Related papers: Symmetric Molecular Dynamics
Granular hydrodynamics predicts symmetry-breaking instability in a two-dimensional (2D) ensemble of nearly elastically colliding smooth hard spheres driven, at zero gravity, by a rapidly vibrating sidewall. Super- and subcritical…
The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to 10 dimensional. The…
In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
We construct symmetric representations of distributions over two-dimensional plane with given mean values as convex combinations of distributions with supports containing not more than three points and with the same mean values.
The regular or chaotic dynamics of an analytical realistic three dimensional model composed of a spherically symmetric central nucleus, a bar and a flat disk is investigated. For describing the properties of the bar we introduce a new…
We give a combinatorial characterization of minimally rigid planar frameworks with orientation-preserving crystallographic symmetry, under the constraint of forced symmetry. The main theorems are proved by extending the methods of the first…
The Courant-Snyder theory for two-dimensional coupled linear optics is presented, based on the systematic use of the real representation of the Dirac matrices. Since any real $4\times 4$-matrix can be expressed as a linear combination of…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
Synthetic molecular dynamics (synMD) trajectories from learned generative models have been proposed as a useful addition to the biomolecular simulation toolbox. The computational expense of explicitly integrating the equations of motion in…
Motivated by the unique physical properties of {\em biological active matter}, e.g., cytoskeletal dynamics in eukaryotic cells, we set up {\em effective} two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin…
Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
Crystal generative models have shown rapid progress for accelerating the discovery of bulk, periodic materials. However, many material systems such as 2D superconductors, thin film semiconductors, and catalytic surfaces are diperiodic,…
A mechanism responsible for the directed transport and molecular separation in a symmetric channel is proposed. We found that under the action of spatial harmonic oscillations of the channel, the system exhibits a directed transport in…
Recent studies aimed at investigating artificial analogs of bacterial colonies have shown that low-density suspensions of self-propelled particles confined in two dimensions can assemble into finite aggregates that merge and split, but have…
We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative algebra. The relationship between these symmetries is…
Self-assembly is one of the crucial mechanisms allowing to design multifunctional materials. Soft hybrid materials contain components of different nature and exhibit competitive interactions which drive self-organisation into structures of…
We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manifolds and canonical relations obtained by localizing them…