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We describe some scaling issues that arise when using lattice Boltzmann methods to simulate binary fluid mixtures -- both in the presence and in the absence of colloidal particles. Two types of scaling problem arise: physical and…
We determine analytically the dependence of the approach to thermal equilibrium of strongly coupled plasmas on the breaking of scale invariance. The theories we consider are the holographic duals to Einstein gravity coupled to a scalar with…
Two-dimensional (2D) nanomaterials exhibit unique properties that are promising for diverse applications, including those relevant to concentration-gradient-driven transport of electrolyte solutions through porous membranes made from these…
A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…
Neural scaling laws approximate a language model's loss as a power-law function of parameter count $N$ and token count $D$. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed…
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion…
We propose an alternative formulation for the exact relations in three-dimensional homogeneous turbulence using two-point statistics. Our finding is illustrated with incompressible hydrodynamic, standard and Hall magnetohydrodynamic…
The nonlinear magnetic induction equation with Hall effect can be used to model magnetic fields, e.g. in astrophysical plasma environments. In order to give reliable results, numerical simulations should be carried out using effective and…
I propose a scaling analysis of the hadron multiplicity ratio measured in Deep Inelastic Scattering on nuclear targets as a tool to distinguish energy loss and nuclear absorption effects on hadron suppression in cold nuclear matter. The…
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product…
Using examples of the square- and triangular-lattice Heisenberg models we demonstrate that the density matrix renormalization group method (DMRG) can be effectively used to study magnetic ordering in two-dimensional lattice spin models. We…
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…
A first-principles scaling law, based on turbulent transport considerations, and a multi-machine database of density limit discharges from the ASDEX Upgrade, JET and TCV tokamaks, show that the increase of the boundary turbulent transport…
We present comparative results from simulations of a lattice and an off-lattice model of a homopolymer, in the context of kinetics of the collapse transition. Scaling laws related to the collapse time, cluster coarsening and aging behavior…
We present new scaling laws for the thrust production and power consumption of three-dimensional combined heaving and pitching hydrofoils by extending the three-dimensional pitching scaling laws introduced by Ayancik et al. (2019). New…
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite…
We address theoretically the puzzling similarity observed in the thermodynamic behaviour of independent clouds of cold dipolar excitons in coupled semiconductor quantum wells. We argue that the condensation of self-trapped exciton gas…
We discuss quantum scale invariance in (scale invariant) gauge theories with both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST invariance is checked in two apparently unrelated approaches using a scale invariant…
We have performed a simulation study of Langmuir turbulence in the Earth's ionosphere by means of a Zakharov model with parameters relevant for the F layer. The model includes dissipative terms to model collisions and Landau damping of the…
Metastability is a formidable challenge to Markov chain Monte Carlo methods. In this paper we present methods for algorithm design to meet this challenge. The design problem we consider is temperature selection for the infinite swapping…