相关论文: Static and Dynamical Phyllotaxis in a Magnetic Cac…

Phyllotactic states are regular lattice-like structures on cylinders and are a botanical classification scheme. In this communication, we report a sequence of transitions between phyllotactic states for particles with a repulsive…

This article consists of two papers: $\textit{Typical dynamics of Newton's method}$ by Steele and $\textit{Erratum to "Typical dynamics of Newton's method"}$ by Dud\'ak and Steele. Let $C^1(M)$ be the space of continuously differentiable…

Leaves of vascular plants are arranged regularly around stems, a phenomenon known as phyllotaxis. A constant angle between two successive leaves is called divergence angle. On the one side, the divergence angle $\alpha_0$ of an initial…

The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a…

We present an application of the basic mathematical concept of complex functions as topological solitons, a most interesting area of research in physics. Such application of complex theory is virtually unknown outside the community of…

Variational principle for a solid in classical mechanics is formulated in terms of a thin elastic 4D bar strain in Minkowsky events space of special relativity. It is shown, that the sum of elastic 4-energies of weak twist and bending under…

In the present paper which is a sequel to [N.B. Volkov and A.M. Iskoldsky The dynamics of vortex structures and states of current: 1;[1]], the dynamics of non-equilibrium phase transitions and states of current in electrophysical systems…

Motivated by Polychronakos' discovery that solitons exist in the hydrodynamic equations of continuum version of the Calogero model, we seek solitons in the classical dynamics of a continuum version of the Haldane-Shastry spin chain. We have…

These notes, written version of a Bourbaki talk, survey Morel-Voevodsky's motivic homotopy theory over a field, with a focus on computations of motivic homotopy sheaves, both stable and unstable. We also describe Isaksen-Wang-Xu's…

Magnetic solitons are nonlinear, local excitations in magnetic systems. In this study, we theoretically and numerically investigate the properties and generation of one-dimensional (1D) topologically trivial magnetic solitons in…

We study the scattering properties of optical dipole-mode vector solitons recently predicted theoretically and generated in a laboratory. We demonstrate that such a radially asymmetric composite self-trapped state resembles ``a molecule of…

Evolution of systems in which Hamiltonians are generators of gauge transformations is a notion that requires more structure than the canonical theory provides. We identify and study this additional structure in the framework of relational…

A general approach allowing to find the analytical expressions for equilibrium magnetic structures in small and flat magnetic nano-sized cylinders of arbitrary shape made of soft magnetic material is presented. The resulting magnetization…

The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…

The O(3) sigma model in two spatial dimensions admits topological (Bogomol'nyi) lower bound on its energy. This paper proposes a lattice version of this system which maintains the Bogomol'nyi bound and allows the explicit construction of…

We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…

We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum…

Soliton dynamics in spin-textured metals generate electrical currents, which produce backaction through spin torques. We modify the Landau-Lifshitz-Gilbert equation and the corresponding solitonic equations of motion to include such…

We study the classical anisotropic ferromagnetic spin chain with frustration. The behavior of soliton and kink solutions in the vicinity of the ground state phase transition from the ferromagnetic to the spiral phase is studied. The…