Related papers: Partial dynamical symmetry as a selection criterio…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
This paper considers the problem of optimal filtering for partially observed signals taking values on the rotation group. More precisely, one or more components are considered not to be available in the measurement of the attitude of a 3D…
A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…
The low-lying spectra of atomic nuclei display diverse behaviors, for example rotational bands, which can be described phenomenologically by simple symmetry groups such as spatial SU(3). This leads to the idea of dynamical symmetry, where…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
The large body of experimental data on nuclear fission is analyzed with a semi-empirical ordering scheme based on the macro-microscopic approach and the separability of compound-nucleus and fragment properties on the fission path. We apply…
One of the interesting aspects in the study of atomic nuclei is the strikingly regular behaviour many display in spite of being complex quantum-mechanical systems, prompting the universal question of how regularity emerges out of…
Non-equilibrium dynamics of many-body systems is important in many branches of science, such as condensed matter, quantum chemistry, and ultracold atoms. Here we report the experimental observation of a phase transition of the quantum…
It is often assumed that few- and many-body systems can be accurately described by considering only pairwise two-body interactions of the constituents. We illustrate that three- and higher-body forces enter naturally in effective field…
Multi-mode expansions in computational quantum dynamics promise convergence toward exact results upon increasing the number of modes. Convergence is difficult to ascertain in practice due to the unfavourable scaling of required resources…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
A symmetry classification of possible interactions in a diatomic molecular chain is provided. For nonlinear interactions the group of Lie point transformations, leaving the lattice invariant and taking solutions into solutions, is at most…
Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true''…
When spatial constraint for the constituents (e.g., atom or particle) of system is once given, disordered structure for non-interacting system in equilibrium states is symmetric with respect to equiatomic composition. Meanwhile, when the…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
Spontaneous symmetry breaking is an essential feature of modern science. We demonstrate that it also plays an important role in the physics of complex plasmas. Complex plasmas can serve as a powerful tool for observing and studying discrete…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
Samples of the spectrum of the 36Ar nucleus are known in different energy windows. In addition to the ground state region (GS), the superdeformed (SD) state is observed, too, and there is a good candidate for the hyperdeformed (HD) one, as…
Statistical body shape models are widely used in 3D pose estimation due to their low-dimensional parameters representation. However, it is difficult to avoid self-intersection between body parts accurately. Motivated by this fact, we…