scholarly journals On the concept of dynamical reduction: the case of coupled oscillators

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190041 ◽  
Author(s):  
Yoshiki Kuramoto ◽  
Hiroya Nakao
Keyword(s):  
Degrees Of Freedom ◽  
Structural Similarity ◽  
Dynamical Interaction ◽  
Phase Reduction ◽  
Dynamical Reduction ◽  
Reduction Methods ◽  
Centre Manifold Reduction ◽  
New Formulation ◽  
Dynamical Degrees ◽  
Discrete Populations

An overview is given on two representative methods of dynamical reduction known as centre-manifold reduction and phase reduction . These theories are presented in a somewhat more unified fashion than the theories in the past. The target systems of reduction are coupled limit-cycle oscillators. Particular emphasis is placed on the remarkable structural similarity existing between these theories. While the two basic principles, i.e. (i) reduction of dynamical degrees of freedom and (ii) transformation of reduced evolution equation to a canonical form, are shared commonly by reduction methods in general, it is shown how these principles are incorporated into the above two reduction theories in a coherent manner. Regarding the phase reduction, a new formulation of perturbative expansion is presented for discrete populations of oscillators. The style of description is intended to be so informal that one may digest, without being bothered with technicalities, what has been done after all under the word reduction . This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

scholarly journals An Existence Theory for Gravity–Capillary Solitary Water Waves

Water Waves ◽  
2021 ◽  
Author(s):  
M. D. Groves
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Applied Mathematics ◽  
Spatial Dynamics ◽  
Existence Theory ◽  
Water Wave Problem ◽  
Reduction Methods ◽  
Centre Manifold Reduction ◽  
Weak Surface ◽  
The One

AbstractIn the applied mathematics literature solitary gravity–capillary water waves are modelled by approximating the standard governing equations for water waves by a Korteweg-de Vries equation (for strong surface tension) or a nonlinear Schrödinger equation (for weak surface tension). These formal arguments have been justified by sophisticated techniques such as spatial dynamics and centre-manifold reduction methods on the one hand and variational methods on the other. This article presents a complete, self-contained account of an alternative, simpler approach in which one works directly with the Zakharov–Craig–Sulem formulation of the water-wave problem and uses only rudimentary fixed-point arguments and Fourier analysis.

Interface Reduction in Craig-Bampton Component Mode Synthesis by Orthogonal Polynomial Series

2017 ◽  
Author(s):  
Luigi Carassale ◽  
Mirko Maurici
Keyword(s):  
Degrees Of Freedom ◽  
Axial Compressor ◽  
Component Mode Synthesis ◽  
Reduction Techniques ◽  
Interface Reduction ◽  
Reduction Methods ◽  
Interface Displacement ◽  
Polynomial Series ◽  
Efficient Representation

The component mode synthesis based on the Craig-Bampton method has two strong limitations that appear when the number of the interface degrees of freedom is large. First, the reduced-order model obtained is overweighed by many unnecessary degrees of freedom. Second, the reduction step may become extremely time consuming. Several interface reduction techniques addressed successfully the former problem, while the latter remains open. In this paper we tackle this latter problem through a simple interface-reduction technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing interface reduction methods on a case study regarding a rotor blade of an axial compressor.

scholarly journals Implementing model reduction to the JuliaFEM platform

2018 ◽  
Vol 51 (1) ◽  
pp. 36-54 ◽  
Author(s):  
Marja Liisa Rapo ◽  
Jukka Aho ◽  
Hannu Koivurova ◽  
Tero Frondelius
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Reduction ◽  
Open Source ◽  
Degrees Of Freedom ◽  
Mass Matrices ◽  
Dynamic Condensation ◽  
Dynamic Analyses ◽  
Reduction Methods ◽  
Large Model

JuliaFEM is an open source finite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper first describes the JuliaFEM concept briefly after which it presents the theory of model reduction, and finally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

scholarly journals SOLUTION TO 2+1 GRAVITY IN DREIBEIN FORMALISM

1994 ◽  
Vol 03 (01) ◽  
pp. 131-137 ◽  
Author(s):  
W.G. UNRUH
Keyword(s):  
General Relativity ◽  
Degrees Of Freedom ◽  
Closed Timelike Curves ◽  
Original Theory ◽  
Arbitrary Genus ◽  
Genus 2 ◽  
Genus Two ◽  
Dynamical Degrees

This paper outlines the reduction of the dreibein formalism of 2+1 General Relativity to the dynamical degrees of freedom for a genus 2 (and by extension for an arbitrary genus) two space. The resulting dynamical variables of the reduced theory are global holonomies and are constants of the motion of the original theory. The relation to geometry and closed timelike curves is briefly described.

Dynamical Degrees of Freedom of DNA Sequences by Local and Global Short-Range Prediction

Fractals ◽  
1997 ◽  
Vol 05 (01) ◽  
pp. 1-10
Author(s):  
M. Ragosta ◽  
C. Serio ◽  
M. T. Lanfredi ◽  
M. Macchiato
Keyword(s):  
Dna Sequences ◽  
Degrees Of Freedom ◽  
Nonlinear Process ◽  
Short Term ◽  
Chaotic Motions ◽  
Deterministic Systems ◽  
Predictive Skill ◽  
Low Dimensional ◽  
Dynamical Degrees ◽  
Insight Into

The dynamical properties of DNA sequence samples have been analyzed on the basis of a procedure able to distinguish chaos from randomness. The procedure relies on the concept of short-term (range) predictability of low-dimensional chaotic motions and can distinguish merely linear stochastic processes, e.g. fractional Brownian motion, from truly nonlinear deterministic systems. The method consists in obtaining forecasts on the basis of past events in the sequence. Two forecasting strategies are used. The local strategy views the sequence as the outcome of a nonlinear process, whereas the global approach considers the series as the outcome of a linear stochastic process. For both approaches, the predictive skill is computed and their inter-comparison allows us to get insight into and an understanding of the structure of DNA sequences. Nucleotidic sequences belonging to different taxonomic and functional groups have been analyzed. Different behaviors have been detected according to the existence of finite correlation dimension for specific groups of sequences.

scholarly journals FROM BRICKS TO QUASINORMAL MODES: A NEW PERSPECTIVE ON BLACK HOLE ENTROPY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342027 ◽  
Author(s):  
MICHELE ARZANO ◽  
STEFANO BIANCO ◽  
OLAF DREYER
Keyword(s):  
Black Hole ◽  
Short Distance ◽  
Degrees Of Freedom ◽  
Quasinormal Modes ◽  
Black Hole Entropy ◽  
Quantum Field ◽  
Extended Region ◽  
New Perspective ◽  
The Right ◽  
Dynamical Degrees

Calculations of black hole entropy based on the counting of modes of a quantum field propagating in a Schwarzschild background need to be regularized in the vicinity of the horizon. To obtain the Bekenstein–Hawking result, the short distance cut-off needs to be fixed by hand. In this note, we give an argument for obtaining this cut-off in a natural fashion. We do this by modeling the black hole by its set of quasinormal modes (QNMs). The horizon then becomes a extended region: the quantum ergosphere. The interaction of the quantum ergosphere and the quantum field provides a natural regularization mechanism. The width of the quantum ergosphere provides the right cut-off for the entropy calculation. We arrive at a dual picture of black hole entropy. The entropy of the black hole is given both by the entropy of the quantum field in the bulk and the dynamical degrees of freedom on the horizon.

Do different national samples yield similar dimensions of national culture?

2015 ◽  
Vol 22 (2) ◽  
pp. 259-277 ◽  
Author(s):  
Michael Minkov ◽  
Michael Harris Bond ◽  
Vesselin Blagoev
Keyword(s):  
National Culture ◽  
Data Reduction ◽  
Structural Similarity ◽  
Skilled Workers ◽  
Content Type ◽  
Value Structures ◽  
National Representation ◽  
Values And Beliefs ◽  
Reduction Methods ◽  
Data Reduction Method

Purpose – Cross-national studies of employees’ values and beliefs have extracted dimensions of national culture from diverse samples of employees. The purpose of this paper is to find out if this sample diversity impacts the nature of the extracted dimensions: is a given dimension replicable across diverse samples (such as managers vs skilled workers?). Design/methodology/approach – The authors analyzed a set of values from the World Values Survey, comparing nation-level value structures from four types of samples in 46 countries: national representation, managers, experts without supervisory duties, and skilled workers. The authors analyzed the data with, and simultaneously compared, two data reduction methods: multidimensional scaling (MDS) plots (Shalom Schwartz’s preferred method) vs exploratory factor analysis (EFA). Findings – MDS plots suggested structural similarity across the four samples, whereas EFA suggests divergence. Research limitations/implications – Whether dimensions of national culture replicate across different samples or not depends on the data reduction method. There is no one best method in an abstract sense. Researchers’ choice of method should be contingent on their research philosophy: theory-driven vs empirical. Originality/value – No such study has been published previously.

scholarly journals Comparative Study of Blades Reduced Order Models With Geometrical Nonlinearities and Contact Interfaces

2020 ◽  
Author(s):  
Elise Delhez ◽  
Florence Nyssen ◽  
Jean-Claude Golinval ◽  
Alain Batailly
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Performance Indicator ◽  
Element Model ◽  
Reduced Order Models ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Reduction Methods ◽  
Blade Tip ◽  
Reduced Space

Abstract This paper investigates the use of different model reduction methods accounting for geometric nonlinearities. These methods are adapted to retain physical degrees-of-freedom in the reduced space in order to ease contact treatment. These reduction methods are applied to a 3D finite element model of an industrial compressor blade (NASA rotor 37). In order to compare the different reduction methods, a scalar indicator is defined. This performance indicator allows to quantify the accuracy of the predicted displacement both locally (at the blade tip) and globally. The robustness of each method with respect to variations of the external excitation is also assessed. The performances of the reduction methods are then compared in the case of frictional contact between the blade tip and the surrounding casing. This work brings evidence that reduced order models provide a computationally efficient alternative to full order finite element models for the accurate prediction of the time response of structures with both distributed and localized nonlinearities.

Inhomogeneous Folding Modes in Infinite Lattices of Rigid Triangulated Miura-ori

2021 ◽  
Author(s):  
Anandaroop Lahiri ◽  
Phanisri P. Pratapa
Keyword(s):  
Degrees Of Freedom ◽  
Null Space ◽  
Acoustic Metamaterials ◽  
One Dimensional ◽  
Infinite Lattices ◽  
Nodal Displacements ◽  
Displacement Based ◽  
New Formulation ◽  
Hinge Model ◽  
Deformation Modes

Abstract Infinite two-dimensional tessellations of triangulated Miura-ori with rigid panels are known to exhibit only homogeneous modes of folding, thereby limiting their usefulness in engineering applications. In this work, we show that the corresponding one-dimensional lattices are less restricted and can exhibit inhomogeneous folding modes of deformation. We demonstrate this by looking at the modes in the null space of Bloch-reduced compatibility matrix in a nodal-displacement-based formulation, that is typically employed in the context of origami structural analysis. We compute the deformation modes that vary non-uniformly across the lattice depending on their wavelength, and identify the minimal number of modes that can represent such deformations. We then present a more efficient formulation based on folding-angles to study the deformation modes of infinite one-dimensional rigid triangulated origami lattices. We derive the degrees of freedom of the tessellations in terms of the minimal number of folding-angles that are required to capture the periodic inhomogeneous deformations of the infinite lattices. Within this formulation, we provide the framework to analytically derive the stiffness matrix of the lattice. Finally, we verify the new formulation by comparing the results with the bar-and-hinge model that is based on nodal-displacements. The observations from our work could have implications for the use of rigid panel origami lattices as acoustic metamaterials.

Improvement of a Reduced Torsional Model by Means of Parameter Identification

1989 ◽  
Vol 111 (1) ◽  
pp. 17-26 ◽  
Author(s):  
P. Schwibinger ◽  
R. Nordmann
Keyword(s):  
Finite Element ◽  
Mechanical Model ◽  
Degrees Of Freedom ◽  
Short Circuit ◽  
Original System ◽  
Element Model ◽  
The Finite Element Method ◽  
System A ◽  
Reduction Methods ◽  
Short Circuits

Turbogenerator sets in operation may be excited to transient torsional vibrations by dynamic electrical moments at the generator due to short-circuits or faulty synchronization. For the solution of the torsional vibration problem it is essential to find an appropriate torsional model of the original system. A common approach is to model the torsional system finely by the finite element method which normally results in a very accurate mechanical model with many degrees of freedom (DOF). However for some applications it is desirable to have a torsional model with a reduced number of DOF which reproduces the original system exactly only in the lower eigenfrequencies and modes. This paper describes a method which allows finding a most accurate reduced torsional model with discrete masses and springs from a finite element model with many DOF. The results for the eigenfrequencies, the modes, and internal moments due to a short-circuit excitation of a 600 MW turbogenerator set are presented. They are compared with other reduction methods.

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