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The paper presents some characteristics of unsteady scalar planar fields and studies their properties that are relevant to research on environmental extremum seeking and tracking environmental boundaries by mobile robots.
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
It is shown, that the requirement of invariance under spatial rotations reveales an intrinsic fractional extended translation-rotation-like property for particles described with the fractional Schroedinger equation, which we call fractional…
Exact solutions of Schroedinger and Pauli equations for charged particles in an external stationary electromagnetic field of an arbitrary configuration are constructed. Green functions of scalar and spinor particles are calculated in this…
We investigate the interaction between an eccentric planet and a less massive external debris disc. This scenario could occur after planet-planet scattering or merging events. We characterise the evolution over a wide range of initial…
We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between…
Deviation from standard dispersion relations for electrons and photons in the form of an extra term proportional to an arbitrarily high power of momentum is studied. It is shown that observational constraints lead to a region in the…
A sample of spectroscopic binaries and a sample of single planetary systems, both having main-sequence solar-type primary components, are selected in order to compare their eccentricities. The positions of the objects in the…
The role of the quintessence field as a probable candidate for the repulsive dark energy, the conditions for tracking and the requisites for tracker fields are examined. The concept of `integrated tracking' is introduced and a new criterion…
The exact range of the joined values of several R\'{e}nyi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied. Like in the case when only two orders of R\'{e}nyi entropies…
An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that…
The polarizability measures how the system responds to an applied electrical field. Computationally, there are many different ways to evaluate this tensorial quantity, some of which rely on the explicit use of the external perturbation and…
Starting with a post-Newtonian description of compact binary systems, we derive a set of equations that describes the evolution of the orbital angular momentum and both spin vectors during inspiral. We find regions of phase space that…
It is shown that relative coordinate and momentum of coherent electron pair have the meaning of observables with the help of quadrupole and magnetic moments. Distributions of quadrupole terms of scalar potential are shown. These…
A conducting 1D line or 2D plane inside (or on the surface of) an insulator is considered.Impurities displace the charges inside the insulator. This results in a long-range fluctuating electric field acting on the conducting line (plane).…
In a recent paper Martin & Lubow showed that a circumbinary disc around an eccentric binary can undergo damped nodal oscillations that lead to the polar (perpendicular) alignment of the disc relative to the binary orbit. The disc angular…
The matrix elements of the electromagnetic current and the energy-momentum tensor for sharply localized states of spin-1 systems are considered. Their interpretation as local spatial densities of various characteristics of the considered…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems with well separated components. We investigate systems with initially circular and coplanar orbits and comparable masses. The technique is based on…
Entanglement entropy of gauge fields is calculated using the partition function in curved spacetime with a boundary. We derive a Gibbons-Hawking-like term from a Becchi-Rouet-Stora-Tyutin (BRST) action and a Wald-entropy-like codimension-2…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…