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

Scaling Exponents in Anisotropic Hydrodynamic Turbulence

In anisotropic turbulence the correlation functions are decomposed in the irreducible representations of the SO(3) symmetry group (with different "angular momenta" $\ell$). For different values of $\ell$ the second order correlation function is characterized by different scaling exponents $\zeta_2(\ell)$. In this paper we compute these scaling exponents in a Direct Interaction Approximation (DIA). By linearizing the DIA equations in small anisotropy we set up a linear operator and find its zero-modes in the inertial interval of scales. Thus the scaling exponents in each $\ell$-sector follow from solvability condition, and are not determined by dimensional analysis. The main result of our calculation is that the scaling exponents $\zeta_2(\ell)$ form a strictly increasing spectrum at least until $\ell=6$, guaranteeing that the effects of anisotropy decay as power laws when the scale of observation diminishes. The results of our calculations are compared to available experiments and simulations.Comment: 10 pages, 4 figures, PRE submitted. Fixed problems with figure

Programmable rate modem utilizing digital signal processing techniques

The need for a Programmable Rate Digital Satellite Modem capable of supporting both burst and continuous transmission modes with either Binary Phase Shift Keying (BPSK) or Quadrature Phase Shift Keying (QPSK) modulation is discussed. The preferred implementation technique is an all digital one which utilizes as much digital signal processing (DSP) as possible. The design trade-offs in each portion of the modulator and demodulator subsystem are outlined

A Constructive Quantum Lov\'asz Local Lemma for Commuting Projectors

The Quantum Satisfiability problem generalizes the Boolean satisfiability problem to the quantum setting by replacing classical clauses with local projectors. The Quantum Lov\'asz Local Lemma gives a sufficient condition for a Quantum Satisfiability problem to be satisfiable [AKS12], by generalizing the classical Lov\'asz Local Lemma. The next natural question that arises is: can a satisfying quantum state be efficiently found, when these conditions hold? In this work we present such an algorithm, with the additional requirement that all the projectors commute. The proof follows the information theoretic proof given by Moser's breakthrough result in the classical setting [Mos09]. Similar results were independently published in [CS11,CSV13]

Kompics: a message-passing component model for building distributed systems

The Kompics component model and programming framework was designedto simplify the development of increasingly complex distributed systems. Systems built with Kompics leverage multi-core machines out of the box and they can be dynamically reconfigured to support hot software upgrades. A simulation framework enables deterministic debugging and reproducible performance evaluation of unmodified Kompics distributed systems. We describe the component model and show how to program and compose event-based distributed systems. We present the architectural patterns and abstractions that Kompics facilitates and we highlight a case study of a complex distributed middleware that we have built with Kompics. We show how our approach enables systematic development and evaluation of large-scale and dynamic distributed systems

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

Anomalous and dimensional scaling in anisotropic turbulence

We present a numerical study of anisotropic statistical fluctuations in homogeneous turbulent flows. We give an argument to predict the dimensional scaling exponents, (p+j)/3, for the projections of p-th order structure function in the j-th sector of the rotational group. We show that measured exponents are anomalous, showing a clear deviation from the dimensional prediction. Dimensional scaling is subleading and it is recovered only after a random reshuffling of all velocity phases, in the stationary ensemble. This supports the idea that anomalous scaling is the result of a genuine inertial evolution, independent of large-scale behavior.Comment: 4 pages, 3 figure