Log-periodic route to fractal functions

Log-periodic oscillations have been found to decorate the usual power law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes characterized by the amplitudes A(n) of the power law series expansion. These two classes are separated by a novel ``critical'' point. Growth processes (DLA), rupture, earthquake and financial crashes seem to be characterized by oscillatory or bounded regular microscopic functions g(x) that lead to a slow power law decay of A(n), giving strong log-periodic amplitudes. In contrast, the regular function g(x) of statistical physics models with ``ferromagnetic''-type interactions at equibrium involves unbound logarithms of polynomials of the control variable that lead to a fast exponential decay of A(n) giving weak log-periodic amplitudes and smoothed observables. These two classes of behavior can be traced back to the existence or abscence of ``antiferromagnetic'' or ``dipolar''-type interactions which, when present, make the Green functions non-monotonous oscillatory and favor spatial modulated patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new demonstration of the source of strong log-periodicity and of a justification of the general offered classification, update of reference lis

A new approach to the inverse problem for current mapping in thin-film superconductors

A novel mathematical approach has been developed to complete the inversion of the Biot-Savart law in one- and two-dimensional cases from measurements of the perpendicular component of the magnetic field using the well-developed Magneto-Optical Imaging technique. Our approach, especially in the 2D case, is provided in great detail to allow a straightforward implementation as opposed to those found in the literature. Our new approach also refines our previous results for the 1D case [Johansen et al., Phys. Rev. B 54, 16264 (1996)], and streamlines the method developed by Jooss et al. [Physica C 299, 215 (1998)] deemed as the most accurate if compared to that of Roth et al. [J. Appl. Phys. 65, 361 (1989)]. We also verify and streamline the iterative technique, which was developed following Laviano et al. [Supercond. Sci. Technol. 16, 71 (2002)] to account for in-plane magnetic fields caused by the bending of the applied magnetic field due to the demagnetising effect. After testing on magneto-optical images of a high quality YBa2Cu3O7 superconducting thin film, we show that the procedure employed is effective

DNA binding kinetics of two response regulators, PlnC and PlnD, from the bacteriocin regulon of Lactobacillus plantarum C11

<p>Abstract</p> <p>Background</p> <p>Bacteriocin production in the lactic acid bacterium <it>Lactobacillus plantarum </it>C11 is regulated through a quorum sensing based pathway involving two highly homologous response regulators (59% identity and 76% similarity), PlnC as a transcriptional activator and PlnD as a repressor. Previous <it>in vitro </it>studies have shown that both regulators bind, as homodimers, to the same DNA regulatory repeats to exert their regulatory functions. As the genes for these two proteins are located on the same auto-regulatory operon, hence being co-expressed upon gene activation, it is plausible that their opposite functions must somehow be differentially regulated, either in terms of timing and/or binding kinetics, so that their activities do not impair each other in an uncontrolled manner. To understand the nature behind this potential differentiation, we have studied the binding kinetics of the two regulators on five target promoters (P_{<it>plnA</it>}, P_{<it>plnM</it>}, P_{<it>plnJ</it>}, P_{<it>plnE </it>}and P_{<it>plnG</it>}) from the bacteriocin regulon of <it>L. plantarum </it>C11.</p> <p>Results</p> <p>By using surface plasmon resonance spectroscopy we obtained parameters such as association rates, dissociation rates and dissociation constants, showing that the two regulators indeed differ greatly from each other in terms of cooperative binding and binding strength to the different promoters. For instance, cooperativity is very strong for PlnC binding to the promoter of the regulatory operon (P_{<it>plnA</it>}), but not to the promoter of the transport operon (P_{<it>plnG</it>}), while the opposite is seen for PlnD binding to these two promoters. The estimated affinity constants indicate that PlnC can bind to P_{<it>plnA </it>}to activate transcription of the key regulatory operon <it>plnABCD </it>without much interference from PlnD, and that the repressive function of PlnD might act through a different mechanism than repression of the regulatory operon.</p> <p>Conclusion</p> <p>We have characterised the DNA binding kinetics of the two regulators PlnC and PlnD from the bacteriocin locus in <it>L. plantarum </it>C11. Our data show that PlnC and PlnD, despite their strong homology to each other, differ greatly from each other in terms of binding affinity and cooperativity to the different promoters of the <it>pln </it>regulon.</p

Theory of Networked Minority Games based on Strategy Pattern Dynamics

We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. The novel feature of the present formalism is its focus on the dynamical pattern of strategy rankings, and its careful treatment of the strategy ties which arise during the system's temporal evolution. We apply it to the Minority Game (MG) with connected populations. Expressions for the mean success rate among the agents and for the mean success rate for agents with $k$ neighbors are derived. We also use the theory to estimate the value of connectivity $p$ above which the Binary-Agent-Resource system with high resource level goes into the high-connectivity state.Comment: 24 pages, 3 figures, submitted to PR

Review of Fluorescence-Based Velocimetry Techniques to Study High-Speed Compressible Flows

This paper reviews five laser-induced fluorescence-based velocimetry techniques that have been used to study high-speed compressible flows at NASA Langley Research Center. The techniques discussed in this paper include nitric oxide (NO) molecular tagging velocimetry (MTV), nitrogen dioxide photodissociation (NO2-to-NO) MTV, and NO and atomic oxygen (O-atom) Doppler-shift-based velocimetry. Measurements of both single-component and two-component velocity have been performed using these techniques. This paper details the specific application and experiment for which each technique has been used, the facility in which the experiment was performed, the experimental setup, sample results, and a discussion of the lessons learned from each experiment

Thin superconducting disk with B-dependent Jc: Flux and current distributions

The critical state in a superconducting thin circular disk with an arbitrary magnetic field dependence of the critical sheet current, Jc(B), is analyzed. With an applied field Ba perpendicular to the disk, a set of coupled integral equations for the flux and current distributions is derived. The equations are solved numerically, and flux and current profiles are presented graphically for several commonly used Jc(B) dependences. It is shown that for small Ba the flux penetration depth can be described by an effective Bean model with a renormalized Jc entering the leading term. We argue that these results are qualitatively correct for thin superconductors of any shape. The results contrast the parallel geometry behavior, where at small Ba the B-dependence of the critical current can be ignored.Comment: RevTeX, 7 pages including 8 figure

Hypersonic Boundary Layer Measurements with Variable Blowing Rates Using Molecular Tagging Velocimetry

Measurements of mean and instantaneous streamwise velocity profiles in a hypersonic boundary layer with variable rates of mass injection (blowing) of nitrogen dioxide (NO2) were obtained over a 10-degree half-angle wedge model. The NO2 was seeded into the flow from a slot located 29.4 mm downstream of the sharp leading edge. The top surface of the wedge was oriented at a 20 degree angle in the Mach 10 flow, yielding an edge Mach number of approximately 4.2. The streamwise velocity profiles and streamwise fluctuating velocity component profiles were obtained using a three-laser NO2->NO photolysis molecular tagging velocimetry method. Observed trends in the mean streamwise velocity profiles and profiles of the fluctuating component of streamwise velocity as functions of the blowing rate are described. An effort is made to distinguish between the effect of blowing rate and wall temperature on the measured profiles. An analysis of the mean velocity profiles for a constant blowing rate is presented to determine the uncertainty in the measurement for different probe laser delay settings. Measurements of streamwise velocity were made to within approximately 120 gm of the model surface. The streamwise spatial resolution in this experiment ranged from 0.6 mm to 2.6 mm. An improvement in the spatial precision of the measurement technique has been made, with spatial uncertainties reduced by about a factor of 2 compared to previous measurements. For the quiescent flow calibration measurements presented, uncertainties as low as 2 m/s are obtained at 95% confidence for long delay times (25 gs). For the velocity measurements obtained with the wind tunnel operating, average single-shot uncertainties of less than 44 m/s are obtained at 95% confidence with a probe laser delay setting of 1 gs. The measurements were performed in the 31-inch Mach 10 Air Tunnel at the NASA Langley Research Center