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Splash in an inhomogeneous gas in one dimension: Exact analysis and molecular dynamics simulations 一维非均匀气体中的飞溅：精确分析和分子动力学模拟
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-27 DOI: 10.1007/s10955-025-03502-0
Amit Kumar, R. Rajesh
{"title":"Splash in an inhomogeneous gas in one dimension: Exact analysis and molecular dynamics simulations","authors":"Amit Kumar,&nbsp;R. Rajesh","doi":"10.1007/s10955-025-03502-0","DOIUrl":"10.1007/s10955-025-03502-0","url":null,"abstract":"<div><p>We investigate the splash phenomenon resulting from the energy input at the interface between a vacuum and an inhomogeneous gas with density profile <span>(rho (r) = rho _0 r^{-beta })</span>. The energy input causes the formation of ballistic spatters that propagate into the vacuum, leading to a decay of the total energy in the inhomogeneous medium following a power law, <span>(E(t) sim t^{-delta _s})</span>. We determine exactly the exponents <span>(delta _s)</span> by solving the Euler equation using a self-similar solution of the second kind for different values of <span>(beta )</span>. These exponents are further validated through event-driven molecular dynamics simulations. The determination of these exponents also allows us to numerically determine the spatio-temporal dependence of the density, velocity and temperature.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 9","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03502-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144905209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and Uniqueness of Weak Solutions for the Generalized Stochastic Navier-Stokes-Voigt Equations 广义随机Navier-Stokes-Voigt方程弱解的存在唯一性
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-18 DOI: 10.1007/s10955-025-03500-2
Ankit Kumar, Hermenegildo Borges de Oliveira, Manil T. Mohan
{"title":"Existence and Uniqueness of Weak Solutions for the Generalized Stochastic Navier-Stokes-Voigt Equations","authors":"Ankit Kumar,&nbsp;Hermenegildo Borges de Oliveira,&nbsp;Manil T. Mohan","doi":"10.1007/s10955-025-03500-2","DOIUrl":"10.1007/s10955-025-03500-2","url":null,"abstract":"<div><p>In this work, we consider the incompressible generalized Navier-Stokes-Voigt equations in a bounded domain <span>(mathcal {O}subset mathbb {R}^d)</span>, <span>(dge 2)</span>, driven by a multiplicative Gaussian noise. The considered momentum equation is given by: </p><div><div><span>$$begin{aligned} textrm{d}left( varvec{u} - kappa Delta varvec{u}right) = left[ varvec{f} +{operatorname {div}} left( -pi textbf{I}+nu |textbf{D}(varvec{u})|^{p-2}textbf{D}(varvec{u})-varvec{u}otimes varvec{u}right) right] textrm{d} t + Phi (varvec{u})textrm{dW}(t). end{aligned}$$</span></div></div><p>In the case of <span>(d=2,3)</span>, <span>(varvec{u})</span> accounts for the velocity field, <span>(pi )</span> is the pressure, <span>(varvec{f})</span> is a body force and the final term represents the stochastic forces. Here, <span>(kappa )</span> and <span>(nu )</span> are given positive constants that account for the kinematic viscosity and relaxation time, and the power-law index <i>p</i> is another constant (assumed <span>(p&gt;1)</span>) that characterizes the flow. We use the usual notation <span>(textbf{I})</span> for the unit tensor and <span>(textbf{D}(varvec{u}):=frac{1}{2}left( nabla varvec{u} + (nabla varvec{u})^{top }right) )</span> for the symmetric part of velocity gradient. For <span>(pin big (frac{2d}{d+2},infty big ))</span>, we first prove the existence of a <i>martingale solution</i>. Then we show the <i>pathwise uniqueness of solutions</i>. We employ the classical <i>Yamada-Watanabe theorem</i> to ensure the existence of a unique <i>probabilistic strong solution</i>.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 9","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Differentiability of Limit Shapes in Continuous First Passage Percolation Models 连续第一通道渗流模型极限形状的可微性
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-12 DOI: 10.1007/s10955-025-03498-7
Yuri Bakhtin, Douglas Dow
{"title":"Differentiability of Limit Shapes in Continuous First Passage Percolation Models","authors":"Yuri Bakhtin,&nbsp;Douglas Dow","doi":"10.1007/s10955-025-03498-7","DOIUrl":"10.1007/s10955-025-03498-7","url":null,"abstract":"<div><p>We introduce and study a class of abstract continuous action minimization problems that generalize continuous first and last passage percolation. In this class of models a limit shape exists. Our main result provides a framework under which that limit shape can be shown to be differentiable. We then describe examples of continuous first passage percolation models that fit into this framework. The first example is of a family of Riemannian first passage percolation models and the second is a discrete time model based on Poissonian points.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-Geodesics in Integrable and Non-Integrable Exclusion Processes 可积和不可积不相容过程中的拟测地线
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-11 DOI: 10.1007/s10955-025-03488-9
Patrik L. Ferrari, Min Liu
{"title":"Quasi-Geodesics in Integrable and Non-Integrable Exclusion Processes","authors":"Patrik L. Ferrari,&nbsp;Min Liu","doi":"10.1007/s10955-025-03488-9","DOIUrl":"10.1007/s10955-025-03488-9","url":null,"abstract":"<div><p>Backwards geodesics for TASEP were introduced in [30]. We consider flat initial conditions and show that under proper scaling the end-point of the geodesic converges to maximizer argument of the <span>(hbox {Airy}_2)</span> process minus a parabola. We generalize its definition to generic non-integrable models including ASEP and speed changed ASEP (call it quasi-geodesics). We numerically verify that its end-point is universal, where the scaling coefficients are analytically computed through the KPZ scaling theory.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03488-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Color symmetry and ferromagnetism in Potts spin glass 波茨自旋玻璃的颜色对称性和铁磁性
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-11 DOI: 10.1007/s10955-025-03499-6
Hong-Bin Chen
{"title":"Color symmetry and ferromagnetism in Potts spin glass","authors":"Hong-Bin Chen","doi":"10.1007/s10955-025-03499-6","DOIUrl":"10.1007/s10955-025-03499-6","url":null,"abstract":"<div><p>We consider the Potts spin glass with additional ferromagnetic interaction parametrized by <i>t</i>. It has long been observed that the Potts color symmetry breaking for the spin glass order parameter is closely related to the ferromagnetic phase transition. To clarify this, we identify a single critical value <span>(t_textrm{c})</span>, which marks the onset of both color symmetry breaking and the transition to ferromagnetism.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Limiting Eigenvalue Distribution of the General Deformed Ginibre Ensemble 广义变形Ginibre系综的极限特征值分布
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-07 DOI: 10.1007/s10955-025-03492-z
Roman Sarapin
{"title":"Limiting Eigenvalue Distribution of the General Deformed Ginibre Ensemble","authors":"Roman Sarapin","doi":"10.1007/s10955-025-03492-z","DOIUrl":"10.1007/s10955-025-03492-z","url":null,"abstract":"<div><p>Consider the <span>(ntimes n)</span> matrix <span>(X_n=A_n+H_n)</span>, where <span>(A_n)</span> is a <span>(ntimes n)</span> matrix (either deterministic or random) and <span>(H_n)</span> is a <span>(ntimes n)</span> matrix independent from <span>(A_n)</span> drawn from complex Ginibre ensemble. We study the limiting eigenvalue distribution of <span>(X_n)</span>. In [45] it was shown that the eigenvalue distribution of <span>(X_n)</span> converges to some deterministic measure. This measure is known for the case <span>(A_n=0)</span>. Under some general convergence conditions on <span>(A_n)</span> we prove a formula for the density of the limiting measure. We also obtain an estimation on the rate of convergence of the distribution. The approach used here is based on supersymmetric integration.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wetting Transition on Trees I: Percolation With Clustering 树木湿润过渡ⅰ：聚类渗透
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-07 DOI: 10.1007/s10955-025-03479-w
Aser Cortines, Itamar Harel, Dmitry Ioffe, Oren Louidor
{"title":"Wetting Transition on Trees I: Percolation With Clustering","authors":"Aser Cortines,&nbsp;Itamar Harel,&nbsp;Dmitry Ioffe,&nbsp;Oren Louidor","doi":"10.1007/s10955-025-03479-w","DOIUrl":"10.1007/s10955-025-03479-w","url":null,"abstract":"<div><p>A new “Percolation with Clustering” (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the degree of clustering in the configuration. Conditions on such “clustering function” are given for the existence of a limiting free energy and a wetting transition, namely the existence of a non-trivial percolation parameter threshold above and only above which the set of “dry” (open) sites have an asymptotic density. Several examples of clustering functions are given and studied using the general theory. The results here will be used in a sequel paper to study the wetting transition for the discrete Gaussian free field on the tree subject to a hard wall constraint.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03479-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Large Time Cumulants of the KPZ Equation on an Interval 区间上KPZ方程的大时间累积量
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-06 DOI: 10.1007/s10955-025-03496-9
Guillaume Barraquand, Pierre Le Doussal
{"title":"Large Time Cumulants of the KPZ Equation on an Interval","authors":"Guillaume Barraquand,&nbsp;Pierre Le Doussal","doi":"10.1007/s10955-025-03496-9","DOIUrl":"10.1007/s10955-025-03496-9","url":null,"abstract":"<div><p>We consider the Kardar-Parisi-Zhang equation on the interval [0, <i>L</i>] with Neumann type boundary conditions and boundary parameters <i>u</i>, <i>v</i>. We show that the <i>k</i>-th order cumulant of the height behaves as <span>(c_k(L,u,v), t)</span> in the large time limit <span>(t rightarrow +infty )</span>, and we compute the coefficients <span>(c_k(L,u,v))</span>. We obtain an expression for the upper tail large deviation function of the height. We also consider the limit of large <i>L</i>, with <span>(u=tilde{u}/sqrt{L})</span>, <span>(u={tilde{v}}/sqrt{L})</span>, which should give the same quantities for the two parameter family <span>(({tilde{u}}, {tilde{v}}))</span> KPZ fixed point on the interval. We employ two complementary methods. On the one hand we adapt to the interval the replica Bethe ansatz method pioneered by Brunet and Derrida for the periodic case. On the other hand, we perform a scaling limit using previous results available for the open ASEP. The latter method allows to express the cumulants of the KPZ equation in terms a functional equation involving an integral operator.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantitative Pointwise Estimates of the Cooling Process for Inelastic Boltzmann Equation 非弹性玻尔兹曼方程冷却过程的定量点态估计
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-08-06 DOI: 10.1007/s10955-025-03494-x
Gayoung An, Jin Woo Jang, Donghyun Lee
{"title":"Quantitative Pointwise Estimates of the Cooling Process for Inelastic Boltzmann Equation","authors":"Gayoung An,&nbsp;Jin Woo Jang,&nbsp;Donghyun Lee","doi":"10.1007/s10955-025-03494-x","DOIUrl":"10.1007/s10955-025-03494-x","url":null,"abstract":"<div><p>In this paper, we study the homogeneous inelastic Boltzmann equation for hard spheres. We first prove that the solution <i>f</i>(<i>t</i>, <i>v</i>) is bounded pointwise from above by <span>(C_{f_0}langle t rangle ^3)</span> and establish that the cooling time is infinite (<span>( T_c = +infty )</span>) under the condition <span>( f_0 in L^1_2 cap L^{infty }_{s} )</span> for <span>( s &gt; 2 )</span>. Away from zero velocity, we further prove that <span>( f(t,v)le C_{f_0, |v|} langle t rangle )</span> for <span>(v ne 0)</span> at any time <span>( t &gt; 0 )</span>. This time-dependent pointwise upper bound is natural in the cooling process, as we expect the density near <span>( v = 0 )</span> to grow rapidly. We also establish an upper bound that depends on the coefficient of normal restitution constant, <span>(alpha in (0,1])</span>. This upper bound becomes constant when <span>(alpha = 1)</span>, restoring the known upper bound for elastic collisions [8]. Consequently, through these results, we obtain Maxwellian upper bounds on the solutions at each time.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Large Deviations Principle for the Fluctuating Boltzmann Equation 波动玻尔兹曼方程的大偏差原理
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-07-31 DOI: 10.1007/s10955-025-03497-8
Liu Hong
{"title":"Large Deviations Principle for the Fluctuating Boltzmann Equation","authors":"Liu Hong","doi":"10.1007/s10955-025-03497-8","DOIUrl":"10.1007/s10955-025-03497-8","url":null,"abstract":"<div><p>The Boltzmann equation is one of the most famous equations and has vast applications in modern science. In the current study, we take the randomness of binary collisions into consideration and generalize the classical Boltzmann equation into a stochastic framework. The corresponding Kolmogorov forward equations and Liouville equation in either discrete or continuous time and state space are derived respectively, whose characteristic line gives the Boltzmann equation as a consequence of the law of large numbers. Then the large deviations principle for these equations is established, which not only explains the probabilistic origin of the H-theorem in the Boltzmann equation, but also provides a natural way to incorporate the Boltzmann equation into a broader Hamiltonian structure. The so-called Hamilton-Boltzmann equation enjoys many significant merits, like time reversibility, the conservation laws of mass, momentum and energy, Maxwellian-Boltzmann distribution as the equilibrium solution, etc. We also present results under the diffusive limit in parallel. Finally, the macroscopic hydrodynamic models including 13 moments are derived with respect to our Hamilton-Boltzmann equation under the BGK approximation. We expect our study can inspire new insights into the classical Boltzmann equation from either the stochastic aspect or a Hamiltonian view.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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