallowing. Focusing on the infant as a co-regulatory partner and embracing a framework of an infant-driven, versus volume-driven, feeding approach are highlighted as best supporting the preterm infant's developmental strivings and long-term well-being.

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A Dynamic Systems Approach to Personality

European Psychologist ◽

10.1027//1016-9040.6.3.172 ◽

2001 ◽

Vol 6 (3) ◽

pp. 172-176 ◽

Cited By ~ 14

Author(s):

Lawrence A. Pervin

Keyword(s):

Dynamic Systems ◽

Systems Approach ◽

Biological Processes ◽

Recent Advances ◽

Dynamic View ◽

The Future ◽

History Of

David Magnusson has been the most articulate spokesperson for a holistic, systems approach to personality. This paper considers three concepts relevant to a dynamic systems approach to personality: dynamics, systems, and levels. Some of the history of a dynamic view is traced, leading to an emphasis on the need for stressing the interplay among goals. Concepts such as multidetermination, equipotentiality, and equifinality are shown to be important aspects of a systems approach. Finally, attention is drawn to the question of levels of description, analysis, and explanation in a theory of personality. The importance of the issue is emphasized in relation to recent advances in our understanding of biological processes. Integrating such advances into a theory of personality while avoiding the danger of reductionism is a challenge for the future.

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Dynamic Systems for Everyone

Contemporary Psychology ◽

10.1037/004523 ◽

1996 ◽

Vol 41 (10) ◽

pp. 1002-1003

Author(s):

Esther Thelen

Keyword(s):

Dynamic Systems

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