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We propose an innovative fast 3D approach for the accurate computation of electromagnetic losses in the metallic armors of submarine cables. In order to develop a scheme that is more efficient with respect to most commonly used 3D simulation methods, typically based on the Finite Element Method (FEM), we proceed by proposing a suitable discretization of an integral formulation. In the proposed approach, each wire of the armor is modeled as filamentary which leads to a dramatic reduction in the number of degrees of freedom in the numerical model and in the overall computational burden. The new approach can be applied to cables where armor wires are stranded either with opposite (contralay) or same (equilay) orientation as the central phase cables. The efficiency of the proposed method is especially notable in latter case for which FEM is very demanding due to the extremely large model size. The reduction in both computation times and memory footprint allows performing extensive sensitivity studies with respect to geometrical parameters and material properties that would be otherwise unaffordable with existing 3D methods.

Recent advances in satellite technologies, statistical and mathematical models, and computational resources have paved the way for operational use of satellite data in monitoring and forecasting natural hazards. We present a review of the use of satellite data for Earth observation in the context of geohazards preventive monitoring and disaster evaluation and assessment. We describe the techniques exploited to extract ground displacement information from satellite radar sensor images and the applicability of such data to the study of natural hazards such as landslides, earthquakes, volcanic activity, and ground subsidence. In this context, statistical techniques, ranging from time series analysis to spatial statistics, as well as continuum or discrete physics-based models, adopting deterministic or stochastic approaches, are irreplaceable tools for modeling and simulating natural hazards scenarios from a mathematical perspective. In addition to this, the huge amount of data collected nowadays and the complexity of the models and methods needed for an effective analysis set new computational challenges. The synergy among statistical methods, mathematical models, and optimized software, enriched with the assimilation of satellite data, is essential for building predictive and timely monitoring models for risk analysis.

The extent of intersystem crossing in the O(3P) + C6H6 reaction, a prototypical system for spin-forbidden reactions in oxygenated aromatic molecules, is theoretically evaluated for the first time. Calculations are performed using nonadiabatic transition-state theory coupled with stochastic master equation simulations and Landau-Zener theory. It is found that the dominant intersystem crossing pathways connect the T2 and S0 potential energy surfaces through at least two distinct minimum-energy crossing points. The calculated channel-specific rate constants and intersystem crossing branching fractions differ from previous literature estimates and provide valuable kinetic data for the investigation of benzene and polycyclic aromatic hydrocarbons oxidation in interstellar, atmospheric, and combustion conditions. The theoretical results are supported by crossed molecular beam experiments with electron ionization mass-spectrometric detection and time-of-flight analysis at 8.2 kcal/mol collision energy. This system is a suitable benchmark for theoretical and experimental studies of intersystem crossing in aromatic species.

A PEEC formulation is applied to compute Joule losses and currents in the wires composing the screens of the phase conductors in a submarine tripolar cable. In order to model the infinite extent of the cable and to reduce the computational burden, simmetries of the geometry are exploited. A good agreement is obtained with brute force FEM simulations, with a dramatic reduction of computational times and memory requirement.

A thin-shell integral equation formulation is applied to the computation of eddy-current losses in submarine ac cables. The continuous helical symmetry of the geometry is exploited for reducing the computational cost of the simulation.

Reliable modeling of hydrocarbon oxidation relies critically on knowledge of the branching fractions (BFs) as a function of temperature (T) and pressure (p) for the products of the reaction of the hydrocarbon with atomic oxygen in its ground state, O(3P). During the past decade, we have performed in-depth investigations of the reactions of O(3P) with a variety of small unsaturated hydrocarbons using the crossed molecular beam (CMB) technique with universal mass spectrometric (MS) detection and time-of-flight (TOF) analysis, combined with synergistic theoretical calculations of the relevant potential energy surfaces (PESs) and statistical computations of product BFs, including intersystem crossing (ISC). This has allowed us to determine the primary products, their BFs, and extent of ISC to ultimately provide theoretical channel-specific rate constants as a function of T and p. In this work, we have extended this approach to the oxidation of one of the most important species involved in the combustion of aromatics: the benzene (C6H6) molecule. Despite extensive experimental and theoretical studies on the kinetics and dynamics of the O(3P) + C6H6 reaction, the relative importance of the C6H5O (phenoxy) + H open-shell products and of the spin-forbidden C5H6 (cyclopentadiene) + CO and phenol adduct closed-shell products are still open issues, which have hampered the development of reliable benzene combustion models. With the CMB technique, we have investigated the reaction dynamics of O(3P) + benzene at a collision energy (Ec) of 8.2 kcal/mol, focusing on the occurrence of the phenoxy + H and spin-forbidden C5H6 + CO and phenol channels in order to shed further light on the dynamics of this complex and important reaction, including the role of ISC. Concurrently, we have also investigated the reaction dynamics of O(1D) + benzene at the same Ec. Synergistic high-level electronic structure calculations of the underlying triplet/singlet PESs, including nonadiabatic couplings, have been performed to complement and assist the interpretation of the experimental results. Statistical (RRKM)/master equation (ME) computations of the product distribution and BFs on these PESs, with inclusion of ISC, have been performed and compared to experiment. In light of the reasonable agreement between the CMB experiment, literature kinetic experimental results, and theoretical predictions for the O(3P) + benzene reaction, the so-validated computational methodology has been used to predict (i) the BF between the C6H5O + H and C5H6 + CO channels as a function of collision energy and temperature (at 0.1 and 1 bar), showing that their increase progressively favors radical (phenoxy + H)-forming over molecule (C5H6 + CO and phenol stabilization)-forming channels, and (ii) channel-specific rate constants as a function of T and p, which are expected to be useful for improved combustion models.

The extent of intersystem crossing in the O(3P) + C6H6 reaction, a prototypical system for spin-forbidden reactions in oxygenated aromatic molecules, is theoretically evaluated for the first time. Calculations are performed using nonadiabatic transition-state theory coupled with stochastic master equation simulations and Landau–Zener theory. It is found that the dominant intersystem crossing pathways connect the T2 and S0 potential energy surfaces through at least two distinct minimum-energy crossing points. The calculated channel-specific rate constants and intersystem crossing branching fractions differ from previous literature estimates and provide valuable kinetic data for the investigation of benzene and polycyclic aromatic hydrocarbons oxidation in interstellar, atmospheric, and combustion conditions. The theoretical results are supported by crossed molecular beam experiments with electron ionization mass-spectrometric detection and time-of-flight analysis at 8.2 kcal/mol collision energy. This system is a suitable benchmark for theoretical and experimental studies of intersystem crossing in aromatic species.

This paper discusses and analyzes two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretized by either Nédélec-type polynomial finite elements or spline-based isogeometric analysis. The first approach is a new isogeometric mortar method and the second one is based on a modal basis for the Lagrange multiplier space, called state-space concatenation in the engineering literature. Spectral correctness and in particular inf-sup stability of both approaches are investigated numerically, and analytical results are obtained for the isogeometric mortar method. The new mortar method is shown to be unconditionally stable. Its construction of the discrete Lagrange multiplier space takes advantage of the high continuity of splines and does not have an analogue for Nédélec finite elements. On the other hand, the approach with modal basis is easier to implement but relies on application knowledge to ensure stability and correctness.

In Africa et al. (Sci Rep 7(1):3803, 2017) a step-by-step procedure was presented that enables to determine the density of states width, the carrier mobility and the injection barrier height of an OTFT! structure by fitting data from simple measurements to suitable numerical simulations. At each step of the procedure only one parameter value is determined, thus highly simplifying the fitting procedure and enhancing its robustness. In this study we apply such procedure to p-type organic polymers. A very satisfactory fitting of experimental measurements is obtained, and physically meaningful values for the aforementioned parameters are extracted thus further confirming the soundness of the parameter extraction method.

There are many applications in which it is required to compute quasi-stationary magnetic fields and related quantities in possibly large regions containing many magnetic and/or conductive thin wires. When analyzing these problems by the finite-element method, one has to discretize the wires into fine elements in order to resolve the skin effect and the space separating the wires. Heavy computational burden is, therefore, needed to solve the resulting equations. To overcome such limitations, we propose a magnetic field integral formulation in the magneto-quasi-static regime that is suitable for computing the magnetic field in a 3-D domain in the presence of thin wires. To reduce the computational complexity, the wires are treated as 1-D manifolds embedded in the surrounding 3-D space. To validate the proposed methodology, we compare the cost and accuracy of our approach to full scale finite-element simulations of an array of wires in a 3-D external magneto-quasi-static field.

PurposeThe purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors. Design/methodology/approachAn approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields. FindingsThe results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost. Research limitations/implicationsLimitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor. Originality/valueThe efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.

The predictive accuracy of state–of–the–art continuum models for charge transport in organic semiconductors is highly dependent on the accurate tuning of a set of parameters whose values cannot be effectively estimated either by direct measurements or by first principles. Fitting the complete set of model parameters at once to experimental data requires to set up extremely complex multi–objective optimization problems whose solution is, on the one hand, overwhelmingly computationally expensive and, on the other, it provides no guarantee of the physical soundness of the value obtained for each individual parameter. In the present study we present a step–by–step procedure that enables to determine the most relevant model parameters, namely the density of states width, the carrier mobility and the injection barrier height, by fitting experimental data from a sequence of relatively simple and inexpensive measurements to suitably devised numerical simulations. At each step of the proposed procedure only one parameter value is sought for, thus highly simplifying the numerical fitting and enhancing its robustness, reliability and accuracy. As a case study we consider a prototypical n-type organic polymer. A very satisfactory fitting of experimental measurements is obtained, and physically meaningful values for the aforementioned parameters are extracted.

A Trefftz-like method is proposed for the evaluation of losses in an array of parallel magnetic and conductive wires subject to an external time-harmonic magneto-quasi-static field. The formulation is tested on a two-dimensional model of a submarine three-core power cable armor. The accuracy of the method is verified by comparison with a reference Finite Element Method solution.

This paper presents a line-integral formulation for the computation of the magnetic field in the vicinity of a network of magnetic and conductive wires. The formulation is valid in the time-harmonic case and considers eddy currents. A comparison with the results obtained with the finite-element method confirms the accuracy of the proposed formulation.

© 2016 Elsevier B.V. All rights reserved. Cavities in linear accelerators suffer from eigenfrequency shifts due to mechanical deformation caused by the electromagnetic radiation pressure, a phenomenon known as Lorentz detuning. Estimating the frequency shift up to the needed accuracy by means of standard Finite Element Methods, is a complex task due to the non exact representation of the geometry and due to the necessity for mesh refinement when using low order basis functions. In this paper, we use Isogeometric Analysis for discretizing both mechanical deformations and electromagnetic fields in a coupled multiphysics simulation approach. The combined high-order approximation of both leads to high accuracies at a substantially lower computational cost. publisher: Elsevier articletitle: Isogeometric simulation of Lorentz detuning in superconducting accelerator cavities journaltitle: Computer Physics Communications articlelink: http://dx.doi.org/10.1016/j.cpc.2015.11.015 content_type: article copyright: Copyright © 2015 Elsevier B.V. All rights reserved. ispartof: COMPUTER PHYSICS COMMUNICATIONS vol:201 issue:1 pages:1-7 ispartof: location:Annecy, France status: published

In this paper, we describe a mathematical model and a numerical simulation method for the condenser component of a novel two-phase thermosiphon cooling system for power electronics applications. The condenser consists of a set of roll-bonded vertically mounted fins among which air flows by either natural or forced convection. In order to deepen the understanding of the mechanisms that determine the performance of the condenser and to facilitate the further optimization of its industrial design, a multiscale approach is developed to reduce as much as possible the complexity of the simulation code while maintaining reasonable predictive accuracy. To this end, heat diffusion in the fins and its convective transport in air are modeled as 2D processes while the flow of the two-phase coolant within the fins is modeled as a 1D network of pipes. For the numerical solution of the resulting equations, a Dual Mixed-Finite Volume scheme with Exponential Fitting stabilization is used for 2D heat diffusion and convection while a Primal Mixed Finite Element discretization method with upwind stabilization is used for the 1D coolant flow. The mathematical model and the numerical method are validated through extensive simulations of realistic device structures which prove to be in excellent agreement with available experimental data.

The broad application of computational design and construction technologies has widely changed the use and perception of computer software in architecture. Thus, we have seen a shift from mere drawing-tools towards mighty parametric design methods. These tools have allowed many architects to form the conception and design of very complex architectural projects.

In the design of electromagnetic devices the accurate representation of the geometry plays a crucial role in determining the device performance. For accelerator cavities, in particular, controlling the frequencies of the eigenmodes is important in order to guarantee the synchronization between the electromagnetic field and the accelerated particles. The main interest of this work is in the evaluation of eigenmode sensitivities with respect to geometrical changes using Monte Carlo simulations and stochastic collocation. The choice of an Isogeometric Analysis approach for the spatial discretization allows for an exact handling of the geometrical domains and their deformations, guaranteeing, at the same time, accurate and highly regular solutions.

Folding strategies have been explored in architecture as a method to generate complex spatial and structural concepts from simple planar surfaces. The folding mechanism of a rigid material may seem as trivial as folding a sheet of paper. The striking elegance of models folded from paper appear more than just visually interesting. A simple crease along a line or a curve dictates a determined movement for both faces. The basic origami folds include valley and mountain folds, pleats, reverse folds, squash folds, and sinks. The number of basic folds is small, but they can be combined in a variety of ways to make intricate designs.

Nanomedicine is the emerging medical research branch which employs nanotechnological devices to improve clinical diagnosis and to design more effective therapeutic methodologies. In particular, functionalized nanoparticles have proved their clinical usefulness for cancer therapy, either as vectors for targeted drug delivery or for hyperthermia treatment. The effectiveness of such novel therapeutic strategies in nanomedicine exploits the capability of the nanoparticles to penetrate into the living tissue through the vascular network and to reach the targeted site. Accordingly, their success is tightly related to the control of the the multi-physics and multiscale phenomena governing the diffusion and transport properties of the nanoparticles, together with the geometrical and chemo-mechanical factors regulating the nanoparticles-tissue interactions. Indeed, the therapeutic effectiveness of earlier approaches was hindered by a limited ability in penetrating within the tumor tissue essentially due to microfluidic effects. Mathematical modeling is often employed in nanomedicine to analyze in silico the key biophysical mechanisms acting at different scales of investigations, providing useful guidelines to foresee and possibly optimize novel experimental techniques. Since these phenomena involve different characteristic time- and length-scales, a multiscale modeling approach is mandatory. In this work we outline how a multiscale analysis starts at the smallest scale, and its results are injected in large-scale models. At the microscale, the transport of nanoparticles is modeled either by the stochastic Langevin equation or by its continuous limit; in both cases short distance interaction forces between particles are considered, such as Coulomb and van der Waals interactions, and small disturbances of the fluid velocity field induced by the presence of nanoparticles are assumed. At the macroscopic scale, the living tissue is typically modeled as a homogeneous (homogenized) porous material of varying permeability, where the fluid flow is modeled by Darcy’s equation and nanoparticle transport is described by a continuum Diffusion-Reaction-Advection equation. One of the most significant features of the model is the ability to incorporate information on the microvascular network based on physiological data. The exploitation of the large aspect ratio between the diameter of a capillary and the intercapillary distance makes it possible to adopt an advanced computational scheme as the embedded multiscale method: with this approach the capillaries are represented as one-dimensional (1D) channels embedded and exchanging mass in a porous medium. Special mathematical operators are used to model the interaction of capillaries with the surrounding tissue. In this general context, we illustrate a bottom-up approach to study the transport and the diffusion of nanoparticles in living materials. We determine the permeability as well as the lumped parameters appearing in the nanoparticle transport equation at the tissue level by means of simulations at the microscale, while the macroscale tissue deposition rate is derived from the results of microscale simulations by means of a suitable upscaling technique.

Purpose – The purpose of this paper is to develop a computational model for the simulation of heterojunction organic photovoltaic devices with a specific application to a light harvesting capacitor (LHC) consisting of a double layer of organic materials connected in series with two insulating layers and an external resistive load. Design/methodology/approach – The model is based on a coupled system of nonlinear partial and ordinary differential equations describing current flow throughout the external resistive load as the result of exciton generation in the bulk, exciton dissociation into bonded pairs at the acceptor-donor material interface, and electron/hole charge generation and drift-diffusion transport in the two device materials. Findings – Numerical simulation results are shown to be in good agreement with measured on-off transient currents and allow for novel insight on the microscopical phenomena which affect the external LHC performance, in particular, the widely different time scales at which such phenomena occur and their relation to the overall device dynamics. Originality/value – The LHC demonstrates the viability of a novel approach for converting light energy into an electric current without a steady state flow of free charge carriers through the semiconducting layers. The new insight about the microscopic working principles that determine the macroscopically observed behavior of the LHC obtained via the model proposed in this paper are expected to serve as a basis for studying techniques for exploiting the full potential of the LHC.

A perturbation approach is used to derive surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors described by means of Brauer's model [1]. A new technique is proposed to solve the nonlinear diffusion equation of the magnetic field in conductive media and then its solution is coupled with a BEM formulation for the case of parallel magnetic conductors in terms of E and B fields.

As relatively new and promising members of the wickless heat pipes family, Pulsating Heat Pipes, with their high effective thermal conductivity, construction simplicity, low weight, and potential high power loads may answer the present industry demand of high heat transfer capability, efficient thermal control, flexibility and low cost. Numerous are the attempts to simulate their complex thermal behavior, but none of the existing models is validated for transient operative conditions and under various gravity levels. Thus, a novel lumped parameters model able to compute the steady state as well as the transient performance of PHPs has been developed. It consists of a two-phase separated flow model applicable to a confined operating regime (slug–plug flow). A complete set of balance differential equations accounts for thermal and fluid-dynamic phenomena. The main originalities of this tool lay in the suppression of the standard assumption of saturated vapor plugs as well as in the consequent embedding of heterogeneous and homogeneous phase changes. In addition, an experimental work has been carried out with a 16 turns copper capillary PHP filled with FC-72. Therefore, the model has been validated in several operative conditions and under various gravity levels by comparison with these experimental data both in normal and hyper-gravity conditions showing very good prediction capability.

Interdependence of chemical structure, thin-film morphology, and transport properties is a key, yet often elusive aspect characterizing the design and development of high-mobility, solution-processed polymers for large-area and flexible electronics applications. There is a specific need to achieve >1 cm2 V−1 s−1 field-effect mobilities (μ) at low processing temperatures in combination with environmental stability, especially in the case of electron-transporting polymers, which are still lagging behind hole transporting materials. Here, the synthesis of a naphthalene-diimide based donor–acceptor copolymer characterized by a selenophene vinylene selenophene donor moiety is reported. Optimized field-effect transistors show maximum μ of 2.4 cm2 V−1 s−1 and promising ambient stability. A very marked film structural evolution is revealed with increasing annealing temperature, with evidence of a remarkable 3D crystallinity above 180 °C. Conversely, transport properties are found to be substantially optimized at 150 °C, with limited gain at higher temperature. This discrepancy is rationalized by the presence of a surface-segregated prevalently edge-on packed polymer phase, dominating the device accumulated channel. This study therefore serves the purpose of presenting a promising, high-electron-mobility copolymer that is processable at relatively low temperatures, and of clearly highlighting the necessity of specifically investigating channel morphology in assessing the structure–property nexus in semiconducting polymer thin films.

In this paper, a singularly perturbed convection diffusion boundary value problem, with discontinuous diffusion coefficient is examined. In addition to the presence of boundary layers, strong and weak interior layers can also be present due to the discontinuities in the diffusion coefficient. A priori layer adapted piecewise uniform meshes are used to resolve any layers present in the solution. Using a Petrov---Galerkin finite element formulation, a fitted finite difference operator is shown to produce numerical approximations on this fitted mesh, which are uniformly second order (up to logarithmic terms) globally convergent in the pointwise maximum norm.

This article deals with the analysis of the functional iteration, denoted Generalized Gummel Map (GGM), proposed in [C. de Falco, A.L. Lacaita, E. Gatti, R. Sacco, Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices, J. Comp. Phys. 204 (2) (2005) 533-561] for the decoupled solution of the Quantum Drift-Diffusion (QDD) model. The solution of the problem is characterized as being a fixed point of the GGM, which permits the establishment of a close link between the theoretical existence analysis and the implementation of a numerical tool, which was lacking in previous non-constructive proofs [N.B. Abdallah, A. Unterreiter, On the stationary quantum drift-diffusion model, Z. Angew. Math. Phys. 49 (1998) 251-275, R. Pinnau, A. Unterreiter, The stationary current-voltage characteristics of the quantum drift-diffusion model, SIAM J. Numer. Anal. 37 (1) (1999) 211-245]. The finite element approximation of the GGM is illustrated, and the main properties of the numerical fixed point map (discrete maximum principle and order of convergence) are discussed. Numerical results on realistic nanoscale devices are included to support the theoretical conclusions.

In this paper we present the spatial discretization of the thermal element model for coupled electrothermal simulation introduced in [1] with a suitable multiscale Finite Element scheme. The structure of the local matrices for the the thermal element is presented in detail and some preliminary numerical results are reported. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we present an approach to coupled electro–thermal circuit simulation. More precisely we derive from the heat diffusion PDE a thermal element model and we show how it can be included in a standard SPICE–like circuit simulator without significant modifications to the solver structure. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Density of States (DOS) is an ingredient of critical importance for the accurate physical understanding of the optoelectronic properties of organic semiconductors. The disordered nature of this class of materials, though, renders the task of determining the DOS far from trivial. Its extraction from experimental measurements is often performed by driving the semiconductor out of thermal equilibrium and therefore requires making assumptions on the charge transport properties of the material under examination. This entanglement of DOS and charge transport models is unfavorable since transport mechanisms in organic semiconductors are themselves still subject of debate. To avoid this, we propose an alternative approach which is based on populating and probing the DOS by means of capacitive coupling in Metal Insulator Semiconductors (MIS) structures while keeping the semiconductor in thermal equilibrium. Assuming a Gaussian shape, we extract the DOS width by numerical fitting of experimental Capacitance–Voltage curves, exploiting the fact that the DOS width affects the spatial distribution of accumulated charge carriers which in turn concurs to define the MIS capacitance. The proposed approach is successfully tested on two benchmark semiconducting polymers, one of n-type and one of p-type and it is validated by verifying the robustness of the extraction procedure with respect to varying the insulator electrical permittivity. Finally, as an example of the usefulness and effectiveness of our approach, we study the static characteristics of thin film transistors based on the aforementioned polymers in the framework of the Extended Gaussian Disorder transport model. Thanks to the extracted DOS widths, the functional dependence of current on the gate voltage is nicely predicted and physical insight on transistor operation is achieved.

This chapter describes the Demonstrator Platform (DP), a framework for simulation of devices, interconnects, circuits, electromagnetic fields, and thermal effects. This framework is used to develop and test new mathematical methods and algorithms. Section 8.1 describes the design of the DP and gives an overview of the available modules. Section 8.2 is a tutorial on how to use the DP focusing on model-order reduction. It shows for the example of a micro-hotplate model all the steps needed to apply model-order reduction, including postprocessing and error estimation. In a second part, a coupled simulation of a circuit combined with a reduced model of a transmission line is presented. Section 8.3 emphasizes the aspect of the DP as a development framework. After introducing the benchmark example of an n-channel power MOS-FET, it is shown how to combine and extend different modules of the DP to a fully coupled electro-thermal simulation of the device.

In this paper, we propose a unified framework for Quantum-corrected drift-diffusion (QCDD) models in nanoscale semiconductor device simulation. QCDD models are presented as a suitable generalization of the classical drift-diffusion (DD) system, each particular model being identified by the constitutive relation for the quantum-correction to the electric potential. We examine two special, and relevant, examples of QCDD models; the first one is the modified DD model named Schrodinger-Poisson-drift-diffusion, and the second one is the quantum-drift-diffusion (QDD) model. For the decoupled solution of the two models, we introduce a functional iteration technique that extends the classical Gummel algorithm widely used in the iterative solution of the DD system. We discuss the finite element discretization of the various differential subsystems, with special emphasis on their stability properties, and illustrate the performance of the proposed algorithms and models on the numerical simulation of nanoscale devices in two spatial dimensions.

International audience; Nanomedicine is the branch of nanotechnology devoted to the miniaturization of devices and to the functionalization of processes for the diagnosis and the design of tools of clinical use. In the perspective to develop patient-specific treatments and effective therapies against currently incurable diseases, biomechanical modelling plays a key role in enabling their translation to clinical practice. Establishing a dynamic interaction with experiments, a modelling approach is expected to allow investigating problems with lower economic burden, evaluating a larger range of conditions. Since biological systems have a wide range of typical characteristic length and timescales, a multiscale modelling approach is necessary both for providing a proper description of the biological complexity at the single scales and for keeping the largest amount of functional interdependence among them. This work starts with a survey both of the common frameworks for modelling a biological system, at scales from atoms to a continuous distribution of matter, and of the available multiscale methods that link the different levels of investigation. In the following, we define an original approach for dealing with the specific case of transport and diffusion of nanoparticles and/or drug-delivery carriers from the systemic circulation to a target tissue microstructure. Using a macro-micro viewpoint, we discuss the existing multiscale approaches and we propose few original strategies for overcoming their limitations in bridging scales. In conclusion, we highlight and critically discuss the future challenges of multiscale modelling for achieving the long-term objective to assist the nanomedical research in proposing more accurate clinical approaches for improved medical benefit.

In this communication, we present a computational model for heterojunction Organic Photovoltaic (OPV) devices consisting of a system of semilinear PDEs and ODEs. The mathematical model is discussed, focusing on the transmission conditions at material interfaces, together with the numerical method used for its solution. Steady-state and transient simulations are performed on realistic devices with various interface morphologies.

This article is an attempt to provide a self consistent picture, including existence analysis and numerical solution algorithms, of the mathematical problems arising from modeling photocurrent transients in Organic-polymer Solar Cells (OSCs). The mathematical model for OSCs consists of a system of nonlinear diffusion-reaction partial differential equations (PDEs) with electrostatic convection, coupled to a kinetic ordinary differential equation (ODE). We propose a suitable reformulation of the model that allows us to prove the existence of a solution in both stationary and transient conditions and to better highlight the role of exciton dynamics in determining the device turn-on time. For the numerical treatment of the problem, we carry out a temporal semi-discretization using an implicit adaptive method, and the resulting sequence of differential subproblems is linearized using the Newton-Raphson method with inexact evaluation of the Jacobian. Then, we use exponentially fitted finite elements for the spatial discretization, and we carry out a thorough validation of the computational model by extensively investigating the impact of the model parameters on photocurrent transient times., 20 pages, 11 figures

In this article, we continue our mathematical study of organic solar cells (OSCs) and propose a two-scale (micro- and macro-scale) model of heterojunction OSCs with interface geometries characterized by an arbitrarily complex morphology. The microscale model consists of a system of partial and ordinary differential equations in an heterogeneous domain, that provides a full description of excitation/transport phenomena occurring in the bulk regions and dissociation/recombination processes occurring in a thin material slab across the interface. The macroscale model is obtained by a micro-to-macro scale transition that consists of averaging the mass balance equations in the normal direction across the interface thickness, giving rise to nonlinear transmission conditions that are parametrized by the interfacial width. These conditions account in a lumped manner for the volumetric dissociation/recombination phenomena occurring in the thin slab and depend locally on the electric field magnitude and orientation. Using the macroscale model in two spatial dimensions, device structures with complex interface morphologies, for which existing data are available, are numerically investigated showing that, if the electric field orientation relative to the interface is taken into due account, the device performance is determined not only by the total interface length but also by its shape.

A model for polymer Solar Cells is presented consisting of a system of nonlinear diffusion-reaction PDEs with electrostatic convection, coupled to a kinetic ODE. A proof of the existence of both stationary and transient solutions is given and an algorithm for computing them is proposed and numerically validated by comparison with experimentally measured data for a photovoltaic cell.

In this article, we carry out the convergence analysis of the dual–mixed hybridized finite volume scheme proposed in (Marco Brera et al., Comput. Methods Appl. Mech. Eng., in press, 2010) for the numerical approximation of transport problems in symmetrizable form. Using the results of (Micheletti et al., SIAM J. Sci. Comput., 23-1:245–270, 2001; Brezzi et al., Discretization of semiconductor device problems (i), Elsevier North-Holland, Amsterdam, 2005) optimal error estimates are obtained for the scalar unknown and the flux in the appropriate graph norm, while using the techniques and analysis of (Arnold and Brezzi, Math. Modeling Numer. Anal., 19-1:7–32, 1985; Brezzi and Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991) the superconvergence of the hybrid variable and of its post-processed (nonconforming) reconstruction are proved. Numerical experiments are included to support the theoretical conclusions.

In this paper we present a novel system for power electronics cooling consisting of a thermosyphon loop composed of an evaporator, to which the power modules are attached, and of a condenser, formed by a set of vertically mounted aluminum panels. To facilitate the optimization of the design of the condenser, which is critical for the whole system performance, we developed a simulation tool based on a multiscale mathematical model valid in the natural convection regime. The mathematical model and the numerical method adopted to solve it have been validated by comparing the simulation results with experimental measurements.

In this work we address the well-posedness of the steady-state and transient problems stemming from the coupling of a network of lumped electric elements and a PDE model of heat diffusion in the chip substrate. In particular we consider the thermal element model presented in [1] and we prove that it can be controlled by any combination of voltage sources (imposing the average current in a region of the chip) and current sources (imposing the Joule power per unit area produced in a region) connected to its temperature nodes. This result justifies the implementation of the element as a linear n-port conductance as carried out in [2].

We present a new strategy to perform chip-level electro-thermal simulation. In our approach electrical behaviour of each circuit element is modeled by standard compact models with an added temperature node (1; 2). Mutual heating is accounted for by a 2-D or 3-D diffusion reaction PDE, which is coupled to the electrical network by enforcing instantaneous energy conservation. To cope with the multiscale nature of heat diffusion in VLSI circuit a suitable spatial discretization scheme is adopted which allows for efficient meshing of large domains with details at a much smaller scale. Preliminary numerical results on a realistic test case are included as a validation of the model and of the numerical method.

We present a numerical method for solving Diffusion Reaction equations on two completely overlapping unstructured meshes which reduces the requirements on mesh generation software when strong local refinement is needed to capture features of the solution that appear on different scales.