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We find an exact closed-form expression for the magnetostatic interaction energy between a point magnet and a ring magnet in terms of complete elliptic integrals. The exact expression for the energy exhibits an equilibrium point close to…
This is the final part of a series of papers where we study perturbations of divergence form second order elliptic operators $-\operatorname{div} A \nabla$ by first and zero order terms, whose complex coefficients lie in critical spaces,…
This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region…
The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several…
Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…
The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The deduced…
The longitudinal relaxation time of the magnetization of a system of two exchange coupled spins subjected to a strong magnetic field is calculated exactly by averaging the stochastic Gilbert-Landau-Lifshitz equation for the magnetization,…
The dipteran flight mechanism of the insects is commonly used to design the nonlinear flight robot system. However, the dynamic response of the click mechanism of the nonlinear robot system with multiple stability still unclear. In this…
This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from…
We discuss the problem of equilibrium spin currents in ferromagnets with inhomogeneous magnetization. Using simple microscopic models we explain the physical origin of equilibrium spin currents. Next we derive the equilibrium spin current…
We shall introduce a stability condition for a coherent sheaf associated to an elliptic surface. Then we study the behavior under relative Fourier-Mukai transforms.
Rotational inertia is stabilizing the frequency of electric power systems against small and large disturbances, but it is also the cause for oscillations between generators. As more and more conventional generators are replaced by renewable…
The derivation of electromagnetic gyrofluid equations is made systematic by using the Hermite polynomial form of the underlying delta-f gyrokinetic distribution function. The gyrokinetic free-energy functional is explicitly used to set up…
Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating…
The coherent manipulation of spin observables in storage rings provides opportunities to test the application of some fundamental dynamical principles. In this context, it is possible to confirm, using gauge invariance and Lorentz…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
This talk presents a list of problems related to the double-elliptic (Dell) integrable systems with elliptic dependence on both momenta and coordinates. As expected, in the framework of Seiberg-Witten theory the recently discovered explicit…
We discuss analytical approximation schemes for the dynamics of diluted spin models. The original dynamics of the complete set of degrees of freedom is replaced by a hierarchy of equations including an increasing number of global…
We compute the entanglement entropy of a massless spin $2$ field in a sphere in flat Minkowski space. We describe the theory with a linearized metric perturbation field $h_{\mu\nu}$ and decompose it in tensor spherical harmonics. We fix the…
In this article we present an efficient algorithm to compute rotation intervals of circle maps of degree one. It is based on the computation of the rotation number of a monotone circle map of degree one with a constant section. The main…