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Understanding the thermal behaviour of superconducting accelerator magnets is essential to ensure their stable and reliable operation. This work presents an extension of the Finite Element Quench Simulator (FiQuS) Multipole module to…
Motivated by recent experiments with proximitized nanowires, we study a mesoscopic s-wave superconductor connected via point contacts to normal-state leads. We demonstrate that at energies below the charging energy the system is described…
Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The…
We study a transmission problem for the time harmonic Maxwell's equations between a classical positive material and a so-called negative index material in which both the permittivity $\varepsilon$ and the permeability $\mu$ take negative…
A geometric theory of the irreducible tensor operators of quantum spin systems. It is based upon the Maxwell-Sylvester geometric representation of the multipolar electrostatic potential. In the latter, an order-$\ell$ multipolar potential…
High-fidelity numerical methods that model the physical layout of a device are essential for the design of many technologies. For methods that characterize electromagnetic effects, these numerical methods are referred to as computational…
In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called…
Several aspects of the general theory for the critical states of a vortex lattice and the magnetic flux dynamics in type-II superconductors are examined by a direct variational optimisation method and widespread physical principles. Our…
The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
To date the most precise estimations of the critical exponent for the Anderson transition have been made using the transfer matrix method. This method involves the simulation of extremely long quasi one-dimensional systems. The method is…
Using Maxwell's mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations $\operatorname{curl} \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$, $\operatorname{curl} \mathbf{H} = \frac{\partial…
Solving coupled nonlinear sine-Gordon equations and Maxwell equations numerically, we study the electromagnetic and superconducting properties of the single crystal of high-$T_c$ superconductor $\rm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ with a…
The predictions of Moore's law are considered by experts to be valid until 2020 giving rise to "post-Moore's" technologies afterwards. Energy efficiency is one of the major challenges in high-performance computing that should be answered.…
A Maxwell solver derived from finite element method with \mathcal{O}(N) computing cost is developed to improve the numerical dispersion properties in relativistic particle-in-cell (PIC) simulations. The correction of the dispersion relation…
We study Maxwell's equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and $L^2$-data. Our first contribution is a direct proof of well-posedness of the…
We present a small computer algebra program for use in Maxwell's theory. The Maxwell equations and the energy-momentum current of the electromagnetic field are formulated in the language of exterior differential forms. The corresponding…
Maxwell equations provide a complete description of the electromagnetic (EM) phenomena, which have been one of the key fundamental-theories of modern physics, such as electromagnetism, optics, quantum theories, etc. The vacuum permittivity…
The superconducting transition in presence of strong columnar disorder parallel to the magnetic field is considered. A solvable model appropriate for description of the broad crossover regime towards the true "glassy" critical behavior is…
Constant-potential molecular dynamics (MD) simulations are indispensable for understanding the capacitance, structure, and dynamics of electrical double layers (EDLs) at the atomistic level. However, the classical constant-potential method,…
Electrical power conversions are common in a large variety of engineering applications. With reference to AC/DC and DC/AC power conversions, a strong research interest resides in multilevel converters, thanks to the many advantages they…