Stationary states in Langevin dynamics under asymmetric L\'evy noises

Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises, which provide natural extension to the Gaussian noise having however a new property mainly a possibility of being asymmetric. Stationary probability densities are examined for a particle moving in parabolic, quartic and in generic double well potential models subjected to the action of $\alpha$-stable noises. Relevant solutions are constructed by methods of stochastic dynamics. In situations where analytical results are known they are compared with numerical results. Furthermore, the problem of estimation of the parameters of stationary densities is investigated.Comment: 9 pages, 9 figures, 3 table

Improving epidemic control strategies by extended detection

The majority of epidemics eradication programs work in a preventive responsive way. The lack of exact information about the epidemiological status of individuals makes responsive actions less efficient. Here, we demonstrate that additional tests can significantly increase the efficiency of “blind” treatment (vaccination or culling). Eradication strategy consisting of “blind” treatment in very limited local neighbourhood supplemented by extra tests in a little bit larger neighbourhood is able to prevent invasion of even highly infectious diseases and to achieve this at a cost lower than for the “blind” strategy. The effectiveness of the extended strategy depends on such parameters as the test efficiency and test cost

Stationary states for underdamped anharmonic oscillators driven by Cauchy noise

Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the damping is strong enough, for potential wells which in the overdamped regime produce multimodal stationary states, stationary states in the underdamped regime can be multimodal with the same number of modes like in the overdamped regime. For the parabolic potential, the stationary density is always unimodal and it is given by the two dimensional $\alpha$-stable density. For the mixture of quartic and parabolic single-well potentials the stationary density can be bimodal. Nevertheless, the parabolic addition, which is strong enough, can destroy bimodlity of the stationary state.Comment: 9 page

Statistics of non-linear stochastic dynamical systems under L\'evy noises by a convolution quadrature approach

This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficient way, independently from the kind of white noise; 2) The particular form of Wiener-Hopf integral transform and its numerical evaluation, both introduced in this study, are generalizations of fractional integro-differential operators of potential type and Gr\"unwald-Letnikov fractional derivatives, respectively.Comment: 20 pages, 5 figure

On distributions of functionals of anomalous diffusion paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Levy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrodinger equations that recently appeared in the literature.Comment: 25 pages, 4 figure

First passage and first hitting times of Lévy flights and Lévy walks

Abstract For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it (‘leapovers’), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms

Value of tissue harmonic imaging (THI) and contrast harmonic imaging (CHI) in detection and characterisation of breast tumours

The purpose of this study was to investigate the extent to which tissue harmonic imaging (THI), speckle reduction imaging (SRI), spatial compounding (SC) and contrast can improve detection and differentiation of breast tumours. We examined 38 patients (14 benign, 24 malignant tumours) with different combinations of THI, SRI and SC. The effect on delineation, margin, tissue differentiation and posttumoral phenomena was evaluated with a three-point score. Additionally, 1oo not palpable tumours (diameters: 4–15 mm) were examined by contrast harmonic imaging (CHI) with power Doppler. After bolus injection (0.5 ml Optison), vascularisation and enhancement were observed for 20 min. The best combination for detection of margin, infiltration, echo pattern and posterior lesion boundary was the combination of SRI level 2 with SC low. THI was helpful for lesions OF more than 1 cm depth. In native Power Doppler, vessels were found in 54 of 100 lesions. Within 5 min after contrast medium (CM) injection, marginal and penetrating vessels increased in benign and malignant tumours and central vessels mostly in carcinomas (p<0.05). A diffuse CM accumulation was observed up to 20 min after injection in malignant tumours only (p<0.05). THI, SRI and SC improved delineation and tissue differentiation. Second-generation contrast agent allowed detection of tumour vascularisation with prolonged enhancement

A Re-examination of the Portevin-Le Chatelier Effect in Alloy 718 in Connection with Oxidation-Assisted Intergranular Cracking

In Alloy 718, a sharp transition exists in the fracture path changing from an intergranular brittle mode to a transgranular ductile mode which is associated with a transition of flow behavior from smooth in the dynamic strain aging regime to a serrated one in the Portevin-Le Chatelier (PLC) regime. In order to better understand both deformation and rupture behavior, PLC phenomenon in a precipitation-hardened nickel-base superalloy was carefully investigated in a wide range of temperatures [573 K to 973 K (300°C to 700°C)] and strain rates (109^-5 to 3.2910^-2 s^-1 ). Distinction was made between two PLC domains characterized by different evolutions of the critical strain to the onset of the first serration namely normal and inverse behavior. The apparent activation energies associated with both domains were determined using different methods. Results showed that normal and inverse behavior domains are related to dynamic interaction of dislocations with, respectively, interstitial and substitutional solutes atoms. This analysis confirms that normal PLC regime may be associated to the diffusion of carbon atoms, whereas the substitutional species involves in the inverse regime is discussed with an emphasis on the role of Nb and Mo

Effectiveness analysis of resistance and tolerance to infection

<p>Abstract</p> <p>Background</p> <p>Tolerance and resistance provide animals with two distinct strategies to fight infectious pathogens and may exhibit different evolutionary dynamics. However, few studies have investigated these mechanisms in the case of animal diseases under commercial constraints.</p> <p>Methods</p> <p>The paper proposes a method to simultaneously describe (1) the dynamics of transmission of a contagious pathogen between animals, (2) the growth and death of the pathogen within infected hosts and (3) the effects on their performances. The effectiveness of increasing individual levels of tolerance and resistance is evaluated by the number of infected animals and the performance at the population level.</p> <p>Results</p> <p>The model is applied to a particular set of parameters and different combinations of values. Given these imputed values, it is shown that higher levels of individual tolerance should be more effective than increased levels of resistance in commercial populations. As a practical example, a method is proposed to measure levels of animal tolerance to bovine mastitis.</p> <p>Conclusions</p> <p>The model provides a general framework and some tools to maximize health and performances of a population under infection. Limits and assumptions of the model are clearly identified so it can be improved for different epidemiological settings.</p