The longest excursion of stochastic processes in nonequilibrium systems

We consider the excursions, i.e. the intervals between consecutive zeros, of stochastic processes that arise in a variety of nonequilibrium systems and study the temporal growth of the longest one l_{\max}(t) up to time t. For smooth processes, we find a universal linear growth \simeq Q_{\infty} t with a model dependent amplitude Q_\infty. In contrast, for non-smooth processes with a persistence exponent \theta, we show that < l_{\max}(t) > has a linear growth if \theta \sim t^{1-\psi} if \theta > \theta_c. The amplitude Q_{\infty} and the exponent \psi are novel quantities associated to nonequilibrium dynamics. These behaviors are obtained by exact analytical calculations for renewal and multiplicative processes and numerical simulations for other systems such as the coarsening dynamics in Ising model as well as the diffusion equation with random initial conditions.Comment: 4 pages,2 figure

Operational loads on a tidal turbine due to environmental conditions

Accurate assessment of the fatigue life of tidal stream turbines and components requires prediction of the unsteady loading of turbine components over a wide range of frequencies. This study focuses on the influence of ambient turbulence, velocity shear and the approach taken to model wave kinematics, on the variation of thrust load imposed on the rotor shaft and supporting tower. Load cycles are assessed based on sea-state occurrence data taken over a five month period for a case study site. The influence of each environmental parameter on component loading is evaluated and the impact on material design parameters assessed. Alternative approaches are considered for modelling turbulent loading and wave loading. The frequency variation of loads due to turbulence are scaled from experimental data from trials of a three-bladed horizontal axis turbine of 1.2 m diameter on a bed-mounted supporting structure. Frequency dependent wave loading is estimated by a relative form of the drag term of the widely used equation of Morison et al. (1950), with the depth decay of kinematics modelled by linear wave theory. Over the five month interval considered a ten year design life can be obtained with a lower design load by accounting for variation of turbulence intensity that occurs during each tidal cycle. This is expected to vary further with the approach taken to model the onset turbulence. A component can also be designed for lower loads over the same time period if irregular waves are modelled instead of regular

Pressure Dependence of the Magnetic Anisotropy in the "Single-Molecule Magnet" [Mn4O3Br(OAc)3(dbm)3]

The anisotropy splitting in the ground state of the single-molecule magnet [Mn4O3Br(OAc)3(dbm)3] is studied by inelastic neutron scattering as a function of hydrostatic pressure. This allows a tuning of the anisotropy and thus the energy barrier for slow magnetisation relaxation at low temperatures. The value of the negative axial anisotropy parameter $D_{\rm cluster}$ changes from -0.0627(1) meV at ambient to -0.0603(3) meV at 12 kbar pressure, and in the same pressure range the height of the energy barrier between up and down spins is reduced from 1.260(5) meV to 1.213(9) meV. Since the $\rm Mn-Br$ bond is significantly softer and thus more compressible than the $\rm Mn-O$ bonds, pressure induces a tilt of the single ion Mn$^{3+}$ anisotropy axes, resulting in the net reduction of the axial cluster anisotropy.Comment: 4 pages, 3 figure

Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution

We introduce an alternative definition of the relative height h^\kappa(x) of a one-dimensional fluctuating interface indexed by a continuously varying real paramater 0 \leq \kappa \leq 1. It interpolates between the height relative to the initial value (i.e. in x=0) when \kappa = 0 and the height relative to the spatially averaged height for \kappa = 1. We compute exactly the distribution P^\kappa(h_m,L) of the maximum h_m of these relative heights for systems of finite size L and periodic boundary conditions. One finds that it takes the scaling form P^\kappa(h_m,L) = L^{-1/2} f^\kappa (h_m L^{-1/2}) where the scaling function f^\kappa(x) interpolates between the Rayleigh distribution for \kappa=0 and the Airy distribution for \kappa=1, the latter being the probability distribution of the area under a Brownian excursion over the unit interval. For arbitrary \kappa, one finds that it is related to, albeit different from, the distribution of the area restricted to the interval [0, \kappa] under a Brownian excursion over the unit interval.Comment: 25 pages, 4 figure

Quantitative magnetic resonance imaging for focal liver lesions: Bridging the gap between research and clinical practice

Magnetic resonance imaging (MRI) is highly important for the detection, characterization, and follow-up of focal liver lesions. Several quantitative MRI-based methods have been proposed in addition to qualitative imaging interpretation to improve the diagnostic work-up and prognostics in patients with focal liver lesions. This includes DWI with apparent diffusion coefficient measurements, intravoxel incoherent motion, perfusion imaging, MR elastography, and radiomics. Multiple research studies have reported promising results with quantitative MRI methods in various clinical settings. Nevertheless, applications in everyday clinical practice are limited. This review describes the basic principles of quantitative MRI-based techniques and discusses the main current applications and limitations for the assessment of focal liver lesions

Dynamic Phase Transitions in Cell Spreading

We monitored isotropic spreading of mouse embryonic fibroblasts on fibronectin-coated substrates. Cell adhesion area versus time was measured via total internal reflection fluorescence microscopy. Spreading proceeds in well-defined phases. We found a power-law area growth with distinct exponents a_i in three sequential phases, which we denote basal (a_1=0.4+-0.2), continous (a_2=1.6+-0.9) and contractile (a_3=0.3+-0.2) spreading. High resolution differential interference contrast microscopy was used to characterize local membrane dynamics at the spreading front. Fourier power spectra of membrane velocity reveal the sudden development of periodic membrane retractions at the transition from continous to contractile spreading. We propose that the classification of cell spreading into phases with distinct functional characteristics and protein activity patterns serves as a paradigm for a general program of a phase classification of cellular phenotype. Biological variability is drastically reduced when only the corresponding phases are used for comparison across species/different cell lines.Comment: 4 pages, 5 figure

Record Statistics for Multiple Random Walks

We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance \sigma^2 of the jump distribution is finite and (II) when \sigma^2 is divergent as in the case of L\'evy flights with index 0 < \mu < 2. In both cases we find that the mean record number grows universally as \sim \alpha_N \sqrt{n} for large n, but with a very different behavior of the amplitude \alpha_N for N > 1 in the two cases. We find that for large N, \alpha_N \approx 2 \sqrt{\log N} independently of \sigma^2 in case I. In contrast, in case II, the amplitude approaches to an N-independent constant for large N, \alpha_N \approx 4/\sqrt{\pi}, independently of 0<\mu<2. For finite \sigma^2 we argue, and this is confirmed by our numerical simulations, that the full distribution of (R_{n,N}/\sqrt{n} - 2 \sqrt{\log N}) \sqrt{\log N} converges to a Gumbel law as n \to \infty and N \to \infty. In case II, our numerical simulations indicate that the distribution of R_{n,N}/\sqrt{n} converges, for n \to \infty and N \to \infty, to a universal nontrivial distribution, independently of \mu. We discuss the applications of our results to the study of the record statistics of 366 daily stock prices from the Standard & Poors 500 index.Comment: 25 pages, 8 figure

Periodic Lamellipodial Contractions Correlate with Rearward Actin Waves

AbstractCellular lamellipodia bind to the matrix and probe its rigidity through forces generated by rearward F-actin transport. Cells respond to matrix rigidity by moving toward more rigid matrices using an unknown mechanism. In spreading and migrating cells we find local periodic contractions of lamellipodia that depend on matrix rigidity, fibronectin binding and myosin light chain kinase (MLCK). These contractions leave periodic rows of matrix bound β3-integrin and paxillin while generating waves of rearward moving actin bound α-actinin and MLCK. The period between contractions corresponds to the time for F-actin to move across the lamellipodia. Shortening lamellipodial width by activating cofilin decreased this period proportionally. Increasing lamellipodial width by Rac signaling activation increased this period. We propose that an actin bound, contraction-activated signaling complex is transported locally from the tip to the base of the lamellipodium, activating the next contraction/extension cycle

Naturalness and Fine Tuning in the NMSSM: Implications of Early LHC Results

We study the fine tuning in the parameter space of the semi-constrained NMSSM, where most soft Susy breaking parameters are universal at the GUT scale. We discuss the dependence of the fine tuning on the soft Susy breaking parameters M_1/2 and m0, and on the Higgs masses in NMSSM specific scenarios involving large singlet-doublet Higgs mixing or dominant Higgs-to-Higgs decays. Whereas these latter scenarios allow a priori for considerably less fine tuning than the constrained MSSM, the early LHC results rule out a large part of the parameter space of the semi-constrained NMSSM corresponding to low values of the fine tuning.Comment: 19 pages, 10 figures, bounds from Susy searches with ~1/fb include

An origin for small neutrino masses in the NMSSM

We consider the Next to Minimal Supersymmetric Standard Model (NMSSM) which provides a natural solution to the so-called mu problem by introducing a new gauge-singlet superfield S. We realize that a new mechanism of neutrino mass suppression, based on the R-parity violating bilinear terms mu_i L_i H_u mixing neutrinos and higgsinos, arises within the NMSSM, offering thus an original solution to the neutrino mass problem (connected to the solution for the mu problem). We generate realistic (Majorana) neutrino mass values without requiring any strong hierarchy amongst the fundamental parameters, in contrast with the alternative models. In particular, the ratio |mu_i/mu| can reach about 10^-1, unlike in the MSSM where it has to be much smaller than unity. We check that the obtained parameters also satisfy the collider constraints and internal consistencies of the NMSSM. The price to pay for this new cancellation-type mechanism of neutrino mass reduction is a certain fine tuning, which get significantly improved in some regions of parameter space. Besides, we discuss the feasibility of our scenario when the R-parity violating bilinear terms have a common origin with the mu term, namely when those are generated via a VEV of the S scalar component from the couplings lambda_i S L_i H_u. Finally, we make comments on some specific phenomenology of the NMSSM in the presence of R-parity violating bilinear terms.Comment: 21 pages, 5 figures, Latex fil