64 research outputs found
Fracture Surfaces as Multiscaling Graphs
Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of
materials, paper) are analyzed as self-affine graphs of height as a
function of length . We show that these are multiscaling, in the sense that
order moments of the height fluctuations across any distance
scale with a characteristic exponent that depends nonlinearly on the order of
the moment. Having demonstrated this, one rules out a widely held conjecture
that fracture in 2D belongs to the universality class of directed polymers in
random media. In fact, 2D fracture does not belong to any of the known kinetic
roughening models. The presence of multiscaling offers a stringent test for any
theoretical model; we show that a recently introduced model of quasi-static
fracture passes this test.Comment: 4 pages, 5 figure
On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence
We propose a new approach to the old-standing problem of the anomaly of the
scaling exponents of nonlinear models of turbulence. We achieve this by
constructing, for any given nonlinear model, a linear model of passive
advection of an auxiliary field whose anomalous scaling exponents are the same
as the scaling exponents of the nonlinear problem. The statistics of the
auxiliary linear model are dominated by `Statistically Preserved Structures'
which are associated with exact conservation laws. The latter can be used for
example to determine the value of the anomalous scaling exponent of the second
order structure function. The approach is equally applicable to shell models
and to the Navier-Stokes equations.Comment: revised version with new data on Navier-Stokes eq
Corporate Crime and Plea Bargains
Corporate entities enjoy legal subjectivity in a variety of forms, but they are not human beings. Hence, their legal capacity to bear rights and obligations of their own is not universal. This article lays out a stylized model that explores, from a normative point of view, one of the limits that ought to be set on corporate capacity to act "as if" they had a human nature-the capacity to commit crime. Accepted wisdom states that corporate criminal liability is justified as a measure to deter criminal behavior. Our analysis supports this intuition in one subset of cases, but also reveals that deterrence might in fact be undermined in another subset of cases, especially in an environment saturated with plea bargains involving serious violations of the law. © 2017 Walter de Gruyter GmbH, Berlin/Boston 2017
Phenomenology of Wall Bounded Newtonian Turbulence
We construct a simple analytic model for wall-bounded turbulence, containing
only four adjustable parameters. Two of these parameters characterize the
viscous dissipation of the components of the Reynolds stress-tensor and other
two parameters characterize their nonlinear relaxation. The model offers an
analytic description of the profiles of the mean velocity and the correlation
functions of velocity fluctuations in the entire boundary region, from the
viscous sub-layer, through the buffer layer and further into the log-layer. As
a first approximation, we employ the traditional return-to-isotropy hypothesis,
which yields a very simple distribution of the turbulent kinetic energy between
the velocity components in the log-layer: the streamwise component contains a
half of the total energy whereas the wall-normal and the cross-stream
components contain a quarter each. In addition, the model predicts a very
simple relation between the von-K\'arm\'an slope and the turbulent
velocity in the log-law region (in wall units): . These
predictions are in excellent agreement with DNS data and with recent laboratory
experiments.Comment: 15 pages, 11 figs, included, PRE, submitte
The Viscous Lengths in Hydrodynamic Turbulence are Anomalous Scaling Functions
It is shown that the idea that scaling behavior in turbulence is limited by
one outer length and one inner length is untenable. Every n'th order
correlation function of velocity differences \bbox{\cal
F}_n(\B.R_1,\B.R_2,\dots) exhibits its own cross-over length to
dissipative behavior as a function of, say, . This length depends on
{and on the remaining separations} . One result of this Letter
is that when all these separations are of the same order this length scales
like with
, with being
the scaling exponent of the 'th order structure function. We derive a class
of scaling relations including the ``bridge relation" for the scaling exponent
of dissipation fluctuations .Comment: PRL, Submitted. REVTeX, 4 pages, I fig. (not included) PS Source of
the paper with figure avalable at http://lvov.weizmann.ac.il/onlinelist.htm
The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer
The statistical objects characterizing turbulence in real turbulent flows
differ from those of the ideal homogeneous isotropic model.They
containcontributions from various 2d and 3d aspects, and from the superposition
ofinhomogeneous and anisotropic contributions. We employ the recently
introduceddecomposition of statistical tensor objects into irreducible
representations of theSO(3) symmetry group (characterized by and
indices), to disentangle someof these contributions, separating the universal
and the asymptotic from the specific aspects of the flow. The different
contributions transform differently under rotations and so form a complete
basis in which to represent the tensor objects under study. The experimental
data arerecorded with hot-wire probes placed at various heights in the
atmospheric surfacelayer. Time series data from single probes and from pairs of
probes are analyzed to compute the amplitudes and exponents of different
contributions to the second order statistical objects characterized by ,
and . The analysis shows the need to make a careful distinction
between long-lived quasi 2d turbulent motions (close to the ground) and
relatively short-lived 3d motions. We demonstrate that the leading scaling
exponents in the three leading sectors () appear to be different
butuniversal, independent of the positions of the probe, and the large
scaleproperties. The measured values of the exponent are , and .
We present theoretical arguments for the values of these exponents usingthe
Clebsch representation of the Euler equations; neglecting anomalous
corrections, the values obtained are 2/3, 1 and 4/3 respectively.Comment: PRE, submitted. RevTex, 38 pages, 8 figures included . Online (HTML)
version of this paper is avaliable at http://lvov.weizmann.ac.il
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
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 firstly 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.Comment: 35 pages, REVTEX, 1 figure, Phys. Rev. E, submitte
Iterated Conformal Dynamics and Laplacian Growth
The method of iterated conformal maps for the study of Diffusion Limited
Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and
related processes. We emphasize the fundamental difference between these
processes: DLA is grown serially with constant size particles, while Laplacian
patterns are grown by advancing each boundary point in parallel, proportionally
to the gradient of the Laplacian field. We introduce a 2-parameter family of
growth patterns that interpolates between DLA and a discrete version of
Laplacian growth. The ultraviolet putative finite-time singularities are
regularized here by a minimal tip size, equivalently for all the models in this
family. With this we stress that the difference between DLA and Laplacian
growth is NOT in the manner of ultraviolet regularization, but rather in their
deeply different growth rules. The fractal dimensions of the asymptotic
patterns depend continuously on the two parameters of the family, giving rise
to a "phase diagram" in which DLA and discretized Laplacian growth are at the
extreme ends. In particular we show that the fractal dimension of Laplacian
growth patterns is much higher than the fractal dimension of DLA, with the
possibility of dimension 2 for the former not excluded.Comment: 13 pages, 12 figures, submitted to Phys. Rev.
Towards a Nonperturbative Theory of Hydrodynamic Turbulence:Fusion Rules, Exact Bridge Relations and Anomalous Viscous Scaling Functions
In this paper we derive here, on the basis of the NS eqs. a set of fusion
rules for correlations of velocity differences when all the separation are in
the inertial interval. Using this we consider the standard hierarchy of
equations relating the -th order correlations (originating from the viscous
term in the NS eq.) to 'th order (originating from the nonlinear term) and
demonstrate that for fully unfused correlations the viscous term is negligible.
Consequently the hierarchic chain is decoupled in the sense that the
correlations of 'th order satisfy a homogeneous equation that may exhibit
anomalous scaling solutions. Using the same hierarchy of eqs. when some
separations go to zero we derive a second set of fusion rules for correlations
with differences in the viscous range. The latter includes gradient fields. We
demonstrate that every n'th order correlation function of velocity differences
{\cal F}_n(\B.R_1,\B.R_2,\dots) exhibits its own cross-over length
to dissipative behavior as a function of, say, . This length depends on
{and on the remaining separations} . When all these
separations are of the same order this length scales like with ,
with being the scaling exponent of the 'th order structure
function. We derive a class of exact scaling relations bridging the exponents
of correlations of gradient fields to the exponents of the 'th
order structure functions. One of these relations is the well known ``bridge
relation" for the scaling exponent of dissipation fluctuations .Comment: PRE, Submitted. REVTeX, 18 pages, 7 figures (not included) PS Source
of the paper with figures avalable at
http://lvov.weizmann.ac.il/onlinelist.htm
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