Related papers: Definition of Systematic, Approximately Separable …
Localized basis ab initio molecular dynamics simulation within the density functional framework has been used to generate realistic configurations of amorphous silicon carbide (a-SiC). Our approach consists of constructing a set of smart…
Numerical data structures for positive dimensional solution sets of polynomial systems are sets of generic points cut out by random planes of complimentary dimension. We may represent the linear spaces defined by those planes either by…
Simplified representations of macromolecules help in rationalising and understanding the outcome of atomistic simulations, and serve to the construction of effective, coarse-grained models. The number and distribution of coarse-grained…
Particle-in-Cell (PIC) methods are widely used computational tools for fluid and kinetic plasma modeling. While both the fluid and kinetic PIC approaches have been successfully used to target either kinetic or fluid simulations, little was…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this…
Physics-inspired molecular representations are the cornerstone of similarity-based learning applied to solve chemical problems. Despite their conceptual and mathematical diversity, this class of descriptors shares a common underlying…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic…
A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries.…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
We present a novel framework for Finite Element Particle-in-Cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining…
An approach to gauge theory in the context of locally conformally flat space-time is described. It is discussed how there are a number of natural principal bundles associated with any given locally conformally flat space-time $X$. The…
Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…
Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with…
The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies both, introduces new challenges. This paper introduces new…
We begin with a description of spacetime by a 4-dimensional cubic lattice $\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\sscripthat$…
Computational studies of chemical reactions in complex environments such as proteins, nanostructures, or on surfaces require accurate and efficient atomistic models applicable to the nanometer scale. In general, an accurate parametrization…
We present a fully variational generalization of the pseudo self-interaction correction (VPSIC) approach previously presented in two implementations based on plane-waves and atomic orbital basis set, known as PSIC and ASIC, respectively.…
Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles,…