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Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as a limiting case of differential advection
2014
Physical Review E
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A one-component bistable reaction-diffusion system with asymmetric nonlocal coup ling is derived as limiting case of a two-component activator-inhibitor reaction -diffusion model with differential advection ...
The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusi on system are then compared to the previously studied case of a system with symm etric nonlocal coupling. ...
ACKNOWLEDGMENT We acknowledge financial support from the German Science Foundation DFG in the framework of SFB 910 "Control of Self-Organizing Nonlinear Systems." ...
doi:10.1103/physreve.89.052909
pmid:25353863
fatcat:dmr7e2nf7rehrbe7xvzc67lszy
Preface to the Issue Nonlocal Reaction-Diffusion Equations
2015
Mathematical Modelling of Natural Phenomena
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Nonlocal reaction-diffusion equations in population dynamics Nonlocal reaction-diffusion equations are intensively studied during the last decade in relation with problems in population dynamics and other ...
In comparison with traditional reaction-diffusion equations they possess new mathematical properties and richer nonlinear dynamics. ...
The dynamics of both interacting populations is described by a reaction-diffusion system with nonlocal terms describing migrations. ...
doi:10.1051/mmnp/201510601
fatcat:xqmxs3fgyfg23eny5lqwwsyzlu
Mathematical models for cell migration: a nonlocal perspective
[article]
2019
arXiv
pre-print
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Following a brief introduction and motivation, we give a systematic classification of available PDE models with respect to the type of featured nonlocalities and review some of the mathematical challenges ...
arising from such models, with a focus on analytical aspects. ...
Analysis of models with spatial nonlocalities in reaction terms The analysis of reaction-diffusion equations featuring nonlocalities in source terms is highly challenging, in large part down to classical ...
arXiv:1911.05200v1
fatcat:4ugyp5m76bexpl6zhob7wkbobu
Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications
[article]
2024
arXiv
pre-print
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Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue ...
Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. ...
RM also acknowledges the support of the BERC 2022-2025 program and the Spanish Ministry of Science, Innovation and Universities through the Agencia Estatal de Investigacion (AEI) BCAM Severo Ochoa excellence ...
arXiv:2401.14651v1
fatcat:dxm4ky6xgzeuvhm6x7nfvd5ciy
Implications for(d,p)reaction theory from nonlocal dispersive optical model analysis ofCa40(d,p)Ca41
2016
Physical Review C
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2016 pre-print arXiv:1610.00177v1 fatcat:ppwb64yh2vcwhckplsarai7m5q
The nonlocal dispersive optical model (NLDOM) nucleon potentials are used for the first time in the adiabatic analysis of a (d,p) reaction to generate distorted waves both in the entrance and exit channels ...
Lett. 112, 162502 (2014)] to constrain relevant single-particle physics in a consistent way by imposing the fundamental properties, such as nonlocality, energy-dependence and dispersive relations, that ...
Soon after the publication of [6] , a nonlocal version of the dispersive optical model (NL-DOM) became available for 40 Ca [9] . ...
doi:10.1103/physrevc.94.034609
fatcat:vrgea7h345ejrdvdtkc47f6kti
Preface
2016
Discrete and Continuous Dynamical Systems. Series A
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He was particularly interested in the large time behavior of solutions of reaction-diffusion systems. ...
While Paul Fife contributed to many fields including fluid dynamics and elliptic regularity theory, his main field of research was the qualitative theory of solutions to nonlinear evolution equations of ...
When the reaction term of a nonlocal equation has a gap region in the space variable, not only a transition front but also a blocking solution by a large gap region are exhibited. ...
doi:10.3934/dcds.201702i
fatcat:ihkao4padfep7eticddo7n5nee
Effects of operator nonlocality on closures for multicomponent reactive flows based on dispersion analysis
[article]
2023
arXiv
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Algebraic closure models with spatially nonlocal operators that are associated with both unresolved advective transport and nonlinear reaction terms in a Reynolds-averaged Navier-Stokes context are presented ...
This work extends model forms from weakly-nonlinear extensions of that dispersion theory and the role of nonlocality in the presence of reactions is studied and captured by analytic expressions. ...
In the following sections, we will first develop a model problem based on laminar flows that can capture dynamics neglected in that work for a linear reaction setup that will capture the effects of nonlocality ...
arXiv:2201.10013v2
fatcat:l4mwa723b5hx5mz3gdmww736mu
Effects of an induced three-body force in the incident channel of ( d,p ) reactions
2019
Physical Review C
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We illustrate the role of these terms for the case of ^40Ca(d,p)^41Ca transfer reactions at incident deuteron energies of 11.8, 20 and 56 MeV, using several parameterisations of nonlocal optical potentials ...
A widely accepted practice for treating deuteron breakup in A(d,p)B reactions relies on solving a three-body A+n+p Schrödinger equation with pairwise A-n, A-p and n-p interactions. ...
III we describe their connection to the dynamical part of the nonlocal dispersive optical model (NLDOM). In Sec. VI we discuss nonlocal scattering inputs for the ADWA with NLDOM. In Sec. ...
doi:10.1103/physrevc.99.064612
fatcat:d3v4kh62ifhutc2x5dtau6kyny
Transition form factor of γ→3π in a nonlocal quark model
2017
Physical Review D
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2017 pre-print arXiv:1701.07171v2 fatcat:lu2xfb6wqff3feijaglojoooqaOther Versions
The transition form factor of a gamma into three pions F_3π are studied in a framework of nonlocal chiral quark model. ...
Availability of nonlocality not change a value of transition form factor in chiral limit. ...
ACKNOWLEDGMENTS I thank A. E. Dorokhov, A. E. Radzhabov, D. V. Karlovets for discussion and for close reading. Author thankful to M. V. Polyakov for motivation to study this subject. ...
doi:10.1103/physrevd.95.074025
fatcat:qvlc2nmovnbhnfjqwrj7ib3yty
Wave Propagation in Periodically Supported Nanoribbons: A Nonlocal Elasticity Approach
2013
Journal of Vibration and Acoustics
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The nonlocal length scale is identified via atomistic finite element (FE) models of graphene nanoribbons with Floquet's boundary conditions. ...
Moreover, the nonlocal elasticity solution proposed in this paper captures the dispersive behavior of nanoribbons when an increasing number of flexural modes are considered. ...
(25) , the term related to the in-plane rotation of the CAC bond is equated to the bending strain energy associated with a deep shear beam model. ...
doi:10.1115/1.4023953
fatcat:z577pu77hrhgjpub77grlyo3sq
One-nucleon transfer reactions and the optical potential
[article]
2015
arXiv
pre-print
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The results of a purely phenomenological potential and the optical potential obtained from the dispersive optical model are compared; both point toward the importance of including nonlocality in transfer ...
We provide a summary of new developments in the area of direct reaction theory with a particular focus on one-nucleon transfer reactions. ...
A similar study was performed using the dispersive optical model [19] . ...
arXiv:1509.04700v1
fatcat:rcjz2eil6ngbdgwmwbc6gcuc3a
Bifurcation analysis of a general activator-inhibitor model with nonlocal dispersal
2017
Discrete and continuous dynamical systems. Series B
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Compared with the "spatial averaging" nonlocal dispersal model, our model admits a larger parameter region supporting pattern formations, which is also true if compared with the local reaction-diffusion ...
In this paper, we are mainly concerned with the effect of nonlocal diffusion and dispersal spread on bifurcations of a general activator-inhibitor system in which the activator has a nonlocal dispersal ...
The authors would like to thank all the members of College of William and Mary for their support and hospitality during their visit. ...
doi:10.3934/dcdsb.2020295
fatcat:czvon4ceh5ebjenne3vyod6syu
Lagrangian formulation of continuum with internal long-range interactions
2011
Theoretical and Applied Mechanics Letters
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By this formulation, elastic wave in a rod with the internal long-range interactions is investigated. The dispersion of the elastic wave is predicted. ...
Based on a new definition of nonlocal variable, this paper establishes the Lagrangian formulation for continuum with internal long-range interactions. ...
This dispersion possibly occurs in nano-structures, but it awaits further verification. Fig. 1 . 1 A rod model with the internal long-range interactions a) Corresponding author. ...
doi:10.1063/2.1104206
fatcat:2e3wysmaurcanatpdqzeecv7ua
Invasion Generates Periodic Traveling Waves (Wavetrains) in Predator-Prey Models with Nonlocal Dispersal
2016
SIAM Journal on Applied Mathematics
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However it is important to comment that there is a relatively large literature on ptws in reaction-diffusion models with nonlocal terms in the kinetics. ...
The paper concludes with a comparison between the predictions of the nonlocal model and the corresponding reaction-diffusion model. ...
models of ptw generation behind invasion and those of models with nonlocal dispersal. ...
doi:10.1137/15m1027991
fatcat:4xc3yfelfnaw7mr27pcrcps2ii
Out-of-Plane Elastic Waves in 2D Models of Solids: A Case Study for a Nonlocal Discretization Scheme with Reduced Numerical Dispersion
2015
Mathematical Problems in Engineering
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A denser mesh of degrees of freedom could be a straightforward solution to mitigate numerical dispersion, since it provides more advantageous relation between the model length scale and considered wavelengths ...
Fourier-based nonlocal discretization for continuum mechanics is introduced for a two-dimensional model undergoing out-of-plane wave propagation. ...
Rimoli acknowledge the partial support of the National Science Foundation under Grant CMMI-1130368. ...
doi:10.1155/2015/584081
fatcat:mdi54t4razg6diys55odujt6ti
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