Propagation of Correlations in a Hard-Sphere System

Gerasimenko, V. I.; Gapyak, I. V.

doi:10.1007/s10955-022-02958-8

Cited by 4 publications

(8 citation statements)

References 21 publications

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“…The cumulants of probability distribution functions are interpreted as correlation functions and are governed by the Liouville hierarchy. The following outlines the approach to the description of the evolution of a state by means of both reduced distribution functions and reduced correlation functions, which is based on the dynamics of correlations [53]. It should be emphasized that on a microscopic scale, the macroscopic characteristics of fluctuations of observables are directly determined by the reduced correlation functions.…”

Section: Hierarchies Of Evolution Equations For Colliding Particlesmentioning

confidence: 99%

“…The evolution of the sequence of correlation functions (2.30) of many hard spheres is determined by the Cauchy problem of the weak formulation of the Liouville hierarchy of the following evolution equations [53]:…”

Section: Criterion a Solution Of Thementioning

confidence: 99%

“…The possibility of redefining of the reduced distribution functions naturally arises as a result of dividing the series in expression (2.39) by the series of the normalization factor. A definition of reduced distribution functions equivalent to definition (2.39) is formulated on the basis of correlation functions (2.33) of a system of hard spheres by means of the following series expansion [53]:…”

Section: Criterion a Solution Of Thementioning

confidence: 99%

“…As is known, on a microscopic scale, the macroscopic characteristics of fluctuations of observables are directly determined by means of the reduced correlation functions. Assuming as a basis an alternative approach to the description of the evolution of states of a hardsphere system within the framework of correlation functions (2.33), then the reduced correlation functions are defined by means of a solution of the Cauchy problem of the Liouville hierarchy (2.31),(2.32) as follows [53]: Such a representation for reduced correlation functions (2.57) can be derived as a result of the fact that the reduced correlation functions are cumulants of reduced distribution functions (2.40). Indeed, traditionally reduced correlation functions are introduced by means of the cluster expansions of the reduced distribution functions similar to the cluster expansions of the probability distribution functions (2.29) and on the set of allowed configurations R 3n zW n they have the form:…”

Section: The Hierarchy Of Nonlinear Evolution Equations For Reduced C...mentioning

confidence: 99%

“…In a particular case, the non-perturbative solutions of these hierarchies are represented in the form of the perturbation (iteration) series as a result of applying analogs of the Duhamel equation to their generating operators. The paper also formulated the Liouville hierarchy of evolution equations for correlation functions of the state and established that the dynamics of correlations underlie the description of the evolution of an infinitely many hard spheres that are governed by the BBGKY hierarchy for the reduced distribution functions or the hierarchy of nonlinear evolution equations for the reduced correlation functions [53].…”

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confidence: 99%

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Досягнення В Теорії Рівнянь Еволюції Багатьох Частинок Із Зіткненнями

Герасименко,

Гап'як

2023

ЗПІМ

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В огляді подано строгі результати теорії фундаментальних еволюційних рівнянь систем багатьох частинок із зіткненнями, а також розглянуто їх зв’язок із нелінійними кінетичними рівняннями, які описують колективну поведінку частинок у скейлінгових наближеннях.

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Section: Hierarchies Of Evolution Equations For Colliding Particlesmentioning

confidence: 99%

Section: Criterion a Solution Of Thementioning

confidence: 99%

Section: Criterion a Solution Of Thementioning

confidence: 99%

Section: The Hierarchy Of Nonlinear Evolution Equations For Reduced C...mentioning

confidence: 99%

mentioning

confidence: 99%

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Досягнення В Теорії Рівнянь Еволюції Багатьох Частинок Із Зіткненнями

Герасименко,

Гап'як

2023

ЗПІМ

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Cluster expansion for a dilute hard sphere gas dynamics

Bodineau

Gallagher

Saint‐Raymond

et al. 2022

Journal of Mathematical Physics

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In a previous paper by the authors, a cluster expansion method had been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the empirical measure, from which the fluctuating Boltzmann equation and large deviation estimates have been deduced. The cluster expansion originally devised by the authors was implemented at the level of the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, which is a standard tool to investigate the deterministic dynamics. In this paper, we introduce an alternative approach in which the cluster expansion is applied directly on real trajectories of the particle system. This offers a fresh perspective on the study of the hard sphere dynamics in the low density limit, allowing us to recover the results previously obtained by the authors and also to describe the actual clustering of particle trajectories.

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Optimizing Energy Storage System Operations and Configuration through a Whale Optimization Algorithm Enhanced with Chaotic Mapping and IoT Data: Enhancing Efficiency and Longevity of Energy Storage Stations

Gao

2023

Wireless Power Transfer

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To enhance the charging and discharging strategy of the energy storage system (ESS) and optimize its economic efficiency, this paper proposes a novel approach based on the enhanced whale algorithm. Recognizing that the standard whale algorithm can sometimes suffer from local optima in high-dimensional multiobjective optimization, this study introduces chaotic mapping and individual information exchange mechanisms to address this challenge. The proposed algorithm explores optimal configurations for different energy device placements and capacities through encircling and bubble searches, evaluating various multiobjective functions for optimization. In addition, the algorithm refines both the system operation model and the ESS configuration model, with the objective function being the analysis of the average annual revenue of the ESS. Model testing results demonstrate that this algorithm yields more moderate energy storage (ES) capacity decay, extending operational time to 3,124 days and achieving a full-life cycle benefit of the ESS as high as 1,821,623.68 yuan. Also, our algorithm demonstrates high efficiency, with minimal test time (68.36 seconds) and quick optimization (0.031 seconds per cycle), regardless of problem complexity.

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Propagation of Correlations in a Hard-Sphere System

Cited by 4 publications

References 21 publications

Досягнення В Теорії Рівнянь Еволюції Багатьох Частинок Із Зіткненнями

Досягнення В Теорії Рівнянь Еволюції Багатьох Частинок Із Зіткненнями

Cluster expansion for a dilute hard sphere gas dynamics

Optimizing Energy Storage System Operations and Configuration through a Whale Optimization Algorithm Enhanced with Chaotic Mapping and IoT Data: Enhancing Efficiency and Longevity of Energy Storage Stations

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