Chaotic diffusion caused by close encounters with several massive asteroids: II. the regions of (10) Hygiea, (2) Pallas, and (31) Euphrosyne

Context. Close encounters with (1) Ceres and (4) Vesta, the two most massive bodies in the main belt, are known to be a mechanism of dynamical mobility able to significantly alter proper elements of minor bodies, and they are the main source of dynamical mobility for medium-sized and large asteroids (D > 20 km, approximately). Recently, it has been shown that drift rates caused by close encounters with massive asteroids may change significantly on timescales of 30 Myr when different models (i.e., different numbers of massive asteroids) are considered. Aims. So far, not much attention has been given to the case of diffusion caused by the other most massive bodies in the main belt: (2) Pallas, (10) Hygiea, and (31) Euphrosyne, the third, fourth, and one of the most massive highly inclined asteroids in the main belt, respectively. Since (2) Pallas is a highly inclined object, relative velocities at encounter with other asteroids tend to be high and changes in proper elements are therefore relatively small. It was thus believed that the scattering effect caused by highly inclined objects in general should be small. Can diffusion by close encounters with these asteroids be a significant mechanism of long-term dynamical mobility? Methods. By performing simulations with symplectic integrators, we studied the problem of scattering caused by close encounters with (2) Pallas, (10) Hygiea, and (31) Euphrosyne when only the massive asteroids (and the eight planets) are considered, and the other massive main belt asteroids and non-gravitational forces are also accounted for. Results. By finding relatively small values of drift rates for (2) Pallas, we confirm that orbital scattering by this highly inclined object is indeed a minor effect. Unexpectedly, however, we obtained values of drift rates for changes in proper semi-major axis a caused by (10) Hygiea and (31) Euphrosyne larger than what was previously found for scattering by (4) Vesta. These high rates may have repercussions on the orbital evolution and age estimate of their respective families. © 2013 ESO.

Numerical solution of the time dependent Ginzburg-Landau equations for mixed (d plus s)-wave superconductors

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-destructive thermal wave method applied to study thermal properties of fast setting time endodontic cement

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

About the minimum time transference in a fractional differential equation

The use of fractional calculus when modeling phenomena allows new queries concerning the deepest parts of the physical laws involved in. Here we will be dealing with an apparent paradox in which the time of transference from zero in a system with fractional derivatives can be strictly shortened relatively to the minimal time transference done in an equivalent system in the frame of the entire derivatives.

Ordinary fractional differential equations are in fact usual entire ordinary differential equations on time scales

Despite the huge number of works considering fractional derivatives or derivatives on time scales some basic facts remain to be evaluated. Here we will be showing that the fractional derivative of monomials is in fact an entire derivative considered on an appropriate time scale.

Column generation for a multitrip vehicle routing problem with time windows, driver work hours, and heterogeneous fleet

This study addresses a vehicle routing problem with time windows, accessibility restrictions on customers, and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can performmultiple routes per day, all starting and ending at a single depot, and it is assigned to a single driverwhose totalwork hours are limited.Acolumn generation algorithmis proposed.The column generation pricing subproblem requires a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performingmultiple routes per day and to address the need to set the workday’s start time within the planning horizon. A constructive heuristic and a metaheuristic based on tabu search are also developed to find good solutions.

A comprehensive study of the 26th December 2004 Sumatra earthquake: possible implications on Earth rotation and investigations on the coseismic and postseismic stress diffusion associated with the seismic rupture

In this work a multidisciplinary study of the December 26th, 2004 Sumatra earthquake has been carried out. We have investigated both the effect of the earthquake on the Earth rotation and the stress field variations associated with the seismic event. In the first part of the work we have quantified the effects of a water mass redistribution associated with the propagation of a tsunami wave on the Earth’s pole path and on the length-of-day (LOD) and applied our modeling results to the tsunami following the 2004 giant Sumatra earthquake. We compared the result of our simulations on the instantaneous rotational axis variations with some preliminary instrumental evidences on the pole path perturbation (which has not been confirmed yet) registered just after the occurrence of the earthquake, which showed a step-like discontinuity that cannot be attributed to the effect of a seismic dislocation. Our results show that the perturbation induced by the tsunami on the instantaneous rotational pole is characterized by a step-like discontinuity, which is compatible with the observations but its magnitude turns out to be almost one hundred times smaller than the detected one. The LOD variation induced by the water mass redistribution turns out to be not significant because the total effect is smaller than current measurements uncertainties. In the second part of this work of thesis we modeled the coseismic and postseismic stress evolution following the Sumatra earthquake. By means of a semi-analytical, viscoelastic, spherical model of global postseismic deformation and a numerical finite-element approach, we performed an analysis of the stress diffusion following the earthquake in the near and far field of the mainshock source. We evaluated the stress changes due to the Sumatra earthquake by projecting the Coulomb stress over the sequence of aftershocks taken from various catalogues in a time window spanning about two years and finally analyzed the spatio-temporal pattern. The analysis performed with the semi-analytical and the finite-element modeling gives a complex picture of the stress diffusion, in the area under study, after the Sumatra earthquake. We believe that the results obtained with the analytical method suffer heavily for the restrictions imposed, on the hypocentral depths of the aftershocks, in order to obtain the convergence of the harmonic series of the stress components. On the contrary we imposed no constraints on the numerical method so we expect that the results obtained give a more realistic description of the stress variations pattern.

Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Real-time evaluation of diffusion of the local anesthetic solution during peribulbar block using ultrasound imaging and clinical correlates of diffusion

The aims of this prospective observational study were to assess the incidence of intraconal spread during peribulbar (extraconal) anesthesia by real-time ultrasound imaging of the retro-orbital compartment and to determine whether a complete sensory and motor block (with akinesia) of the eye is directly related to the intraconal spread.

Spinal Cord Diffusion-Tensor Imaging and Motor-evoked Potentials in Multiple Sclerosis Patients: Microstructural and Functional Asymmetry

Purpose: To assess possible association between intrinsic structural damage and clinical disability by correlating spinal cord diffusion-tensor (DT) imaging data with electrophysiological parameters in patients with a diagnosis of multiple sclerosis (MS). Materials and Methods: This study was approved by the local ethical committee according to the declaration of Helsinki and written informed consent was obtained. DT images and T1- and T2-weighted images of the spinal cord were acquired in 28 healthy volunteers and 41 MS patients. Fractional anisotropy (FA) and apparent diffusion coefficients were evaluated in normal-appearing white matter (NAWM) at the cervical level and were correlated with motor-evoked potentials (n = 34). Asymmetry index was calculated for FA values with corresponding left and right regions of interest as percentage of the absolute difference between these values relative to the sum of the respective FA values. Statistical analysis included Spearman rank correlations, Mann-Whitney test, and reliability analysis. Results: Healthy volunteers had low asymmetry index (1.5%-2.2%). In MS patients, structural abnormalities were reflected by asymmetric decrease of FA (asymmetry index: 3.6%; P = .15). Frequently asymmetrically affected among MS patients was left and right central motor conduction time (CMCT) to abductor digiti minimi muscle (ADMM) (asymmetry index, 15%-16%) and tibialis anterior muscle (TAM) (asymmetry index, 9.5%-14.1%). Statistically significant correlations of functional (ie, electrophysiological) and structural (ie, DT imaging) asymmetries were found (P = .005 for CMCT to ADMM; P = .007 for CMCT to TAM) for the cervical lateral funiculi, which comprise the crossed pyramidal tract. Interobserver reliability for DT imaging measurements was excellent (78%-87%). Conclusion: DT imaging revealed asymmetric anatomic changes in spinal cord NAWM, which corresponded to asymmetric electrophysiological deficits for both arms and legs, and reflected a specific structure-function relationship in the human spinal cord. © RSNA, 2013.

Calcium waves driven by "sensitization" wave-fronts

OBJECTIVE: Cellular Ca(2+) waves are understood as reaction-diffusion systems sustained by Ca(2+)-induced Ca(2+) release (CICR) from Ca(2+) stores. Given the recently discovered sensitization of Ca(2+) release channels (ryanodine receptors; RyRs) of the sarcoplasmic reticulum (SR) by luminal SR Ca(2+), waves could also be driven by RyR sensitization, mediated by SR overloading via Ca(2+) pump (SERCA), acting in tandem with CICR. METHODS: Confocal imaging of the Ca(2+) indicator fluo-3 was combined with UV-flash photolysis of caged compounds and the whole-cell configuration of the patch clamp technique to carry out these experiments in isolated guinea pig ventricular cardiomyocytes. RESULTS: Upon sudden slowing of the SERCA in cardiomyocytes with a photoreleased inhibitor, waves indeed decelerated immediately. No secondary changes of Ca(2+) signaling or SR Ca(2+) content due to SERCA inhibition were observed in the short time-frame of these experiments. CONCLUSIONS: Our findings are consistent with Ca(2+) loading resulting in a zone of RyR 'sensitization' traveling within the SR, but inconsistent with CICR as the predominant mechanism driving the Ca(2+) waves. This alternative mode of RyR activation is essential to fully conceptualize cardiac arrhythmias triggered by spontaneous Ca(2+) release.