scholarly journals Hydrodynamic limits of the nonlinear Schrödinger equation with the Chern-Simons gauge fields

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jeongho Kim ◽  
Bora Moon
Keyword(s):  
Quantum Correction ◽  
Hydrodynamic Limit ◽  
Energy Estimate ◽  
Correction Term ◽  
Euler System ◽  
Entropy Method ◽  
Planck Constant ◽  
Nonlinear Schrödinger ◽  
Relative Entropy Method ◽  
Chern Simons

<p style='text-indent:20px;'>We present two types of the hydrodynamic limit of the nonlinear Schrödinger-Chern-Simons (SCS) system. We consider two different scalings of the SCS system and show that each SCS system asymptotically converges towards the compressible and incompressible Euler system, coupled with the Chern-Simons equations and Poisson equation respectively, as the scaled Planck constant converges to 0. Our method is based on the modulated energy estimate. In the case of compressible limit, we observe that the classical theory of relative entropy method can be applied to show the hydrodynamic limit, with the additional quantum correction term. On the other hand, for the incompressible limit, we directly estimate the modulated energy to derive the desired asymptotic convergence.</p>

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.

scholarly journals Hydrodynamic limit of the kinetic Cucker–Smale flocking model

2014 ◽  
Vol 25 (01) ◽  
pp. 131-163 ◽  
Author(s):  
Trygve K. Karper ◽  
Antoine Mellet ◽  
Konstantina Trivisa
Keyword(s):  
Hyperbolic Conservation Laws ◽  
Hydrodynamic Limit ◽  
Entropy Method ◽  
Singular Limit ◽  
Local Alignment ◽  
Stat Phys ◽  
Hyperbolic Conservation ◽  
Starting Point ◽  
Free Transport ◽  
Relative Entropy Method

The hydrodynamic limit of a kinetic Cucker–Smale flocking model is investigated. The starting point is the model considered in [Existence of weak solutions to kinetic flocking models, SIAM Math. Anal.45 (2013) 215–243], which in addition to free transport of individuals and a standard Cucker–Smale alignment operator, includes Brownian noise and strong local alignment. The latter was derived in [On strong local alignment in the kinetic Cucker–Smale equation, in Hyperbolic Conservation Laws and Related Analysis with Applications (Springer, 2013), pp. 227–242] as the singular limit of an alignment operator first introduced by Motsch and Tadmor in [A new model for self-organized dynamics and its flocking behavior, J. Stat. Phys.141 (2011) 923–947]. The objective of this work is the rigorous investigation of the singular limit corresponding to strong noise and strong local alignment. The proof relies on a relative entropy method. The asymptotic dynamics is described by an Euler-type flocking system.

scholarly journals Relative Entropy Method Applied for the Fatigue Life Distribution of Carbon Fiber/Epoxy Composites

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 224
Author(s):  
Changsheng Yuan ◽  
Yingjie Liang
Keyword(s):  
Experimental Data ◽  
Carbon Fiber ◽  
Relative Entropy ◽  
Least Squares Method ◽  
Entropy Method ◽  
Epoxy Composites ◽  
Order Moment ◽  
Kolmogorov Smirnov ◽  
Relative Entropy Method ◽  
Carbon Fiber Epoxy

This paper verifies the feasibility of the relative entropy method in selecting the most suitable statistical distribution for the experimental data, which do not follow an exponential distribution. The efficiency of the relative entropy method is tested through the fractional order moment and the logarithmic moment in terms of the experimental data of carbon fiber/epoxy composites with different stress amplitudes. For better usage of the relative entropy method, the efficient range of its application is also studied. The application results show that the relative entropy method is not very fit for choosing the proper distribution for non-exponential random data when the heavy tail trait of the experimental data is emphasized. It is not consistent with the Kolmogorov–Smirnov test but is consistent with the residual sum of squares in the least squares method whenever it is calculated by the fractional moment or the logarithmic moment. Under different stress amplitudes, the relative entropy method has different performances.

A COMBINATION WEIGHTING ALGORITHM USING RELATIVE ENTROPY FOR DOCUMENT CLUSTERING

2014 ◽  
Vol 28 (03) ◽  
pp. 1453002 ◽  
Author(s):  
BO JI ◽  
YANGDONG YE ◽  
YU XIAO
Keyword(s):  
Relative Entropy ◽  
Document Clustering ◽  
Multiple Attribute Decision Making ◽  
Entropy Method ◽  
Data Object ◽  
Information Bottleneck ◽  
Subjective Weight ◽  
Multiple Attribute ◽  
Sequential Information ◽  
Relative Entropy Method

This paper proposes a combination weighting algorithm using relative entropy for document clustering. Combination weighting is widely used in multiple attribute decision making (MADM) problem. However, there exist two difficulties to hinder the applications of combination weighting on document clustering. First, combination weighting is based on the integration of subjective weighting and objective weighting. However, there are so many attributes in documents that the subjective weights which rely on manual annotation by experts are impracticable. Secondly, a document data object might contain hundreds or even thousands of features. It is an extremely time-consuming task to calculate the combination weights. To address the issues, we suggest to simplify the combination weighting by not distinguishing subjective weight and objective weight. Meanwhile, we choose relative entropy method to reduce running time. In our algorithm, we obtain a combination weight set with 14 combination forms. The experiments on real document data show that both on the AC/PR/RE measures and the mutual information (MI) measure, the proposed CWRE-sIB algorithm is superior to the original sequential information bottleneck (sIB) algorithm and a series of weighting-sIB algorithms, which are built by applying a single weighting scheme to the original sIB algorithm.

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