219 research outputs found

    Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes

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    Different initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved by exploiting the connection with Brownian motion and the heat equation. The analysis of the fractional version (of order Μ\nu) of the Fresnel equation is also performed and, in detail, some specific cases, like Μ=1/2\nu=1/2, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process F(t)F(t), t>0t>0 with real sign-varying density is constructed and some of its properties examined. The equation of vibrations of plates is considered and the case of circular vibrating disks CRC_R is investigated by applying the methods of planar orthogonally reflecting Brownian motion within CRC_R. The composition of F with reflecting Brownian motion BB yields the law of biquadratic heat equation while the composition of FF with the first passage time TtT_t of BB produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure

    Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion

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    We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.”Marco Polo Programme” (University of Bologna

    Analytical tools for solitons and periodic waves corresponding to phonons on Lennard-Jones lattices in helical proteins

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    9 pages, 13 figures.-- PACS nrs.: 05.45.Yv, 87.15.-v.-- PMID: 15783440 [PubMed].We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jones potential, the solitons can be characterized analytically with a good quantitative agreement using formulas for a Toda potential with parameters fitted to the Lennard-Jones potential. We also discuss and show the robustness of the family of periodic solutions called cnoidal waves, corresponding to phonons. The soliton phenomena described in the simulations of alpha helices may help to explain recent x-ray experiments on long alpha helices in Rhodopsin where a long lifetime of the vibrational modes has been observed.Peer reviewe

    Noise-induced macroscopic bifurcations in globally-coupled chaotic units

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    Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived through an order parameter expansion.Comment: Phys. Rev. Lett., accepte

    Lagrangian transport through an ocean front in the North-Western Mediterranean Sea

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    We analyze with the tools of lobe dynamics the velocity field from a numerical simulation of the surface circulation in the Northwestern Mediterranean Sea. We identify relevant hyperbolic trajectories and their manifolds, and show that the transport mechanism known as the `turnstile', previously identified in abstract dynamical systems and simplified model flows, is also at work in this complex and rather realistic ocean flow. In addition nonlinear dynamics techniques are shown to be powerful enough to identify the key geometric structures in this part of the Mediterranean. In particular the North Balearic Front, the westernmost part of the transition zone between saltier and fresher waters in the Western Mediterranean is interpreted in terms of the presence of a semipermanent ``Lagrangian barrier'' across which little transport occurs. Our construction also reveals the routes along which this transport happens. Topological changes in that picture, associated with the crossing by eddies and that may be interpreted as the breakdown of the front, are also observed during the simulation.Comment: 34 pages, 6 (multiple) figures. Version with higher quality figures available from http://www.imedea.uib.es/physdept/publications/showpaper_en.php?indice=1764 . Problems with paper size fixe

    Convolution-type derivatives, hitting-times of subordinators and time-changed C0C_0-semigroups

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    In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by means of convolution-type integro-differential operators similar to the fractional derivatives. Furthermore we will discuss the concept of time-changed C0C_0-semigroup in case the time-change is performed by means of the hitting-time of a subordinator. We will show that such time-change give rise to bounded linear operators not preserving the semigroup property and we will present their governing equations by using again integro-differential operators. Such operators are non-local and therefore we will investigate the presence of long-range dependence.Comment: Final version, Potential analysis, 201

    Near-surface transport pathways in the north Atlantic Ocean : looking for throughput from the subtropical to the subpolar gyre

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    Author Posting. © American Meteorological Society, 2011. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 41 (2011): 911–925, doi:10.1175/2011JPO4498.1.Motivated by discrepancies between Eulerian transport estimates and the behavior of Lagrangian surface drifters, near-surface transport pathways and processes in the North Atlantic are studied using a combination of data, altimetric surface heights, statistical analysis of trajectories, and dynamical systems techniques. Particular attention is paid to the issue of the subtropical-to-subpolar intergyre fluid exchange. The velocity field used in this study is composed of a steady drifter-derived background flow, upon which a time-dependent altimeter-based perturbation is superimposed. This analysis suggests that most of the fluid entering the subpolar gyre from the subtropical gyre within two years comes from a narrow region lying inshore of the Gulf Stream core, whereas fluid on the offshore side of the Gulf Stream is largely prevented from doing so by the Gulf Stream core, which acts as a strong transport barrier, in agreement with past studies. The transport barrier near the Gulf Stream core is robust and persistent from 1992 until 2008. The qualitative behavior is found to be largely independent of the Ekman drift.This work was supported by the National Science Foundation Grants CMG-82469600 and CMG-82579600 and by the Office of Naval Research Grant ONR-13108700

    Platelet activation in the postoperative period after lung transplantation

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    Objective During lung transplantation, cells in the pulmonary parenchyma are subjected to ischemia, hypothermic storage, and reperfusion injury. Platelets, whose granular contents include adhesion receptors, chemokines, and coactivating substances that activate inflammatory and coagulant cascades, likely play a critical role in the lung allograft response to ischemia and reperfusion. The platelet response to the pulmonary allograft, however, has never been studied. Here we report significant platelet activation immediately after lung transplantation. Methods We performed a prospective cohort study comparing markers of platelet activation in patients undergoing lung transplantation and patients undergoing nontransplant thoracotomy. Plasma levels of soluble P-selectin, soluble CD40 ligand, and platelet–leukocyte conjugates were measured before surgery, after skin closure, and at 6 postoperative hours. Results Both soluble P-selectin and soluble CD40 ligand levels increased significantly after lung transplantation but not after thoracotomy. Additionally, platelet–monocyte conjugate fluorescence was significantly higher after lung transplantation than after thoracotomy alone. Conclusion These findings suggest that platelet activation is significantly increased after lung transplantation beyond that expected from the postoperative state. The increase in circulating platelet–monocyte conjugates suggests an important interaction between platelets and inflammatory cells. Further research should examine whether platelet activation affects early graft function after lung transplantation
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