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Michal Demetrian

Publications and source records attributed to Michal Demetrian.

17 recordsLinked to original sources
arXiv2026

Aggregate models of liquidity-profit dynamics

We discuss the problem of limit cycles in an aggregate-type models of liquidity growth proposed and studied both theoretically and numerically by W. Semmler and M. Sieveking in \cite{SemmlerSieveking}. Their model is locally of predator-prey type with cannibalism in predator (profit) and logistic bound on prey's population (liquidity). We modify the model to include the weak Allee effect in liquidity and to study the local bifurcations of equilibria and limit cycles by means of the Hopf-Andronov theory. The main motivation for this study follows the economic theory of the so-called corridors of stability introduced by Leijonhuvud in \cite{Leijonh}. Similar importance of these effects is, however, found also in the originally developed dynamical models in biology, especially in mathematical ecology.

econ.TH↗
arXiv2012

On computation of clustering coefficient in a class of random networks

The random networks enriched with additional structures as metric and group-symmetry in background metric space are investigated. The important quantities like he clustering coefficient as well as the mean degree of separation in such networks are effectively computed with help of additional structures. Representative models are discussed in details.

math.ST↗
arXiv2008

On Emergence of Dominating Cliques in Random Graphs

Emergence of dominating cliques in Erdös-Rényi random graph model ${\bbbg(n,p)}$ is investigated in this paper. It is shown this phenomenon possesses a phase transition. Namely, we have argued that, given a constant probability $p$, an $n$-node random graph $G$ from ${\bbbg(n,p)}$ and for $r= c \log_{1/p} n$ with $1 \leq c \leq 2$, it holds: (1) if $p > 1/2$ then an $r$-node clique is dominating in $G$ almost surely and, (2) if $p \leq (3 - \sqrt{5})/2$ then an $r$-node clique is not dominating in $G$ almost surely. The remaining range of probability $p$ is discussed with more attention. A detailed study shows that this problem is answered by examination of sub-logarithmic growth of $r$ upon $n$.

math.CO↗
arXiv2006

Study of the Coleman - de Luccia instanton of the second order

We study the second order Coleman - de Luccia instanton which appears as the curvature of the effective potential reaches a sufficiently large value. We show how one can find the approximative formula for this instanton by perturbative expansion in the case when the second derivative of the effective potential divided by the Hubble parameter squared is close to -10, and we perform a numerical study of this instanton in the case of quasi-exponential potential.

gr-qc↗
arXiv2006

Particle in a box at high temperature

High temperature expansion of the partition function for a particle on a segment of a line is found to show an example of the quantum system that thermodynamical functions do not approach the thermodynamical functions of its classical counterpart at high temperature. The problem might be interesting for the students and teachers because by a collection of noninteracting particles trapped in a box at sufficiently high temperature and low density one imitates the classical ideal gas.

physics.ed-ph↗
arXiv2006

Motion of a testing particle in gravitational field of a ring

The planar motion of a testing body in the field of gravity of the massive ring is studied. The "perihelion" precession due to non-relativistic reasons is demonstrated on this simple example of planar motion in the radially symmetric (in the plane of motion) situation. The ring as the source of the gravitational field can serve as the toy model for quasi-planar sources of gravity appearing in the galactic dynamics, etc. The results are used to estimate the real perihelion shift of the planet Mercury due to gravitational quadrupole moment of the Sun.

physics.class-ph↗
arXiv2006

False vacuum decay in a brane world cosmological model

The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein's theory of relativity.

gr-qc↗
arXiv2005

False vacuum decay with gravity in a critical case

The vacuum decay in a de Sitter universe is studied within semiclassical approximation for the class of effective inflaton potentials whose curvature at the top is close to a critical value. By comparing the actions of the Hawking - Moss instanton and the Coleman - de Luccia instanton(s) the mode of vacuum decay is determined. The case when the fourth derivative of the effective potential at its top is less than a critical value is discussed.

gr-qc↗
arXiv2003

A criterion for bubble formation in de Sitter universe

The influence of the shape of scalar field potential on the outcome of vacuum decay in de Sitter universe is studied. Sufficient condition for vacuum decay via bubble formation, described by Coleman - de Luccia instanton, is revisited and necessary condition is found. Both conditions require that the curvature of the potential is greater than 4 $\times$ (Hubble constant)$^2$, but while the sufficient condition states that this inequality is to be valid at the top of the barrier, the necessary condition requires that it holds at least somewhere throughout the barrier. The conditions leave a 'grey zone' in parameter space, which however seems to be forbidden for quartic potential as well as for quadratic potential with a narrow peak proposed by Linde in the context of open inflation.

gr-qc↗
arXiv2002

Quantum mechanics on non-commutative plane

One of the simplest example of non-commutative (NC) spaces is the NC plane. In this article we investigate the consequences of the non-commutativity to the quantum mechanics on a plane. We derive corrections to the standard (commutative) Hamiltonian spectrum for hydrogen-like atom and isotropic linear harmonic oscillator (LHO) and formulate the problem of the potential scattering on the NC plane. In the case of LHO we consider the noncommutativity of the momentum operators, too.

hep-th↗
arXiv2002

How to Introduce A World Time to A Part of Two Dimensional de Sitter Manifold

We define 1+1 dimensional de Sitter manifold in this paper and we consider various coordinate systems on it. Some interesting aspects of the general theory of relativity are demonstrated by using the transformations between the considered coordinate systems. The problem might be of interest for physics and mathematics students as well as for physics teachers.

physics.ed-ph↗
arXiv2002

Casimir effect in four simple situations - including a noncommutative two-sphere

A computation of the Casimir effect for a real scalar field in four situations: on a segment of a line, on a circle and on both standard commutative and noncommutative two-spheres is given in this paper. The main aim of this paper is to discuss the Casimir energy on the noncommutative sphere within the theory with commutative time. The comparison with the noncommutative cylinder is also done.

hep-th↗