A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models

GASTROINTESTINAL DIGESTION OF KAHAI PROTEIN CONCENTRATE (CARYODENDRON ORINOCENSE KARST)

Objective: The aim of this study was to obtain kahai protein concentrate from Caryodendron orinocense karst cultivated in the region Amazonia of Ecuador and characterizes its gastric and duodenal hydrolysates using the sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) electrophoresis method and the reversed-phase ultra-high-performance liquid chromatography (RP-UHPLC) method.Methods: Kahai seeds (C. orinocense karst) were utilized to obtain kahai protein concentrate at pH 5.0 using the isoelectric precipitation method and then subject to gastric hydrolysis with pepsin enzyme (2000 U/mg of protein) at pH 1.2, pH 2.0, and pH 3.2 at 37°C for 2 h with agitation in simulated gastric fluids and then to duodenal hydrolysis with pancreatin (mix enzymes) at pH 7.0 at 37°C for 3 h with agitation in simulated intestinal fluid. Gastric and duodenal hydrolysates from kahai were characterized using the SDS-PAGE electrophoresis method and the RP-UHPLC chromatography method.Results: Proteins obtained from kahai (C. orinocense karst) were hydrolyzed with pepsin, only one protein with molecular weight of 100 kDa presented resistance to hydrolysis with pepsin at all pHs assayed. All proteins from kahai protein concentrate were totally hydrolyzed with pancreatin in in vitro conditions.Conclusion: This study suggests that kahai protein concentrates have a high grade of digestibility in vitro when using the gastroduodenal model of digestion. Kahai protein can be a good source of alternative vegetal proteins to be consumed by animals and humans

Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions $d\geq 2$ and in all of space for $d\geq 3$, the uniqueness being a result previously not known for PKS with degenerate diffusion. We generalize the notion of criticality for PKS and show that subcritical problems are globally well-posed. For a fairly general class of problems, we prove the existence of a critical mass which sharply divides the possibility of finite time blow up and global existence. Moreover, we compute the critical mass for fully general problems and show that solutions with smaller mass exists globally. For a class of supercritical problems we prove finite time blow up is possible for initial data of arbitrary mass.Comment: 31 page

Rotating Hele-Shaw cells with ferrofluids

We investigate the flow of two immiscible, viscous fluids in a rotating Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining the instability of the fluid-fluid interface is analyzed. The linear stability analysis of the problem shows that a non-uniform, azimuthal magnetic field, applied tangential to the cell, tends to stabilize the interface. We verify that maximum growth rate selection of initial patterns is influenced by the applied field, which tends to decrease the number of interface ripples. We contrast these results with the situation in which a uniform magnetic field is applied normally to the plane defined by the rotating Hele-Shaw cell.Comment: 12 pages, 3 ps figures, RevTe

Efectos moduladores de la personalidad y la valoración subjetiva en la respuesta autonómica ante una tarea de hablar en público

El objetivo de este estudio fue examinar en una muestra de 16 mujeres, el efecto los de rasgos de personalidad y la valoración subjetiva ante un estresor social de laboratorio (hablar en público) en la respuesta cardiovascular y electrodérmica. Se midieron las respuestas de conductancia de la piel, la frecuencia cardiaca (FC) y el volumen del pulso periférico (VPP) durante un periodo de descanso, preparación, tarea y recuperación ante un discurso académico. Los sujetos fueron clasificados según sus puntuaciones altas o bajas en el cuestionario de personalidad EPQ, el STAI y en las medidas subjetivas. Los sujetos mostraron un aumento de la activación fisiológica significativo durante las fases de preparación y ejecución del discurso, esta activación estuvo modulada por las variables de personalidad y la valoración subjetiva. Los sujetos más extrovertidos mostraron mayor frecuencia de respuestas electrodérmicas (RED) a lo largo de todo el registro. Los sujetos que percibieron la tarea como más difícil mostraron los valores más altos en frecuencia cardiaca. Por último, aquéllos que percibieron un mayor estrés y esfuerzo mostraron un porcentaje de cambio mayor en volumen de pulso. Estos resultados apoyan el uso de la tarea de hablar en público como un buen estresor de laboratorio y la importancia de la experiencia subjetiva y los rasgos de personalidad del individuo como variables que modulan dicha respuesta

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters

Intrinsic noise-induced phase transitions: beyond the noise interpretation

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Ito vs. Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Ito. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau type model. A detailed discussion of new numerical algorithms used in both interpretations is also presented.Comment: 9 pages, 8 figures, to be published in Phys. Rev.