Related papers: On the kinetic description of the objective molecu…
Numerical simulations of turbulent flows are well known to pose extreme computational challenges due to the huge number of dynamical degrees of freedom required to correctly describe the complex multi-scale statistical correlations of the…
While Born-Oppenheimer molecular dynamics (BOMD) has been widely studied by resorting to powerful methods in mathematical analysis, this paper presents a geometric formulation in terms of Hamilton's variational principle and…
Within the framework of linear-scaling Kohn-Sham density functional theory, a robust method for maintaining compact localized orbitals close to the ground state is coupled with nuclear dynamics. This allows to obviate the commonly employed…
A new numerical continuum \textit{one-domain} approach (ODA) solver is presented for the simulation of the transfer processes between a free fluid and a porous medium. The solver is developed in the \textit{mesoscopic} scale framework,…
Neither molecular kinetics nor continuum fluid dynamics alone is adequate to describe multiscale gas flows across different regimes. Bridging these regimes within a single self-consistent framework has long been a central challenge in fluid…
Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach…
We develop a general framework in the renormalization-group (RG) method for extracting a mesoscopic dynamics from an evolution equation by incorporating some excited (fast) modes as additional components to the invariant manifold spanned by…
We introduce a general and systematic theoretical framework for Operational Dynamic Modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of…
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach…
In this paper we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic…
Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical…
We propose a multiscale computational method for thin-layer flows of complex fluids, termed the synchronized molecular dynamics (SMD) method, which directly couples local molecular dynamics (MD) simulations with a macroscopic lubrication…
To study simultaneously the hydrodynamic and thermodynamic behaviors in compressible flow systems with spherical or cylindrical symmetry, we present a theoretical framework for constructing Discrete Boltzmann Model(DBM) with spherical or…
Multi-particle collision dynamics is an appealing numerical technique aiming at simulating fluids at the mesoscopic scale. It considers molecular details in a coarse-grained fashion and reproduces hydrodynamic phenomena. Here, the…
Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…
We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…
Basic problems of the semiclassical microscopic modelling of strongly interactingsystems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic…
We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…
Based on a novel concept of multiplicative multiscale decomposition, we have derived a multiscale micromorphic molecular dynamics (MMMD)to extent the (Andersen)-Parrinello-Rahman molecular dynamics to mesoscale and macroscale. The…
We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the…