Riccardo Sacco

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I got a Master of Science in Electronic Engineering and a PhD in Applied Mathematics. Presently, I am Associate Professor in Numerical Analysis with an habilitation to Full Professorship. My interests range from Computational Biology to Numerical Modeling in Applied Sciences.

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Aidy Ali

Universiti Pertahanan Nasional Malaysia

BORA YILDIRIM

Hacettepe University

Michele Brun

University of Cagliari

Petko Kiriazov

Bulgarian Academy of Sciences

Iolanda Craifaleanu

Technical University Of Civil Engineering, Bucharest

Daniel Ribeiro

University of Otago

Mikail F Lumentut

National Taiwan University

Aashique Rezwan

University of Wisconsin-Madison

pasztai zoltan

University of Oradea

Isad Saric

University of Sarajevo

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Papers by Riccardo Sacco

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences, 2019

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Mixed finite volume methods for semiconductor device simulation

Numerical Methods for Partial Differential Equations, May 1, 1997

ABSTRACT We deal with the two-dimensional numerical solution of the Van Roosbroeck system, widely... more ABSTRACT We deal with the two-dimensional numerical solution of the Van Roosbroeck system, widely employed in modern semiconductor device simulation. Using the well-known Gummel&#39;s decoupled algorithm leads to the iterative solution of a nonlinear Poisson equation for the electric potential and two linearized continuity equations for the electron and hole current densities. The numerical approximation is based on the dual mixed formulation for a self-adjoint second-order elliptic operator by using the Raviart-Thomas (RT) finite elements of lowest degree on a triangular partition of the device domain. In this article, we propose a suitable variant of the RT method, based on the diagonalization of the element mass matrix. This is achieved by use of an appropriate numerical integration that eliminates the fluxes and gives rise to a cell-centered finite volume scheme for the scalar unknown with the same approximation properties of the mixed approach, but at a reduced computational cost. The above procedure suggests also a natural way to introduce in the frame of the classical Box Method (BM) suitable vector basis functions (edge elements) to represent the current field over each mesh triangle. This issue may be profitably employed both as a postprocessing tool, as well as a technique for solving the current continuity equations when source terms depending on the current itself are included in the mathematical model. Simulations of realistic semiconductor devices are then included to demonstrate the accuracy and stability of the new method. © 1997 John Wiley &amp; Sons, Inc.

Neurodegenerative Disorders of the Eye and of the Brain: A Perspective on Their Fluid-Dynamical Connections and the Potential of Mechanism-Driven Modeling

Frontiers in Neuroscience, Nov 12, 2020

Neurodegenerative disorders (NDD) such as Alzheimer's and Parkinson's diseases are significant ca... more Neurodegenerative disorders (NDD) such as Alzheimer's and Parkinson's diseases are significant causes of morbidity and mortality worldwide. The pathophysiology of NDD is still debated, and there is an urgent need to understand the mechanisms behind the onset and progression of these heterogenous diseases. The eye represents a unique window to the brain that can be easily assessed via non-invasive ocular imaging. As such, ocular measurements have been recently considered as potential sources of biomarkers for the early detection and management of NDD. However, the current use of ocular biomarkers in the clinical management of NDD patients is particularly challenging. Specifically, many ocular biomarkers are influenced by local and systemic factors that exhibit significant variation among individuals. In addition, there is a lack of methodology available for interpreting the outcomes of ocular examinations in NDD. Recently, mathematical modeling has emerged as an important tool capable of shedding light on the pathophysiology of multifactorial diseases and enhancing analysis and interpretation of clinical results. In this article, we review and discuss the clinical evidence of the relationship between NDD in the brain and in the eye and explore the potential use of mathematical modeling to facilitate NDD diagnosis and management based upon ocular biomarkers.

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Ocular Fluid Dynamics

Modeling and simulation in science, engineering & technology, 2019

The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more

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Coding of Examples Using Matlab Scripts

Abstract This chapter complements Parts 1 , 4 , 5 , and 6 of the book with a series of examples t... more Abstract This chapter complements Parts 1 , 4 , 5 , and 6 of the book with a series of examples that address specific theoretical issues treated in the book chapters. In some cases, examples are devoted to problem solving with the purpose of quantitatively verifying the mathematical properties of models and methods. In other cases, examples are selected to treat situations of interest in biology and/or bioengineering that are characterized by realistic values of model parameters. In all cases, the reader is asked to adopt a critical approach that connects the development of the solution of the problem at hand with the theoretical foundations and, ultimately, with the analysis of the obtained results in the light of biophysical reliability. Examples are always accompanied by a quantitative implementation of models and methods through numerical algorithms that are based on the use of Matlab built-in functions and Matlab codes illustrated in Chapter 29 .

Nanoparticle-based organic polymer retinal prostheses: modeling, solution map and simulation

Mathematics in engineering, 2023

In this article we investigate a mathematical model for a retinal prosthesis made of organic poly... more In this article we investigate a mathematical model for a retinal prosthesis made of organic polymer nanoparticles (NP) in the stationary regime. The model consists of a Drift-Diffusion system to describe free charge transport in the NP bulk; a Poisson-Nernst-Planck system to describe ion electrodiffusion in the solution surrounding the NP; and nonlinear transmission conditions at the NP-solution interface. To solve the model we use an iteration procedure for which we prove the existence and briefly comment the uniqueness of a fixed point under suitable smallness assumptions on model parameters. For system discretization we use a stabilized finite element method to prevent unphysical oscillations in the electric potential, carrier number densities and ion molar densities. Model predictions describe the amount of active chemical molecule accumulating at the neuron surface and highlight electrostatic effects induced by the sole presence of the nanoparticle. These results support the use of mathematical modeling as a virtual laboratory for the optimal design of bio-hybrid systems, whose investigation may be impervious due to experimental limits.

Electric Analogy to Fluid Flow

Clinical assessment of intraocular pressure: a whole-eye dynamic model

Journal for modeling in ophthalmology, Jun 18, 2018

The aim of this work is to provide a quantitative description of how geometrical and material pro... more

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Approssimazione di problemi ai limiti

Unitext, 2008

Quest'opera è protetta dalla legge sul diritto d'autore e la sua riproduzione è ammessa solo ed e... more Quest'opera è protetta dalla legge sul diritto d'autore e la sua riproduzione è ammessa solo ed esclusivamente nei limiti stabiliti dalla stessa. Le fotocopie per uso personale possono essere effettuate nei limiti del 15% di ciascun volume dietro pagamento alla SIAE del compenso previsto dall'art. 68. Le riproduzioni per uso non personale e/o oltre il limite del 15% potranno avvenire solo a seguito di specifica autorizzazione rilasciata da AIDRO,

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Multiphysics Computational Modeling in Cartilage Tissue Engineering

Studies in mechanobiology, tissue engineering and biomaterials, 2011

A common technique for in vitro cartilage regeneration is to seed a porous matrix with cartilage ... more A common technique for in vitro cartilage regeneration is to seed a porous matrix with cartilage cells and to culture the construct in static conditions or under medium perfusion in a bioreactor. An essential step toward the development of functional cartilage is to understand and control the tissue growth phenomenon in such systems. The growth process depends on various space- and time-varying biophysical variables of the environment surrounding the cartilage cells, primarily mass transport and mechanical variables, all involved in the cell biological response. Moreover, the growth process is inherently multiscale, since cell size (10 μm), scaffold pore size (100 μm), and cellular construct size (10 mm) pertain to three separate spatial scales. To obtain a quantitative understanding of cartilage growth in this complex multiphysics and multiscale system, advanced mathematical models and efficient scientific computing techniques have been developed. In this chapter, we discuss the existing knowledge in this field and we present the most recent advancements for the numerical simulation of cartilage tissue engineering.

Stabilized Mixed Finite Volume Methods for Convection-Diffusion Problems

East-West Journal of Mathematics, 1997

ABSTRACT A finite volume method is proposed for convection-diffusion problems on two-dimensional ... more ABSTRACT A finite volume method is proposed for convection-diffusion problems on two-dimensional domains. The singularly perturbed case is stabilized by lumping and by the addition of an artificial viscosity, such that the numerical solution is exact if the problem has constant coefficients and no source term. It is shown that the discretization produces an M-matrix for all values of the cell Péclet number. Computations to illustrate the method are presented.

A Discretization Scheme for an Extended Drift-Diffusion Model Including Trap-Assisted Phenomena

Journal of Computational Physics, Apr 1, 2000

An extended drift-diffusion model is considered to account for the kinetics of electrons trapped ... more An extended drift-diffusion model is considered to account for the kinetics of electrons trapped in defect states within a semiconductor material. A discretization scheme based on Newton-Krylov iterations and mixed finite volumes is then proposed and applied to the model, even in the presence of Schottky contacts (i.e., Robintype boundary conditions). Numerical results concerning the simulation of an electrooptical device in several working conditions are presented last.

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Hybridization of Galerkin and Petrov–Galerkin Mixed Finite Element Methods for 2nd Order Elliptic Problems

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Preliminary Considerations on Constitutive Modeling

Abstract This chapter investigates three fundamental concepts that are pivotal for the constituti... more Abstract This chapter investigates three fundamental concepts that are pivotal for the constitutive modeling of materials. The first concept is the mathematical description of incompressibility. The second concept is the mathematical description of homogeneity. The third concept is the difference between material domain and observational domain and its consequences on transport theorems. These concepts are widely utilized throughout the book.

Cellular Components and Functions: A Brief Overview

Abstract This chapter gives a basic introduction to cellular biology by providing a glossary of t... more Abstract This chapter gives a basic introduction to cellular biology by providing a glossary of the components of a cell that are relevant to the study under investigation, with a short description of the functions of each component. Special attention is devoted to illustrating functional units with a marked electrochemical character, such as ion channels and ion pumps. Then, the basic concepts of cellular biology are applied to describe the signaling pathway connecting the transmission of an electric signal along a nerve fiber to the production of vasoactive agents by an astrocyte.

Functional Spaces and Functional Inequalities

Abstract This chapter reviews the elements of functional analysis that are needed to support the ... more Abstract This chapter reviews the elements of functional analysis that are needed to support the theoretical analysis of the methodologies and algorithms for the solution of the mathematical models illustrated in the book. In the first part of the chapter, the basic concepts of function spaces and their associated topology and norms are introduced. In the second part of the chapter, the principal category of metric complete normed spaces, the so-called Banach spaces, is presented. In the third part of the chapter, a notable member of the family of Banach spaces, the so-called Hilbert function spaces, is illustrated. Several examples are provided to support the theoretical presentation and definitions.

Balance Laws in Local Form

Abstract This chapter illustrates the derivation of a balance law in local form, starting from th... more Abstract This chapter illustrates the derivation of a balance law in local form, starting from the corresponding balance law in integral form, to describe the time rate of change of a scalar quantity or a vector-valued quantity associated with a material volume. The key mathematical tool to perform the passage from the integral to the local form is the transport theorem. Examples of derivation of balance laws in local form are given for mass, electric charge, energy, linear momentum, and angular momentum. Balance laws in local form are first derived in the Eulerian framework and, as a second step, in the Lagrangian framework.

Finite Element Approximation of a Unified Model for Linear Elastic Materials

Abstract This chapter addresses the numerical approximation of the mathematical model for a linea... more Abstract This chapter addresses the numerical approximation of the mathematical model for a linear elastic material. The model is able to treat both compressible and incompressible regimes under a unified framework known as Herrmann formulation of linear elasticity, based on the introduction of a further dependent variable, called pressure parameter, in addition to the solid displacement. The pressure parameter coincides with the hydrostatic pressure in the incompressible limit, where the Herrmann model formally coincides with the Stokes equations for a viscous incompressible fluid in stationary conditions. Weak formulation and finite element approximation of the Herrmann model are illustrated and the compatibility between the approximation spaces for displacement and pressure is analyzed in order to provide sufficient conditions for the numerical method to be stable and convergent. Examples of stable and unstable finite element spaces for displacement and pressure are discussed and computationally investigated in the solution of two-dimensional test cases.

Time Semidiscretization and Weak Formulations for Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type

Abstract This chapter illustrates the weak formulation of an initial value/boundary value problem... more Abstract This chapter illustrates the weak formulation of an initial value/boundary value problem in one spatial dimension including advective, diffusive, and reactive terms. The approach consists of two steps. In the first step, a temporal semidiscretization of the initial value/boundary value problem with the backward Euler method reduces the time-dependent problem into a finite sequence of boundary value problems of advection–diffusion–reaction type in which the unknown depends on the sole spatial variable. In the second step, two weak formulations of the advection–diffusion–reaction boundary value problem are considered, namely, the so-called displacement-based weak formulation and the so-called mixed weak formulation. Well-posedness of the considered weak formulations is proved by means of a theoretical tool of functional analysis, the Lax–Milgram lemma.

Constitutive Relations in Electromagnetism and Ion Electrodynamics

Elsevier eBooks, 2019

Abstract This chapter applies the theory of multicomponent mixtures to a charged mixture comprisi... more Abstract This chapter applies the theory of multicomponent mixtures to a charged mixture comprising ions, a fluid component, and, possibly, a solid component. In the first part of the chapter, the constitutive laws for production terms, total forces, and energy of each component of the mixture are derived on the basis of biophysically motivated assumptions. In the second part of the chapter, the system of equations modeling the electrodynamics of a charged mixture is derived. Two special instances of the general multicomponent charged mixture theory are considered, namely, the Poisson–Nernst–Planck model for ion electrodynamics and the drift-diffusion model for electron and hole charge transport in a semiconductor.