On MRI turbulence quantification

Turbulent flow, characterized by velocity fluctuations, accompanies many forms of cardiovascular disease and may contribute to their progression and hemodynamic consequences. Several studies have investigated the effects of turbulence on the magnetic resonance imaging (MRI) signal. Quantitative MRI turbulence measurements have recently been shown to have great potential for application both in human cardiovascular flow and in engineering flow. In this article, potential pitfalls and sources of error in MRI turbulence measurements are theoretically and numerically investigated. Data acquisition strategies suitable for turbulence quantification are outlined. The results show that the sensitivity of MRI turbulence measurements to intravoxel mean velocity variations is negligible, but that noise may degrade the estimates if the turbulence encoding parameter is set improperly. Different approaches for utilizing a given amount of scan time were shown to influence the dynamic range and the uncertainty in the turbulence estimates due to noise. The findings reported in this work may be valuable for both in vitro and in vivo studies employing MRI methods for turbulence quantification.     

On the nature of turbulence

A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.The research was supported by the Netherlands Organisation for the Advancement of Pure Research (Z.W.O.).     

On the nature of turbulence

A concept of turbulence is presented that is based on the results of an investigation of the structure of a gas flow in a tube with a square cross section in front of a nonsteady-state moving flame front. It is shown that a region of elevated pressure, consisting of alternating condensations, is formed in the gas flow near the tube walls. These condensations are the sources of waves which form a distribution of velocity fluctuations in the gas flow over a wide range of amplitudes, frequencies and directions. The dynamics of the perturbations at the walls and the configuration of the wave in the gap make it possible to consider the fluctuations in the flow as pseudochaotic and to use statistical methods to describe them. Zh. éksp. Teor. Fiz. 113, 191–203 (January 1998)     

On the spherical symmetry of a static perfect fluid

A globally static space-time with asymptotically Euclidean behavior representing a finite body of a perfect fluid and a vacuum region is shown to be diffeomorphic to Euclidean space and its metric spherically symmetric whenever the magnitude of the gravitational field strength is only a function of the gravitational potential. Under some additional physical assumptions it is then proved that this spherically symmetric solution is not deformable, that is, does not admit a nontrivial first order perturbation that is also a static, asymptotically Euclidean perfect fluid with the same equation of state and the same central value of the pressure and the gravitational potential.This work was supported in part by the United States Atomic Energy Commission under contract number AT (04-3)-34, Project Agreement No. 125.     

On dynamical symmetry breakdown

We investigate the possibility of dynamical symmetry breaking, that is the appearance of 〈?〉 ≠ 0 due to radiative corrections in scalar theory with the interaction λ?⁴, scalar electrodynamics and non-Abelian gauge theories. We show that in the one-loop approximation at small coupling constant the dynamical symmetry breaking is absent and the only mechanism of spontaneous symmetry breaking remains the Goldstone-Higgs-Kibble effect.     

On the stability of Kolmogorov spectra of a weak turbulence

The stability problem of Kolmogorov spectra of a weak turbulence is analytically solved for the first time in the framework of a three-wave kinetic equation. The spectrum of isotropic perturbations of a stationary not-in-equilibrium distribution is found for the capillary waves on a shallow water surface. It is shown, in the isotropic case, that the Kolmogorov solution is stable with respect to excitations local in k-space. The perturbations drift to the damping region without growth of the magnitude. The structural instability of the isotropic spectrum is found by computer simulation: a small pumping anisotropy causes the spectrum to be essentially anisotropic within the inertial range.     

On characteristic exponents in turbulence

Ruelle has found upper bounds to the magnitude and to the number of non-negative characteristic exponents for the Navier-Stokes flow of an incompressible fluid in a domain . The latter is particularly important because it yields an upper bound to the Hausdorff dimension of attracting sets. However, Ruelle's bound on the number has three deficiences: (i) it relies on some unproved conjectures about certain constants; (ii) it is valid only in dimensions 3 and not 2; (iii) it is valid only in the limit . In this paper these deficiences are remedied and, in addition, the final constants in the inequality are improved.Work partially supported by U.S. National Science Foundation grant No. PHY-8116101-A01     

On developed hydrodynamic turbulence spectra

New results in the theory of the developed hydrodynamic turbulence spectra are reviewed. Within the limits of the hypothesis of interaction locality it is shown that the series of equations for the moments has a scale-invariant solution with the Kolmogorov index values. With the help of the Wyld diagram technique the equations in the Direct Interaction Approximation are formulated which accurately take into account the transfer effect and have the precise solution in the form of the Kolmogorov spectrum. In the framework of these equations the corrections to the Kolmogorov spectrum due to gyrotropy and compressibility are found.     

Transmittance of partially coherent flat topped beam with circular and elliptical symmetry in turbulence

Average relative power transmittance is evaluated, for partially coherent flat topped beams with circular and elliptical symmetry, propagated through turbulent atmosphere. We have shown that for partially coherent flat topped beams with the mentioned symmetry, power transmittance is enhanced as the order of flat topped beam increase, but the full coherent one does not show this behavior. Also we have shown that there is a transition region (R_C) for full and partial coherent flat topped beams with circular and elliptical symmetry. We investigated the dependency of the power transmittance in turbulent media with respect to the structure constant.     

Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group

The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we first consider the needed general theory, and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.     

On the structure of symmetry generators

In a field theoretic framework we investigate generators of symmetry transformations induced by conserved local, not necessarily translationally covariant currents. Assuming the invariance of the vacuum and a mass gap, it is shown that the generator on one-particle states in general can be any polynomial of the generators of the Poincaré group and the internal symmetries. We give an example showing that the generator, defined as an integral over a conserved current, in spite of leaving the vacuum invariant, need not be self-adjoint.Supported by a DAAD grant     

On spatial symmetry. II

The goal of the present work is to find all the possible objects which transform linearly and intransitively under arbitrary transformations of coordinates in an x-space. As a result of these investigations it was established that there exist, in all, three types of geometric entities: transors, tensors, and M-objects. While transors and tensors are described by a finite number of components, M-objects are described only by an infinite number of components. 1 is found that some dimensionality constant of length plays an important role in the transformation properties of M-objects.Translated from Izvestiya VUZ. Fizika, No. 6, pp. 89–93, June, 1973.     

Vacco动力学方程的Mei对称性、Lie对称性和Noether对称性

研究Vacco动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Vacco动力学方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一 个例子说明结果的应用. 关键词： Vacco动力学方程 Mei对称性 Noether对称性 Lie对称性 守恒量     

On the symmetry of real-space renormalisation

A geometric structure, arising from the embedding into a Hilbert space of the parametrised probability measure for a given lattice model, is applied here to study the symmetry properties of real-space renormalisation group (RG) flow. In the projective state space this flow is shown to have two contributions: a gradient term, which generates a projective automorphism of the state space for each given length scale; and a correction term due to the scale change. We argue that this structure implies the absence of any symmetry of a geodesic type for the RG flow when restricted to the parameter space submanifold of the state space. This is demonstrated explicitly via a study of the one-dimensional Ising model in an external field. In this example we construct exact expressions for the beta functions associated with the flow induced by infinitesimal rescaling. These constitute a generating vector field for RG diffeomorphisms on the parameter space manifold, and we analyse the symmetry properties of this transformation. The results indicate an approximate conformal Killing symmetry near the critical point, but no generic symmetry of the RG flow globally on the parameter space.     

On the use of permutation symmetry

We study the S₃-symmetrical model proposed by Harari, Haut and Weyers to calculate both the Cabibbo angle and the m_d/m_s mass ratio. We show that supplementary terms are needed in the lagrangian to recover their results.