1,720,971 research outputs found
VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D
Full text linkWe present a Virtual Element MATLAB solver for elliptic and parabolic, linear and semilinear Partial Differential Equations (PDEs) in two and three space dimensions, which is coined VEMcomp. Such PDEs are widely applicable to describing problems in material sciences, engineering, cellular and developmental biology, among many other applications. The library covers linear and nonlinear models posed on different simple and complex geometries, involving time-dependent bulk, surface, and bulk-surface PDEs. The solver employs the Virtual Element Method (VEM) of lowest polynomial order k=1 on general polygonal and polyhedral meshes, including the Finite Element Method (FEM) of order k=1 as a special case when the considered mesh is simplicial. VEMcomp has three main purposes. First, VEMcomp generates polygonal and polyhedral meshes optimized for fast matrix assembly. Triangular and tetrahedral meshes are encompassed as special cases. For surface PDEs, VEMcomp is compatible with the well-known Matlab package DistMesh for mesh generation. Second, given a mesh for the considered geometry, possibly generated with an external package, VEMcomp computes all the matrices (mass and stiffness) required by the VEM or FEM method. Third, for multiple classes of stationary and time-dependent bulk, surface and bulk-surface PDEs, VEMcomp solves the considered PDE problem with the VEM or FEM in space and IMEX Euler in time, through a user-friendly interface. As an optional post-processing, VEMcomp comes with its own functions for plotting the numerical solutions and evaluating the error when possible. An extensive set of examples illustrates the usage of the library
Turing patterns in a 3D morpho-chemical bulk-surface reaction-diffusion system for battery modeling
Full text linkIn this paper we introduce a bulk-surface reaction-diffusion (BSRD) model in three space dimensions that extends the DIB morphochemical model to account for the electrolyte contribution in the application, in order to study structure formation during discharge-charge processes in batteries. Here we propose to approximate the model by the Bulk-Surface Virtual Element Method on a tailor-made mesh that proves to be competitive with fast bespoke methods for PDEs on Cartesian grids. We present a selection of numerical simulations that accurately match the classical morphologies found in experiments. Finally, we compare the Turing patterns obtained by the coupled 3D BS-DIB model with those obtained with the original 2D version.25 pages, 11 figures, 1 tabl
The Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs: Analysis and Applications
No full textBulk-surface partial differential equations (BS-PDEs) are prevalent in many applications such as cellular, developmental and plant biology as well as in engineering and material sciences. Novel numerical methods for BS-PDEs in three space dimensions (3D) are sparse. In this work, we present a bulk-surface virtual element method (BS-VEM) for bulk-surface reaction-diffusion systems, a form of semilinear parabolic BS-PDEs in 3D. Unlike previous studies in two space dimensions (2D), the 3D bulk is approximated with general polyhedra, whose outer faces constitute a flat polygonal approximation of the surface. For this reason, the method is restricted to the lowest order case where the geometric error is not dominant. The BS-VEM guarantees all the advantages of polyhedral methods such as easy mesh generation and fast matrix assembly on general geometries. Such advantages are much more relevant than in 2D. Despite allowing for general polyhedra, general nonlinear reaction kinetics and general surface curvature, the method only relies on nodal values without needing additional evaluations usually associated with the quadrature of general reaction kinetics. This latter is particularly costly in 3D. The BS-VEM as implemented in this study retains optimal convergence of second order in space
Virtual element method for the Laplace-Beltrami equation on surfaces
Full text linkWe present and analyze a Virtual Element Method (VEM) for the Laplace-Beltrami equa-
tion on a surface in R3, that we call Surface Virtual Element Method (SVEM). The method combines
the Surface Finite Element Method (SFEM) [Dziuk, Eliott, Finite element methods for surface PDEs,
2013] and the recent VEM [Beirao da Veiga et al, Basic principles of virtual element methods, 2013] in
order to allow general polygonal approximation of the surface. We account for the error arising from
the geometry approximation and in the case of polynomial order k = 1 we extend to surfaces the error
estimates for the interpolation in the virtual element space. We prove existence, uniqueness and first
order H1 convergence of the numerical solution.We highlight the differences between SVEM and VEM
from the implementation point of view. Moreover, we show that the capability of SVEM of handling
nonconforming and discontinuous meshes can be exploited in the case of surface pasting. We provide
some numerical experiments to confirm the convergence result and to show an application of mesh
pasting
Analysing technological specificities of industrial sectors using corporate patent profiles with a gravity center modelling
No full textThis paper investigates the possibility of developing a correspondence between the industrial sector (based on ICB classification) which is attributed to a corporation and the technological composition of this corporation's patent portfolio (based on WIPO technological fields) using a mathematical model based on gravity center.Exploiting data characterising 1288 large corporations from the Corporate Invention Board database, we carry out a two steps analysis. In the first place we compute average patent profiles for different industrial sectors. Then, we test the discriminating power of these average patent profiles by checking to what extent the analysis of a given corporate patent portfolio makes it possible to correctly predict the industrial sector to which this corporation actually belongs.The results show that this modelling, although providing quite precise predictive information for some industrial sectors (e.g. Healthcare, Automobiles or Chemical), does not fit for some industrial sectors which produce mainly very generic (i.e. not specific) technologies (e.g. Consumer Services or Support Services)
The economic sustainability of optimizing feedstock imports with environmental constraints
No full textThe energetic crisis jeopardizes the safety of nations and people in multiple ways. In addressing the problem of commodity production out of feedstock imports, an eco-environmentally rational agent aims at minimizing the cost of feedstock imports and their increasingly expensive transportation, but also the water footprint of the feedstock production process and the water scarcity in the exporting countries. This implies the need for more accurate feedstock import strategies, that account for the increased multiplicity of factors at play. This study proves the existence of solutions and quantitatively demonstrates that transportation costs and nonuniform feedstock characteristics inhibit feedstock interchangeability, by solving a novel nonlinear program
that accounts for the complexity of the factors at play. Moreover, it is shown that the interplay between water footprint and water scarcity across countries can inhibit or foster feedstock interchangeability. Model validation strategies and a sensitivity analysis complete the study
Virtual element method for elliptic bulk-surface PDEs in three space dimensions
Full text linkIn this work we present a novel bulk-surface virtual element method (BSVEM)
for the numerical approximation of elliptic bulk-surface partial differential
equations (BSPDEs) in three space dimensions. The BSVEM is based on the
discretisation of the bulk domain into polyhedral elements with arbitrarily
many faces. The polyhedral approximation of the bulk induces a polygonal
approximation of the surface. Firstly, we present a geometric error analysis of
bulk-surface polyhedral meshes independent of the numerical method. Then, we
show that BSVEM has optimal second-order convergence in space, provided the
exact solution is in the bulk and on the surface, where the
additional is due to the combined effect of surface curvature and
polyhedral elements close to the boundary. We show that general polyhedra can
be exploited to reduce the computational time of the matrix assembly. To
demonstrate optimal convergence results, a numerical example is presented on
the unit sphere.Comment: 25 pages, 4 figures, 1 table. This replacement improves figures,
updates references, and avoids redundancies. arXiv admin note: substantial
text overlap with arXiv:2002.1174
Turing pattern formation on the sphere for a morphochemical reaction-diffusion model for electrodeposition
Full text linkThe present paper deals with the pattern formation properties of a specific morpho- electrochemical reaction-diffusion model on a sphere. The physico-chemical background to this study is the morphological control of material electrodeposited onto spherical parti- cles. The particular experimental case of interest refers to the optimization of novel metal- air flow batteries and addresses the electrodeposition of zinc onto inert spherical supports. Morphological control in this step of the high-energy battery operation is crucial to the energetic efficiency of the recharge process and to the durability of the whole energy- storage device. To rationalise this technological challenge within a mathematical modeling perspective, we consider the reaction-diffusion system for metal electrodeposition intro- duced in [Bozzini et al., J. Solid State Electr.17, 467–479 (2013)] and extend its study to spherical domains. Conditions are derived for the occurrence of the Turing instability phe- nomenon and the steady patterns emerging at the onset of Turing instability are investi- gated. The reaction-diffusion system on spherical domains is solved numerically by means of the Lumped Surface Finite Element Method (LSFEM) in space combined with the IMEX Euler method in time. The effect on pattern formation of variations in the domain size is investigated both qualitatively, by means of systematic numerical simulations, and quan- titatively by introducing suitable indicators that allow to assign each pattern to a given morphological class. An experimental validation of the obtained results is finally presented for the case of zinc electrodeposition from alkaline zincate solutions onto copper spheres
What lies behind the success of Italian GIs products? Questioning tradition in consortia via aggregated conditional efficiency
No full textFirms and territories are considered extremely interrelated, especially approaching the market of agri-food
products detaining the PDO (Protected Designation of Origin) and PGI (Protected Geographical Indication)
labels. By aiming at reducing costs and simultaneously exploiting potential benefits, entrepreneurial realities
often collaborate through consortia. This aspect takes on a crucial relevance when considering the Italian
context, widely known for its high-quality products, the vocation to cooperate, and the high adaptability to
insidious locations. In this light, this study assesses the efficiency level of in-the-consortia Italian firms by
conditioning for two external factors affecting the input–output process evaluated, i.e. physical riskiness and
vocation to cooperate. The Data Envelopment Analysis (DEA) scores are aggregated by using firms’ membership
in the consortia as the DEA aggregation criterion. More than 600 firms aggregated in 50 consortia allow for
a capillary and locally-based study over the 2011–2020 period. The study signals tips about geographical
concentration and proximity since it tests whether tradition and attitude to cooperate motivate the agri-food
industry efficiency level, in line with the historical regional background of these organizational forms. Finally,
suggestions to exploit the market of certified products are discussed both for policy-makers and practitioners,
as well as new opportunities for future research
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