Nonperturbative Spectrum of Anomalous Scaling Exponents in the Anisotropic Sectors of Passively Advected Magnetic Fields

We address the scaling behavior of the covariance of the magnetic field in the three-dimensional kinematic dynamo problem when the boundary conditions and/or the external forcing are not isotropic. The velocity field is gaussian and $\delta$-correlated in time, and its structure function scales with a positive exponent $\xi$. The covariance of the magnetic field is naturally computed as a sum of contributions proportional to the irreducible representations of the SO(3) symmetry group. The amplitudes are non-universal, determined by boundary conditions. The scaling exponents are universal, forming a discrete, strictly increasing spectrum indexed by the sectors of the symmetry group. When the initial mean magnetic field is zero, no dynamo effect is found, irrespective of the anisotropy of the forcing. The rate of isotropization with decreasing scales is fully understood from these results.Comment: 22 pages, 2 figures. Submitted to PR

The decay of homogeneous anisotropic turbulence

We present the results of a numerical investigation of three-dimensional decaying turbulence with statistically homogeneous and anisotropic initial conditions. We show that at large times, in the inertial range of scales: (i) isotropic velocity fluctuations decay self-similarly at an algebraic rate which can be obtained by dimensional arguments; (ii) the ratio of anisotropic to isotropic fluctuations of a given intensity falls off in time as a power law, with an exponent approximately independent of the strength of the fluctuation; (iii) the decay of anisotropic fluctuations is not self-similar, their statistics becoming more and more intermittent as time elapses. We also investigate the early stages of the decay. The different short-time behavior observed in two experiments differing by the phase organization of their initial conditions gives a new hunch on the degree of universality of small-scale turbulence statistics, i.e. its independence of the conditions at large scales.Comment: 9 pages, 17 figure

CATS: linearizability and partition tolerance in scalable and self-organizing key-value stores

Distributed key-value stores provide scalable, fault-tolerant, and self-organizing storage services, but fall short of guaranteeing linearizable consistency in partially synchronous, lossy, partitionable, and dynamic networks, when data is distributed and replicated automatically by the principle of consistent hashing. This paper introduces consistent quorums as a solution for achieving atomic consistency. We present the design and implementation of CATS, a distributed key-value store which uses consistent quorums to guarantee linearizability and partition tolerance in such adverse and dynamic network conditions. CATS is scalable, elastic, and self-organizing; key properties for modern cloud storage middleware. Our system shows that consistency can be achieved with practical performance and modest throughput overhead (5%) for read-intensive workloads

Anisotropic Homogeneous Turbulence: hierarchy and intermittency of scaling exponents in the anisotropic sectors

We present the first measurements of anisotropic statistical fluctuations in perfectly homogeneous turbulent flows. We address both problems of intermittency in anisotropic sectors and hierarchical ordering of anisotropies on a direct numerical simulation of a three dimensional random Kolmogorov flow. We achieved an homogeneous and anisotropic statistical ensemble by randomly shifting the forcing phases. We observe high intermittency as a function of the order of the velocity correlation within each fixed anisotropic sector and a hierarchical organization of scaling exponents at fixed order of the velocity correlation at changing the anisotropic sector.Comment: 6 pages, 3 eps figure

Molecular adaptation to calsequestrin 2 (CASQ2) point mutations leading to catecholaminergic polymorphic ventricular tachycardia (CPVT): comparative analysis of R33Q and D307H mutants

Homozygous calsequestrin 2 (CASQ2) point mutations leads to catecholaminergic polymorphic ventricular tachycardia: a common pathogenetic feature appears to be the drastic reduction of mutant CASQ2 in spite of normal transcription. Comparative biochemical analysis of R33Q and D307H knock in mutant mice identifies different pathogenetic mechanisms for CASQ2 degradation and different molecular adaptive mechanisms. In particular, each CASQ2 point mutation evokes specific adaptive cellular and molecular processes in each of the four adaptive pathways investigated. Thus, similar clinical phenotypes and identical cellular mechanism for cardiac arrhythmia might imply different molecular adaptive mechanisms

Statistics of pressure and of pressure-velocity correlations in isotropic turbulence

Some pressure and pressure-velocity correlation in a direct numerical simulations of a three-dimensional turbulent flow at moderate Reynolds numbers have been analyzed. We have identified a set of pressure-velocity correlations which posseses a good scaling behaviour. Such a class of pressure-velocity correlations are determined by looking at the energy-balance across any sub-volume of the flow. According to our analysis, pressure scaling is determined by the dimensional assumption that pressure behaves as a ``velocity squared'', unless finite-Reynolds effects are overwhelming. The SO(3) decompositions of pressure structure functions has also been applied in order to investigate anisotropic effects on the pressure scaling.Comment: 21 pages, 8 figur

Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents

The first example of a turbulent system where the failure of the hypothesis of small-scale isotropy restoration is detectable both in the `flattening' of the inertial-range scaling exponent hierarchy, and in the behavior of odd-order dimensionless ratios, e.g., skewness and hyperskewness, is presented. Specifically, within the kinematic approximation in magnetohydrodynamical turbulence, we show that for compressible flows, the isotropic contribution to the scaling of magnetic correlation functions and the first anisotropic ones may become practically indistinguishable. Moreover, skewness factor now diverges as the P\'eclet number goes to infinity, a further indication of small-scale anisotropy.Comment: 4 pages Latex, 1 figur

Statistical conservation laws in turbulent transport

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. We propose that with very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments (without forcing the transported fields) we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas

Mean value coordinates–based caricature and expression synthesis

We present a novel method for caricature synthesis based on mean value coordinates (MVC). Our method can be applied to any single frontal face image to learn a specified caricature face pair for frontal and 3D caricature synthesis. This technique only requires one or a small number of exemplar pairs and a natural frontal face image training set, while the system can transfer the style of the exemplar pair across individuals. Further exaggeration can be fulfilled in a controllable way. Our method is further applied to facial expression transfer, interpolation, and exaggeration, which are applications of expression editing. Additionally, we have extended our approach to 3D caricature synthesis based on the 3D version of MVC. With experiments we demonstrate that the transferred expressions are credible and the resulting caricatures can be characterized and recognized