Related papers: Modeling Magnetic Fields with Helical Solutions to…
We study a semilinear equation involving the fractional Laplacian on the hyperbolic space $\mathbb{H}^n$. Unlike in conformally compact Einstein manifolds, the fractional Laplacian on $\mathbb{H}^n$ does not enjoy conformal covariance. By…
In the presence of cosmic chiral asymmetry, chiral-vorticity and chiral-magnetic effects can play an important role in the generation and evolution of magnetic fields in the early universe. We include these chiral effects in the magnetic…
The Earth's magnetic field can be decomposed into spherical harmonics, and the exact coefficients of the decomposition can be determined through a few measurements of its value at different locations. Using measurements from a magnetometer…
A thermodynamic model for the generation of magnetic fields in the planets is proposed, considering crossed effects between gravitational and electric forces. The magnetic field of the Earth is estimated and found to be in agreement with…
Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory.…
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…
In this paper we present the analytical calculations to derive the magnetic field of a solenoid by solving exactly a fractional integral with the use of a novel method. Starting from the Biot-Savart law, we consider a coil of negligible…
Rotating magnetic structures are common in astrophysics, from vortex tubes and tornados in the Sun all the way to jets in different astrophysical systems. The physics of these objects often combine inertial, magnetic, gas pressure and…
Development of quantum engineering put forward new theoretical problems. Behavior of a single mesoscopic cell (device) we may usually describe by equations of quantum mechanics. However if experimentators gather hundreds of thousands of…
We present all second order classical integrable systems of the cylindrical type in a three dimensional Euclidean space $\mathbb{E}_3$ with a nontrivial magnetic field. The Hamiltonian and integrals of motion have the form $H…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar…
A new method for derivation of the equation of motion from the field equation is proposed. The problem of embedding the singularities in a field satisfying the field equations is discussed.
We explain the (non)helical dynamo process using a field-structure model based on magnetic induction equation in an intuitive way. We show how nonhelical kinetic energy converts into magnetic energy and cascades toward smaller eddies in a…
It is well known that helical magnetic fields undergo a so-called inverse cascade by which their correlation length grows due to the conservation of magnetic helicity in classical ideal magnetohydrodynamics (MHD). At high energies above…
We present a solvable ladder model which displays magnetization plateaus at fractional values of the total magnetization. Plateau signatures are also shown to exist along special lines. The model has isotropic Heisenberg interactions with…
We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
On a metric measure space $X$ that supports a regular, strongly local resistance form we consider a magnetic energy form that corresponds to the magnetic Laplacian for a particle confined to $X$. We provide sufficient conditions for…
The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an…