Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a channel is developed. This is based on the global study of the phase space structure of the low-dimensional ODE's defined by the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail, and general proofs concerning properties of fixed points and existence of finite-time singularities for broad classes of solutions are given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. The main conclusion is that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space spanning a sufficiently large set of initial conditions, are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding of them does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is discussed as the key point for a generic Dynamical Solvability Scenario which is proposed for a general context of interfacial pattern selection.Comment: 3 figures added, major rewriting of some sections, submitted to Phys. Rev.

Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation

A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies drastically the scenario of formation of finite-time cusp singularities. For a subclass of solutions, we show that, for any given initial condition, there exists a critical rotation rate above which cusp formation is prevented. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions. This condition admits a simple interpretation related to the linear stability problem.Comment: 4 pages, 2 figure

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev

Two-finger selection theory in the Saffman-Taylor problem

We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two \it unequal \rm fingers advancing with the same velocity but with different relative widths $\lambda_1$ and $\lambda_2$ and different tip positions. For vanishingly small dimensionless surface tension $d_0$, an infinite discrete set of values of the total filling fraction $\lambda = \lambda_1 + \lambda_2$ and of the relative individual finger width $p=\lambda_1/\lambda_2$ are selected out of a two-parameter continuous degeneracy. They scale as $\lambda-1/2 \sim d_0^{2/3}$ and $|p-1/2| \sim d_0^{1/3}$. The selected values of $\lambda$ differ from those of the single finger case. Explicit approximate expressions for both spectra are given.Comment: 4 pages, 3 figure

Equilibration of Concentrated Hard Sphere Fluids

We report a systematic molecular dynamics study of the isochoric equilibration of hard-sphere fluids in their metastable regime close to the glass transition. The thermalization process starts with the system prepared in a non-equilibrium state with the desired final volume fraction {\phi} but with a prescribed non-equilibrium static structure factor S_0(k; {\phi}). The evolution of the {\alpha}- relaxation time {\tau}{\alpha} (k) and long-time self-diffusion coefficient DL as a function of the evolution time tw is then monitored for an array of volume fractions. For a given waiting time the plot of {\tau}{\alpha} (k; {\phi}, tw) as a function of {\phi} exhibits two regimes corresponding to samples that have fully equilibrated within this waiting time ({\phi} \leq {\phi}(c) (tw)), and to samples for which equilibration is not yet complete ({\phi} \geq {\phi}(c) (tw)). The crossover volume fraction {\phi}(c) (tw) increases with tw but seems to saturate to a value {\phi}(a) \equiv {\phi}(c) (tw \rightarrow \infty) \approx 0.582. We also find that the waiting time t^(eq)_w({\phi}) required to equilibrate a system grows faster than the corresponding equilibrium relaxation time, t^(eq)({\phi}) \approx 0.27 \times [{\tau}{\alpha} (k; {\phi})]^1.43, and that both characteristic times increase strongly as {\phi} approaches {\phi}^(a), thus suggesting that the measurement of equilibrium properties at and above {\phi}(a) is experimentally impossible

General Non-equilibrium Theory of Colloid Dynamics

A non-equilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n(r,t) of a colloidal liquid in terms of the coupled time evolution equations of its mean value n(r,t) and of the covariance {\sigma}(r,r';t) \equiv of its fluctuations {\delta}n(r, t) = n(r, t) - n(r, t). These two coarse-grained equations involve a local mobility function b(r, t) which, in its turn, is written in terms of the memory function of the two-time correlation function C(r, r' ; t, t') \equiv <{\delta}n(r, t){\delta}n(r',t')>. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance n^0(r) and {\sigma}^0(r,r') towards its equilibrium state characterized by the equilibrium local concentration profile n^(eq)(r) and equilibrium covariance {\sigma}^(eq)(r,r'). This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities

Elogios honorificos y sublimes priuilegios de la cabeza del Serafico doctor de la Iglesia S. Buenauentura : propuestos al ... Concurso de Religiones Sagradas, Doctores, y Maestros de la Vniuersidad de Alcalà, que asistieron a la celebridad de su Translacion en el Conuento de S. Diego

Copia digital. Madrid : Ministerio de Cultura. Subdirección General de Coordinación Bibliotecaria, 2008Sign.: ¶\p6\s, A-B\p4\s, C\p2\sPort. con orla tip

Topological gravity on plumbed V-cobordisms

An ensemble of cosmological models based on generalized BF-theory is constructed where the role of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed V-cobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions. PACS numbers: 0420G, 0240, 0460Comment: 29 page

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.Comment: 17 pages in revtex. changes: 1 reference adde

A bibliographic analysis of transformer literature 1990-2000

This paper presents an analysis of the bibliography on transformers covering the period from 1990 to 2000. It contains all the transformer subjects: a) Transformer design, b) Transformer protection, c) Transformer connections, d) Transformer diagnostics, e) Transformer failures, f) Transient analysis of transformers (overvoltages, overcurrents), g) Modeling and analysis of transformer using FEM (thermal modeling, losses modeling, insulation modeling, windings modeling). Several international journals were investigated including the following: Advances in Electrical and Computer Engineering, Canadian Journal of Electrical and Computer Engineering, COMPEL (The International Journal for Computation and Mathematics in Electrical and Electronic Engineering), Electrical Engineering, Electric Power Components and Systems, Electric Power Systems Research, European Transactions on Electrical Power, IEEE Transactions on Magnetics, IEEE Transactions on Power Delivery, International Journal of Electrical Power and Energy Systems, and IET Generation Transmission & Distribution. Due to the high number of publication in journals, we are not considering publications of conferences and symposia. A total of 700 publications are analyzed in this paper. The research presented in this paper is important because it contains and analyzes the best research papers on transformers coming from many countries all over the world and published in top rated scientific electrical engineering journals