相关论文: Scale-independent mixing laws

We present a thermodynamic formulation for scale-invariant systems based on the principle of extreme information. We create an analogy between these systems and the well-known thermodynamics of gases and fluids, and study as a compelling…

The description of fluid mixtures molecular behavior is significant for various industry fields due to the complex composition of fluid found in nature. Statistical mechanics approaches use intermolecular interaction potential to predict…

Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…

The universal theory of order parameter fluctuations (delta scaling laws) is applied to a wide range of intermediate energy heavy-ion collision data obtained with INDRA. This systematic study confirms that the observed fragment production…

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…

Sum rules relating the masses of ground-state baryons and mesons are obtained in a constituent quark model. The interaction is assumed to be independent of quark spins except for a spin-dependent part that can be treated as a perturbation.…

In a mixture of scalar fields undergoing diffusive processes governed by Fick's law, the concentration at each point evolves linearly in the concentrations at all points and independently from the other concentrations, when one considers a…

Scaling laws for characteristic length scales (in time or in the model parameters) are both experimentally robust and accessible for rigorous analysis. In multiscale situations cross--overs between different scaling laws are observed. We…

We present a phenomenological model for the mixing length used in turbulence models. It has the advantage of naturally accounting for the object's geometry while satisfying the standard symmetries of the Navier-Stokes equations. We employ…

We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…

In this study we apply the maximum entropy principle to derive the properly scaled velocity distribution function of Boltzmann equations for mixtures, which leads to a non-isothermal Maxwell-Stefan diffusion model. We also analyze the…

We formulate multifractal models for velocity differences and gradients which describe the full range of length scales in turbulent flow, namely: laminar, dissipation, inertial, and stirring ranges. The models subsume existing models of…

We discuss the scaling of the interaction energy with particle numbers for a harmonically trapped two-species mixture at thermal equilibrium experiencing interactions of arbitrary strength and range. In the limit of long-range interactions…

Multiscale mixing efficiencies for passive scalar advection are defined in terms of the suppression of variance weighted at various length scales. We consider scalars maintained by temporally steady but spatially inhomogeneous sources,…

In a series of three lectures, I review the theory and phenomenology of heavy quark masses and mixing angles and the status of their determination. In addition, I give an introduction to heavy quark symmetry, with the main emphasis on the…

We have shown in this investigation that the partial pressure can be defined uniquely as each wall pressure exerted by a component in liquid mixtures, and is an important observable physical quantity. As a consequence of this definition,…

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

Stochastic Master equations or quantum filtering equations for mixed states are well known objects in quantum physics. Building a mathematically rigorous theory of these equations in infinite-dimensional spaces is a long standing open…

A new computational framework for the simulation of turbulent flow through complex objects and along irregular boundaries is presented. This is motivated by the application of metal foams in compact heat-transfer devices, or as catalyst…

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship…