Upper critical dimension of the KPZ equation

Numerical results for the Directed Polymer model in 1+4 dimensions in various types of disorder are presented. The results are obtained for system size considerably larger than that considered previously. For the extreme strong disorder case (Min-Max system), associated with the Directed Percolation model, the expected value of the meandering exponent, zeta = 0.5 is clearly revealed, with very week finite size effects. For the week disorder case, associated with the KPZ equation, finite size effects are stronger, but the value of seta is clearly seen in the vicinity of 0.57. In systems with "strong disorder" it is expected that the system will cross over sharply from Min-Max behavior at short chains to weak disorder behavior at long chains. This is indeed what we find. These results indicate that 1+4 is not the Upper Critical Dimension (UCD) in the week disorder case, and thus 4+1 does not seem to be the upper critical dimension for the KPZ equation

Dynamical Inequality in Growth Models

A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the Molecular Beam Equation, the situation is more interesting, where the exponents saturate the inequality. As the acid test for the relative strength of four popular approximation schemes we apply the inequality to the exponents obtained for two Non Local KPZ systems. We find that all methods but one, the Self Consistent Expansion, violate the inequality in some regions of parameter space. To further demonstrate the usefulness of the inequality, we apply it to a specific model, which belongs to a family of models in which the inequality becomes an equality. We thus show that the inequality can easily yield results, which otherwise have to rely either on approximations or general beliefs.Comment: 6 pages, 4 figure

Assessment of the relationships between myocardial contractility and infarct tissue revealed by serial magnetic resonance imaging in patients with acute myocardial infarction

Imaging changes in left ventricular (LV) volumes during the cardiac cycle and LV ejection fraction do not provide information on regional contractility. Displacement ENcoding with Stimulated Echoes (DENSE) is a strain-encoded cardiac magnetic resonance (CMR) technique that measures strain directly. We investigated the relationships between strain revealed by DENSE and the presence and extent of infarction in patients with recent myocardial infarction (MI). 50 male subjects were invited to undergo serial CMR within 7 days of MI (baseline) and after 6 months (follow-up; n = 47). DENSE and late gadolinium enhancement (LGE) images were acquired to enable localised regional quantification of peak circumferential strain (Ecc) and the extent of infarction, respectively. We assessed: (1) receiver operating characteristic (ROC) analysis for the classification of LGE, (2) strain differences according to LGE status (remote, adjacent, infarcted) and (3) changes in strain revealed between baseline and follow-up. 300 and 258 myocardial segments were available for analysis at baseline and follow-up respectively. LGE was present in 130/300 (43 %) and 97/258 (38 %) segments, respectively. ROC analysis revealed moderately high values for peak Ecc at baseline [threshold 12.8 %; area-under-curve (AUC) 0.88, sensitivity 84 %, specificity 78 %] and at follow-up (threshold 15.8 %; AUC 0.76, sensitivity 85 %, specificity 64 %). Differences were observed between remote, adjacent and infarcted segments. Between baseline and follow-up, increases in peak Ecc were observed in infarcted segments (median difference of 5.6 %) and in adjacent segments (1.5 %). Peak Ecc at baseline was indicative of the change in LGE status between baseline and follow-up. Strain-encoded CMR with DENSE has the potential to provide clinically useful information on contractility and its recovery over time in patients with MI

Classical and quantum regimes of the superfluid turbulence

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with 1/q playing the same role as the Reynolds number Re=UR/\nu in classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re >> 1 in classical hydrodynamics, and q << 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is the superfluid Reynolds number Re_s=UR/\kappa, which contains the circulation quantum \kappa characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; and (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. The phase diagram of the dynamical vortex states is suggested.Comment: 12 pages, 1 figure, version accepted in JETP Letter

Rain, power laws, and advection

Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws are generated by treating rain as a passive tracer undergoing advection in a velocity field generated by a two-dimensional system of point vortices.Comment: 7 pages, 4 figure

Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties

We analyze the statistical properties of three-dimensional ($3d$) turbulence in a rotating fluid. To this end we introduce a generating functional to study the statistical properties of the velocity field $\bf v$. We obtain the master equation from the Navier-Stokes equation in a rotating frame and thence a set of exact hierarchical equations for the velocity structure functions for arbitrary angular velocity $\mathbf \Omega$. In particular we obtain the {\em differential forms} for the analogs of the well-known von Karman-Howarth relation for $3d$ fluid turbulence. We examine their behavior in the limit of large rotation. Our results clearly suggest dissimilar statistical behavior and scaling along directions parallel and perpendicular to $\mathbf \Omega$. The hierarchical relations yield strong evidence that the nature of the flows for large rotation is not identical to pure two-dimensional flows. To complement these results, by using an effective model in the small-$\Omega$ limit, within a one-loop approximation, we show that the equal-time correlation of the velocity components parallel to $\mathbf \Omega$ displays Kolmogorov scaling $q^{-5/3}$, where as for all other components, the equal-time correlators scale as $q^{-3}$ in the inertial range where $\bf q$ is a wavevector in $3d$. Our results are generally testable in experiments and/or direct numerical simulations of the Navier-Stokes equation in a rotating frame.Comment: 24 pages in preprint format; accepted for publication in Phys. Rev. E (2011

On the nature of transport in near-critical dissipative-trapped-electron-mode turbulence: Effect of a subdominant diffusive channel

9 pages, 4 figures.-- PACS nrs.: 52.35.Ra, 52.55.-s.The change in nature of radial transport in numerical simulations of near-critical dissipative-trapped-electron-mode turbulence is characterized as the relative strength of an additional diffusive transport channel (subdominant to turbulence) is increased from zero. In its absence, radial transport exhibits the lack of spatial and temporal scales characteristic of self-organized-critical systems. This dynamical regime survives up to diffusivity values which, for the system investigated here, greatly exceeds the expected neoclassical value. These results, obtained using a novel Lagrangian method, complete and extend previous works based instead on the use of techniques imported from the study of cellular automata [ J. A. Mier et al., Phys. Plasmas 13, 102308 (2006) ]. They also shed further light on why some features of self-organized criticality seem to be observed in magnetically confined plasmas in spite of the presence of mechanisms which apparently violate the conditions needed for its establishment.This research was sponsored by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2006-15244-C03-01/FTN. Research sponsored in part by the Laboratory Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. Research supported in part by DOE Office of Science Grant No. DEFG02-04ER5741 at the University of Alaska.Publicad

A Physiological Analysis of Color Vision in Batoid Elasmobranchs

The potential for color vision in elasmobranchs has been studied in detail; however, a high degree of variation exists among the group. Evidence for ultraviolet (UV) vision is lacking, despite the presence of UV vision in every other vertebrate class. An integrative physiological approach was used to investigate color and ultraviolet vision in cownose rays and yellow stingrays, two batoids that inhabit different spectral environments. Both species had peaks in UV, short, medium, and long wavelength spectral regions in dark-, light-, and chromatic-adapted electroretinograms. Although no UV cones were found with microspectrophotometric analysis, both rays had multiple cone visual pigments with λmax at 470 and 551 nm in cownose rays (Rhinoptera bonasus) and 475, 533, and 562 nm in yellow stingrays (Urobatis jamaicensis). The same analysis demonstrated that both species had rod λmax at 500 and 499 nm, respectively. The lens and cornea of cownose rays maximally transmitted wavelengths greater than 350 nm and greater than 376 nm in yellow stingrays. These results support the potential for color vision in these species and future investigations should reveal the extent to which color discrimination is significant in a behavioral context