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The timeline of the Earth's history reveals quasi-periodicity of the geological record over the last 542 Myr, on timescales close, in the order of magnitude, to 1 Myr. What is the origin of this quasi-periodicity? What is the nature of the…
Experimentally observed magnetic fields with nanoscale variations are theoretically modeled by a piece-wise constant function with jump discontinuity along a smooth curve, the magnetic edge. Assuming the edge is a closed curve with an axis…
The electron motion in a strong perpendicular magnetic field close to the impenetrable stripe is considered by making use of the singular integral equation technique. The energy spectrum is calculated and compared with the energy spectrum…
Ballistic transport properties in a two dimensional electron gas are studied numerically, where magnetic fields are perpendicular to the plane of two dimensional electron systemsand periodically modulated both in $x$ and $y$ directions. We…
We consider the electron gas moving on the surface of a sphere in a uniform magnetic field. An exact solution of the problem is found in terms of oblate spheroidal functions, depending on the parameter $p= \Phi/\Phi_0$, the number of flux…
The critical behaviour of the Ising model in the absence of an external magnetic field can be specified either through spontaneous symmetry breaking (thermal criticality) or through cluster percolation (geometric criticality). We extend…
In this paper we prove that every locally minimizing curve with constant speed in a prox-regular subset of a Riemannian manifold is a weak geodesic. Moreover, it is shown that under certain assumptions, every weak geodesic is locally…
Although systematic measurements of the solar polar magnetic field exist only from mid 1970s, other proxies can be used to infer the polar field at earlier times. The observational data indicate a strong correlation between the polar field…
The earthquake-like model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach…
We consider a charged particle following the boundary of a two-dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering…
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
The motion of a charged particle in a straight magnetic field ${\bf B} = B(y)\,\wh{\sf z}$ with a constant perpendicular gradient is solved exactly in terms of elliptic functions and integrals. The motion can be decomposed in terms of a…
Magnetic fields are present on all scales in the Universe. While we understand the processes which amplify the fields fairly well, we do not have a "natural" mechanism to generate the small initial seed fields. By using fully relativistic…
We consider Ising models in two and three dimensions with nearest neighbor ferromagnetic interactions and long range, power law decaying, antiferromagnetic interactions. If the strength of the ferromagnetic coupling J is larger than a…
The secondary electron emission process is essential for the optimal operation of a wide range of applications, including fusion reactors, high-energy accelerators, or spacecraft. The process can be influenced and controlled by the use of a…
The problem of extracting the work from a quantum-thermodynamic system driven by slowly varying external parameters is discussed. It is shown that there naturally emerges a gauge-theoretic structure. The field strength identically vanishes…
A yoke-based permanent magnet, which has been employed in many watt balances at national metrology institutes, is supposed to generate strong and uniform magnetic field in an air gap in the radial direction. However, in reality the fringe…
Periodically driven dynamics of a particle moving in the field Coulomb plus confining potential is treated for one and three dimensional cases. Critical value of the external field strength at which chaotization will occur is evaluated…
Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In…