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

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 $\nu$) of the Fresnel equation is also performed and, in detail, some specific cases, like $\nu=1/2$, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process $F(t)$, $t>0$ 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 $C_R$ is investigated by applying the methods of planar orthogonally reflecting Brownian motion within $C_R$. The composition of F with reflecting Brownian motion $B$ yields the law of biquadratic heat equation while the composition of $F$ with the first passage time $T_t$ of $B$ produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure

Growth, competition and cooperation in spatial population genetics

We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space is continuous and the total density of competing individuals fluctuates due to demographic stochasticity. By means of analytics and numerical simulations, we study the behavior of fixation probabilities, fixation times, and heterozygosity, in a neutral setting and in cases where the two species can compete or cooperate. By concluding with examples in which individuals are transported by fluid flows, we argue that this model is a natural choice to describe competition in marine environments.Comment: 29 pages, 14 figures; revised version including a section with results in the presence of fluid flow

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

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 $C_0$-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

Population dynamics in compressible flows

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible turbulence is relevant for population dynamics in the ocean and we consider cases both where the velocity field is turbulent and when it is static. Furthermore, we investigate populations in terms of a continuos density field and when the populations are treated via discrete particles. In the last case we focus on the competition and fixation of one species compared to anotherComment: 16 pages, talk delivered at the Geilo Winter School 201

Controlling chaotic transients: Yorke's game of survival

5 pages, 4 figures.-- PACS nr.: 05.45.Gg, 05.45.Pq.-- PMID: 14995689 [PubMed].We consider the tent map as the prototype of a chaotic system with escapes. We show analytically that a small, bounded, but carefully chosen perturbation added to the system can trap forever an orbit close to the chaotic saddle, even in presence of noise of larger, although bounded, amplitude. This problem is focused as a two-person, mathematical game between two players called "the protagonist" and "the adversary." The protagonist's goal is to survive. He can lose but cannot win; the best he can do is survive to play another round, struggling ad infinitum. In the absence of actions by either player, the dynamics diverge, leaving a relatively safe region, and we say the protagonist loses. What makes survival difficult is that the adversary is allowed stronger "actions" than the protagonist. What makes survival possible is (i) the background dynamics (the tent map here) are chaotic and (ii) the protagonist knows the action of the adversary in choosing his response and is permitted to choose the initial point x(0) of the game. We use the "slope 3" tent map in an example of this problem. We show that it is possible for the protagonist to survive.J.A. and M.S.J. acknowledge financial support from the Spanish Ministry of Science and Technology under project BFM2000-0967, and from the Universidad Rey Juan Carlos under projects URJC-PGRAL-2001/02 and URJC-PIGE-02-04. F.d'O. acknowledges financial support from MCyT (Spain) and FEDER, project REN2001-0802-C02-01/MAR (IMAGEN).Peer reviewe

Risk assessment for the spread of Serratia marcescens within dental-unit waterline systems using Vermamoeba vermiformis

Vermamoeba vermiformis is associated with the biofilm ecology of dental-unit waterlines (DUWLs). This study investigated whether V. vermiformis is able to act as a vector for potentially pathogenic bacteria and so aid their dispersal within DUWL systems. Clinical dental water was initially examined for Legionella species by inoculating it onto Legionella selective-medium plates. The molecular identity/profile of the glassy colonies obtained indicated none of these isolates were Legionella species. During this work bacterial colonies were identified as a non-pigmented Serratia marcescens. As the water was from a clinical DUWL which had been treated with Alpron™ this prompted the question as to whether S. marcescens had developed resistance to the biocide. Exposure to Alpron™ indicated that this dental biocide was effective, under laboratory conditions, against S. marcescens at up to 1x108 colony forming units/millilitre (cfu/ml). V. vermiformis was cultured for eight weeks on cells of S. marcescens and Escherichia coli. Subsequent electron microscopy showed that V. vermiformis grew equally well on S. marcescens and E. coli (p = 0.0001). Failure to detect the presence of S. marcescens within the encysted amoebae suggests that V. vermiformis is unlikely to act as a vector supporting the growth of this newly isolated, nosocomial bacterium

Integration of safety in IFMIF-DONES design

The IFMIF-DONES (International Fusion Material Irradiation Facility-DEMO Oriented NEutron Source) facility is being designed with the general objective of providing irradiation of representative samples of power fusion machine materials under prototypical conditions. A linear accelerator will deliver deuterons at high intensity to circulating lithium in a loop, which will produce neutrons capable of obtaining the required damage conditions. As a result of this process, radionuclides will be produced as a by-product, which is characterized by several degrees of mobility. Shielding and radiation protection measures will be required in the facility. IFMIF-DONES will be classified as a first class radioactive facility according to national regulations, with Spain being the European candidate to site the facility. Several aspects of the main safety instructions affecting the facility’s design are explained and discussed in this pape

Characterisation and radioimmunotherapy of L19-SIP, an anti-angiogenic antibody against the extra domain B of fibronectin, in colorectal tumour models

Angiogenesis is a characteristic feature of tumours and other disorders. The human monoclonal antibody L19- SIP targets the extra domain B of fibronectin, a marker of angiogenesis expressed in a range of tumours. The aim of this study was to investigate whole body distribution, tumour localisation and the potential of radioimmunotherapy with the L19-small immunoprotein (SIP) in colorectal tumours. Two colorectal tumour models with highly different morphologies, the SW1222 and LS174T xenografts, were used in this study. Localisation and retention of the L19-SIP antibody at tumour vessels was demonstrated using immunohistochemistry and Cy3-labelled L19-SIP. Whole body biodistribution studies in both tumour models were carried out with 125I-labelled L19-SIP. Finally, 131I-labelled antibody was used to investigate the potential of radioimmunotherapy in SW1222 tumours. Using immunohistochemistry, we confirmed extra domain B expression in the tumour vasculature. Immunofluorescence demonstrated localisation and retention of injected Cy3-labelled L19-SIP at the abluminal side of tumour vessels. Biodistribution studies using a 125I-labelled antibody showed selective tumour uptake in both models. Higher recorded values for localisation were found in the SW1222 tumours than in the LS174T (7.9 vs 6.6 %ID g−1), with comparable blood clearance for both models. Based on these results, a radioimmunotherapy study was performed in the SW1222 xenograft using 131I-Labelled L19-SIP (55.5 MBq), which showed selective tumour uptake, tumour growth inhibition and improved survival. Radio- and fluorescence-labelled L19-SIP showed selective localisation and retention at vessels of two colorectal xenografts. Furthermore, 131I-L19-SIP shows potential as a novel treatment of colorectal tumours, and provides the foundation to investigate combined therapies in the same tumour models