Michal Demetrian

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 Einsteins theory of relativity.

The Stability of Normal Equilibrium Point and the Existence of Limit Cycles in a Simple Keynesian Macrodynamic Model of Monetary Policy

In this chapter, a simple Keynesian macroeconomic model of monetary policy describing the development of nominal rate of interest, expected rate of inflation, and nominal money supply in the period of deflationary depression, which was introduced by Asada (2011) is investigated rigorously. The normal equilibrium point of the model is derived and its dynamic stability is investigated. Questions concerning the existence of limit cycles are studied analytically. The bifurcation equation is found. The formulae for the calculation of its coefficients are gained. A numerical example is presented by means of numerical simulations.

False Vacuum Decay with Gravity in a Critical Case

The vacuum decay in a de Sitter universe is studied for the class of effective inflaton potentials that curvature at the top is less than as well as greater than a critical value determined previously. By comparing the actions of the Hawking - Moss instanton and the Coleman - de Luccia instanton(s) the mode of vacuum decay is determined in this critical situation.

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.

On dynamics in a Keynesian model of monetary and fiscal stabilization policy mix with twin debt accumulation

In this paper, a six‐dimensional model of flexible prices with the monetary and fiscal policy mix, describing the development of the firms’ private debt, the output, the expected rate of inflation, the rate of interest, government expenditure, and government bonds are analyzed. The stress put on the “twin debt accumulation” means that in our model both private debt accumulation and the public debt (government bond) accumulation are explicitly introduced. Questions concerning the existence of limit cycles around its normal equilibrium point are investigated. The bifurcation equation is found. The formulae for the calculation of its coefficients are gained. Numerical example illustrating the results attained is presented by means of numerical simulations.

On Liu´s Criterion in Asada´s Model of Monetary and Fiscal Policy

It is known that a simple Hopf bifurcation in a dynamic model can arise if the Jacobian matrix of the model has a pair of purely imaginary eigenvalues and others have negative real parts. Liu ́s criterion gives conditions under which the eigenvalues have required properties. In this paper, a six-dimensional dynamic model of Asada (2014), describing the development of the firms ́ private debt, the output, the expected rate of inflation, the rate of interest, the government expenditures, and the government bond is introduced. There are found conditions on the parameters of the model under which Liu ́s criterion is satisfied. A numerical example illustrates the reached result.

A detailed study of the dominating cliques phase transition in random graphs

A subset of nodes S ⊆V of a graph G =(V , E ) is a dominating clique if S is a dominating set and a clique of G . The phase transition of dominating cliques in Erdos-Renyi random graph model is investigated in this paper. Lower and upper bounds on the edge probability p for the existence of an r -node dominating clique are established in this paper. We prove therein that given an n -node random graph G from for r =c log1/p n with 1≤c ≤2 it holds: (1) if p >1/2 then an r -clique is dominating in G with a high probability and, (2) if

Coleman–de Luccia Instanton of the Second Order in a Brane World

p \leq ( 3 - \sqrt{5})/2

Euclidean action for vacuum decay in a de Sitter universe

then an r -clique is not dominating in G with a high probability. The remaining range of the probability p is discussed with more attention. Within such a range, we provide intervals of r where a dominating clique existence probability is zero, positive but less than one, and one, respectively.

A Criterion for bubble formation in de Sitter universe

The second order Coleman–de Luccia instanton and its action in the Randall–Sundrum type II model are investigated and the comparison with the results in Einstein’s general relativity is done in the present paper.