Related papers: Multipole Distributions and Hyper-Flux Fields
At the surfaces of materials, the bulk symmetry of the charge density is broken and electron spill-out into the vacuum region creates a surface dipole. Such spill-out has been historically calculated by Lang and Kohn [Phys. Rev. B…
We discuss the continuum field theory limit of the physical scenario described in Ref. [1], the universe arising from the interpretation of the most general collection of logical codes in terms of distributions of units of energy along…
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with…
The behavior of the magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge. In addition to the usual inverse distance singularity,…
The concept of electromotive force (emf) may be introduced in various ways in an undergraduate course of theoretical electromagnetism. The multitude of alternate expressions for the emf is often the source of confusion to the student. We…
The method of image charges is a powerful and elegant technique in electrostatics, commonly used to determine the electric field generated by point charges near conductors of various shapes. While standard problems focus on single charges…
We present an application of the basic mathematical concept of complex functions as topological solitons, a most interesting area of research in physics. Such application of complex theory is virtually unknown outside the community of…
A topological flux function is introduced to quantify the topology of magnetic braids: non-zero line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a…
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are…
Dense distributions of string-like objects in material media are considered in terms of continuum field theory. The strings are assumed to carry a quantized abelian topological charge, such as the Burgers vector of dislocations in solids or…
We develop a numerical statistical method to study linear cosmological fluctuations in inflationary scenarios with multiple fields, and apply it to an ensemble of six-field inflection point models in string theory. The latter are concrete…
We give a description of cell diffusion in a soft tissue, paying special attention to the coupling of force, matter, and microforce balance laws through a suitable dissipation principle. To this end, we cast our framework into a multi-level…
We discuss a simple and experimentally available realization of fracton physics. We note that superfluid vortices form a Hamiltonian system that conserves total dipole moment and trace of the quadrupole moment of vorticity; thereby…
A long-standing controversy concerning the causes of the magnetic field in and around a parallel-plate capacitor is examined. Three possible sources of contention are noted and detailed. The first is the ambiguous initial impression given…
The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase-boundaries, i.e. the boundaries between a condensed phase and its vapor and the boundaries between two or multiple…
The purpose of this course is to provide an introduction to Electromagnetic Theory. The foundations of electrodynamics starting from the nature of electrical force up to the level of Maxwell equations solutions are presented. It starts with…
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of all constituting ions. One feature of active…
In this comment, we discuss some features of the multipolar expansion of the power radiated by a confined system of charges and currents, and the possibility of generalization to a higher arbitrary order of the multipolar expansion.
We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular…
The problem of the charged-particle motion in crossed electric and magnetic fields is investigated, and the validity of the guiding-center representation is assessed in comparison with the exact particle dynamics. While the magnetic field…