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The study of continuous-time information diffusion has been an important area of research for many applications in recent years. When only the diffusion traces (cascades) are accessible, cascade-based network inference and influence…
Generative models have made significant impacts across various domains, largely due to their ability to scale during training by increasing data, computational resources, and model size, a phenomenon characterized by the scaling laws.…
The scaling argument developed by Larichev and Held (1995) for eddy amplitudes and fluxes in a horizontally homogeneous, two-layer model on an f-plane is extended to a beta-plane. In terms of the non-dimensional number x =…
It is conjectured that the size scaling of the nearest level spacing in the critical spectral region, $S(N)\propto N^{-\lambda}$, remains qualitatively the same within phases of extended and critical states. The exponent $\lambda$ is…
The self-similarity of a passive scalar in homogeneous isotropic decaying turbulence is investigated by the method of line segments (M. Gauding et al., Physics of Fluids 27.9 (2015): 095102). The analysis is based on a highly resolved…
The diffusivity of tagged particles is demonstrated to be heterogeneous on time scales comparable to or less than the structural relaxation time %taking place at the interparticle distance in a highly supercooled liquid via 3D molecular…
We investigated theoretically water evaporation from concentrated supramolecular mixtures, such as solutions of polymers or amphiphilic molecules, using numerical resolutions of a one dimensional model based on mass transport equations.…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…
We establish new scaling properties for the universality class of Model C, which describes relaxational critical dynamics of a nonconserved order parameter coupled to a conserved scalar density. We find an anomalous diffusion phase, which…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a…
The intermittent burst dynamics during the slow drainage of a porous medium is studied experimentally. We have shown that this system satisfies a set of conditions known to be true for critical systems, such as intermittent activity with…
A diffusion-deposition model for glassy dynamics in compacting granular systems is treated by time scaling and by a method that provides the exact asymptotic (long time) behavior. The results include Vogel-Fulcher dependence of rates on…
Understanding the nature of compressible fluctuations in a broad range of turbulent plasmas, from the intracluster medium to the solar wind, has been an active field of research in the past decades. Theoretical frameworks for weakly…
We consider the asymmetric exclusion process. We start from a profile which is constant along the drift direction and prove that the density profile, under a diffusive rescaling of time, converges to the solution of a parabolic equation.
We study the phase ordering colloids suspended in a thermotropic nematic liquid crystal below the clearing point Tni and the resulting aggregated structure. Small (150nm) PMMA particles are dispersed in a classical liquid crystal matrix,…
We investigate the ground-state properties of trapped fermion systems described by the Hubbard model with an external confining potential. We discuss the universal behaviors of systems in different regimes: from few particles, i.e. in…
Membrane configurations in the Banks-Fischler-Shenker-Susskind matrix model are unstable due to the existence of flat directions in the potential and the decay process can be seen as a realization of chaotic scattering. In this note, we…
Agent-based cellular models simulate tissue evolution by capturing the behavior of individual cells, their interactions with neighboring cells, and their responses to the surrounding microenvironment. An important challenge in the field is…