285 research outputs found
Energy levels and their correlations in quasicrystals
Quasicrystals can be considered, from the point of view of their electronic
properties, as being intermediate between metals and insulators. For example,
experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have
conductivities far smaller than those of the metals that these alloys are
composed from. Wave functions in a quasicrystal are typically intermediate in
character between the extended states of a crystal and the exponentially
localized states in the insulating phase, and this is also reflected in the
energy spectrum and the density of states. In the theoretical studies we
consider in this review, the quasicrystals are described by a pure hopping
tight binding model on simple tilings. We focus on spectral properties, which
we compare with those of other complex systems, in particular, the Anderson
model of a disordered metal.Comment: 15 pages including 19 figures. Review article, submitted to Phil. Ma
Scaling laws and vortex profiles in 2D decaying turbulence
We use high resolution numerical simulations over several hundred of turnover
times to study the influence of small scale dissipation onto vortex statistics
in 2D decaying turbulence. A self-similar scaling regime is detected when the
scaling laws are expressed in units of mean vorticity and integral scale, as
predicted by Carnevale et al., and it is observed that viscous effects spoil
this scaling regime. This scaling regime shows some trends toward that of the
Kirchhoff model, for which a recent theory predicts a decay exponent .
In terms of scaled variables, the vortices have a similar profile close to a
Fermi-Dirac distribution.Comment: 4 Latex pages and 4 figures. Submitted to Phys. Rev. Let
Persistence exponents of non-Gaussian processes in statistical mechanics
Motivated by certain problems of statistical physics we consider a stationary
stochastic process in which deterministic evolution is interrupted at random
times by upward jumps of a fixed size. If the evolution consists of linear
decay, the sample functions are of the "random sawtooth" type and the level
dependent persistence exponent \theta can be calculated exactly. We then
develop an expansion method valid for small curvature of the deterministic
curve. The curvature parameter g plays the role of the coupling constant of an
interacting particle system. The leading order curvature correction to \theta
is proportional to g^{2/3}. The expansion applies in particular to exponential
decay in the limit of large level, where the curvature correction considerably
improves the linear approximation. The Langevin equation, with Gaussian white
noise, is recovered as a singular limiting case.Comment: 20 pages, 3 figure
Probability distribution of the maximum of a smooth temporal signal
We present an approximate calculation for the distribution of the maximum of
a smooth stationary temporal signal X(t). As an application, we compute the
persistence exponent associated to the probability that the process remains
below a non-zero level M. When X(t) is a Gaussian process, our results are
expressed explicitly in terms of the two-time correlation function,
f(t)=.Comment: Final version (1 major typo corrected; better introduction). Accepted
in Phys. Rev. Let
Self-gravitating Brownian particles in two dimensions: the case of N=2 particles
We study the motion of N=2 overdamped Brownian particles in gravitational
interaction in a space of dimension d=2. This is equivalent to the simplified
motion of two biological entities interacting via chemotaxis when time delay
and degradation of the chemical are ignored. This problem also bears some
similarities with the stochastic motion of two point vortices in viscous
hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We
analytically obtain the density probability of finding the particles at a
distance r from each other at time t. We also determine the probability that
the particles have coalesced and formed a Dirac peak at time t (i.e. the
probability that the reduced particle has reached r=0 at time t). Finally, we
investigate the variance of the distribution and discuss the proper form
of the virial theorem for this system. The reduced particle has a normal
diffusion behaviour for small times with a gravity-modified diffusion
coefficient =r_0^2+(4k_B/\xi\mu)(T-T_*)t, where k_BT_{*}=Gm_1m_2/2 is a
critical temperature, and an anomalous diffusion for large times
~t^(1-T_*/T). As a by-product, our solution also describes the growth of
the Dirac peak (condensate) that forms in the post-collapse regime of the
Smoluchowski-Poisson system (or Keller-Segel model) for T<T_c=GMm/(4k_B). We
find that the saturation of the mass of the condensate to the total mass is
algebraic in an infinite domain and exponential in a bounded domain.Comment: Revised version (20/5/2010) accepted for publication in EPJ
Numerical renormalization group of vortex aggregation in 2D decaying turbulence: the role of three-body interactions
In this paper, we introduce a numerical renormalization group procedure which
permits long-time simulations of vortex dynamics and coalescence in a 2D
turbulent decaying fluid. The number of vortices decreases as ,
with instead of the value predicted by a na\"{\i}ve
kinetic theory. For short time, we find an effective exponent
consistent with previous simulations and experiments. We show that the mean
square displacement of surviving vortices grows as .
Introducing effective dynamics for two-body and three-body collisions, we
justify that only the latter become relevant at small vortex area coverage. A
kinetic theory consistent with this mechanism leads to . We find that
the theoretical relations between kinetic parameters are all in good agreement
with experiments.Comment: 23 RevTex pages including 7 EPS figures. Submitted to Phys. Rev. E
(Some typos corrected; see also cond-mat/9911032
A telerehabilitation approach to chronic facial paralysis in the COVID-19 pandemic scenario: what role for electromyography assessment?
There is a lack of data on patient and diagnostic factors for prognostication of complete recovery in patients with peripheral facial palsy. Thus, the aim of this study was to evaluate the role of a telerehabilitave enhancement through the description of a case report with the use of short-wave diathermy and neuromuscular electrical stimulation combined to facial proprioceptive neuromuscular facilitation (PNF) rehabilitation in unrecovered facial palsy, in a COVID-19 pandemic scenario describing a paradigmatic telerehabilitation report. A 43-year-old woman underwent a facial rehabilitation plan consisting of a synergistic treatment with facial PNF rehabilitation, short-wave diathermy, and neuromuscular electrical stimulation (12 sessions lasting 45 min, three sessions/week for 4 weeks). Concerning the surface electromyography evaluation of frontal and orbicularis oris muscles, the calculated ratio between amplitude of the palsy side and normal side showed an improvement in terms of movement symmetry. At the end of the outpatient treatment, a daily telere-habilitation protocol with video and teleconsultation was provided, showing a further improvement in the functioning of a woman suffering from unresolved facial paralysis. Therefore, an adequate telerehabilitation follow-up seems to play a fundamental role in the management of patients with facial palsy
Persistence properties of a system of coagulating and annihilating random walkers
We study a d-dimensional system of diffusing particles that on contact either
annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1).
In 1-dimension, the system models the zero temperature Glauber dynamics of
domain walls in the q-state Potts model. We calculate P(m,t), the probability
that a randomly chosen lattice site contains a particle whose ancestors have
undergone exactly (m-1) coagulations. Using perturbative renormalization group
analysis for d < 2, we show that, if the number of coagulations m is much less
than the typical number M(t), then P(m,t) ~ m^(z/d) t^(-theta), with theta=d Q
+ Q(Q-1/2) epsilon + O(epsilon^2), z=(2Q-1) epsilon + (2 Q-1) (Q-1)(1/2+A Q)
epsilon^2 +O(epsilon^3), where Q=(q-1)/q, epsilon =2-d and A =-0.006. M(t) is
shown to scale as t^(d/2-delta), where delta = d (1 -Q)+(Q-1)(Q-1/2) epsilon+
O(epsilon^2). In two dimensions, we show that P(m,t) ~ ln(t)^(Q(3-2Q))
ln(m)^((2Q-1)^2) t^(-2Q) for m << t^(2 Q-1). The 1-dimensional results
corresponding to epsilon=1 are compared with results from Monte Carlo
simulations.Comment: 12 pages, revtex, 5 figure
Impact of rehabilitation on fatigue in post-COVID-19 patients: a systematic review and meta-analysis
The post-COVID-19 syndrome may affect patients after the COVID-19 post-acute phase. In particular, the 69% of patients reported persistent fatigue at the discharge. To date, no clear data are available regarding the most effective rehabilitative approaches for the treatment of this condition. Thus, this systematic review aimed to evaluate the rehabilitation treatment’s efficacy on fatigue in post-COVID-19 patients. We systematically searched PubMed, Scopus, and Web of Science databases to find longitudinal study designs presenting: post-COVID-19 patients as participants; a rehabilitative approach aimed to reduce post-COVID-19 syndrome as intervention; and fatigue intensity assessed through an evaluation tool that quantified the perceived exertion (i.e., fatigue severity scale, FSS; Borg Scale (BS); Borg Category Ratio 10, CR10; Checklist Individual Strength (CIS) fatigue scale; FACIT (Functional Assessment of Chronic Illness Therapy) fatigue scale). The present systematic review protocol was registered on PROSPERO (registration number CRD42021284058). Out of 704 articles, 6 studies were included. Nearly all patients showed COVID-19-related fatigue, and after the rehabilitation treatment, only 17% of subjects reported the persistency of symptoms. The overall effect size reported a −1.40 decrease in Borg Category Ratio 10 with a SE of 0.05 and a 95% CI between −1.50 and −1.30 (p < 0.001). The present systematic review and meta-analysis underlines the rehabilitation role in the fatigue reduction in patients affected by post-COVID-19 syndrome
Conformal Field Theory Approach to the 2-Impurity Kondo Problem: Comparison with Numerical Renormalization Group Results
Numerical renormalization group and conformal field theory work indicate that
the two impurity Kondo Hamiltonian has a non-Fermi liquid critical point
separating the Kondo-screening phase from the inter-impurity singlet phase when
particle-hole (P-H) symmetry is maintained. We clarify the circumstances under
which this critical point occurs, pointing out that there are two types of P-H
symmetry. Only one of them guarantees the occurance of the critical point. Much
of the previous numerical work was done on models with the other type of P-H
symmetry. We analyse this critical point using the boundary conformal field
theory technique. The finite-size spectrum is presented in detail and compared
with about 50 energy levels obtained using the numerical renormalization group.
Various Green's functions, general renormalization group behaviour, and a
hidden are analysed.Comment: 38 pages, RevTex. 2 new sections clarify the circumstances under
which a model will exhibit the non-trivial critical point (hence potentially
resolving disagreements with other Authors) and explain the hidden SO(7)
symmetry of the model, relating it to an alternative approach of Sire et al.
and Ga
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