Neutral Equations of Mixed Type

In this dissertation we consider neutral equations of mixed type. In particular, we con- sider the associated linear Fredholm theory and nerve fiber models that are written as systems of neutral equations of mixed type. In Chapter 2, we extend the existing Fredholm theory for mixed type functional differential equations developed by Mallet-Paret to the case of implicitly defined mixed type functional differential equations. In Chapter 3, we apply the theory to an example arising from modeling signal prop- agation in nerve fibers. In this two-dimensional system, we rely on the Lyapunov- Schmidt method to demonstrate the existence of traveling wave solutions. With the aid of numerical computations, a saddle-node bifurcation was detected. In Chapter 4, we consider an extension of the parallel nerve fiber model examining in Chapter 3 and present the results of a numerical study. In this chapter, an additional form of coupling is examined not considered in the model from Chapter 3. This second type of coupling may be excitatory or inhibitory depending on the sign of the coupling parameter. Within a continuation framework, we employ a pseudo-spectral approach utilizing Chebyshev polynomials as basis functions. The chebfun package, consisting of Chebyshev tools, was utilized to manipulate the polynomials

Dynamics of poroelastic filaments

We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition to the usual terms for the bending of an elastic rod, we find a term that arises from fluid-solid interaction. Using the poroelastica equation as a starting point, we consider the load controlled and displacement controlled planar buckling of a slender rod, as well as the closely related instabilities of a rod subject to twisting moments and compression when embedded in an elastic medium. This work has applications to the active and passive mechanics of thin filaments and sheets made from gels, plant organs such as stems, roots and leaves, sponges, cartilage layers and bones.Comment: 34 pages, 13 figures, to appear in the Proceeding of the Royal Societ

Stochastic evolutionary game dynamics

In this review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations.Comment: To appear in "Reviews of Nonlinear Dynamics and Complexity" Vol. II, Wiley-VCH, 2009, edited by H.-G. Schuste

List of contents

Rev. iberoam. bioecon. cambio clim. Vol.1(1) 2015; 95-114Los cambios medioambientales globales hacen pensar en un aumento futuro de la aridez, por ello es necesario buscar alternativas que permitan un uso más eficiente del agua y reducir su consumo, teniendo en cuenta que es un recurso limitado. En la actualidad, aproximadamente el 59,7% del total de agua planificada para todos los usos en Cuba se utiliza en la agricultura, pero no más del 50% de esa agua se convierte directamente en productos agrícolas. El estudio de las funciones agua-rendimiento y su uso dentro de la planificación del agua para riego es una vía importante para trazar estrategias de manejo que contribuyan al incremento en la producción agrícola. Utilizando los datos de agua aplicada por riego y los rendimientos obtenidos en más de 100 experimentos de campo realizados fundamentalmente en suelo Ferralítico Rojo de la zona sur de La Habana y con ayuda de herramientas de análisis de regresión en este trabajo se estiman las funciones agua aplicada-rendimientos para algunos cultivos agrícolas y se analizan las posibles estrategias de optimización del riego a seguir en función de la disponibilidad de agua. Seleccionar una estrategia de máxima eficiencia del riego puede conducir a reducciones de agua a aplicar entre un 21,6 y 46,8%, incrementos de la productividad del agua entre 17 y 32% y de la relación beneficios/costo estimada de hasta un 3,4%. Lo anterior indica la importancia desde el punto de vista económico que puede llegar a alcanzar el uso de esta estrategia en condiciones de déficit hídrico. El conocimiento de las funciones agua aplicada por riego-rendimiento y el uso de la productividad del agua, resultan parámetros factibles de introducir como indicadores de eficiencia en el planeamiento del uso del agua en la agricultura, con lo cual es posible reducir los volúmenes de agua a aplicar y elevar la relación beneficio-costo actual.Rev. iberoam. bioecon. cambio clim. Vol.1(1) 2015; 95-11

Large Time Behaviour of Neutral Delay Systems

UBL - phd migration 201

Trapping and Wiggling: Elastohydrodynamics of Driven Microfilaments

We present a general theoretical analysis of semiflexible filaments subject to viscous drag or point forcing. These are the relevant forces in dynamic experiments designed to measure biopolymer bending moduli. By analogy with the ``Stokes problems" in hydrodynamics (fluid motion induced by that of a wall bounding a viscous fluid), we consider the motion of a polymer one end of which is moved in an impulsive or oscillatory way. Analytical solutions for the time-dependent shapes of such moving polymers are obtained within an analysis applicable to small-amplitude deformations. In the case of oscillatory driving, particular attention is paid to a characteristic length determined by the frequency of oscillation, the polymer persistence length, and the viscous drag coefficient. Experiments on actin filaments manipulated with optical traps confirm the scaling law predicted by the analysis and provide a new technique for measuring the elastic bending modulus. A re-analysis of several published experiments on microtubules is also presented.Comment: RevTex, 24 pages, 15 eps figs, uses cite.sty, Biophysical