<abstract><title style='display:none'>Abstract</title> The semi-Lagrangian numerical method, in conjunction with semi-implicit time integration, provides numerical weather prediction models with numerical stability for large time steps, accurate modes of interest, and good representation of hydrostatic and geostrophic balance. Drawing on the legacy of dynamical cores at the Met Office, the use of the semi-implicit semi-Lagrangian method in an operational numerical weather prediction context is surveyed, together with details of the solution approach and associated issues and challenges. The numerical properties and performance of the current operational version of the Met Office’s numerical model are then investigated in a simplified setting along with the impact of different modelling choices.</abstract>

Semi-implicit semi-Lagrangian modelling of the atmosphere: a Met Office perspective

<abstract><title style='display:none'>Abstract</title> We present a comparison of the forecasting performances of three Dynamic Factor Models on a large monthly data panel of macroeconomic and financial time series for the UE economy. The first model relies on static principal-component and was introduced by Stock and Watson (2002a, b). The second is based on generalized principal components and it was introduced by Forni, Hallin, Lippi and Reichlin (2000, 2005). The last model has been recently proposed by Forni, Hallin, Lippi and Zaffaroni (2015, 2016). The data panel is split into two parts: the calibration sample, from February 1986 to December 2000, is used to select the most performing specification for each class of models in a in- sample environment, and the proper sample, from January 2001 to November 2015, is used to compare the performances of the selected models in an out-of-sample environment. The metholodogical approach is analogous to Forni, Giovannelli, Lippi and Soccorsi (2016), but also the size of the rolling window is empirically estimated in the calibration process to achieve more robustness. We find that, on the proper sample, the last model is the most performing for the Inflation. However, mixed evidencies appear over the proper sample for the Industrial Production.</abstract>

A forecasting performance comparison of dynamic factor models based on static and dynamic methods

<abstract><title style='display:none'>Abstract</title>In this paper we study the model of the chemical reaction of fully competitive inhibition and determine the appropriate parameter <italic>∊</italic> (related to the chemical constants of the model), for the application of singular perturbation techniques. We determine the inner and the outer solutions up to the first perturbation order and the uniform expansions. Some numerical results are discussed.</abstract>

A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

<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>Rheumatoid arthritis is an autoimmune disease of unknown etiology that manifests as a persistent inflammatory synovitis and eventually destroys the joints. The immune system recognizes synovial cells as <italic>not self</italic> and consequently causes lymphocyte and antibody proliferation that is promoted by the pro-inflammatory cytokines, the most significant being tumor necrosis factor TNF-<italic>α</italic>. In the treatment of rheumatoid arthritis either monoclonal antibodies or soluble receptors are used to neutralize the TNF-<italic>α</italic> bioactivity, such as sTNFR2, Etanercept and Infliximab. In [M. Jit <italic>et al.</italic> Rheumatology 2005;44:323-331] a mathematical model that represents the TNF-<italic>α</italic> dynamics in the inflamed synovial joint within which locally produced TNF-<italic>α</italic> can bind to cell-surface receptors was proposed. It consists of four coupled ordinary differential equations, that were integrated numerically assuming a range of estimates of the key parameters. In this paper we complement the previous work by determining the general solution of those equations for specific conditions on the parameters. Then we characterize the behavior of TNF-<italic>α</italic> in the presence of different inhibitors and also evaluate the inhibitors effectiveness in the treatment of rheumatoid arthritis.</abstract>

Solution of a mathematical model for the treatment of rheumatoid arthritis

<abstract><title style='display:none'>Abstract</title>We summarize features and results on the problem of the existence of Ground States for the Nonlinear Schrödinger Equation on doubly-periodic metric graphs. We extend the results known for the two–dimensional square grid graph to the honeycomb, made of infinitely-many identical hexagons. Specifically, we show how the coexistence between one–dimensional and two–dimensional scales in the graph structure leads to the emergence of threshold phenomena known as dimensional crossover.</abstract>

Quantum graphs and dimensional crossover: the honeycomb

<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>
This paper concerns the existence of global weak solutions <italic>á la Leray</italic> for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.
</abstract>

Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law

<abstract>
<title style='display:none'>Abstract</title>
This survey offers a unified up-to-date presentation of macroscopic models of traffic flow, pointing out their main characteristics and possible drawbacks. The presentation is completed by several pictures illustrating the models’ features. Some open problems and future research directions are also given to inspire the reader.
</abstract>

Macroscopic traffic flow modelling: from kinematic waves to autonomous vehicles

<abstract>
<title style='display:none'>Abstract</title>
Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean–field limit and show well–posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings.
</abstract>

Continuous limits of residual neural networks in case of large input data

<abstract>
<title style='display:none'>Abstract</title>
The luxury car market has demanding product development standards aimed at providing state-of-the-art features in the automotive domain. Handling performance is amongst the most important properties that must be assessed when developing a new car model. In this work, we analyse the problem of predicting subjective evaluations of automobiles handling performances from objective records of driving sessions. A record is a multi-dimensional time series describing the temporal evolution of the mechanical state of an automobile. A categorical variable quantifies the evaluations of handling properties. We describe an original deep learning system, featuring a denoising autoencoder and hierarchical attention mechanisms, that we designed to solve this task. Attention mechanisms intrinsically compute probability distributions over their inputs’ components. Combining this feature with the saliency maps technique, our system can compute <italic>heatmaps</italic> that provide a visual aid to identify the physical events conditioning its predictions.
</abstract>

Deep learning-assisted analysis of automobiles handling performances

<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> In this paper we present, in a framework of 1D-membrane Micro-Electro-Mechanical- Systems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steady- state case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychono's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results. </abstract>

Electrostatic field in terms of geometric curvature in membrane MEMS devices

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Volume 14 (2023): Issue 1 (January 2023)

Volume 13 (2022): Issue 1 (January 2022)

Volume 12 (2021): Issue 1 (January 2021)

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Volume 10 (2019): Issue 2 (January 2019) Special Issue on Mathematical Models and Methods in Biology, Medicine and Physiology. Guest Editors: Michele Piana, Luigi Preziosi

Volume 10 (2019): Issue 1 (February 2019)

Volume 9 (2018): Issue 2 (December 2018) Special Issue on Mathematical modelling for complex systems: multi-agents methods. Guest Editor: Elena De Angelis

Volume 9 (2018): Issue 1 (February 2018)

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Volume 7 (2016): Issue 3 (September 2016) "Special Issue on New Trends in Semi-Lagrangian Methods,
Guest Editors: Luca Bonaventura, Maurizio Falcone and Roberto Ferretti

Volume 7 (2016): Issue 2 (June 2016) Special Issue on Constitutive Equations for Heat Conduction in Nanosystems and Non-equilibrium Processes. Guest Editors: Vito Antonio Cimmelli and David Jou