相关论文: Conservation Laws in Field Dynamics or Why Boundar…
We consider a scalar conservation law with source in a bounded open interval $\Omega\subseteq\mathbb R$. The equation arises from the macroscopic evolution of an interacting particle system. The source term models an external effort driving…
We repeat the numerical experiments for diffusion limited aggregation (DLA) and show that there is a potentially infinite set of conserved quantities for the long time asymptotics. We connect these observations with the exact integrability…
Two-dimensional driven dissipative flows are generally integrable via a conservation law that is singular at equilibria. Nonintegrable dynamical systems are confined to n*3 dimensions. Even driven-dissipative deterministic dynamical systems…
We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for…
It has been known for some time that for a large class of non-linear field theories in Minkowski space with two-dimensional target space the complex eikonal equation defines integrable submodels with infinitely many conservation laws. These…
The dynamics of classical field theories is usually governed by field equations, but when fields are constrained to bounded domains it is also dependent on its boundary conditions. Usually boundary conditions are constrained by the…
One dimensional systems sometimes show pathologically slow decay of currents. This robustness can be traced to the fact that an integrable model is nearby in parameter space. In integrable models some part of the current can be conserved,…
This paper focuses on infinite-horizon optimal control problems for dissipative systems and the relations to their finite-horizon formulations. We show that, for a large class of problems, dissipativity of the state equation, when a…
Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
An action in which the Ricci scalar is nonminimally coupled with a scalar field and contains higher order curvature invariant terms carries a conserved current under certain conditions that decouples geometric part from the scalar field.…
Thin, solid bodies with metric symmetries admit a restricted form of reparameterization invariance. Their dynamical equilibria include motions with both rigid and flowing aspects. On such configurations, a quantity is conserved along the…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
Hyperbolic conservation laws are conventionally solved by evolving reconstructed floating-point fields, incurring both computational overhead and structural diffusion near discontinuities. Here we introduce the Fast Quantised Numerical…
An intrinsic version of the integrability theorem for the classical Backlund theorem is presented. It is characterized by a one-form which can be put in the form of a Riccati system. It is shown how this system can be linearized. Based on…
We give a full analysis of the conservation along null surfaces of generalized energy and super-momenta, for gravitational systems enclosed by a finite boundary. In particular we interpret the conservation equations in a canonical manner,…
It is well known that (possibly non-unique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In Ref. [J. Math. Phys. {\bf 21}, 2802 (1980)], Wald derived a…
We study field theory models in the context of a gravitational theory based on the requirement that the measure of integration in the action is not necessarily \sqrt{-g} but it is determined dynamically through additional degrees of…