Related papers: A symmetry and Noether charge preserving discretiz…
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…
Noether's 2nd theorem applied to a total system states that a global symmetry which is a part of local symmetries does not provide a physically meaningful conserved charge but it instead leads to off-shell constraints as a form of conserved…
We consider the system of partial differential equations stemming from the time discretization of the two-field formulation of the Biot's model with the backward Euler scheme. A typical difficulty encountered in the space discretization of…
In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the…
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
This paper studies the reduced phase space formulation (relational formalism) of gravity coupling to the Brown-Kucha\v r dust for asymptotic flat spacetimes. A set of boundary conditions for the asymptotic flatness are formulated for Dirac…
Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of…
We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied…
In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…
This article deals with a simultaneous abstract evolution equation. This includes a parabolic-hyperbolic phase-field system as an example which consists of a parabolic equation for the relative temperature coupled with a semilinear damped…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
We find exact cosmological solutions when the Newton parameter and the cosmological term are dynamically evolving in a renormalization-group improved Hamiltonian approach. In our derivation we use the Noether symmetry approach, leading to…
It has been noticed that for a large class of cosmological models, the gauge fixing of the time-reparametrization invariance does not completely fix the clock. Instead, the system enjoys a surprising residual Noether symmetry under a…
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
Existence of strong solutions of an abstract Cauchy problem for a class of doubly nonlinear evolution inclusion of second order is established via a semi-implicit time discretization method. The principal parts of the operators acting on…