A Fractional Model of Complex Permittivity of Conductor Media with Relaxation: Theory vs. Experiments

Moving from the study of plasmonic materials with relaxation, in this work we propose a fractional Abraham-Lorentz-like model of the complex permittivity of conductor media. This model extends the Ciancio-Kluitenberg, based on the Mazur-de Groot non-equilibrium thermodynamics theory (NET). The approach based on NET allows us to link the phenomenological function of internal variables and electrodynamics variables for a large range of frequencies. This allows us to closer reproduce experimental data for some key metals, such as Cu, Au and Ag. Particularly, our fitting significantly improves those obtained by Rakic and coworkers and we were able to operate in a larger range of energy values. Moreover, in this work we also provide a definition of a substantial fractional derivative, and we extend the fractional model proposed by Flora et al

Thermomechanics of Interstitial Working at Liquid Boundaries

A model of material interface, for which the metric tensor is regarded as an internal variable, is considered. Both a local and a non-local evolution equation for such a variable are analyzed. The consequences of the second law of thermodynamics are derived in both cases

On Systems of Active Particles Perturbed by Symmetric Bounded Noises: A Multiscale Kinetic Approach

We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by a multidimensional Hypo-Elliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integro-differential Equation with hypo-elliptical terms. In the numerical simulations we focus on a simple case where the unperturbed dynamics of the agents is of logistic type and the bounded perturbations are of the Doering–Cai–Lin noise or the Arctan bounded noise. We then find the evolution and the steady state of the HEFPE. The steady state density is, in some cases, multimodal due to noise-induced transitions. Then we assume the steady state density as the initial condition for the full system evolution. Namely we modeled the vital dynamics of the agents as logistic nonlocal, as it depends on the whole size of the population. Our simulations suggest that both the steady states density and the total population size strongly depends on the type of bounded noise. Phenomena as transitions to bimodality and to asymmetry also occur

Architectural self-fabrication

The paper will focus on the role of computational design and digital fabrication in the processes of urban and architectural self-regeneration of existing infrastructures and buildings. The Architectural Fabrication research agenda takes inspiration from some of the concepts mentioned in Christopher Alexander’s essay ‘Systems generating systems’ (1968). It aims at introducing ways in which systems thinking and computer aided manufacturing can be most directly applied to the built environment. Hacking architectural spaces, by evolving their genetic spatial and structural codes, is developing the idea of optimizing resources involving inhabitants rather than generating other top down architectural solutions. During the last decades (starting from the book of Mario Carpo, ‘The Digital Turn in Architecture’) the digital shift in architectural design has generated a new discipline with the aim to define an innovative way to bridge the notion of nature with the one of teknè. From such a cultural milieu many research agenda were focusing on the concepts of morphogenesis and evolutionary thinking inspired by the work of French philosophers Gilles Deleuze and Felix Guattari based on the theory of complex systems. Despite this interest in bridging an evolutionary approach with the notion of emergent technologies in architecture (well described in the book ‘The Architecture of Emergence’ of Michael Weinstock) only a very few researchers have investigated on the potential of computational design as a driver for the ecological rehabilitation of existing infrastructures. As a matter of fact, the computational designers were so worried to claim for a new aesthetical identity of their discipline while a new opportunity was emerging for applying this evolutionary approach in order to hack existing structures. The idea of living infrastructures is related to the possibility of developing contextual algorithms in order to customize standard solutions with a post-human process that creates diversified spatial configurations out of very rigid organizational systems. Therefore, the paper will also talk about the Hacking Gomorra project as a possible paradigm of experimenting a 3D printing protocol for the environmental rehabilitation of a mega-structural housing building in Naples (Italy)

On a mathematical model of immune competition

AbstractThis work deals with the qualitative analysis of a nonlinear integro-differential model of immune competition with special attention to the dynamics of tumor cells contrasted by the immune system. The analysis gives evidence of how initial conditions and parameters influence the asymptotic behavior of the solutions

On a Mathematical Model of Immune Competition

This work deals with the qualitative analysis of a nonlinear integro-differential model of immune competition with special attention to the dynamics of tumor cells contrasted by the immune system. The analysis gives evidence of how initial conditions and parameters influence the asymptotic behavior of the solutions

Dynamic behavior of anisotropic plates with various combinations of edge conditions

En el presente trabajo se determinan las frecuencias naturales de vibración en placas delgadas rectangulares anisótropas, sustentadas en sus cuatro bordes por combinaciones diferentes de las clásicas condiciones de vínculos. Se consideran tres conjuntos de condiciones de contorno: 1) un par de bordes opuestos empotrado-empotrado y el otro par de bordes empotrado-simplemente apoyado, 2) tres bordes empotrados y el restante libre, 3) ambos pares de bordes empotrado-simplemente apoyado. Se considera la incidencia de la anisotropía del material, examinando el efecto de esta variable sobre las frecuencias naturales y formas modales de placas cuadrangulares con distintas relaciones de lados. Se utiliza el método variacional de Ritz, empleando como funciones aproximantes del desplazamiento las denominadas “funciones viga” en cada dirección coordenada principal. Es importante destacar el hecho de que en un trabajo pionero sobre el tema del cual son autores Mohan and Kingsbury5 se realiza un grave error desde el punto de vista matemático, ya que se utiliza el método variacional de Galerkin para obtener el algoritmo de cálculo siendo que las funciones coordenadas utilizadas no satisfacen condiciones naturales en varios casos. Por consiguiente, los resultados obtenidos no son lícitos en la mayoría de los casos tratados en el trabajo mencionado. Se realiza una implementación computacional que permite optimizar los tiempos para la obtención de re-sultados. A partir de la condición de anisotropía se efectúa la particularización al caso isótropo y ortótropo. Para validar la metodología empleada se comparan los resultados obtenidos con los disponibles en la literatura científica. Los resultados de este trabajo muestran que las frecuencias naturales son afectadas directamente por las condiciones de contorno y por la anisotropía del material y que el comportamiento dinámico de las mismas no puede predecirse sobre la base del análisis convencional de placas isótropas y ortótropas.Peer Reviewe