scholarly journals Hydrodynamic limit of a coupled Cucker–Smale system with strong and weak internal variable relaxation

2021 ◽  
pp. 1-73
Author(s):  
Jeongho Kim ◽  
David Poyato ◽  
Juan Soler
Keyword(s):  
Hydrodynamic Limit ◽  
Particle Interaction ◽  
Type Equation ◽  
Coupled System ◽  
Internal Variable ◽  
Inertial Effects ◽  
Self Organized ◽  
Weakly Singular ◽  
Background Population ◽  
Two Populations

In this paper, we present the hydrodynamic limit of a multiscale system describing the dynamics of two populations of agents with alignment interactions and the effect of an internal variable. It consists of a kinetic equation coupled with an Euler-type equation inspired by the thermomechanical Cucker–Smale (TCS) model. We propose a novel drag force for the fluid-particle interaction reminiscent of Stokes’ law. While the macroscopic species is regarded as a self-organized background fluid that affects the kinetic species, the latter is assumed sparse and does not affect the macroscopic dynamics. We propose two hyperbolic scalings, in terms of a strong and weak relaxation regime of the internal variable towards the background population. Under each regime, we prove the rigorous hydrodynamic limit towards a coupled system composed of two Euler-type equations. Inertial effects of momentum and internal variable in the kinetic species disappear for strong relaxation, whereas a nontrivial dynamics for the internal variable appears for weak relaxation. Our analysis covers both the case of Lipschitz and weakly singular influence functions.

scholarly journals The emergence and resilience of self-organized governance in coupled infrastructure systems

2020 ◽  
Vol 117 (9) ◽  
pp. 4617-4622 ◽  
Author(s):  
Rachata Muneepeerakul ◽  
John M. Anderies
Keyword(s):  
System Analysis ◽  
Coupled System ◽  
Small Scale ◽  
Shared Resources ◽  
Infrastructure Systems ◽  
Self Organized ◽  
Trade Offs ◽  
Wide Range ◽  
Rigorous Treatment ◽  
Coupled Infrastructure Systems

Studies of small-scale, self-organized social-ecological systems have contributed to our understanding of successful governance of shared resources. However, the lack of formal analytically tractable models of such coupled infrastructure systems makes it difficult to connect this understanding to such concepts as stability, robustness, and resilience, which are increasingly important in considering such systems. In this paper, we mathematically operationalize a widely used conceptual framework via a stylized dynamical model. The model yields a wide range of system outcomes: sustainability or collapse, infrastructure at full or partial capacity, and social agents seeking outside opportunities or exclusively engaging in the system. The low dimensionality of the model enables us to derive these conditions in clear relationships of biophysical and social factors describing the coupled system. Analysis of the model further reveals regime shifts, trade-offs, and potential pitfalls that one may face in governing these self-organized systems. The intuition and insights derived from the model lay ground for more rigorous treatment of robustness and resilience of self-organized coupled infrastructure systems, which can lead to more effective governance.

Logistic Models for Symbiosis, Predator-Prey, and Competition

2010 ◽  
pp. 838-847 ◽  
Author(s):  
Ricardo Lopez-Ruiz ◽  
Danièle Fournier-Prunaret
Keyword(s):  
Logistic Models ◽  
Type Equation ◽  
Coupled System ◽  
Stationary Regime ◽  
Economic Networks ◽  
Predator Prey ◽  
Logistic Equations ◽  
Complex Interactions ◽  
Logistic Mapping ◽  
Dynamical Properties

If one isolated species (corporation) is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species (corporations) can be expressed by a coupled system of two discrete logistic equations. As three basic relationships between two species are present in nature, namely symbiosis, predator-prey, and competition, three different models are obtained. Each model is a cubic two-dimensional discrete logistic-type equation with its own dynamical properties: stationary regime, periodicity, quasi-periodicity, and chaos. We also propose that these models could be useful for thinking in the different interactions happening in the economic world, as for instance for the competition and the collaboration between corporations. Furthermore, these models could be considered as the basic ingredients to construct more complex interactions in the ecological and economic networks.

scholarly journals Asymptotic analysis of Vlasov-type equations under strong local alignment regime

2015 ◽  
Vol 25 (11) ◽  
pp. 2153-2173 ◽  
Author(s):  
Moon-Jin Kang ◽  
Alexis F. Vasseur
Keyword(s):  
Kinetic Equation ◽  
Hyperbolic Conservation Laws ◽  
Hydrodynamic Limit ◽  
Local Equilibrium ◽  
Euler System ◽  
Entropy Method ◽  
Local Alignment ◽  
Hyperbolic Conservation ◽  
Self Organized ◽  
Relative Entropy Method

We consider the hydrodynamic limit of a collisionless and non-diffusive kinetic equation under strong local alignment regime. The local alignment is first considered by Karper, Mellet and Trivisa in [On strong local alignment in the kinetic Cucker–Smale model, in Hyperbolic Conservation Laws and Related Analysis with Applications, Springer Proceedings in Mathematics & Statistics, Vol. 49 (Springer, 2014), pp. 227–242], as a singular limit of an alignment force proposed by Motsch and Tadmor in [A new model for self-organized dynamics and its flocking behavior, J. Statist. Phys. 141 (2011) 923–947]. As the local alignment strongly dominates, a weak solution to the kinetic equation under consideration converges to the local equilibrium, which has the form of mono-kinetic distribution. We use the relative entropy method and weak compactness to rigorously justify the weak convergence of our kinetic equation to the pressureless Euler system.

A model of axonal transport drug delivery

Open Physics ◽  
2012 ◽  
Vol 10 (2) ◽  
Author(s):  
Andrey Kuznetsov
Keyword(s):  
Drug Delivery ◽  
Axonal Transport ◽  
Targeted Drug Delivery ◽  
Coupled System ◽  
Physical Significance ◽  
First Order ◽  
Pharmaceutical Agent ◽  
Active Motor ◽  
Parameter Values ◽  
Two Populations

AbstractIn this paper a model of targeted drug delivery by means of active (motor-driven) axonal transport is developed. The model is motivated by recent experimental research by Filler et al. (A.G. Filler, G.T. Whiteside, M. Bacon, M. Frederickson, F.A. Howe, M.D. Rabinowitz, A.J. Sokoloff, T.W. Deacon, C. Abell, R. Munglani, J.R. Griffiths, B.A. Bell, A.M.L. Lever, Tri-partite complex for axonal transport drug delivery achieves pharmacological effect, Bmc Neuroscience 11 (2010) 8) that reported synthesis and pharmacological efficiency tests of a tri-partite complex designed for axonal transport drug delivery. The developed model accounts for two populations of pharmaceutical agent complexes (PACs): PACs that are transported retrogradely by dynein motors and PACs that are accumulated in the axon at the Nodes of Ranvier. The transitions between these two populations of PACs are described by first-order reactions. An analytical solution of the coupled system of transient equations describing conservations of these two populations of PACs is obtained by using Laplace transform. Numerical results for various combinations of parameter values are presented and their physical significance is discussed.

On the Low Strain Rate Regime of Structural Superplasticity - an Internal Variable Approach

2005 ◽  
Vol 475-479 ◽  
pp. 3007-3012
Author(s):  
Won Kyu Bang ◽  
J.E. Park ◽  
Yong Nam Kwon ◽  
Chong Soo Lee ◽  
Young Won Chang
Keyword(s):  
Threshold Stress ◽  
Type Equation ◽  
Internal Variable ◽  
Mechanical Tests ◽  
Variable Theory ◽  
Fine Grained ◽  
Size Refinement ◽  
Variable Approach ◽  
Internal Variable Theory ◽  
Constitutive Parameters

The superplastic deformation behavior of a fine-grained 7075 Al has been investigated to clarify the issue of threshold stress. A series of mechanical tests has been conducted at various temperatures for the specimens with various grain sizes. The quantitative constitutive parameters have been determined from load relaxation test by applying the internal variable theory of structural superplaticity (SSP) proposed by Chang et al. The GBS flow could be formulated as a viscosity-type equation, characterized by the Newtonian exponent of 1.0. The unresolved issue of threshold stress is clarified and identified as a critical stress required for the GBS. The micro-mechanical roll of grain size refinement has also been manifested in terms of proposed constitutive parameters.

Problem behavior in autism spectrum disorders: A paradigmatic self-organized perspective of network structures

2019 ◽  
Vol 42 ◽  
Author(s):  
Lucio Tonello ◽  
Luca Giacobbi ◽  
Alberto Pettenon ◽  
Alessandro Scuotto ◽  
Massimo Cocchi ◽  
...  
Keyword(s):  
Autism Spectrum Disorder ◽  
Problem Behaviors ◽  
Autism Spectrum ◽  
The Self ◽  
Network Structures ◽  
Self Organized ◽  
Critical Equilibrium ◽  
Self Organized Criticality ◽  
Acute Agitation ◽  
Spectrum Disorders

AbstractAutism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.

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