Equations of state for strongly anharmonic crystals with a complex lattice

On the basis of a nonsymmetrized self-consistent-field approximation, thermal and caloric equations of state for strongly anharmonic crystals with a complex lattice are considered, allowing, in principle, anharmonism of any desired (basically, even) order to be taken into account. These equations include the moments of single-particle distribution functions, which are the solutions of some system of transcendental equations. More detailed consideration is given to the case of binary crystals with strong fourth-order anharmonism. The possibility of obtaining corrections to the approximation adopted is also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 40–44, November, 1979.     

Synchronization of excitatory neurons with strongly heterogeneous phase responses

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, the dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a method to solve the self-consistent equations for order parameters by using formal complex-valued phase variables, and apply our theory to networks of in vitro cortical neurons. We find a novel state transition that is not observed in previous oscillator network models.     

Statistical equilibrium solutions of the shallow water equations

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2D fluid flow with a free surface, is described. The model contains a competing acoustic turbulent direct energy cascade, and a 2D turbulent inverse energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrains the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.     

潜体在非均质流体中的平衡位置与平衡过程

以探空气球为例,讨论潜体在非均质流体中的平衡位置与平衡过程.     

On the sound field of a shallow spherical shell in an infinite baffle

A method is presented for calculating the far field sound radiation from a shallow spherical shell in an acoustic medium. The shell has a concentrated ring mass boundary condition at its perimeter representing a loudspeaker voice coil and is excited by a concentrated ring force exerted by the end of the voice coil. A Green's function is developed for a shallow spherical shell, which is based upon Reissner's solution to the shell wave equation [Q. Appl. Math. 13, 279-290 (1955)]. The shell is then coupled to the surrounding acoustic medium using an eigenfunction expansion, with unknown coefficients, for its deflection. The resulting surface pressure distribution is solved using the King integral together with the free space Green's function in cylindrical coordinates. In order to eliminate the need for numerical integration, the radiation (coupling) integrals are solved analytically to yield fast converging expansions. Hence, a set of simultaneous equations is obtained which is solved for the coefficients of the eigenfunction expansion. These coefficients are finally used in formulas for the far field sound radiation.     

Experimental study of surface wave propagation in strongly heterogeneous media

In the present paper, the propagation of Rayleigh waves in a strongly heterogeneous medium is discussed. Scattering of stress waves is a difficult scientific problem. Specifically, the interaction of surface waves with distributed inhomogeneity seems highly complicated due to the existence of two displacement components. Rayleigh waves undergo significant attenuation and velocity change depending on the frequency and the inhomogeneity content. The aim of this study is to highlight the dispersive behavior of concrete, especially when damaged, and increase the experimental data in an area where the work is limited.     

Percolation on patchwise heterogeneous surfaces under equilibrium conditions

The site percolation problem on square lattices whose sites are grouped in two types of energetically different patches is studied. Several lattices formed by collections of either randomly or orderly localized and no overlapped patches of different sizes are generated. The system is characterized by two parameters, namely, the size of each patch, l, and the energy difference between the two kind of sites, ΔE. Particles are adsorbed at equilibrium on the lattice. The critical coverage is determined by means of Monte Carlo simulations and finite-size scaling analysis. The percolative behavior of the system as a function of the parameters characterizing the heterogeneity of the energetic surface topography is presented and discussed.     

On the measurement of frequency-dependent ultrasonic attenuation in strongly heterogeneous materials

This paper deals with the measurement of frequency-dependent ultrasonic attenuation in strongly heterogeneous materials, such as cementitious materials. To improve the measurement of this parameter on this kind of materials, a linear swept–frequency signal is used to drive an emitter transducer to conduct a through-transmission inspection in immersion. To filter out undesirable frequency content, time–frequency filtering and detection process are performed. The use of this method has been compared with two excitation techniques, the broadband and the narrowband pulses. The results obtained using the swept–frequency excitation together with the time–frequency filtering, allows the determination of the attenuation curves with high accuracy over a wide frequency range without the need for complicated equipment, and improves the effective bandwidth by using a unique pair of transducers.     

Nonthermal fixed points: effective weak coupling for strongly correlated systems far from equilibrium

Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The nonthermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early Universe after inflation and the question of fast thermalization in heavy-ion collision experiments.     

Relative equilibrium and collapse configurations of heterogeneous vortex triple rings

Configurations of point vortices in a 2D fluid that are placed at the vertices of concentric regular m-gons, i.e. point vortex rings, are considered. The number of configurations that rotate uniformly-relative equilibria-is shown to be finite in the case of three rings with arbitrary circulations, subject to a few circulation constraints. Similar finiteness results for collapse configurations of three rings are also obtained, and an effective computational method is described.     

Dual‐fermion approach to non‐equilibrium strongly correlated problems

We present a generalization of the recently developed dual‐fermion approach introduced for correlated lattices to non‐equilibrium problems. In its local limit, the approach has been used to devise an efficient impurity solver, the superperturbation solver for the Anderson impurity model (AIM). Here we show that the general dual perturbation theory can be formulated on the Keldysh contour. Starting from a reference Hamiltonian system, in which the time‐dependent solution is found by exact diagonalization, we make a dual perturbation expansion in order to account for the relaxation effects from the fermionic bath. Simple test results for closed as well as open quantum systems in a fermionic bath are presented.     

Correlation functions for a strongly correlated boson system

The correlation functions for a strongly correlated exactly solvable one-dimensional boson system on a finite chain as well as in the thermodynamic limit are calculated explicitly. This system, which we call the phase model, is the strong coupling limit of the integrable q-boson hopping model. The results are presented as determinants.