Related papers: Symmetric Molecular Dynamics
The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…
The filtration of fluid in 2D porous medium is simulated by the molecular dynamics technique. The high concentration of fluid is created at the initial point in time and the number of fluid particles is investigated in all porous. The…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
We expand on the known result that the Carroll algebra in $2+1$ dimensions admits two non-trivial central extensions by computing the associated Lie group, which we call extended Carroll group. The symplectic geometry associated to this…
We introduce a simple model for DNA-cationic-lipid complexes in which galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices that couple orientationally and positionally to lattices in neighboring galleries. We…
In this paper, we develop a multiscale hierarchy framework for objective molecular dynamics (OMD), a reduced order molecular dynamics with a certain symmetry, that connects it to the statistical kinetic equation, and the macroscopic…
We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…
We study the dynamics of particles in a multi-component 2d Lennard-Jones (LJ) fluid in the limiting case where {\it all the particles are different} (APD). The equilibrium properties of this APD system were studied in our earlier work…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of…
In many scientific fields, there is an interest in understanding the way in which complex chemical networks evolve. The chemical networks which researchers focus upon, have become increasingly complex and this has motivated the development…
We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear…
We present a symmetry-based exhaustive approach to explore the structural and compositional richness of two-dimensional materials. We use a ``combinatorial engine'' that constructs potential compounds by occupying all possible Wyckoff…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
We develop a Hamiltonian theory for 2D soliton equations. In particular, we identify the spaces of doubly periodic operators on which a full hierarchy of commuting flows can be introduced, and show that these flows are Hamiltonian with…
The application of generative models in crystal structure prediction (CSP) has gained significant attention. Conditional generation--particularly the generation of crystal structures with specified stability or other physical properties has…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
A kinetic approach for the evolution of ultracold neutral plasmas including interionic correlations and the treatment of ionization/excitation and recombination/deexcitation by rate equations is described in detail. To assess the…
With exquisite precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometer-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and…
We present Molecular Dynamics (MD), Quasi Harmonic Lattice Dynamics (QHLD) and Energy Minimization (EM) calculations for the crystal structure of Ne, Ar, Kr and Xe as a function of pressure and temperature. New Lennard-Jones (LJ) parameters…