Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number $n_0$ of the sites in the system leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on $n_0$. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in $n_0$ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum Path-Integral Monte Carlo calculations.Comment: 12 pages, 8 Postscript figure

Model of the Belousov-Zhabotinsky reaction

The article describes results of the modified model of the Belousov-Zhabotinsky reaction, which resembles rather well the limit set observed upon experimental performance of the reaction in the Petri dish. We discuss the concept of the ignition of circular waves and show that only the asymmetrical ignition leads to the formation of spiral structures. From the qualitative assumptions on the behavior of dynamic systems, we conclude that the Belousov-Zhabotinsky reaction likely forms a regular grid.Comment: 17 pages, 12 figure

New model for system of mesoscopic Josephson contacts

Quantum fluctuations of the phases of the order parameter in 2D arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free of the incorrect application of the phase operator. The proposed model employs trigonometric phase operators and makes it possible to study arrays of small superconducting granules, pores filled with superfluid helium, or Josephson junctions in which the average number of particles $n_0$ (effective bosons, He atoms, and so on) is small, and the standard approach employing the phase operator and the particle number operator as conjugate ones is inapplicable. There is a large difference in the phase diagrams between arrays of macroscopic and mesoscopic objects for $n_0 < 5$ and $U<J$ ($U$ is the characteristic interaction energy of the particle per granule and $J$ is the Josephson coupling constant). Reentrant superconductivity phenomena are discussed.Comment: 4 pages, 3 Postscript figure

Stochastic Turing patterns in the Brusselator model

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross diffusive terms, often neglected in the heuristic derivation of reaction diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.Comment: modified version submitted to Phys Rev. E. 5. 3 Figures (5 panels) adde

Legal and economic components of modern accounting transformation

Complex transformational process characteristics of modern accounting have significantly influenced its three components; the economic, mathematical and legal aspect of modern accounting. Currently the predominant role belongs to the first one, but in the conditions of the digital economy development it is the mathematical one. It should be noted that the importance of commercial secrets prevent the transition to the information flows transparency while significant decrease of the legal accounting aspect can lead to certain quality deterioration of the accounting information. The main idea of this article is not only to discover the negative aspects connected with the weakening of legal accounting aspects, but also to show possible options of modern legal issues and implementations into the accounting practice. One of the main theoretical and methodological problems in this area is the intensive expansion of the multivariate accounting, based on professional judgment, which decreases the accounting procedures’ regulatory role. The authors consider necessary to propose a harmonious and balanced system of informational enrichment of public institutions’ activity of all the ties between the taxation process and its accounting support. As a result of this research, the authors came to the conclusion to structure formal and informal institutions that could influence the organization of accounting at a particular economic level moving from the advisory options of the accounting policy to the elements of discrete financial and business law based on the development of internal standards of economic entities.peer-reviewe

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

Transformation of value and income indicators and their accounting and analytical support

Purpose: The objective of the article is to identify and evaluate transformational changes related to the degree of usefulness of effective financial indicators formed on the accounting basis. These indicators are extremely important for choosing the most effective investment and economic policy of the stakeholders. Structure/Methodology/Approach: To improve the quality and the value of accounting information, as well as to manage the profits and the value of business entities, the following has been revealed: first, the impact of static and dynamic concept of accounting; second, capabilities and limitations of integration of various accounting models and procedures; third, recommendations allowing adoption of accounting tools to the procedures of increasing standardization in financial statements. Findings: In order to reveal the impact of modern accounting procedures on the system of financial and economic performance indicators, a system of accounting procedures and indicators has been proposed. Practical Implications: The results of this study can be implemented into management practice to improve efficiency of property management for business units. Originality/Value: The core value of the study is to shift emphasis onto the aggregation of accounting and analytical tools for evaluation of property and inclusion of information reliability parameters into the system of financial and economic forecasting of business development.peer-reviewe

Quantum orientational melting of mesoscopic clusters

By path integral Monte Carlo simulations we study the phase diagram of two - dimensional mesoscopic clusters formed by electrons in a semiconductor quantum dot or by indirect magnetoexcitons in double quantum dots. At zero (or sufficiently small) temperature, as quantum fluctuations of particles increase, two types of quantum disordering phenomena take place: first, at small values of quantum de Boer parameter q < 0.01 one can observe a transition from a completely ordered state to that in which different shells of the cluster, being internally ordered, are orientationally disordered relative to each other. At much greater strengths of quantum fluctuations, at q=0.1, the transition to a disordered (superfluid for the boson system) state takes place.Comment: 4 pages, 6 Postscript figure