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A quantum model of universe is constructed in which values of dimensionless coupling constants of the fundamental interactions (including the cosmological constant) are determined via certain topological invariants of manifolds forming…
On the basis of a qualitative and numerical analysis of a cosmological model based on an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields -- one classical and one phantom, peculiarities of the behavior of the…
The precise sequence of aminoacids plays a central role in the tertiary structure of proteins and their functional properties. The Hydrophobic-Polar lattice models have provided valuable insights regarding the energy landscape. We…
We investigate loosely bound composite states made of dark matter, where the binding energy for constituent particles is less than the constituent mass. We focus on models of nuclear and molecular dark matter, where constituents are…
We present an information-based total-energy optimization method to produce nearly defect-free structural models of amorphous silicon. Using geometrical, structural and topological information from disordered tetrahedral networks, we have…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation…
Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…
We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystal's bonds. In particular, we show the…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
We study ballistic aggregation on a two dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: in the…
Using the combinatorics of two interpenetrating face centered cubic lattices together with the part of calculus naturally encoded in combinatorial topology, we construct from first principles a lattice model of 3D incompressible…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
In this paper I propose a new model for representing the formation energies of multicomponent crystalline alloys as a function of atom types. In the cases when displacements of atoms from their equilibrium positions are not large, the…
We consider a 1D lattice gas model in which the atoms interact via an infinite number of cluster interactions within contiguous atomic chains plus the next nearest neighbor pairwise interaction. All interactions are of arbitrary strength.…
In this study, we employ dynamical systems methods to analyse the large-scale structure by considering two distinct interaction models (linear and non-linear) within the dark sector, associated with a specific dynamical dark energy model…
We discuss a systematic construction of dimensionless quantum-mechanical equations. The process reduces the number of independent model parameters to a minimum and, at the same time, provides the natural units of length, energy, etc. in a…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
Most large engineering structures are described as assemblies of plates and shells and they are computed as such using adhoc Finite Element packages. In fact their computation in 3D would be much too costly. In this framework, the…
Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…