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Identifiability of interaction kernels in mean-field equations of interacting particles [article]

Quanjun Lang, Fei Lu
2022 arXiv   pre-print
We provide a complete characterization of the identifiability of interaction kernels in mean-field equations for interacting particle systems.  ...  We consider two data adaptive L^2 spaces, one with the Lebesgue measure and the other with an exploration measure intrinsic to the mean-field equation.  ...  Introduction We study the identifiability of the interaction kernel K true from data consisting a solution of the McKean-Vlasov mean-field equation of interacting particles B t u " ν∆u `divrupK true ˚uqs  ... 
arXiv:2106.05565v3 fatcat:s6byzlolsjeofa4vfrj7rzwi5e

Particle-Based Fluid Simulation for Interactive Applications [article]

Matthias Müller, David Charypar, Markus Gross
2003 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation - SCA '04  
Our animation method is fast enough to be used in interactive systems and to allow for user interaction with models consisting of up to 5000 particles.  ...  In addition, the particles can directly be used to render the surface of the fluid.  ...  is symmetric because it uses the arithmetic mean of the pressures of interacting particles.  ... 
doi:10.2312/sca03/154-159 fatcat:knaqshc6tbdbxmg5i5cfjzxvw4

PAIRING CORRELATIONS BEYOND THE MEAN FIELD

M. BENDER, T. DUGUET
2007 International Journal of Modern Physics E  
We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations  ...  are done using an energy functional in the spirit of a naive generalized density functional theory.  ...  Robledo for many inspiring and clarifying discussions on the appearance and interpretation of, and the threat posed by, the divergence and step in particle-number projected EDF.  ... 
doi:10.1142/s0218301307005673 fatcat:re2cn6dag5esffoqi5xzx7wbnq

Fluctuations impact on a pattern-forming model of population dynamics with non-local interactions

Cristóbal López, Emilio Hernández-García
2004 Physica D : Non-linear phenomena  
A model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters.  ...  To this end, a deterministic mean-field description, including a linear stability and a weakly nonlinear analysis, is given and compared with the particle model.  ...  C.L. is a "Ramón y Cajal" fellow of the Spanish MEC.  ... 
doi:10.1016/j.physd.2004.08.016 fatcat:enaqtdfo7vbitdo3ebv53bgtne

Synthetic Flux Attachment [article]

Gerard Valentí-Rojas, Niclas Westerberg, Patrik Öhberg
2020 arXiv   pre-print
At a mean field level, we recover the action of a "charged" superfluid minimally coupled to both a background and a Chern-Simons gauge field.  ...  In doing so, we identify the U(1) Chern-Simons gauge field as a singular density-dependent gauge potential, which in turn can be expressed as a Berry connection.  ...  It is tempting to try to find an interaction kernel for which a simple choice of the laser phase would yield equation (5a).  ... 
arXiv:2003.14339v4 fatcat:r3kn63wesffllmwb7ip4glovce

Anyonic defect braiding and spontaneous chiral symmetry breaking in dihedral liquid crystals [article]

Alexander Mietke, Jörn Dunkel
2021 arXiv   pre-print
Analytic solutions and simulations of the mean-field theory further predict a novel spontaneous chiral symmetry breaking transition in anti-aligning DLCs, in quantitative agreement with the patterns observed  ...  in particle simulations.  ...  Universal mean-field equation In the limit of a constant particle density, a unified mean-field description of 2D monodisperse DLCs can be given in terms of a complex-valued scalar order parameter field  ... 
arXiv:2011.04648v3 fatcat:foiijnmyzne37ckdcr24xalqge

Nonequilibrium dynamics of charged particles in a quantized electromagnetic field: causal, stable and self-consistent dynamics from 1/cexpansion

C H Fleming, P R Johnson, B L Hu
2012 Journal of Physics A: Mathematical and Theoretical  
We derive from a microscopic Hamiltonian a set of stochastic equations of motion for a system of spinless charged particles in an electromagnetic (EM) field based on a consistent application of a dimensionful  ...  With self-consistent backreaction of the EM field included we show that this approach yields causal and runaway-free equations of motion, provides new insights into charged particle backreaction, and naturally  ...  ACKNOWLEDGMENTS We would like to thank Albert Roura for discussions of his related work on the radiation-reaction problem.  ... 
doi:10.1088/1751-8113/45/25/255002 fatcat:qvresjkinjcfbhkfps3msb4ogm

Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods

Eric Bertin, Aparna Baskaran, Hugues Chaté, M. Cristina Marchetti
2015 Physical Review E  
We first show that in the simple case of point-like particles with only alignment interactions, the continuum equations obtained have the same structure in both cases.  ...  Considering systems of self-propelled polar particles with nematic interactions ("rods"), we compare the continuum equations describing the evolution of polar and nematic order parameters, derived either  ...  APPENDIX: NONLOCAL AVERAGE TORQUE In this Appendix, we briefly sketch the derivation of the Fourier transform of the Smoluchowski equation in the case of weakly nonlocal interactions affecting the torque  ... 
doi:10.1103/physreve.92.042141 pmid:26565202 fatcat:sj4zbyw4zjgyvkt47ipi3edszi

Smoothed Particles: A new paradigm for animating highly deformable bodies [chapter]

Mathieu Desbrun, Marie-Paule Gascuel
1996 Eurographics  
Animation requires a linear complexity in the number of particles, offering reasonable time and memory use. * iMAGIS is a joint project  ...  They ensure valid and stable simulation of state equations that describe the physical behavior of the material.  ...  Aknowledgements The authors would like to thank Eugene Fiume for pointing us to SPH and for early discussions, Andy Hanson for his continuous help, and François Faure and Rémi Cozot for a full re-reading of  ... 
doi:10.1007/978-3-7091-7486-9_5 fatcat:qqpmu4ytnvgyjfzdobfgkguggu

Phase separation of polymer-bound particles induced by loop-mediated one dimensional effective long-range interactions

G. David, J.-C. Walter, C. P. Broedersz, J. Dorignac, F. Geniet, A. Parmeggiani, N.-O. Walliser, J. Palmeri
2020 Physical Review Research  
We argue that 1D phase transitions exist in such systems for both Gaussian and self-avoiding polymers and, using a variational method that goes beyond mean-field theory, we obtain the complete mean occupation-temperature  ...  Phase separation of polymer-bound particles induced by loop-mediated one dimensional effective longrange interactions. The cellular cytoplasm is organized into compartments.  ...  Kernel -Mean Field Asympt. Kernel -Var. Method Complete Kernel -Mean Field Complete Kernel -Var. Method FIG. 4.  ... 
doi:10.1103/physrevresearch.2.033377 fatcat:qj4lvenlrzgeflug6437khutcy

Efficient and realistic simulation of phase coexistence

G. J. A. Sevink, E. M. Blokhuis, X. Li, G. Milano
2020 Journal of Chemical Physics  
Our results illustrate the key role of the particle density per field grid cell and show that projection based on a Gaussian kernel is preferred over the standard cloud-in-cell projection.  ...  They also suggest that the behavior of hPF-MD close to the critical point is non-classical, i.e., in agreement with a critical exponent for a pure particle description, despite the mean-field origin of  ...  by "soft" mean-field interactions between particle concentration fields, while treating the intramolecular interactions associated with particles in a molecule in the spirit of MD.  ... 
doi:10.1063/5.0027778 pmid:33380071 fatcat:kjgvmghdkrdujpberuuezi6lyy

Learning Mean-Field Equations from Particle Data Using WSINDy [article]

Daniel A. Messenger, David M. Bortz
2021 arXiv   pre-print
In particular, we use concepts from mean-field theory of IPS in combination with the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) to provide a fast and reliable system identification  ...  We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number N and offering robustness  ...  Discussion We have developed a weak-form method for sparse identification of governing equations for interacting particle systems using the formalism of mean-field equations.  ... 
arXiv:2110.07756v1 fatcat:pzlc3gak45fwpmulgagzzzowpi

Two-species-coagulation approach to consensus by group level interactions

Carlos Escudero, Fabricio Macià, Juan J. L. Velázquez
2010 Physical Review E  
This is achieved by means of introducing explicitly solvable kernels which have a clear physical meaning.  ...  The corresponding solutions are calculated in the long time limit, in which consensus may or may not be reached. The lack of consensus is characterized by means of scaling limits of the solutions.  ...  (2) and we will consider a family of kernels of an apparent physical meaning.  ... 
doi:10.1103/physreve.82.016113 pmid:20866695 fatcat:xskfeogpajbxxasein5luccyya

Nuclear superfluidity at finite temperature [article]

Elena Litvinova, Peter Schuck
2021 arXiv   pre-print
In this framework, we obtained the closed system of equations for the fermionic particle-hole and particle-particle propagators.  ...  Within the Matsubara formalism, the Dyson-type Bethe-Salpeter equation (Dyson-BSE) with the frequency-dependent interaction kernel is obtained.  ...  The full interaction kernel of Eq. ( 21 ) can then be written as: K = Ñ −1 (K (0) + K (r) ) Ñ −1 , and the symbol " ˜" indicates the mean-field character of the quantity.  ... 
arXiv:2105.12832v3 fatcat:a7nz25ez4nadjdtt55j54wubni

Page 334 of Mathematical Reviews Vol. 17, Issue 3 [page]

1956 Mathematical Reviews  
The electro- magnetic angular momentum is identified with the spin of the particle.  ...  The kernel of the one-time equation is given in terms of a power expansion of the coupling constant and its unique relationship to the many-time kernel is discussed.  ... 
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