We propose a Hamiltonian model for gravity waves on the surface of a uid layer surrounding a gravitating sphere. The general equations of motion are non-local and can be used as a starting point for simpler model equations, which can be derived systematically by expanding the Hamiltonian functional. In this paper, we study in detail the small wave amplitude regime. The rst order non-linear term...

Abstract The method of characteristics is extended to set-valued Hamilton-Jacobi equations. This problem arises from a calculus variations’ with multicriteria Lagrangian function: through an embedding into framework, equation derived, where the Hamiltonian function Fenchel conjugate function. In this paper described and some results are given for conjugate.

In this paper, we propose a constructive procedure to modify the Hamiltonian function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for nonzero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network modeling of physical systems, is to embed the system into a larger Hamiltonian system for which a...

We study the off-equilibrium dynamics of the Edwards–Anderson spin glass in four dimensions under the influence of a non-Hamiltonian perturbation (i.e. with asymmetric couplings). We find that for small asymmetry the model behaves like the Hamiltonian model, while for large asymmetry the behaviour of the model can be well described by an interrupted ageing scenario. The autocorrelation function...

We propose an intensity-dependent pion-nucleon coupling Hamiltonian within a unitary multiparticle-production model of the Auerbach-Avin-Blankenbecler-Sugar (AABS) type in which the pion field is represented by the thermal-density matrix. Using this Hamiltonian, we explain the appearance of the negative-binomial (NB) distribution for pions and the well-known empirical relation, the so-called Wr...

We demonstrate a method to characterise the general Heisenberg Hamiltonian with non-uniform couplings by mapping the entanglement it generates as a function of time. Identification of the Hamiltonian in this way is possible as the coefficients of each operator control the oscillation frequencies of the entanglement function. The number of measurements required to achieve a given precision in th...

Numerical simulations of lattice field theories are usually performed in the Lagrangian formulation. The alternative approach of the Hamiltonian formulation [1] has received very little attention so far. Nonetheless, we think there are very good reasons to develop numerical simulation techniques for the Hamiltonian approach: powerful many-body techniques are available [2], which allow the direc...

This paper studies the injection process into a storage ring and presents an analytic model for the nonstationary particle distribution after m ismatched or off-axis injection. The effects of nonlinear fields as well as coupling to the longitudinal motion are described by analytic expressions for the first moments of the particle distribution. The result contains two distinct approximations: fi...

In this thesis, we consider smooth optimal control systems that evolve on Lie groups. Pontryagin’s maximum principle allows us to search for local solutions of the optimal control problem by studying an associated Hamiltonian dynamical system. When the associated Hamiltonian function possess symmetries, we can often study the Hamiltonian system in a vector space whose dimension is lower than th...

We consider a Hamiltonian setup (M, ω,H,L,Γ,P), where (M, ω) is a symplectic manifold, L is a distribution of Lagrangian subspaces in M, P a Lagrangian submanifold of M, H is a smooth time dependent Hamiltonian function on M and Γ : [a, b] 7→ M is an integral curve of the Hamiltonian flow ~ H starting at P . We do not require any convexity property of the Hamiltonian function H . Under the assu...