相关论文: Miquel Dynamics, Clifford Lattices and the Dimer M…

Starting from the hypothesis that the tubulin dimer is a conformationally bistable molecule - fluctuating between a curved and a straight configuration at room temperature - we develop a model for polymorphic dynamics of the microtubule…

Using our mathematical framework developed in \cite{cresson-pierret_scale} called \emph{scale dynamics}, we propose in this paper a new way of interpreting the problem of adding or modifying potentials in mechanics and specifically in…

We implement a standard Monte Carlo algorithm to study the slow, equilibrium dynamics of a silica melt in a wide temperature regime, from 6100 K down to 2750 K. We find that the average dynamical behaviour of the system is in quantitative…

The Standard Model of particle physics is derived from first principles from the free Dirac Lagrangian in 8-dimensional spacetime. Motivated by second quantization arguments, we embed the 4-dimensional Clifford algebra of the Dirac…

We derive the general continuum model for a bilayer system of staggered-flux square lattices, with arbitrary elastic deformation in each layer. Applying this general continuum model to the case where the two layers are rigidly rotated…

In this paper, we introduce a Clifford algebra framework for Julia-type dynamics driven by the geometric product. The nonlinear iteration \[ f(\vec{x}) = (\vec{x}\diamond \vec{n})^p \diamond \vec{n} + \vec{c}, \qquad p \ge 2, \] is studied…

It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a…

We generalize the Vicsek model to describe the collective behaviour of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise…

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…

We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. The latter algebra is a manifold, called Clifford space, which is assumed to be the arena in which physics takes place. A Clifford space…

A novel formulation of fluid dynamics as a kinetic theory with tailored, on-demand constructed particles removes any restrictions on Mach number and temperature as compared to its predecessors, the lattice Boltzmann methods and their…

Dirac, Fock, and Podolsky [Ref. 1] devised a relativistic model in 1932 in which a fixed number of $N$ Dirac electrons interact through a second-quantized electromagnetic field. It is formulated with the help of a multi-time wave function…

The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…

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 investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving 3 tiles which sample the tiling sets {\em via} Monte Carlo Markov chains. We determine…

The paper emphasizes asymptotic behaviors, as stability, instability, dichotomy and trichotomy for skew-evolution semiflows, defined by means of evolution semiflows and evolution cocycles and which can be considered generalizations for…

This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdorff setting, we provide an explicit…

We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…

We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann…

We formulate Dirac-Kaehler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac-Kaehler action requires to choose the lattice structure having both orientabilities…