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Identifiability of interaction kernels in mean-field equations of interacting particles
[article]
2022
arXiv
pre-print
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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]
2003
Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation - SCA '04
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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
2007
International Journal of Modern Physics E
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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
2004
Physica D : Non-linear phenomena
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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]
2020
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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
2012
Journal of Physics A: Mathematical and Theoretical
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2011 pre-print arXiv:1106.1886v1 fatcat:7cbymvqiyvgknkxgco7xyzuepi
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
2015
Physical Review E
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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]
1996
Eurographics
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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
2020
Physical Review Research
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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
2020
Journal of Chemical Physics
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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]
2021
arXiv
pre-print
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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
2010
Physical Review E
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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]
2021
arXiv
pre-print
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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
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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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