Effects of wall compliance on the laminar–turbulent transition of torsional Couette flow

Torsional Couette flow between a rotating disk and a stationary wall is studied experimentally. The surface of the disk is either rigid or covered with a compliant coating. The influence of wall compliance on characteristic flow instabilities and on the laminar–turbulent flow transition is investigated. Data obtained from analysing flow visualizations are discussed. It is found that wall compliance favours two of the three characteristic wave patterns associated with the transition process and broadens the parameter regime in which these patterns are observed. The results for the effects of wall compliance on the third pattern are inconclusive. However, the experiments indicate that the third pattern is not a primary constituent of the laminar–turbulent transition process of torsional Couette flow

Creep via dynamical functional renormalization group

We study a D-dimensional interface driven in a disordered medium. We derive finite temperature and velocity functional renormalization group (FRG) equations, valid in a 4-D expansion. These equations allow in principle for a complete study of the the velocity versus applied force characteristics. We focus here on the creep regime at finite temperature and small velocity. We show how our FRG approach gives the form of the v-f characteristics in this regime, and in particular the creep exponent, obtained previously only through phenomenological scaling arguments.Comment: 4 pages, 3 figures, RevTe

Minimal Conflicting Sets for the Consecutive Ones Property in ancestral genome reconstruction

A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1's on each row are consecutive. A Minimal Conflicting Set is a set of rows that does not have the C1P, but every proper subset has the C1P. Such submatrices have been considered in comparative genomics applications, but very little is known about their combinatorial structure and efficient algorithms to compute them. We first describe an algorithm that detects rows that belong to Minimal Conflicting Sets. This algorithm has a polynomial time complexity when the number of 1's in each row of the considered matrix is bounded by a constant. Next, we show that the problem of computing all Minimal Conflicting Sets can be reduced to the joint generation of all minimal true clauses and maximal false clauses for some monotone boolean function. We use these methods on simulated data related to ancestral genome reconstruction to show that computing Minimal Conflicting Set is useful in discriminating between true positive and false positive ancestral syntenies. We also study a dataset of yeast genomes and address the reliability of an ancestral genome proposal of the Saccahromycetaceae yeasts.Comment: 20 pages, 3 figure

Drift of a polymer chain in disordered media

We consider the drift of a polymer chain in a disordered medium, which is caused by a constant force applied to the one end of the polymer, under neglecting the thermal fluctuations. In the lowest order of the perturbation theory we have computed the transversal fluctuations of the centre of mass of the polymer, the transversal and the longitudinal size of the polymer, and the average velocity of the polymer. The corrections to the quantities under consideration, which are due to the interplay between the motion and the quenched forces, are controlled by the driving force and the degree of polymerization. The transversal fluctuations of the Brownian particle and of the centre of mass of the polymer are obtained to be diffusive. The transversal fluctuations studied in the present Letter may also be of relevance for the related problem of the drift of a directed polymer in disordered media and its applications.Comment: 11 pages, RevTex, Accepted for publication in Europhysics Letter

The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension

We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.Comment: accepted for publication in Phys. Rev.

Functional renormalization group at large N for random manifolds

We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for large embedding space dimension N. This yields a functional renormalization group equation valid for any d, which contains both the O(epsilon=4-d) results of Balents-Fisher and some of the non-trivial results of the Mezard-Parisi solution thus shedding light on both. Corrections are computed at order O(1/N). Applications to the problems of KPZ, random field and mode coupling in glasses are mentioned

Arguments hydrogéochimiques en faveur de Trias évaporitique non affleurant dans le massif du Djurdjura (dorsale kabyle, élément des Maghrébides)

L'analyse des eaux pose à nouveau la question de l'importance des faciès gypso-salifères dans le Trias de la dorsale kabyle du Djurdjura. Cette dernière est un élément de l'orogène alpin périméditerranéen où le Trias est décrit comme étant formé essentiellement de grès et de pélites avec des niveaux marneux et dolomitiques. Dans les régions telliennes, plus méridionales, il est représenté par des formations marno-gypsifères de grande épaisseur (Trias tellien), en position tectonique constamment anormale. On ne rencontre généralement pas de formations évaporitiques en surface dans le massif du Djurdjura. Les analyses chimiques de la majorité des sources le confirment. Toutefois la source de Tinzert, dont l'impluvium est constitué essentiellement de calcaires montre un cortège d'éléments d'origine évaporitique (fortes teneurs en chlorures, sodium et sulfates et la présence du strontium) et plaide pour la présence de niveaux évaporitiques du Trias, à la base de l'aquifère drainé par cette source. Le rapport Sr2+/Ca2+ (en ‰) de la source de Tinzert (3 1000 mg·l-1), sodium (> 500 mg·l-1), sulfates (> 200 mg·l-1) and potassium (> 25 mg·l-1).During flood periods, because of dilution and quick conduit flows in the upper calcareous zones, the water type becomes calcium bicarbonate. During this period, waters flowing out of the spring are traced by the limestone shallow waters (transit of epikarstic waters). On top and upstream from Tinzert, less than 20 metres to the South, Tala Agouni Lansar displays a very different chemical type, calcium bicarbonate. This fact demonstrates that Tinzert sodium chloride content is acquired by water which stays in the deep saturated zone (Figs. 3 et 4), and that longitudinal faults divide the lithological units into segments.Analyses of strontium in waters demonstrate that most of the springs (ABDESSELAM, 1995) have low Sr2+ contents (0.06-0.23 mg·l-1). Tinzert spring has a much higher content (0.35-1.83 mg·l-1 ; Table 1). The use of the Sr2+ /Ca2+ ratio (‰) enabled us to distinguish among aquifers completely developed in limestones, others related to Triassic sandstones and one related to salty layers. The map of Sr2+ /Ca2+ ratios indicates that the springs related to Triassic outcrops have the higher values (Fig. 3).According to the Sr2+ /Ca2+ ratio (‰), three groups can be distinguished:- springs related to limestones, with no relationship with Triassic formations, have a low Sr2+/Ca2+ ratio ( 5‰) classifies this water into the category of waters originating from the alpine Triassic evaporites (MEYBECK, 1984). This high ratio is coupled with the high sulfate, and especially the chloride and sodium content of these waters. This spring is situated on the trace of a north-east thrust sheet sole that probably includes Triassic in its lower part, which concerns the whole Haïzer massif of about 8 km. The water transit is probably either in the upper thrust sheet, or in the lower one, following the East-West axis lowering of the structure.The springs of the Djurdjura display well-differentiated hydrochemical responses. Several springs that only drain limestone have a standard calcium bicarbonate chemical type (Sr2+/Ca2+ < 1 ‰). Other springs (Sr2+/Ca2+ =1 - 1.5 ‰) are characteristic of waters that have flowed in the sandstone and dolomitic Triassic layers, which are observed on the outcrops. Tinzert spring at least, which drains the middle part of the limestone range (Fig. 4, Sr2+/Ca2+=3 - 8.77 ‰), is characterised by waters which have transited through the evaporitic Triassic. The waters of Tinzert spring have also high chloride, sodium and sulfate contents.In the Djurdjura, where evaporitic Triassic formations do not generally outcrop, except in very small lenses, an argument can be made for the existence of deep evaporitic Triassic deposits on the basis of the hydrochemical response of perennial springs

Functional Renormalization Group and the Field Theory of Disordered Elastic Systems

We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the renormalization group functions beyond 1-loop order. Even worse, observables such as the 2-point correlation function exhibit the same problem already at 1-loop order. These difficulties are due to the non-analyticity of the renormalized disorder correlator at zero temperature, which is inherent to the physics beyond the Larkin length, characterized by many metastable states. As a result, 2-loop diagrams, which involve derivatives of the disorder correlator at the non-analytic point, are naively "ambiguous''. We examine several routes out of this dilemma, which lead to a unique renormalizable field-theory at 2-loop order. It is also the only theory consistent with the potentiality of the problem. The beta-function differs from previous work and the one at depinning by novel "anomalous terms''. For interfaces and random bond disorder we find a roughness exponent zeta = 0.20829804 epsilon + 0.006858 epsilon^2, epsilon = 4-d. For random field disorder we find zeta = epsilon/3 and compute universal amplitudes to order epsilon^2. For periodic systems we evaluate the universal amplitude of the 2-point function. We also clarify the dependence of universal amplitudes on the boundary conditions at large scale. All predictions are in good agreement with numerical and exact results, and an improvement over one loop. Finally we calculate higher correlation functions, which turn out to be equivalent to those at depinning to leading order in epsilon.Comment: 42 pages, 41 figure

2-loop Functional Renormalization Group Theory of the Depinning Transition

We construct the field theory which describes the universal properties of the quasi-static isotropic depinning transition for interfaces and elastic periodic systems at zero temperature, taking properly into account the non-analytic form of the dynamical action. This cures the inability of the 1-loop flow-equations to distinguish between statics and quasi-static depinning, and thus to account for the irreversibility of the latter. We prove two-loop renormalizability, obtain the 2-loop beta-function and show the generation of "irreversible" anomalous terms, originating from the non-analytic nature of the theory, which cause the statics and driven dynamics to differ at 2-loop order. We obtain the roughness exponent zeta and dynamical exponent z to order epsilon^2. This allows to test several previous conjectures made on the basis of the 1-loop result. First it demonstrates that random-field disorder does indeed attract all disorder of shorter range. It also shows that the conjecture zeta=epsilon/3 is incorrect, and allows to compute the violations, as zeta=epsilon/3 (1 + 0.14331 epsilon), epsilon=4-d. This solves a longstanding discrepancy with simulations. For long-range elasticity it yields zeta=epsilon/3 (1 + 0.39735 epsilon), epsilon=2-d (vs. the standard prediction zeta=1/3 for d=1), in reasonable agreement with the most recent simulations. The high value of zeta approximately 0.5 found in experiments both on the contact line depinning of liquid Helium and on slow crack fronts is discussed.Comment: 32 pages, 17 figures, revtex

Monte Carlo Dynamics of driven Flux Lines in Disordered Media

We show that the common local Monte Carlo rules used to simulate the motion of driven flux lines in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss a class of generalized Monte Carlo algorithms where an arbitrary number of line elements may move at the same time. We prove that all these dynamical rules have the same value of the critical force and possess phase spaces made up of a single ergodic component. A variant Monte Carlo algorithm allows to compute the critical force of a sample in a single pass through the system. We establish dynamical scaling properties and obtain precise values for the critical force, which is finite even for an unbounded distribution of the disorder. Extensions to higher dimensions are outlined.Comment: 4 pages, 3 figure