Доразработка остаточных запасов нефти на Майском нефтяном месторождении (Томская область)

Анализ проблем разработки остаточных запасов нефти на Майском нефтяном месторождении, предложен комплекс геолого-технических мероприятий. Приведены расчеты, на основе которых, доказаны технологическая и экономическая эффективность.Analysis of the problems of residual oil development of the Mayskoye oil field, was proposed a complex of geological and technical measures. Calculations are given, on the basis of which, proven technological and economic efficiency

Finite-time blowup for a complex Ginzburg-Landau equation

We prove that negative energy solutions of the complex Ginzburg-Landau equation $e^{-i\theta} u_t = \Delta u+ |u|^{\alpha} u$ blow up in finite time, where \alpha >0 and \pi /2<\theta <\pi /2. For a fixed initial value $u(0)$, we obtain estimates of the blow-up time $T_{max}^\theta$ as $\theta \to \pm \pi /2$. It turns out that $T_{max}^\theta$ stays bounded (respectively, goes to infinity) as $\theta \to \pm \pi /2$ in the case where the solution of the limiting nonlinear Schr\"odinger equation blows up in finite time (respectively, is global).Comment: 22 page

Statistics and Characteristics of Spatio-Temporally Rare Intense Events in Complex Ginzburg-Landau Models

We study the statistics and characteristics of rare intense events in two types of two dimensional Complex Ginzburg-Landau (CGL) equation based models. Our numerical simulations show finite amplitude collapse-like solutions which approach the infinite amplitude solutions of the nonlinear Schr\"{o}dinger (NLS) equation in an appropriate parameter regime. We also determine the probability distribution function (PDF) of the amplitude of the CGL solutions, which is found to be approximately described by a stretched exponential distribution, $P(|A|) \approx e^{-|A|^\eta}$, where $\eta < 1$. This non-Gaussian PDF is explained by the nonlinear characteristics of individual bursts combined with the statistics of bursts. Our results suggest a general picture in which an incoherent background of weakly interacting waves, occasionally, `by chance', initiates intense, coherent, self-reinforcing, highly nonlinear events.Comment: 7 pages, 9 figure

Analytic solutions and Singularity formation for the Peakon b--Family equations

Using the Abstract Cauchy-Kowalewski Theorem we prove that the $b$-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to $H^s$ with $s > 3/2$, and the momentum density $u_0 - u_{0,{xx}}$ does not change sign, we prove that the solution stays analytic globally in time, for $b\geq 1$. Using pseudospectral numerical methods, we study, also, the singularity formation for the $b$-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity approaches the real axis, estimating the rate of decay of the Fourier spectrum

Optimal prediction for moment models: Crescendo diffusion and reordered equations

A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to study moment closure generally within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, e.g. $P_N$, diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered $P_N$ equations, that are similar to the simplified $P_N$ equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.Comment: Revised version: 17 pages, 6 figures, presented at Workshop on Moment Methods in Kinetic Gas Theory, ETH Zurich, 2008 2 figures added, minor correction

Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in \Er^2

In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed

Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrödinger equations

The dynamic stability of vortex solutions to the Ginzburg-Landau and nonlinear Schrödinger equations is the basic assumption of the asymptotic particle plus field description of interacting vortices. For the Ginzburg-Landau dynamics we prove that all vortices are asymptotically nonlinearly stable relative to small radial perturbations. Initially finite energy perturbations of vortices decay to zero in L p (ℝ 2 ) spaces with an algebraic rate as time tends to infinity. We also prove that under general (nonradial) perturbations, the plus and minus one-vortices are linearly dynamically stable in L 2 ; the linearized operator has spectrum equal to (−∞, 0] and generates a C 0 semigroup of contractions on L 2 (ℝ 2 ). The nature of the zero energy point is clarified; it is resonance , a property related to the infinite energy of planar vortices. Our results on the linearized operator are also used to show that the plus and minus one-vortices for the Schrödinger (Hamiltonian) dynamics are spectrally stable, i.e. the linearized operator about these vortices has ( L 2 ) spectrum equal to the imaginary axis. The key ingredients of our analysis are the Nash-Aronson estimates for obtaining Gaussian upper bounds for fundamental solutions of parabolic operator, and a combination of variational and maximum principles.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46494/1/220_2005_Article_BF02099719.pd

Quantum Energy-Transport and Drift-Diffusion Models

We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an � expansion of these models, � 2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the Drift-Diffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.

Chapman--Enskog approach to flux-limited diffusion theory

Using the technique developed by Chapman and Enskog for deriving the Navier--Stokes equations from the Boltzmann equation, a framework is set up for deriving diffusion theories from the transport equation. The procedure is first applied to give a derivation of isotropic diffusion theory and then of a completely new theory which is naturally flux-limited. This new flux-limited diffusion theory is then compared with asymptotic diffusion theory