On a rigorous interpretation of the quantum Schrödinger–Langevin operator in bounded domains with applications

AbstractIn this paper we make it mathematically rigorous the formulation of the following quantum Schrödinger–Langevin nonlinear operator for the wavefunctionAQSL=iℏ∂t+ℏ22mΔx−λ(Sψ−〈Sψ〉)−Θℏ[nψ,Jψ] in bounded domains via its mild interpretation. The a priori ambiguity caused by the presence of the multi-valued potential λSψ, proportional to the argument of the complex-valued wavefunctionψ=|ψ|exp{iℏSψ}, is circumvented by subtracting its positional expectation value,〈Sψ〉(t):=∫ΩSψ(t,x)nψ(t,x)dx, as motivated in the original derivation (Kostin, 1972 [45]). The problem to be solved in order to find Sψ is mostly deduced from the modulus-argument decomposition of ψ and dealt with much like in Guerrero et al. (2010) [37]. Here ℏ is the (reduced) Planck constant, m is the particle mass, λ is a friction coefficient, nψ=|ψ|2 is the local probability density, Jψ=ℏmIm(ψ¯∇xψ) denotes the electric current density, and Θℏ is a general operator (eventually nonlinear) that only depends upon the macroscopic observables nψ and Jψ. In this framework, we show local well-posedness of the initial-boundary value problem associated with the Schrödinger–Langevin operator AQSL in bounded domains. In particular, all of our results apply to the analysis of the well-known Kostin equation derived in Kostin (1972) [45] and of the Schrödinger–Langevin equation with Poisson coupling and enthalpy dependence (Jüngel et al., 2002 [41])

Monitoring in a Lotka-Volterra model

The problem of monitoring arises when in an ecosystem, in particular in a system of several populations, observing some components, we want to recover the state of the whole system in function of time. Due to the difficulty to construct exactly this state process, we look for an auxiliary system called observer, the solution of which reproduces this process with certain approximation. This means, that the solution of the observer tends to that of the original system. For this work an important concept is observability which means, that from the observation it is possible to recover the state process in a unique way, however without determining a constructive method to obtain it. If observability holds for the original system, it guarantees the existence of an auxiliary matrix which makes it possible to construct an observer of the system. The considered system of populations is described by the classical Lotka-Volterra model with one predator and two preys and the construction of its observer is illustrated with a numerical example. Finally, it is shown how the observer can be used for the estimation of the level of an abiotic effect on the population system

Development of recombinant PRRS vaccine candidates produced by using the baculovirus expression system

The Porcine Respiratory and Reproductive Syndrome (PRRS) is one of the viral diseases with the greatest impact in the swine industry, causing great economic losses due to causes abortions, infertility, pneumonia and even mortality in the farms.Currently there are two types of commercial vaccines based on live modified PRRS virus (MLV) or based on killed virus (KV). These vaccines are not able to tackle the disease. On one hand, they cannot raise universal immunity against the circulating serotypes of the virus, and, on the other hand, they are unsafe because of the risk of mutating into virulent forms when interacting with circulating viruses.For this reason, ADL-Bionatur Solutions is developing an alternative recombinant vaccine, aimed to be safer than current vaccines and with greater protective capacity and universality. To do this, the design of the vaccine candidates has been based on pontentiating the cell-mediated component of the immune response, while addressing humoral immunity against more conserved antigens of the virus.The expression of vaccine candidates was carried out by using the ADL-Bionatur' FLYLIFE platform, which allows the expression of recombinant proteins in larvae of Trichoplusia ni (T.ni) infected with a baculovirus expression vector. For this purpose, recombinant baculoviruses were generated and the expression of the proteins of interest was studied in T.ni. Subsequently, the solubilization and purification protocols were optimized for optimizing the recovery of the proteins of interest.The results showed that the proteins of interest were correctly expressed in larvae of T.ni. The solubilization and purification protocols were developed and optimized allowing a good recovery performance and a purity higher than 80%, which will allow carrying out in vivo efficacy assays

An Iterative Scheme for Solving Systems of Nonlinear Fredholm Integrodifferential Equations

Using fixed-point techniques and Faber-Schauder systems in adequate Banach spaces, we approximate the solution of a system of nonlinear Fredholm integrodifferential equations of the second kind.This research is partially supported by Junta de Andalucía Grant FQM359 and the ETSIE of the University of Granada, Spain

Observation and control in a model of a cell population affected by radiation

The effect of radiation on a cell population is described by a two-dimensional nonlinear system of differential equations. If the radiation rate is not too high, the system is known to have an asymptotically stable equilibrium. First, for the monitoring of this effect, the concept of observability is applied. For the case when the total number of cells is observed, without distinction between healthy and affected cells, a so-called observer system is constructed, which, at least near the equilibrium state, makes it possible to recover the dynamics of both the healthy and the affected cells, from the observation of the total number of cells without distinction. Results of simulations with illustrative data are also presented. If we want to control the system into a required new equilibrium state, and maintain this new equilibrium by a constant control, a technique of theory of optimal control can be applied to construct a feedback control system

Statistical detection of spatial plant patterns under the effect of forest use

The analysis of the consequences of land use (in particular forest use) may be considered as a partial step towards an integrated modelling of a land system. In the paper a forest territory is considered, where a gap-cut is made, and after a given time period the eventual change in the spatial distribution of undergrowth plants and tree seedlings is to be detected. Floristic data are collected along a line transect. A method for the detection of the change in the plant distributions along the transect is proposed to see whether this occurs at the geometric frontier of the human intervention. Since in the considered case the distribution of the change-point estimate is not known, as a substitute of its confidence interval, the so-called change-interval is calculated, using an adaptation of the bootstrap method. As an illustration, for a concrete plant species, the maximum likelihood estimation of the change-point and the calculation of the above mentioned change-interval is presented. Finally, the validation of the proposed method against some typical ecological situations is also presented, which provides a justification of the used algorithms

Change-Point Method Applied to the Detection of Temporal Variations in Seafloor Bacterial Mat Coverage

The paper is aimed at a methodological development of change-point detection, applicable in dentifying abrupt changes in temporal or spatial data sequences. In earlier papers we developed a method for detecting a change in the parameters of a discrete distribution, with the simultaneous estimation of the (deterministic but unknown) distribution parameters before and after the change. In this paper we not only extend this method to the case of normal distributions, but also provide a new algorithm for the iterative refining of the estimation of the change-point, based on a "cleaning" of mixed-up parts of the samples. The appropriate size of reduced part of the sample is analytically calculated for the case of normal distributions. This "cleaning" is combined with our original change-point detection method. Our new algorithm is not only validated on artificial data, but also applied to a real environmental data set collected and analysed by other authors in a seafloor observatory. Our results detecting abrupt changes of bacterial mat coverage of a seafloor area are in harmony with the biological fluctuations and changes in the abiotic environment, analysed recently by other authors using a different method. We also provide a comparison with other existing change-point detection methods: a one-dimensional version of the gradient method widely used for edge detection, and a maximum type statistical method well-known in environmental studies. Although normality conditions of our method are rather restrictive, its application potential for environmental data sets is also demonstrated

Change-Point Method Applied to the Detection of Temporal Variations in Seafloor Bacterial Mat Coverage

The paper is aimed at a methodological development of change-point detection, applicable in identifying abrupt changes in temporal or spatial data sequences. In earlier papers we developed a method for detecting a change in the parameters of a discrete distribution, with the simultaneous estimation of the (deterministic but unknown) distribution parameters before and after the change. In this paper we not only extend this method to the case of normal distributions, but also provide a new algorithm for the iterative refining of the estimation of the change-point, based on a "cleaning" of mixed-up parts of the samples. The appropriate size of reduced part of the sample is analytically calculated for the case of normal distributions. This "cleaning" is combined with our original change-point detection method. Our new algorithm is not only validated on artificial data, but also applied to a real environmental data set collected and analysed by other authors in a seafloor observatory. Our results detecting abrupt changes of bacterial mat coverage of a seafloor area are in harmony with the biological fluctuations and changes in the abiotic environment, analysed recently by other authors using a different method. We also provide a comparison with other existing change-point detection methods: a one-dimensional version of the gradient method widely used for edge detection, and a maximum type statistical method well-known in environmental studies. Although normality conditions of our method are rather restrictive, its application potential for environmental data sets is also demonstrated

La metodología de aprendizaje basado en proyectos (ABP) aplicada a asignaturas de ciencia de los materiales en ingeniería en la red IdM@ti

En este trabajo se va a presentar una experiencia docente llevada a cabo de forma coordinada entre profesorado de la red de innovación docente en ciencia de materiales IdM@ti. Se trata por tanto de una experiencia interuniversitaria que se ha desarrollado entre cuatro universidades públicas españolas de manera simultánea. Concretamente, el presente trabajo muestra la implementación y el desarrollo de la aplicación de la metodología de aprendizaje basado en proyectos en asignaturas de grados de ingeniería en el ámbito de ciencia de los materiales e ingeniería metalúrgica. Se presentan las experiencias llevadas a cabo durante los últimos cuatro años, mostrando los puntos fuertes y débiles de esta metodología, así como la problemática asociada a la implementación de la misma en asignaturas de curso general de grado. Se presentarán también los resultados obtenidos, así como las principales conclusiones a las que ha llegado el equipo de trabajo de la red IdM@ti

Conservation Strategy for Palm Groves: Optimal Chemical Control Model for Red Palm Weevil, Rhynchophorus ferrugineus

Rhynchophorus ferrugineus (Olivier, 1790) is an invasive pest species that constitutes one of the most important problems around the Mediterranean region and has been responsible for the loss of over 100,000 palm trees with an estimated annual cost of EUR several hundred million since its introduction into Europe. Methodological approaches of conservation ecology, such as multidisciplinary modelling, also apply in the management of cultural landscapes concerning ornamental plants, such as palm trees of the area. In this paper, we propose a dynamic model for the control of the red palm weevil, contributing in this way to the sustainability of an existing cultural landscape. The primary data set collected is a sample from the density-time function of a two-cohort pest population. This data set suggests a bimodal analytic description. If, from this data set, we calculate a sample from the accumulated density-time function (the integral of the density-time function), it displays a double sigmoid function (with two inflections). A good candidate for the analytical description of the latter is the sum of two logistic functions. As for the dynamic description of the process, a two-dimensional system of differential equations can be obtained, where the solution’s second component provides the analytical description of the original density-time function for the two-cohort population. Since the two-cohort waves appear in all three cycle stages, this reasoning applies to the subpopulations of larvae, pupae and adults. The model fitting is always performed using the SimFit package. On this basis, a mathematical model is proposed, which is sufficiently versatile to be of help in the control of this pest species in other geographical areas