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The concept of the partial osmotic pressure of ions in an electrolyte solution is critically examined. In principle these can be defined by introducing a solvent-permeable wall and measuring the force per unit area which can certainly be…
Existence and uniqueness are investigated for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial…
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis…
In this work single capacitor paradox (a variation of the remarkable two capacitor paradox) is considered in a new, quantum discrete form. Simply speaking we consider well-known usual, photoelectric effect experimental device, i.e. photo…
In the thesis, first, the cancellation of infrared divergences in QED is reviewed. Next, two examples in QCD, the quark-quark scattering and the quark-gluon scattering are examined at one loop, from which the importance of Ward-Takahashi…
We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties. Besides…
Using area-preserving curve shortening flow, and a new inequality relating the potential generated by a set to its curvature, we study a non-local isoperimetric problem which arises in the study of di-block copolymer melts, also referred to…
Application of a strong electric field to insulators induces a finite current. This phenomenon is called dielectric breakdown and is known as a fundamental nonequilibrium and nonlinear transport phenomenon in solids. Here, we study the…
Parameters of a high frequency capacitive discharge in argon in axially symmetric chambers of different geometries are studied in experiments and by means of two-dimensional kinetic modeling by the Particle-in-Cell method. It is…
Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of…
We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bounded from below by a positive constant and the case of…
The theory of singular dislocations is placed within the framework of the theory of continuous dislocations using de Rham currents. For a general $n$-dimensional manifold, an $(n-1)$-current describes a local layering structure and its…
Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened…
In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equation has solutions which show characteristics…
We study a 2D system of identical mobile particles on the surface of a cylinder of finite length $d$ and circumference $W$, immersed in a medium of dielectric constant $\varepsilon$. The two end-circles of the cylinder are like-charged with…
The charge distribution at the interface between two electrolytes is studied for the case of non-vanishing ion fluxes. The analysis is an extension of the established Verwey-Niessen theory to non-equilibrium situations. Applying matched…
We analyze the problem of gravitational collapse considering the matching of an exterior region described by the Vaidya's metric and an interior region described by a spherically symmetric shear-free inhomogeneous geometry sourced by a…
We investigate the black holes properties with a very simple and semi-classical model of spacetime discretization. In this context, we apply the Heisenberg's uncertainty principle and the equipartition energy theorem to thereto, obtaining…
Highly efficient sources of indistinguishable single photons that can operate at room temperature would be very beneficial for many applications in quantum technology. We show that the implementation of such sources is a realistic goal…
The formation of electron groups is a common phenomenon in gas discharges and space plasmas. We describe similarities between electron kinetics in solar wind, cathode region of glow discharges, and magnetic nozzles. Remarkable resemblances…