Related papers: From electrostatic potentials to yet another trian…
A criterion to locate tricritical points in phase diagrams is proposed. The criterion is formulated in the framework of the Elementary Catastrophe Theory and encompasses all the existing criteria in that it applies to systems described by a…
The concept of complex harmonic potential in a doubly connected condenser (capacitor) is introduced as an analogue of the real-valued potential of an electrostatic vector field. In this analogy the full differential of a complex potential…
Most physical systems, whether classical or quantum mechanical, exhibit spherical symmetry. Angular momentum, denoted as $\ell$, is a conserved quantity that appears in the centrifugal potential when a particle moves under the influence of…
In this work, we present an explanation of the electric charge quantization based on a semi-classical model of electrostatic fields. We claim that in electrostatics, an electric charge must be equal to a rational multiple of the elementary…
The use of electrostatic ion beam traps require to set many potentials on the electrodes (ten in our case), making the tuning much more difficult than with quadrupole traps. In order to obtain the best trapping conditions, an analytical…
We develop a method for investigating the relationship between the shape of a 1-particle distribution and non-linear electrostatic oscillations in a collisionless plasma, incorporating transverse thermal motion. A general expression is…
We present an analytic ansatz to find the effective electrostatic potential and Coulomb correlations in multicenter problems, specifically homogeneous and doped clusters of metal atoms. The approach is based on a quasi-classical…
The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other…
In this paper, the approach for considering fast charged particles scattering on targets of complex structure, which contains some isolated substructures, was expanded to account quadratic potential terms. Based on this approach, the…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Partial results obtained in a previous paper are completed to represent accurately…
We propose a consistent approach to the definition of electric, magnetic, and toroidal multipole moments. Electric and magnetic fields are split into potential, vortex, and radiative terms, with the latter ones dropped off in the…
We derive Huygens' principle for electrodynamics in terms of 4-vector potentials defined as distributions supported on a surface surrounding the charge-current density. By combining the Pauli algebra with distribution theory, a compact and…
We derive several versions of the cell theory for a crystal phase of hard equilateral triangles. To that purpose we analytically calculated the free area of a frozen oriented or freely rotating particle inside the cavity formed by its…
New exact solutions are derived for the gravitational potential inside and outside a homogeneous torus as rapidly converging series of toroidal harmonics. The approach consists of splitting the inter- nal potential into a known solution to…
We develop an efficient Ewald method of molecular dynamics simulation for calculating the electrostatic interactions among charged and polar particles between parallel metallic plates, where we may apply an electric field with an arbitrary…
Homogeneous nucleation of a new phase near an Ising-like critical point of another phase transition is studied. A scaling analysis shows that the free energy barrier to nucleation contains a singular term with the same scaling as the order…
We examine the spatial distribution of electric charges within an extended, non-conductive cylinder featuring an inner radius denoted as $r_{0}$. Our investigation unveils the emergence of a distinct modified attractive-inverse square…
We present a theoretical study of the unielectronic energy spectra, electron localization, and optical absorption of triangular core-shell quantum rings. We show how these properties depend on geometric details of the triangle, such as side…
Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of…
Spin-conserving and spin-flip opaque reflections of electrons from a potential barrier in heterostructures are described. An electric field of the barrier is considered to be the only source of energy spin splitting in the presence of…