Mesoscopic and microscopic dipole clusters: Structure and phase transitions

Two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. For clusters of N < 81 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are found. Monte Carlo and molecular dynamic methods are used to study in detail the order - disorder transition (the "melting" of clusters). In mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower temperatures an intershell orientational disordering of pairs of shells takes place; at higher temperatures the intershell diffusion sets in and the shell structure disappears. In "macroscopic" clusters (N > 37) an orientational "melting" of only the outer shell is possible. The most stable clusters (having both maximal lowest nonzero eigenfrequencies and maximal temperatures of total melting) are that of completed crystal shells which are concentric groups of nodes of 2D hexagonal lattice with a number of nodes placed in the center of them. The study of different quantities shows that the melting temperature is a nonmonotonic function of the number of particles in the system. The dynamical equilibrium between "solidlike" and "orientationally disordered" forms of clusters is considered.Comment: 12 pages, 16 Postscript figures. Submitted to Phys. Rev.

Volterra-series approach to stochastic nonlinear dynamics: linear response of the Van der Pol oscillator driven by white noise

The Van der Pol equation is a paradigmatic model of relaxation oscillations. This remarkable nonlinear phenomenon of self-sustained oscillatory motion underlies important rhythmic processes in nature and electrical engineering. Relaxation oscillations in a real system are usually coupled to environmental noise, which further enriches their dynamics, but makes theoretical analysis of such systems and determination of the equation's parameter values a difficult task. In a companion paper we have proposed an analytic approach to a similar problem for another classical nonlinear model, the bistable Duffing oscillator. Here we extend our techniques to the case of the Van der Pol equation driven by white noise. We analyze the statistics of solutions and propose a method to estimate parameter values from the oscillator's time series. We use experimental data of active oscillations in a biological system to demonstrate how our method applies to real observations and how it can be generalized for more complex models.Comment: 12 pages, 6 figures, 1 tabl

Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields

The quantum dynamics of a $\hat{\mathbf{J}}^2=(\hat{\mathbf{j}}_1+\hat{\mathbf{j}}_2)^2$-conserving Hamiltonian model describing two coupled spins $\hat{\mathbf{j}}_1$ and $\hat{\mathbf{j}}_2$ under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of $\hat{\mathbf{J}}^2$ is dynamically invariant and the Hamiltonian of the total system restricted to any one of such $(j_1+j_2)-|j_1-j_2|+1$ eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins $\hat{\mathbf{j}}_1$ and $\hat{\mathbf{j}}_2$ between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau-Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.Comment: 11 pages, 5 figure

Bouncing off the walls : the influence of gas-kinetic and van der Waals effects in drop impact

A model is developed for liquid drop impact on a solid surface that captures the thin film gas flow beneath the drop, even when the film’s thickness is below the mean free path in the gas so that gas kinetic effects (GKE) are important. Simulation results agree with experiments, with the impact speed threshold between bouncing and wetting reproduced to within 5 least 50 mapped and provides experimentally verifiable predictions. There are two principal modes of contact leading to wetting and both are associated with a van der Waals driven instability of the film

Development of Methods and Algorithms for Spectral Data Analysis for Vibroacoustic Diagnostics of Diesel-Generator Sets at NPPs

In this article, the main methods and algorithms for spectral data analysis for vibroacoustic diagnostics of diesel-generator sets at nuclear power plants are considered. To collect the diagnostic data, an experimental setup was developed, thanks to which the sound signals of the diesel generator were obtained under various operating conditions. The recording and processing of signals was carried out using the application package and MATLAB programming language. The article describes the application of correlation and spectral analysis for data processing and analysis. Also, the authors apply regression analysis to find the dependence of the speed of the diesel engine on the frequency of acoustic oscillations. The prediction of the number of revolutions from the frequency of sound vibrations makes it possible in the future to build a more accurate mathematical model of engine operation, and also to find diagnostic features for detecting malfunctions and anomalies in the operation of a diesel generator

Phase diagram of 2D array of mesoscopic granules

A lattice boson model is used to study ordering phenomena in regular 2D array of superconductive mesoscopic granules, Josephson junctions or pores filled with a superfluid helium. Phase diagram of the system, when quantum fluctuations of both the phase and local superfluid density are essential, is analyzed both analytically and by quantum Monte Carlo technique. For the system of strongly interacting bosons it is found that as the boson density $n_0$ is increased the boundary of ordered superconducting state shifts to {\it lower temperatures} and at $n_0 > 8$ approaches its limiting position corresponding to negligible relative fluctuations of moduli of the order parameter (as in an array of "macroscopic" granules). In the region of weak quantum fluctuations of phases mesoscopic phenomena manifest themselves up to $n_0 \sim 10$. The mean field theory and functional integral $1/n_0$ - expansion results are shown to agree with that of quantum Monte Carlo calculations of the boson Hubbard model and its quasiclassical limit, the quantum XY model.Comment: 7 pages, 5 Postscript 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