Related papers: Symmetry reduction for central force problems
We consider the dynamics and symplectic reduction of the 2-body problem on a sphere of arbitrary dimension. It suffices to consider the case for when the sphere is 3-dimensional and where we take the group of symmetries to be $SO(4)$. As…
We discuss some examples of equations of the three-body problem with the oscillating asymptotics at large momentum: (i) the fixed-center approximation, (ii) the unitarized equation in the fixed-center approximation, (iii)…
A more conventional realization of a symmetry which had been proposed towards the solution of cosmological constant problem is considered. In this study the multiplication of the coordinates by the imaginary number $i$ in the literature is…
For the Casimir piston filled with an inhomogeneous medium, the Casimir energy is regularized and expressed with cylinder kernel coefficients by using the first-order perturbation theory. When the refraction index of the medium is smoothly…
We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples…
The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…
We carry out a sequence of coordinate changes for the planar three-body problem which successively eliminate the translation and rotation symmetries, regularize all three double collision singularities and blow-up the triple collision.…
Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving non-relativistically with constant velocity. We use…
In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a…
In this paper we study a generalized symplectic fixed point problem, first considered by J. Moser in \cite{M}, from the point of view of some relatively recently discovered symplectic rigidity phenomena. This problem has interesting…
Quantities associated with Casimir forces are calculated in a model wave system of one spatial dimension with Dirichlet or Neumann boundary conditions. 1)Due to zero-point fluctuations, a partition is attracted to the walls of a box if the…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
In this paper, we investigate the asymptotic symmetry and monotonicity of positive solutions to a reaction-diffusion equation in the unit ball, utilizing techniques from elliptic geometry. Firstly, we discuss the properties of solutions in…
The asymptotic symmetry group of three-dimensional (anti) de Sitter space is the two dimensional conformal group with central charge $c=3\ell/2G$. Usually the asymptotic charge algebra is derived using the symplectic structure of the bulk…
Diverse experimental constraints now motivate models of supersymmetry breaking in which some superpartners have masses well above the weak scale. Three alternatives are focus point supersymmetry and inverted hierarchy models, which embody a…
The Casimir effect, the dispersion force attracting neutral objects to each other, may be understood in terms of multiple scattering of light between the interacting bodies. We explore the simple model in which the bodies are assumed to…
We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
We present a new Monte Carlo method to calculate Casimir forces acting on objects in a near-critical fluid, considering the two basic cases of a wall and a sphere embedded in a two-dimensional Ising medium. During the simulation, the…
We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In…