相关论文: Data-Driven Constitutive Relation Reveals Scaling …

With several advantages and as an alternative to predict physics field, machine learning methods can be classified into two distinct types: data-driven relying on training data and physics-driven using physics law. Choosing heat conduction…

Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…

The aim of this paper is to prove the existence of weak solution for a quasi-static evolution of thermo-visco-elastic model with Norton-Hoff law of plasticity. The dependence on temperature occurs both in the elastic constitutive equations…

Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…

In the context of a nonequilibrium statistical thermodynamics, based on a nonequilibrium statistical ensemble formalism, a generalized hydrodynamics of fluids under driven flow and shear stress is derived. At the thermodynamic level, the…

In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For…

Earth's magnetic field is generated by processes in the electrically conducting, liquid outer core, subsumed under the term `geodynamo'. In the last decades, great effort has been put into the numerical simulation of core dynamics following…

Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates, with fluid properties similar to the values of seawater. The DDC flow is driven by an unstable salinity difference and…

Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective…

Constitutive relations close the balance laws of continuum mechanics and serves as the surrogate for a material in the design and engineering process. The problem of obtaining the constitutive relations is an indirect inverse problem where…

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the…

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…

There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both…

Integrating high-dimensional biological data into data-driven mechanistic modeling requires rigorous practical identifiability to ensure interpretability and generalizability. However, coordinate identifiability analysis often suffers from…

We examine the dynamics of two coalescing liquid drops in the `inertial regime', where the effects of viscosity are negligible and the propagation of the bridge front connecting the drops can be considered as `local'. The solution fully…

Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition softwares/hardwares are providing vast amounts of data for various complex phenomena, ranging from those in atomospheric…

We consider a spring-block model with both dry and viscous frictions, subjected to a periodic driving allowing mechanically stable configurations to be sampled. We show that under strong driving, the scaling of the correlation length with…

We investigate interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid-vapor interfaces in non-equilibrium. Conventional Navier-Stokes-Korteweg (NSK) formulations often fail to…

Transport coefficients are of crucial importance in theoretical as well as experimental studies. Despite substantial research on classical hard sphere/disk gases in low and high density regimes, a thorough investigation of transport…

Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…