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We present a general solution and formulation framework to Bellman's lost-in-a-forest problem. The forest boundary is known and may take any shape. The starting point and the orientation are unspecified. We convert the problem into…
This study uses very simple symmetry and consistency considerations to put constraints on possible Friedmann equations for modified gravity models in curved spaces. As an example, it is applied to loop quantum cosmology.
Recovering spherical magnetizations $m$ from magnetic field data in the exterior is a highly non-unique problem. A spherical Hardy-Hodge decomposition supplies information on what contributions of the magnetization $m$ are recoverable but…
We summarize exact solutions of closed superstrings in a constant magnetic field, from a view point of the regularization criterion. Some models will be excluded according to this criterion. The spectrum-generating algebra is also…
In the present work, a Klein Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is discussed from a more direct and physical perspective, via the heat kernel approach. It is shown that the…
Materials with spin-momentum locked surface or interface states provide an interesting playground for studying physics and application of charge-spin current conversion. To characterize their non-equilibrium magnetic and transport…
The pure traction problem of elasticity appears frequently in engineering applications, and its complexity stems from the fact that its solution is unique only up to (infinitesimal) rigid body motions. When finite elements are employed to…
We present a high order numerical method for the solution of the Neumann Green's function in two dimensions. For a general closed planar curve, our computational method resolves both the interior and exterior Green's functions with the…
There is not a unique solution to the electro- or magnetostatic problem where the "boundary condition" is merely a specification of the fields along a line. As a practical example, we consider the case where it is desired to have a magnetic…
In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We show that the renormalized problem is well defined, the…
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…
We propose an all optical ultrafast method to highly magnetize general quantum magnets using a circularly polarized terahertz laser. The key idea is to utilize a circularly polarized laser and its chirping. Through this method, one can…
For a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$, we consider the problem of restoring the metric $g$ and the magnetic potential $\alpha$ from the values of the Ma\~n\'e action potential between…
Equations of the magnetization dynamics are derived for an arbitrary curved 2D surface. General static solutions are obtained in the limit of a strong anisotropy of both signs (easy-surface and easy-normal cases). It is shown that the…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
We give existence results for simple closed curves with prescribed geodesic curvature on $S^{2}$, which correspond to periodic orbits of a charge in a magnetic field.
Magnetization reversal in a fine ferromagnetic grain is simulated for the case of an instantaneously applied reversal magnetic field. The Hamiltonian of the system contains the exchange interaction, the uniaxial anisotropy, the Zeeman…
We give a Morse-theoretic characterization of simple closed geodesics on Riemannian $2$-spheres. On any Riemannian $2$-sphere endowed with a generic metric, we show there exists a simple closed geodesic with Morse index $1$, $2$ and $3$. In…
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used.
We propose a new type of interaction of closed superstrings with the electromagnetic field, other than the usual Kaluza-Klein type or a gauge field with internal gauge group origin. This model with a constant magnetic field is also shown to…