The Landau–Khalatnikov Relaxation Mechanism in Smectic Liquid Crystals

Journal of Experimental and Theoretical Physics - The idea proposed and implemented by Landau and Khalatnikov to describe the dispersion and absorption of sound in superfluid helium is applied to...     

Simulation of Three-Phase Displacement Mechanisms Using a 2D Lattice-Boltzmann Model

Using a numerical technique, known as the lattice-Boltzmann method, we study immiscible three-phase flow at the pore scale. An important phenomenon at this scale is the spreading of oil onto the gas–water interface. In this paper, we recognize from first principles how injected gas remobilizes initially trapped oil blobs. The two main flow mechanisms which account for this type of remobilization are simulated. These are the double-drainage mechanism and (countercurrent) film flow of oil. The simulations agree qualitatively with experimental findings in the literature. We also simulate steady-state three-phase flow (fixed and equal saturations) in a small segment of a waterwet porous medium under both spreading and nonspreading conditions. The difference between the two conditions with respect to the coefficients in the generalized law of Darcy (which also includes viscous coupling) is investigated.     

Numerical simulation of a solitonic gas in KdV and KdV–BBM equations

The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV–BBM type models. Some high resolution numerical results are presented in both integrable and nonintegrable cases. Moreover, the free surface elevation probability distribution is shown to be quasi-stationary. Finally, we employ the asymptotic methods along with the Monte Carlo simulations in order to study quantitatively the dependence of some important statistical characteristics (such as the kurtosis and skewness) on the Stokes–Ursell number (which measures the relative importance of nonlinear effects compared to the dispersion) and also on the magnitude of the BBM term.     

Jump boundary-value problem on a contour with elongate singularities

Let Γ be image of interval (0, 1) under one-to-one continuous mapping φ: (0, 1) → C. If closure of Γ differs from the set Γ bymore than two points, then we call Γ the contour with elongate singularities.We study boundary-value jump problems for analytical functions on that contours, and obtain new criteria for their solvability.     

Physical mechanisms of the rogue wave phenomenon

A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (Benjamin–Feir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrödinger equation, the Davey–Stewartson system, the Korteweg–de Vries equation, the Kadomtsev–Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon.     

Exact solutions of problems of fluid inflow into a well with a vertical hydrofracture and their use in numerical models of flow through porous media

The plane steady flow of a homogeneous incompressible fluid in a reservoir containing a vertical elliptic hydrofracture is considered. The flow in the reservoir and fracture obeys Darcy's law. Exact solutions of the problem of inflow into a fracture of finite conductivity are obtained both in the case of a uniform reservoir and in the presence in the neighborhood of the fracture of a zone with permeability different from that of the rest of the reservoir. On the basis of the solutions obtained, the effect of the parameters of the polluted zone in the vicinity of the well on its production rate is estimated in the presence of a fracture of finite conductivity, the efficiency of hydraulic fracture of the producing and injection wells is analyzed for regular development systems, and a method of taking hydrofractures of arbitrary orientation and length into account is proposed for finite-difference models of flow through porous media in a system of wells.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 69–80, November–December, 1996.     

Motion of the interface of two fluids in a porous medium

In this study we obtain the Integro-differential equation for the motion of the interface of two incompressible fluids in various well areal arrangement systems. The solution of the equation is presented for a five-point system in the form of a power series with respect to time. Formulas are assumed which describe the motion of the particles belonging to the interface along invariant streamlines for five-point, seven-point, and nine-point well arrangement systems. The stratum sweeping coefficients for the fluid which is displacing the stratum oil are calculated (under conditions of the five-point system) at the instant when the fluid breaks through into the operation wells. The results of the calculations are compared with experimental data [1].The author wishes to thank V. L. Danilov for valuable counsel and comments.     

Revivals in Caldeira–Leggett Hamiltonian dynamics

We reconsider the problem of quantum system interacting with a complex environment discussed by Caldeira and Leggett (CL), and generalize their results for a quantum oscillator coupled to a reservoir R with dense discrete spectrum of oscillators with close to ${\omega }_s$ frequencies. Dynamics consists of recurrence cycles with partial revivals of the initial state. This revival or Loschmidt echo appears in each cycle. Width and number of the Loschmidt echo components increase with the recurrence cycle number leading to irregular, stochastic-like time evolution.