<abstract><title style='display:none'>Abstract</title> A new class of high-order accuracy numerical methods based on a semi-Lagrangian formulation for the BGK model of the Boltzmann equation has been recently proposed in [1]. In this paper semi-Lagrangian schemes for the BGK equation have been extended to treat boundary conditions, in particular the diffusive ones. Two different techniques are proposed, using or avoiding iterative procedures. Numerical simulations illustrate the accuracy properties of these approaches and the agreement with the results available in literature.</abstract>

Dipartimento di Matematica e Informatica Università degli Studi di Parma,

Dipartimento di Matematica e Informatica Università degli Studi di Catania,

Boundary conditions for semi-Lagrangian methods for the BGK model

<abstract><title style='display:none'>Abstract</title> In this paper we obtain the chord length distribution function of a non-convex equilateral hexagon and then derive the associated density function. Finally, we calculate the expected value of the chord length. </abstract>

The chord length distribution function of a non-convex hexagon

<abstract><title style='display:none'>Abstract</title> The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case.</abstract>

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

<abstract><title style='display:none'>Abstract</title>The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The performance of different theories is compared in case of heat pulse experiments.</abstract>

Theories and heat pulse experiments of non-Fourier heat conduction

<abstract>
<title style='display:none'>Abstract</title>
This note aims at illustrating the application of the Virtual Element Method to elasticity problems in mixed form, following the Hellinger-Reissner variational principle. In order to highlight the potential and the flexibility of our approach, we focus on a three-dimensional low-order Virtual Element scheme, but similar considerations apply to two-dimensional and higher-order methods.
</abstract>

Virtual Element Methods for three-dimensional Hellinger-Reissner elastostatic problems

<abstract><title style='display:none'>Abstract</title> The electro-thermal transport in silicon carbide semiconductors can be described by an extended hydrodynamic model, obtained by taking moments from kinetic equations, and using the Maximum Entropy Principle. By performing appropriate scaling, one can obtain reduced transport models such as the Energy transport and the drift-diffusion ones, where the transport coefficients are explicitly determined.</abstract>

A hierarchy of hydrodynamic models for silicon carbide semiconductors

<abstract>
<title style='display:none'>Abstract</title>
The application of the Partition of Unity Method (PUM) to signal approximation on graphs represents a recent advancement of this versatile and efficient interpolation technique. Given the novelty of this approach, little is yet known regarding the role of kernel parameters employed in constructing the associated Graph Basis Functions (GBFs). In order to shed light on this aspect, this study proposes several numerical tests obtained using GBFs generated by heat kernels and variational spline kernels.
</abstract>

Exploration of Kernel Parameters in Signal GBF-PUM Approximation on Graphs

<abstract>
<title style='display:none'>Abstract</title>
In the framework of the theory of Landscape Ecology, a review of Lotka-Volterrra type models is proposed. Such models can be considered useful tools in order to represent and evaluate the dynamical behavior and the ecological stability of an environmental system which, as known, is subjected during time to several transformations. At this purpose, after such a review and presentation of different models, an application to an important wine region in France is performed using a model recently introduced in literature.
</abstract>

Mathematical Models for the Assessment of an Environmental System in Landscape Ecology

<abstract>
<title style='display:none'>Abstract</title>
Mathematics has been applied to physics and engineering in the last few centuries, substantially contributing to the various phases of the industrial revolution. Its application to biology is instead relatively more recent. In this paper we provide an overview of some problems in a few fields mainly related to ecology. The models discussed help in fighting pests in agriculture to improve crop harvesting and to combat the phenomenon of alien species invasions, that due to worldwide trading and climate changes is affecting the temperate regions, threatening the survival of the native species. A pair of examples related to primary oxygen production and fallacies of our linear way of thinking are also presented, to stress the fact that raising temperatures entail huge unforeseen problems. Finally we delve briefly in the vaste field of epidemiology, that would deserve a review on its own, to discuss models for diseases in the environment and one instance related epidemics affecting humans, prompted by the important role of asymptomatics played in them.
</abstract>

The usefulness of mathematics in agriculture, for the environment and in contrasting diseases: insights from a wide range of simple models

<abstract>
<title style='display:none'>Abstract</title>
We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an evolutionary Γ-convergence approach, we prove that the solutions of the nonlocal problem converge to the solution of the local problem, when the peridynamic horizon tends to 0, that is, in the nonlocal-to-local limit.
</abstract>

Nonlocal-to-local limit in linearized viscoelasticity

<abstract>
<title style='display:none'>Abstract</title>
The paper presents a complete (to the best of the author’s knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the model, weak and strong local well-posedness, global well-posedness, classification and stability (orbital and asymptotic) of the standing waves, blow-up analysis and derivation from the standard NLS equation with shrinking potentials. Also some related problem is mentioned.
</abstract>

A general review on the NLS equation with point-concentrated nonlinearity

<abstract>
<title style='display:none'>Abstract</title>
We survey results concerning the problem of identifying depth profiles at coastal zone, which evolve in time due to natural as well as anthropic activities. This issue is relevant to control the modifications of the environment occurring near sea coastlines, but also in river's estuaries and harbors. One of the main goals is to predict the time evolution of the depth profile in the long-term (i.e., over years or decades, say), and to do this on the basis of <italic>real</italic> observed and measured <italic>data</italic>, available in several databases. Most mathematical models are formulated in terms of partial differential equations of the diffusive type, in one or two space dimensions. Consequently, from the mathematical standpoint, the aforementioned identification problem takes on the form of an inverse problem for some given parabolic equation associated with suitable initial and boundary conditions.
</abstract>

Modelling and predicting coastal zone depth profile evolution: a survey

<abstract><title style='display:none'>Abstract</title> Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results. </abstract>

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

<abstract><title style='display:none'>Abstract</title>We provide an overview on the problem of modeling heat transport at nanoscale and in far-from-equilibrium processes. A survey of recent results is summarized, and a conceptual discussion of them in the framework of Extended Irreversible Thermodynamics is developed.</abstract>

Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, Catalonia, Spain

Institut d’Estudis Catalans, Barcelona, Catalonia, Spain

Department of Mathematics, Computer Science and Economics, University of Basilicata, Potenza, Italy

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

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