891 research outputs found
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 -correlated in time, and its structure function scales with a
positive exponent . 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
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
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
Inhomogeneous Anisotropic Passive Scalars
We investigate the behaviour of the two-point correlation function in the
context of passive scalars for non homogeneous, non isotropic forcing
ensembles. Exact analytical computations can be carried out in the framework of
the Kraichnan model for each anisotropic sector. It is shown how the
homogeneous solution is recovered at separations smaller than an intrinsic
typical lengthscale induced by inhomogeneities, and how the different Fourier
modes in the centre-of-mass variable recombine themselves to give a ``beating''
(superposition of power laws) described by Bessel functions. The pure power-law
behaviour is restored even if the inhomogeneous excitation takes place at very
small scales.Comment: 14 pages, 5 figure
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
Strong Universality in Forced and Decaying Turbulence
The weak version of universality in turbulence refers to the independence of
the scaling exponents of the th order strcuture functions from the
statistics of the forcing. The strong version includes universality of the
coefficients of the structure functions in the isotropic sector, once
normalized by the mean energy flux. We demonstrate that shell models of
turbulence exhibit strong universality for both forced and decaying turbulence.
The exponents {\em and} the normalized coefficients are time independent in
decaying turbulence, forcing independent in forced turbulence, and equal for
decaying and forced turbulence. We conjecture that this is also the case for
Navier-Stokes turbulence.Comment: RevTex 4, 10 pages, 5 Figures (included), 1 Table; PRE, submitte
Completeness of classical spin models and universal quantum computation
We study mappings between distinct classical spin systems that leave the
partition function invariant. As recently shown in [Phys. Rev. Lett. 100,
110501 (2008)], the partition function of the 2D square lattice Ising model in
the presence of an inhomogeneous magnetic field, can specialize to the
partition function of any Ising system on an arbitrary graph. In this sense the
2D Ising model is said to be "complete". However, in order to obtain the above
result, the coupling strengths on the 2D lattice must assume complex values,
and thus do not allow for a physical interpretation. Here we show how a
complete model with real -and, hence, "physical"- couplings can be obtained if
the 3D Ising model is considered. We furthermore show how to map general
q-state systems with possibly many-body interactions to the 2D Ising model with
complex parameters, and give completeness results for these models with real
parameters. We also demonstrate that the computational overhead in these
constructions is in all relevant cases polynomial. These results are proved by
invoking a recently found cross-connection between statistical mechanics and
quantum information theory, where partition functions are expressed as quantum
mechanical amplitudes. Within this framework, there exists a natural
correspondence between many-body quantum states that allow universal quantum
computation via local measurements only, and complete classical spin systems.Comment: 43 pages, 28 figure
On Sylow normalizers of finite groups
Electronic version of an article published as Journal of Algebra and Its Applications
Vol. 13, No. 3 (2014) 1350116 (20 pages). DOI 10.1142/S0219498813501168. © [copyright World Scientific Publishing Company] http://www.worldscientific.com/[EN] The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent Hall subgroups for given sets of primes are exactly the subgroup- closed saturated formations satisfying the following property: a group belongs to the class if and only if its Sylow normalizers do so. The paper analyzes the extension of this research to the universe of all finite groups.The second and third authors have been supported by Proyecto MTM2010-19938C03-02, Ministerio de Econom ia y Competitividad, Spain. The first author would like to thank the Universitat de Valencia and the Universitat Politecnica de Valencia for their warm hospitality during the preparation of this paper. He has been also supported by RFBR Project 13-01-00469.Kazarin, L.; MartĂnez Pastor, A.; Perez Ramos, MD. (2014). On Sylow normalizers of finite groups. Journal of Algebra and Its Applications. 13(3):1-20. https://doi.org/10.1142/S0219498813501168S12013
Scaling and universality in turbulent convection
Anomalous correlation functions of the temperature field in two-dimensional
turbulent convection are shown to be universal with respect to the choice of
external sources. Moreover, they are equal to the anomalous correlations of the
concentration field of a passive tracer advected by the convective flow itself.
The statistics of velocity differences is found to be universal, self-similar
and close to Gaussian. These results point to the conclusion that temperature
intermittency in two-dimensional turbulent convection may be traced back to the
existence of statistically preserved structures, as it is in passive scalar
turbulence.Comment: 4 pages, 6 figure
Quantitative SPECT/CT parameters of myocardial 99mTechnetium-3,3-diphosphono-1,2-propanodicarboxylic acid (DPD) uptake in suspected cardiac transthyretin amyloidosis
Background: 99mTc-labelled bisphosphonates are used for imaging assessment of patients with transthyretin cardiac amyloidosis (ATTR). Present study evaluates whether quantitative SPECT/CT measurement of absolute myocardial 99mTc-labelled 3,3-diphosphono-1,2-propanodicarboxylic acid (Tc-DPD) uptake can diagnose patients with suspected ATTR. / Methods: Twenty-eight patients (25 male, age 80.03 ± 6.99 years) with suspected ATTR referred for Tc-DPD imaging had planar and SPECT/CT imaging of the chest. Three operators independently obtained Tc-DPD myocardial SUVmax and SUVmean above threshold (SMaT) (20, 40 and 60% of SUVmax), using a semi-automated threshold segmentation method. Results were compared to visual grading (0–3) of cardiac uptake. / Results: Twenty-two patients (78%) had cardiac uptake (2 grade 1, 15 grade 2, 5 grade 3). SUVmax and SMaT segmentation thresholds enabled separating grades 2/3 from 0/1 with excellent inter- and intra-reader correlation. Cut-off values 6.0, 2.5, 3 and 4 for SUVmax, SMaT20,40,60, respectively, separated between grades 2/3 and 0 /1 with PPV and NPV of 100%. SMaT20,40,60(cardiac)/SUVmean (liver) and SMaT20,40,60(cardiac)/SUVmean(liver/lung) separated grades 2 and 3. / Conclusion: Quantitative SPECT/CT parameters of cardiac Tc-DPD uptake are robust, enabling separation of patients with grades 2 and 3 cardiac uptake from grades 0 and 1. Larger patient cohorts will determine the incremental value of SPECT/CT quantification for ATTR management
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