相关论文: The rigid body and the pendulum revisited
A famous result by Delort about the two-dimensional incompressible Euler equations is the existence of weak solutions when the initial vorticity is a diffuse bounded Radon measure with distinguished sign. In this paper we are interested in…
A complete description of twisting somersaults is given using a reduction to a time-dependent Euler equation for non-rigid body dynamics. The central idea is that after reduction the twisting motion is apparent in a body frame, while the…
We show that the integrability of the dynamical system recently proposed by Calogero and characterized by the Hamiltonian $ H = \sum_{j,k}^{N} p_j p_k \{\lambda + \mu cos [ \nu ( q_j - q_k)] \} $ is due to a simple algebraic structure . It…
We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
Although repulsive effects have been predicted for quantum vacuum forces between bodies with nontrivial electromagnetic properties, such as between a perfect electric conductor and a perfect magnetic conductor, realistic repulsion seems…
Alternative to the embedding formalism, we provide a group theoretic approach to the conformal primary basis for the massless field with arbitrary helicity. To this end, we first point out that $sl(2,\mathds{C})$ isometry gets enhanced to…
We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
The deformation theory of hyperbolic and Euclidean cone-manifolds with all cone angles less then 2{\pi} plays an important role in many problems in low dimensional topology and in the geometrization of 3-manifolds. Furthermore, various old…
We describe a three-dimensional geometry that exhibits a repulsive Casimir force using ordinary metallic materials, as computed via an exact numerical method (no uncontrolled approximations). The geometry consists of a zippelike,…
For the chiral oscillator described by a second order and degenerate Lagrangian with special Euclidean group of symmetries, we show, by cotangent bundle Hamiltonian reduction, that reduced equations are Lie-Poisson on dual of oscillator…
The vacuum expectation values of the energy--momentum tensor are investigated for massless scalar fields satisfying Dicichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on…
The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal fluid and plasma dynamics, is addressed in the…
The Robert-Sommeria-Miller equilibrium statistical mechanics predicts the final organization of two dimensional flows. This powerful theory is difficult to handle practically, due to the complexity associated with an infinite number of…
Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of…
Using a path integral approach we rederive a recently found representation of the Casimir energy for a sphere and a cylinder in front of a plane and derive the first correction to the proximity force theorem.
This survey gives a short and comprehensive introduction to a class of finite-dimensional integrable systems known as hypersemitoric systems, recently introduced by Hohloch and Palmer in connection with the solution of the problem how to…
We study the equation of motion of the Euclidean IKKT matrix model, and realize a new type of classical saddle that only exists in $N\rightarrow\infty$ limit. Under the assumption that the matrices are the generators of…
We construct explicitly a Kac-Moody algebra associated to SL$(2, \mathbb R)$ in two different but equivalent ways: either by identifying a Hilbert basis of $L^2($SL$(2, \mathbb R))$ or by the Plancherel Theorem. Central extensions and…