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In this work we present a mathematical model for the description of the dynamical and thermodynamical evolution of a system consisting of an icefield locally underlaid by a subglacial lake occupying a bed depression. The representation of the phase change ice-water is the clue of the model. The numerical solution is based on a finite volume technique. The computational code is tested to describe a portion of the Amundsenisen Icefield, South-Spitsbergen, Svalbard, where the existence of subglacial lake has been hypothesized. The contribution of firn and snow upper layers to the system in terms of temperature fied, density and water content is shown to be non-negligible in the modelling, as it supports ice to overcome its metastable state and change into liquid phase thus forming the subglacial lake. Lake cavity depth (or, better, the bottom surface area) appears to be critical for the formation of the lake, being directly proportional to the amount of geothermal heat coming in. Numerical simulation results are consistent with the existence of the conjectured subglacial lake within the environmental conditions fixed to measured data. Improvements of ice water content modelling and boundary condition formulation are in progress.

In this paper, the lab-on-chip section for a protein assay is designed and optimized. To avoid severe reliability problems related to activated surface stability, a dynamic assay approach is adopted: protein-to-protein neutralization is performed while proteins diffuse freely in the reaction chamber. The related refraction index change is detected via an integrated interferometer. The structure is also design to provide a functional test of the reference protein solution, which is generally required for qualification for medical uses.

We consider a variational model for image segmentation proposed in Sandberg et al. (2010) [12]. In such a model the image domain is partitioned into a finite collection of subsets denoted as phases. The segmentation is unsupervised, i.e., the model finds automatically an optimal number of phases, which are not required to be connected subsets. Unsupervised segmentation is obtained by minimizing a functional of the Mumford-Shah type (Mumford and Shah, 1989 [1]), but modifying the geometric part of the Mumford-Shah energy with the introduction of a suitable scale term. The results of computer experiments discussed in [12] show that the resulting variational model has several properties which are relevant for applications. In this paper we investigate the theoretical properties of the model. We study the existence of minimizers of the corresponding functional, first looking for a weak solution in a class of phases constituted by sets of finite perimeter. Then we find various regularity properties of such minimizers, particularly we study the structure of triple junctions by determining their optimal angles.

We consider the regularization of linear inverse problems by means of the minimization of a functional formed by a term of discrepancy to data and a Mumford-Shah functional term. The discrepancy term penalizes the L 2 distance between a datum and a version of the unknown function which is filtered by means of a non-invertible linear operator. Depending on the type of the involved operator, the resulting variational problem has had several applications: image deblurring, or inverse source problems in the case of compact operators, and image inpainting in the case of suitable local operators, as well as the modeling of propagation of fracture. We present counterexamples showing that, despite this regularization, the problem is actually in general ill-posed. We provide, however, existence results of minimizers in a reasonable class of smooth functions out of piecewise Lipschitz discontinuity sets in two dimensions. The compactness arguments we developed to derive the existence results stem from geometrical and regularity properties of domains, interpolation inequalities, and classical compactness arguments in Sobolev spaces.

In the fracture model presented in this paper, the basic assumption is that the energy is the sum of two terms, one elastic and one cohesive, depending on the elastic and inelastic part of the deformation, respectively. Two variants are examined: a local model, and a nonlocal model obtained by adding a gradient term to the cohesive energy. While the local model only applies to materials which obey Drucker's postulate and only predicts catastrophic failure, the nonlocal model describes the softening regime and predicts two collapse mechanisms, one for brittle fracture and one for ductile fracture. In its nonlocal version, the model has two main advantages over the models existing in the literature. The first is that the basic elements of the theory (the yield function, hardening rule, and evolution laws) are not assumed, but are determined as necessary conditions for the existence of solutions in incremental energy minimization. This reduces to a minimum the number of independent assumptions required to construct the model. The second advantage is that, with appropriate choices of the analytical shape of the cohesive energy, it becomes possible to reproduce, with surprising accuracy, a large variety of observed experimental responses. In all cases, the model provides a description of the entire evolution, from the initial elastic regime to final rupture.

We extend the analysis of Chiba et al. [Phys. Rev. D 75, 124014 (2007)] of Solar System constraints on f(R) gravity to a class of nonminimally coupled (NMC) theories of gravity. These generalize f(R) theories by replacing the action functional of general relativity with a more general form involving two functions f1(R) and f2(R) of the Ricci scalar curvature R. While the function f1(R) is a nonlinear term in the action, analogous to f(R) gravity, the function f2(R) yields a NMC between the matter Lagrangian density Lm and the scalar curvature. The developed method allows for obtaining constraints on the admissible classes of functions f1(R) and f2(R), by requiring that predictions of NMC gravity are compatible with Solar System tests of gravity. Then we consider a NMC model which accounts for the observed accelerated expansion of the Universe and we show that such a model cannot be constrained by the present method.

A model for describing the dynamics of two mutually interacting neurons is considered. In such a context, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point of the membrane potential of one of the two neurons when a spike of the other one occurs. We give an approximation for the interspike time interval probability density function of both neurons within any parametric configurations driving the evolution of the membrane potentials in the so-called subthreshold regimen.

The role of protein Z (PZ) in the etiology of human disorders is unclear. A number of PZ gene variants, sporadic or polymorphic and found exclusively in the serine protease domain, have been observed. Crystal structures of PZ in complex with the PZ-dependent inhibitor (PZI) have been recently obtained. The aim of this study was a structural investigation of the serine protease PZ domain, aiming at finding common traits across disease-linked mutations. We performed 10-20 ns molecular dynamics for each of the observed PZ mutants to investigate their structure in aqueous solution. Simulation data were processed by novel tools to analyse the residue-by-residue backbone flexibility. Results showed that sporadic mutations are associated with anomalous flexibility of residues belonging to specific regions. Among them, the most important is a loop region which is in contact with the longest I helix of PZI. Other regions have been identified, which hold anomalous flexibility associated with potentially protective gene variants. In conclusion, a possible interpretation of effects associated with observed gene variants is provided. The exploration of PZ/PZI interactions seems essential in explaining these effects.

The modeling of various physical questions in plasma kinetics and heat conduction lead to nonlinear boundary value problems involving a nonlocal operator, such as the integral of the unknown solution, which depends on the entire function in the domain rather than at a single point. This talk concerns a particular nonlocal boundary value problem recently studied in [1] by J.R.Cannon and D.J.Galiffa, who proposed a numerical method based on an interval-halving scheme. Starting from their results, we provide a more general convergence theorem and suggest a different iterative procedure to handle the nonlinearity of the discretized problem. References: [1] J.R.Cannon, D.J.Galiffa (2011) On a numerical method for a homogeneous, nonlinear, nonlocal, elliptic boundary problem, Nonlinear Analysis, Vol. 74, pp. 1702-1713.

This paper deals with models of living complex systems, chiefly human crowds, by methods of conservation laws and measure theory. We introduce a modeling framework which enables one to address both discrete and continuous dynamical systems in a unified manner using common phenomenological ideas and mathematical tools as well as to couple these two descriptions in a multiscale perspective. Furthermore, we present a basic theory of well-posedness and numerical approximation of initial-value problems and we discuss its implications on mathematical modeling. Questo articolo riguarda la modellizzazione matematica di sistemi complessi viventi, in particolare le folle, mediante leggi di conservazione e metodi della teoria della misura. Introdurremo un quadro modellistico che permette di trattare sistemi dinamici discreti e continui mediante idee fenomenologiche e strumenti matematici comuni, nonché di accoppiare le due descrizioni in un'ottica multiscala. Inoltre presenteremo una teoria qualitativa di buona positura e approssimazione numerica dei problemi ai valori iniziali e discuteremo le sue implicazioni sulla modellistica.

In this paper, we analyze the above issues and provide a solution for a specific problem that, nevertheless, is quite representative for a generic class of problems in the above setting: computing a vectorial function over a set of nodes. In particular, we introduce AntiCheetah, a novel autonomic multi-round approach performing the assignment of input elements to cloud nodes as an autonomic, self-configuring and self-optimizing cloud system. AntiCheetah is resilient against misbehaving nodes, and it is effective even in worst-case scenarios and against smart cheaters that behave according to complex strategies. Further, we discuss benefits and pitfalls of the AntiCheetah approach in different scenarios. Preliminary experimental results over a custom-built, scalable, and flexible simulator (SofA) show the quality and viability of our solution. Outsourced computing is increasingly popular thanks to the effectiveness and convenience of cloud computing *-as-a-Service offerings. However, cloud nodes can potentially misbehave in order to save resources. As such, some guarantee over the correctness and availability of results is needed. Exploiting the redundancy of cloud nodes can be of help, even though smart cheating strategies render the detection and correction of fake results much harder to achieve in practice.

A mathematical model and the simulation of subsoil decontamination by bioventing will be presented. The bases for the model construction are the following: (1) the pollutant is considered as immobile and confined in the unsaturated zone; (2) only oxygen is injected in the subsoil by wells; (3) the bacteria acting the pollutant removal are immobile and their growth depends on oxygen and pollutant concentration.

Large-scale simulations of blood flow allow for the optimal evaluation of endothelial shear stress for real-life case studies in cardiovascular pathologies. The procedure for anatomic data acquisition, geometry and mesh generation are particularly favorable if used in conjunction with the Lattice Boltzmann method and the underlying cartesian mesh. The methodology allows to accommodate red blood cells in order to take into account the corpuscular nature of blood in multi-scale scenarios and its complex rheological response, in particular, in proximity of the endothelium. Taken together, the Lattice Boltzmann framework has become a powerful computational tool for studying sections of the human circulatory system.