相关论文: The birational Lalanne-Kreweras involution

We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…

The geometry of a Lagrangian mechanical system is determined by its associated evolution semispray. We uniquely determine this semispray using the symplectic structure and the energy of the Lagrange space and the external force field. We…

We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as involutive subbundles of $TM+\wedge^k TM^*$ satisfying a weak version of the…

We develop a general optimization-theoretic framework for Bregman-Variational Learning Dynamics (BVLD), a new class of operator-based updates that unify Bayesian inference, mirror descent, and proximal learning under time-varying…

The transverse, spatial structure of protons is an area revealing fundamental properties of matter, and provides key input for deeper understanding of emerging collective phenomena in high energy collisions of protons, as well as collisions…

Birational rowmotion is a discrete dynamical system on the set of all positive real-valued functions on a finite poset, which is a birational lift of combinatorial rowmotion on order ideals. It is known that combinatorial rowmotion for a…

Convection in a layer inclined against gravity is a thermally driven non-equilibrium system, in which both buoyancy and shear forces drive spatio-temporally complex flow. As a function of the strength of thermal driving and the angle of…

The Levy-flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus, this processes is a kind of continuous-time random walks (CTRW),…

We study a birational map associated to any finite poset P. This map is a far-reaching generalization (found by Einstein and Propp) of classical rowmotion, which is a certain permutation of the set of order ideals of P. Classical rowmotion…

An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to…

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger-Feynman-Dyson perturbation expansion and detailed rules are derived for computations. Complexification…

Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer's light-cone and light propagation to obtain observables. Cosmological perturbation theory in the…

Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting…

The Loewner equation is known as a one-dimensional reduction of the Benney chain as well as the dispersionless KP hierarchy. We propose a reverse process showing that time splitting in the Loewner or the Loewner-Kufarev equation leads to…

This is a survey on recent results on the Loewner theory in one and several complex manifolds

We review two numerical methods related to the Schramm-Loewner evolution (SLE). The first simulates SLE itself. More generally, it finds the curve in the half-plane that results from the Loewner equation for a given driving function. The…

In this paper, for the first time a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi-detailed balance. Starting from a coupled BBGKY hierarchy…

Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case…

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a…

We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…