Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

Mean first-passage time for system driven by the coin-toss square wave

We study the mean-first-passage-time problem for systems driven by the coin-toss square-wave signal. Exact analytic solutions are obtained for the driftless case. We also obtain approximate solutions for the potential case. The mean-first-passage time exhibits discontinuities and a remarkable nonsmooth oscillatory behavior which, to our knowledge, has not been observed for other kinds of driving noise.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

On a class of exact solutions to the Fokker-Planck equations

In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models.

The problem of physical coordinates in predictive Hamiltonian systems

In the Hamiltonian formulation of predictive relativistic systems, the canonical coordinates cannot be the physical positions. The relation between them is given by the individuality differential equations. However, due to the arbitrariness in the choice of Cauchy data, there is a wide family of solutions for these equations. In general, those solutions do not satisfy the condition of constancy of velocities moduli, and therefore we have to reparametrize the world lines into the proper time. We derive here a condition on the Cauchy data for the individuality equations which ensures the constancy of the velocities moduli and makes the reparametrization unnecessary.

A family of inhomogeneous cosmological Einstein - Rosen metrics

Some generalized soliton solutions of the cosmological EinsteinRosen type defined in the space-time region t2=z2 in terms of canonical coordinates are considered. Vacuum solutions are studied and interpreted as cosmological models. Fluid solutions are also considered and are seen to represent inhomogeneous cosmological models that become homogeneous at t?8. A subset of them evolve toward isotropic FriedmannRobertsonWalker metrics.

Bilateral symmetry of radial pulse in high-level tennis players : implications for the validity of central aortic pulse wave analysis

Rapport de synthèse Ce travail de thèse s'articule autour de l'importance de l'évaluation de la fonction vasculaire et des répercussions au niveau central, cardiaque, des perturbations du réseau vasculaire. Les maladies cardiovasculaires sont prédominantes dans notre société et causes de morbidité et mortalité importante. La mesure de la pression artérielle classique reste le moyen le plus utilisé pour suivre la santé des vaisseaux, mais ne reflète pas directement ce qui se passe au niveau du coeur. La tonométrie d'aplanation permet depuis quelques années de mesurer l'onde de pouls radial, et par le biais d'une fonction mathématique de transfert validée, il est possible d'en déduire la forme et Γ amplitude de l'onde de pouls central, donc de la pression aortique centrale. Cette dernière est un reflet bien plus direct de la post-charge cardiaque, et de nombreuses études cliniques actuelles s'intéressent à cette mesure pour stratifier le risque ou évaluer l'effet d'un traitement vasculaire. Toutefois, bien que cet outil soit de plus en plus utilisé, il est rarement précisé si la latéralité de la mesure joue un rôle, sachant que certaines propriétés des membres supérieurs peuvent être affectées par un usage préférentiel (masse musculaire, densité osseuse, diamètre des artères, capillarisation musculaire, et même fonction endothéliale). On a en effet observé que ces divers paramètre étaient tous augmentés sur un bras entraîné. Dès lors on peut se poser la question de l'influence de ces adaptations physiologiques sur la mesure indirecte effectuée par le biais du pouls radial. Nous avons investigué les deux membres supérieurs de sujets jeunes et sédentaires (SED), ainsi que ceux de sujets sportifs avec un développement fortement asymétrique des bras, soit des joueurs de tennis de haut niveau (TEN). Des mesures anthropométriques incluant la composition corporelle et la circonférence des bras et avant-bras ont montré que TEN présente une asymétrie hautement significative aux deux mesures entre le bras dominant (entraîné) et l'autre, ce qui est aussi présent pour la force de serrage (mesurée au dynamomètre de Jamar). L'analyse des courbes centrales de pouls ne montre aucune différence entre les deux membres dans chaque groupe, par contre on peut observer une différence entre SED et TEN, avec un index d'augmentation diastolique qui est 50 % plus élevé chez TEN. Les index d'augmentation systolique sont identiques dans les deux groupes. On peut retenir de cette étude la validité de la méthode de tonométrie d'aplanation quel que soit le bras utilisé (dominant ou non-dominant) et ce même si une asymétrie conséquente est présente. Ces données sont clairement nouvelles et permettent de s'affranchir de cette variable dans la mesure d'un paramètre cardiovasculaire dont l'importance est actuellement grandissante. Les différences d'index diastolique sont expliquées par la fréquence cardiaque et la vitesse de conduction de l'onde de pouls plus basses chez TEN, causant un retard diastolique du retour de l'onde au niveau central, phénomène précédemment bien décrit dans la littérature.

Viscoelasticity in Achilles Tendonopathy: Quantitative Assessment by Using Real-time Shear-Wave Elastography.

Purpose To investigate the differences in viscoelastic properties between normal and pathologic Achilles tendons ( AT Achilles tendon s) by using real-time shear-wave elastography ( SWE shear-wave elastography ). Materials and Methods The institutional review board approved this study, and written informed consent was obtained from 25 symptomatic patients and 80 volunteers. One hundred eighty ultrasonographic (US) and SWE shear-wave elastography studies of AT Achilles tendon s without tendonopathy and 30 studies of the middle portion of the AT Achilles tendon in patients with tendonopathy were assessed prospectively. Each study included data sets acquired at B-mode US (tendon morphology and cross-sectional area) and SWE shear-wave elastography (axial and sagittal mean velocity and relative anisotropic coefficient) for two passively mobilized ankle positions. The presence of AT Achilles tendon tears at B-mode US and signal-void areas at SWE shear-wave elastography were noted. Results Significantly lower mean velocity was shown in tendons with tendonopathy than in normal tendons in the relaxed position at axial SWE shear-wave elastography (P < .001) and in the stretched position at sagittal (P < .001) and axial (P = .0026) SWE shear-wave elastography . Tendon softening was a sign of tendonopathy in relaxed AT Achilles tendon s when the mean velocity was less than or equal to 4.06 m · sec(-1) at axial SWE shear-wave elastography (sensitivity, 54.2%; 95% confidence interval [ CI confidence interval ]: 32.8, 74.4; specificity, 91.5%; 95% CI confidence interval : 86.3, 95.1) and less than or equal to 5.70 m · sec(-1) at sagittal SWE shear-wave elastography (sensitivity, 41.7%; 95% CI confidence interval : 22.1, 63.3; specificity, 81.8%; 95% CI confidence interval : 75.3, 87.2) and in stretched AT Achilles tendon s, when the mean velocity was less than or equal to 4.86 m · sec(-1) at axial SWE shear-wave elastography (sensitivity, 66.7%; 95% CI confidence interval : 44.7, 84.3; specificity, 75.6%; 95% CI confidence interval : 68.5, 81.7) and less than or equal to 14.58 m · sec(-1) at sagittal SWE shear-wave elastography (sensitivity, 58.3%; 95% CI confidence interval : 36.7, 77.9; specificity, 83.5%; 95% CI confidence interval : 77.2, 88.7). Anisotropic results were not significantly different between normal and pathologic AT Achilles tendon s. Six of six (100%) partial-thickness tears appeared as signal-void areas at SWE shear-wave elastography . Conclusion Whether the AT Achilles tendon was relaxed or stretched, SWE shear-wave elastography helped to confirm and quantify pathologic tendon softening in patients with tendonopathy in the midportion of the AT Achilles tendon and did not reveal modifications of viscoelastic anisotropy in the tendon. Tendon softening assessed by using SWE shear-wave elastography appeared to be highly specific, but sensitivity was relatively low. © RSNA, 2014.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Suppression of scroll wave turbulence by noise

Rotating scroll waves are dynamical spatiotemporal structures characteristic of three-dimensional active media. It is well known that, under low excitability conditions, scroll waves develop an intrinsically unstable dynamical regime that leads to a highly disorganized pattern of wave propagation. Such a ¿turbulent¿ state bears some resemblance to fibrillation states in cardiac tissue. We show here that this unstable regime can be controlled by using a spatially distributed random forcing superimposed on a control parameter of the system. Our results are obtained from numerical simulations but an explicit analytical argument that rationalizes our observations is also presented.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.