1,096 research outputs found
Equilibrium states and invariant measures for random dynamical systems
Random dynamical systems with countably many maps which admit countable
Markov partitions on complete metric spaces such that the resulting Markov
systems are uniformly continuous and contractive are considered. A
non-degeneracy and a consistency conditions for such systems, which admit some
proper Markov partitions of connected spaces, are introduced, and further
sufficient conditions for them are provided. It is shown that every uniformly
continuous Markov system associated with a continuous random dynamical system
is consistent if it has a dominating Markov chain. A necessary and sufficient
condition for the existence of an invariant Borel probability measure for such
a non-degenerate system with a dominating Markov chain and a finite (16) is
given. The condition is also sufficient if the non-degeneracy is weakened with
the consistency condition. A further sufficient condition for the existence of
an invariant measure for such a consistent system which involves only the
properties of the dominating Markov chain is provided. In particular, it
implies that every such a consistent system with a finite Markov partition and
a finite (16) has an invariant Borel probability measure. A bijective map
between these measures and equilibrium states associated with such a system is
established in the non-degenerate case. Some properties of the map and the
measures are given.Comment: The article is published in DCDS-A, but without the 3rd paragraph on
page 4 (the complete removal of the paragraph became the condition for the
publication in the DCDS-A after the reviewer ran out of the citation
suggestions collected in the paragraph
Quantum Iterated Function Systems
Iterated functions system (IFS) is defined by specifying a set of functions
in a classical phase space, which act randomly on an initial point. In an
analogous way, we define a quantum iterated functions system (QIFS), where
functions act randomly with prescribed probabilities in the Hilbert space. In a
more general setting a QIFS consists of completely positive maps acting in the
space of density operators. We present exemplary classical IFSs, the invariant
measure of which exhibits fractal structure, and study properties of the
corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include
Synthetic Turbulence, Fractal Interpolation and Large-Eddy Simulation
Fractal Interpolation has been proposed in the literature as an efficient way
to construct closure models for the numerical solution of coarse-grained
Navier-Stokes equations. It is based on synthetically generating a
scale-invariant subgrid-scale field and analytically evaluating its effects on
large resolved scales. In this paper, we propose an extension of previous work
by developing a multiaffine fractal interpolation scheme and demonstrate that
it preserves not only the fractal dimension but also the higher-order structure
functions and the non-Gaussian probability density function of the velocity
increments. Extensive a-priori analyses of atmospheric boundary layer
measurements further reveal that this Multiaffine closure model has the
potential for satisfactory performance in large-eddy simulations. The
pertinence of this newly proposed methodology in the case of passive scalars is
also discussed
Approximation of rough functions
For given p ∈ [1,∞] and g ∈ L p(R), we establish the existence and uniqueness of solutions f ∈ L p(R), to the equation f (x) − a f (bx) = g(x), where a ∈ R, b ∈ R\ {0}, and |a| ̸= |b|1/p. Solutions include well-known nowhere differentiable functions such as those of Bolzano,Weierstrass, Hardy, and many others. Connections and consequences in the theory of fractal interpolation, approximation theory, and Fourier analysis are established.M. F. Barnsley, B. Harding, A. Vince, P. Viswanatha
On the "Mandelbrot set" for a pair of linear maps and complex Bernoulli convolutions
We consider the "Mandelbrot set" for pairs of complex linear maps,
introduced by Barnsley and Harrington in 1985 and studied by Bousch, Bandt and
others. It is defined as the set of parameters in the unit disk such
that the attractor of the IFS is
connected. We show that a non-trivial portion of near the imaginary axis is
contained in the closure of its interior (it is conjectured that all non-real
points of are in the closure of the set of interior points of ). Next we
turn to the attractors themselves and to natural measures
supported on them. These measures are the complex analogs of
much-studied infinite Bernoulli convolutions. Extending the results of Erd\"os
and Garsia, we demonstrate how certain classes of complex algebraic integers
give rise to singular and absolutely continuous measures . Next we
investigate the Hausdorff dimension and measure of , for
in the set , for Lebesgue-a.e. . We also obtain partial results on
the absolute continuity of for a.e. of modulus greater
than .Comment: 22 pages, 5 figure
A differential method for bounding the ground state energy
For a wide class of Hamiltonians, a novel method to obtain lower and upper
bounds for the lowest energy is presented. Unlike perturbative or variational
techniques, this method does not involve the computation of any integral (a
normalisation factor or a matrix element). It just requires the determination
of the absolute minimum and maximum in the whole configuration space of the
local energy associated with a normalisable trial function (the calculation of
the norm is not needed). After a general introduction, the method is applied to
three non-integrable systems: the asymmetric annular billiard, the many-body
spinless Coulombian problem, the hydrogen atom in a constant and uniform
magnetic field. Being more sensitive than the variational methods to any local
perturbation of the trial function, this method can used to systematically
improve the energy bounds with a local skilled analysis; an algorithm relying
on this method can therefore be constructed and an explicit example for a
one-dimensional problem is given.Comment: Accepted for publication in Journal of Physics
Harmonic analysis of iterated function systems with overlap
In this paper we extend previous work on IFSs without overlap. Our method
involves systems of operators generalizing the more familiar Cuntz relations
from operator algebra theory, and from subband filter operators in signal
processing.Comment: 37 page
Coherent States Measurement Entropy
Coherent states (CS) quantum entropy can be split into two components. The
dynamical entropy is linked with the dynamical properties of a quantum system.
The measurement entropy, which tends to zero in the semiclassical limit,
describes the unpredictability induced by the process of a quantum approximate
measurement. We study the CS--measurement entropy for spin coherent states
defined on the sphere discussing different methods dealing with the time limit
. In particular we propose an effective technique of computing
the entropy by iterated function systems. The dependence of CS--measurement
entropy on the character of the partition of the phase space is analysed.Comment: revtex, 22 pages, 14 figures available upon request (e-mail:
[email protected]). Submitted to J.Phys.
UK survey of occupational therapist’s and physiotherapist’s experiences and attitudes towards hip replacement precautions and equipment
Background: Total hip replacement (THR) is one of the most common orthopaedic procedures in the United Kingdom (UK). Historically, people following THR have been provided with hip precautions and equipment such as: raised toilet seats and furniture rises, in order to reduce the risks of dislocation post-operation. The purpose of this study was to determine current practices in the provision of these interventions in the UK for people following primary THR. Methods: A 27-question, self-administered online survey was developed and distributed to UK physiotherapists and occupational therapists involved in the management of people following primary THR (target respondents). The survey included questions regarding the current practices in the provision of equipment and hip precautions for THR patients, and physiotherapist’s and occupational therapist’s attitudes towards these practices. The survey was disseminated through print and web-based/social media channels. Results: 170 health professionals (87 physiotherapists and 83 occupational therapists), responded to the survey. Commonly prescribed equipment in respondent’s health trusts were raised toilet seats (95%), toilet frames and rails (88%), furniture raises (79%), helping hands/grabbers (77%), perching stools (75%) and long-handled shoe horns (75%). Hip precautions were routinely prescribed by 97% of respondents. Hip precautions were most frequently taught in a pre-operative group (52% of respondents). Similarly equipment was most frequently provided pre-operatively (61% respondents), and most commonly by occupational therapists (74% respondents). There was variability in the advice provided on the duration of hip precautions and equipment from up to six weeks post-operatively to life-time usage. Conclusions: Current practice on hip precautions and provision of equipment is not full representative of clinician’s perceptions of best care after THR. Future research is warranted to determine whether and to whom hip precautions and equipment should be prescribed post-THR as opposed to the current ‘blanket’ provision of equipment and movement restriction provided in UK practice
Stationary Properties of a Randomly Driven Ising Ferromagnet
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics
under the influence of a fast switching, random external field. Analytic
results for the stationary state are presented in mean-field approximation,
exhibiting a novel type of first order phase transition related to dynamic
freezing. Monte Carlo simulations performed on a quadratic lattice indicate
that many features of the mean field theory may survive the presence of
fluctuations.Comment: 5 pages in RevTex format, 7 eps/ps figures, send comments to
"mailto:[email protected]", submitted to PR
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