相关论文: A note on two Collatz evolution flows

We consider evolution operators $G(t,s)$ associated to a class of nonautonomous elliptic operators with unbounded coefficients, in the space of bounded and continuous functions over $\mathbb{R}^d$. We prove some new pointwise estimates for…

In statistical physics, the Nakajima-Mori-Zwanzig projection operator formalism is used to derive an integro-differential equation for observables in a Hilbert space, the generalized Langevin equation (GLE). This technique relies on the…

The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called {\it evolution loops}). We make a detailed…

In this paper we study the discrete-time dynamical systems associated with gonosomal algebras used as algebraic model in the sex-linked genes inheritance. We show that the class of gonosomal algebras is disjoint from the other…

We present a mathematical framework within which Discrete Dislocation Dynamics in three dimensions is well-posed. By considering smooth distributions of slip, we derive a regularised energy for curved dislocations, and rigorously derive the…

We prove long-time existence for the negative $L^2$-gradient flow of the $p$-elastic energy, $p\geq 2$, with an additive positive multiple of the length of the curve. To achieve this result we regularize the energy by adding a small…

The Generalized SU(2) Proca (GSU2P) theory has recently garnered attention for its potential to describe key phases of cosmic evolution, including primordial inflation and late-time accelerated expansion. However, its full cosmological…

Non-Hermitian Hamiltonians and Lindblad operators are some of the most important generators of dynamics for describing quantum systems interacting with different kinds of environments. The first type differs from conservative evolution by…

We consider the problem of dynamical stability for the $n$-vortex of the Ginzburg-Landau model. Vortices are one of the main examples of topological solitons, and their dynamic stability is the basic assumption of the asymptotic ``particle…

We perform numerical simulations to investigate tidal evolution of two single-planet systems, that is, WASP-50 and GJ 1214 and a two-planet system CoRoT-7. The results of orbital evolution show that tidal decay and circularization may play…

(abridged) Aims: To study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods: We use the test field method together with 3D numerical simulations of turbulent…

Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…

We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between…

In this paper, we study stationary structures near the planar Couette flow in Sobolev spaces on a channel $\mathbb{T}\times[-1,1]$, and asymptotic behavior of Couette flow in Gevrey spaces on $\mathbb{T}\times\mathbb{R}$ for the…

We consider a Bose-Einstein condensate driven by periodic delta-kicks. In contrast to first-order descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate…

We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…

We consider the relation between so called continuous localization models - i.e. non-linear stochastic Schr\"odinger evolutions - and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW…

The evolution operator method is used to solve the generalized Fokker-Planck equations and the generalized diffusion-wave equations in the (1+1) dimensional space in which $x\in\mathbb{R}$ and $t\in\mathbb{R}_+$. These equations contain…

Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…

We investigate the evolution of phase transition of the classical fully compact dimer model on the bipartite square lattice with second nearest bonds at finite temperatures. We use the numeric Monte Carlo method with the directed-loop…