Related papers: Multipole Distributions and Hyper-Flux Fields
We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem…
The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The…
A charge-monopole theory is derived from simple and self-evident postulates. Charges and monopoles take an analogous theoretical structure. It is proved that charges interact with free waves emitted from monopoles but not with the…
Electrodynamics is usually written with a polarization vector field to describe the response of matter to electric fields, or more specifically, to describe changes in distribution of charge as an electric field is changed. This approach…
We analyze the flow into inflation for generic "single-clock" systems, by combining an effective field theory approach with a dynamical-systems analysis. In this approach, we construct an expansion for the potential-like term in the…
The problem of the motion of a charged particle in an electric dipole field is used to illustrate that the Hamilton-Jacobi method does not necessarily give all solutions to the equations of motion of a mechanical system. The mathematical…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
We report an analytical investigation of the force and torque acting upon a magnetic dipole placed in the vicinity of a moving electrically conducting nonmagnetic plate. This problem is relevant to contactless electromagnetic flow…
The behavior of a distributed charge in a Coulomb potential well is considered. It is shown that elements of a distributed charge can move along different trajectories, thus forming actually motion of a charge wave. Propagation over…
The concept of the moduli space allows for a simple, universally applicable description of the low-energy dynamics of topological solitons. This description is remarkably insensitive to the properties of the underlying theory, whose details…
The excess power, energy and intensity of a random electromagnetic field above a high threshold level are characterized based on a Slepian--Kac model for upcrossings. For quasi-static fields, the probability distribution of the excess…
The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second order effect comes from the non-central electric dipole…
We present an analytical study, validated by numerical simulations, of electroosmotic flow in a Hele-Shaw cell with non-uniform surface charge patterning. Applying the lubrication approximation and assuming thin electric double layer, we…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
We obtain the fields and electromagnetic self-force of a charge distributed on the surface of a sphere undergoing rigid motion at constant proper acceleration, where the charge distribution has axial symmetry about the direction of motion.…
I investigate the properties of forces on bodies in theories governed by the generalized Poisson equation div[mu(abs(grad_phi))grad_phi]=G rho, for the potential phi produced by a distribution of sources rho. This equation describes, inter…
We develop a general theory of buoyancy instabilities in the electron-ion plasma with the electron heat flux based not upon MHD equations, but using a multicomponent plasma approach in which the momentum equation is solved for each species.…
It is well understood that various alternatives are available within EM theory for the definitions of energy density, momentum transfer, EM stress-energy tensor, and so forth. Although the various options are all compatible with the basic…
In this pedagogical introduction, I discuss theoretical aspects of superfluidity and superconductivity, mostly using a field-theoretical formalism. While the emphasis is on general concepts and mechanisms behind superfluidity, I also…
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.