Related papers: Emergence of rigid Polycrystals from atomistic Sys…
We analyze a lattice model closely related to the one-dimensional inelastic gas with periodic boundary condition. The one-dimensional inelastic gas tends to form high density clusters of particles with almost the same velocity, separated by…
The formation of correlated structures is of importance in many diverse contexts such as strongly coupled plasmas, soft matter, and even biological mediums. In all these contexts the dynamics are mainly governed by electrostatic…
The behavior of identical particles interacting through the harmonic-repulsive pair potential has been studied in 3D using molecular dynamics simulations at a number of different densities. We found that at many densities, as the…
In exact density functional theory (DFT) the total ground-state energy is a series of linear segments between integer electron points, a condition known as "piecewise linearity". Deviation from this condition is indicative of poor…
A binary mixture of particles interacting with spherically-symmetric potentials leading to microsegregation is studied by theory and molecular dynamics (MD) simulations. We consider spherical particles with equal diameters and volume…
We study pattern formation within the $J_1$-$J_3$ - spin model on a two-dimensional square lattice in the case of incompatible (ferromagnetic) boundary conditions on the spin field. We derive the discrete-to-continuum $\Gamma$-limit at the…
Architected materials derive their properties from the geometric arrangement of their internal structural elements. Their designs rely on continuous networks of members to control the global mechanical behavior of the bulk. Here, we…
We analytically examine the pair interaction for parallel, discrete helices of charge. Symmetry arguments allow for the energy to be decomposed into a sum of terms, each of which has an intuitive geometric interpretation. Truncated Fourier…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
We consider a simple model for the assembly of chiral molecules in two dimensions driven by maximization of the contact area. We derive a macroscopic model described by a parameter taking nine possible values corresponding to the possible…
The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural…
Motivated by solid-solid phase transitions in elastic thin films, we perform a Gamma-convergence analysis for a singularly perturbed energy describing second order phase transitions in a domain of vanishing thickness. Under a two-wells…
A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either…
We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of…
The theory of Bloembergen and Pershan for the light waves at the boundary of nonlinear media is extended to a nonlinear two-dimensional atomic crystal, i.e. a single planar atomic lattice, placed in between linear bulk media. The crystal is…
Making use of the energetics and equations of state of defective uranium dioxide that calculated with first-principles method, we demonstrate a possibility of constraining the formation energy of point defects by measuring the transition…
This paper deals with the energy transport properties of charged particles with time-dependent damping force. Based on the proposed nonlinear dimensionless mapping,the stability and dynamical evolution of the particle system is analyzed…
Crystalline or polycrystalline systems governed by odd elastic responses are known to exhibit complex dynamical behaviors involving self-propelled dynamics of topological defects with spontaneous self-rotation of chiral crystallites.…
While classical theory of phase transitions deals with systems where shape variation is energetically neutral, the account of rigidity can lead to the emergence of new thermodynamic features. One of them is a special type of critical points…
Impact of single particle onto a rigid substrate leads to its deformation and fragmentation. The flow associated with the particle spreading on a solid substrate after impact is extremely complicated. In this theoretical study a simplified…