Fluctuations and stability in front propagation

Propagating fronts arising from bistable reaction-diffusion equations are a purely deterministic effect. Stochastic reaction-diffusion processes also show front propagation which coincides with the deterministic effect in the limit of small fluctuations (usually, large populations). However, for larger fluctuations propagation can be affected. We give an example, based on the classic spruce-budworm model, where the direction of wave propagation, i.e., the relative stability of two phases, can be reversed by fluctuations.Comment: 5 pages, 5 figure

Bound of dissipation on a plane Couette dynamo

Variational turbulence is among the few approaches providing rigorous results in turbulence. In addition, it addresses a question of direct practical interest, namely the rate of energy dissipation. Unfortunately, only an upper bound is obtained as a larger functional space than the space of solutions to the Navier-Stokes equations is searched. Yet, in general, this upper bound is in good agreement with experimental results in terms of order of magnitude and power law of the imposed Reynolds number. In this paper, the variational approach to turbulence is extended to the case of dynamo action and an upper bound is obtained for the global dissipation rate (viscous and Ohmic). A simple plane Couette flow is investigated. For low magnetic Prandtl number $P_m$ fluids, the upper bound of energy dissipation is that of classical turbulence (i.e. proportional to the cubic power of the shear velocity) for magnetic Reynolds numbers below $P_m^{-1}$ and follows a steeper evolution for magnetic Reynolds numbers above $P_m^{-1}$ (i.e. proportional to the shear velocity to the power four) in the case of electrically insulating walls. However, the effect of wall conductance is crucial : for a given value of wall conductance, there is a value for the magnetic Reynolds number above which energy dissipation cannot be bounded. This limiting magnetic Reynolds number is inversely proportional to the square root of the conductance of the wall. Implications in terms of energy dissipation in experimental and natural dynamos are discussed.Comment: In this new version, amistake (in equation 23 of the first version) is correcte

Variational bound on energy dissipation in plane Couette flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from [email protected]

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation

Velocity and processivity of helicase unwinding of double-stranded nucleic acids

Helicases are molecular motors which unwind double-stranded nucleic acids (dsNA) in cells. Many helicases move with directional bias on single-stranded (ss) nucleic acids, and couple their directional translocation to strand separation. A model of the coupling between translocation and unwinding uses an interaction potential to represent passive and active helicase mechanisms. A passive helicase must wait for thermal fluctuations to open dsNA base pairs before it can advance and inhibit NA closing. An active helicase directly destabilizes dsNA base pairs, accelerating the opening rate. Here we extend this model to include helicase unbinding from the nucleic-acid strand. The helicase processivity depends on the form of the interaction potential. A passive helicase has a mean attachment time which does not change between ss translocation and ds unwinding, while an active helicase in general shows a decrease in attachment time during unwinding relative to ss translocation. In addition, we describe how helicase unwinding velocity and processivity vary if the base-pair binding free energy is changed.Comment: To appear in special issue on molecular motors, Journal of Physics - Condensed Matte

Hammerhead, an ultrahigh resolution ePix camera for wavelength-dispersive spectrometers

Wavelength-dispersive spectrometers (WDS) are often used in synchrotron and FEL applications where high energy resolution (in the order of eV) is important. Increasing WDS energy resolution requires increasing spatial resolution of the detectors in the dispersion direction. The common approaches with strip detectors or small pixel detectors are not ideal. We present a novel approach, with a sensor using rectangular pixels with a high aspect ratio (between strips and pixels, further called "strixels"), and strixel redistribution to match the square pixel arrays of typical ASICs while avoiding the considerable effort of redesigning ASICs. This results in a sensor area of 17.4 mm x 77 mm, with a fine pitch of 25 $\mu$m in the horizontal direction resulting in 3072 columns and 176 rows. The sensors use ePix100 readout ASICs, leveraging their low noise (43 e$^-$, or 180 eV rms). We present results obtained with a Hammerhead ePix100 camera, showing that the small pitch (25 $\mu$m) in the dispersion direction maximizes performance for both high and low photon occupancies, resulting in optimal WDS energy resolution. The low noise level at high photon occupancy allows precise photon counting, while at low occupancy, both the energy and the subpixel position can be reconstructed for every photon, allowing an ultrahigh resolution (in the order of 1 $\mu$m) in the dispersion direction and rejection of scattered beam and harmonics. Using strixel sensors with redistribution and flip-chip bonding to standard ePix readout ASICs results in ultrahigh position resolution ($\sim$1 $\mu$m) and low noise in WDS applications, leveraging the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development complexity through sharing the ASIC, hardware, software and DAQ development with existing versions of ePix cameras.Comment: 8 pages, 6 figure

Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field

We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the stationary limit. If magnetic field is smaller compared to the critical value, determined by frictional anisotropy, the relaxation of the correlation is non-oscillating in time. However, in a larger magnetic field this relaxation becomes oscillating. The phenomenon is related to the statistical dependence of the components of transformed random force caused by the simultaneous influence of magnetic field and anisotropic dissipation.Comment: 7 pages, 2 figure

CalMagNet ? an array of search coil magnetometers monitoring ultra low frequency activity in California

International audienceThe California Magnetometer Network (CalMagNet) consists of sixty-eight triaxial search-coil magnetometer systems measuring Ultra Low Frequency (ULF), 0.001?16 Hz, magnetic field fluctuations in California. CalMagNet provides data for comprehensive multi-point measurements of specific events in the Pc 1?Pc 5 range at mid-latitudes as well as a systematic, long-term study of ULF signals in active fault regions in California. Typical events include geomagnetic micropulsations and spectral resonant structures associated with the ionospheric Alfvén resonator. This paper provides a technical overview of the CalMagNet sensors and data processing systems. The network is composed of ten reference stations and fifty-eight local monitoring stations. The primary instruments at each site are three orthogonal induction coil magnetometers. A geophone monitors local site vibration. The systems are designed for future sensor expansion and include resources for monitoring four additional channels. Data is currently sampled at 32 samples per second with a 24-bit converter and time tagged with a GPS-based timing system. Several examples of representative magnetic fluctuations and signals as measured by the array are given