Article
Materials Science, Multidisciplinary
Basile Audoly, Claire Lestringant
Summary: The proposed method provides a way to derive equivalent one-dimensional models for slender non-linear structures, handling various conditions and capturing detailed shape of cross-sections through a kinematic parameterization. It is effective when macroscopic strain and rod properties vary slowly in the longitudinal direction, resulting in a more accurate equivalent rod model.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Mathematics, Applied
Marco Bonacini, Sergio Conti, Flaviana Iurlano
Summary: In this paper, a notion of irreversibility for crack evolution in the presence of cohesive forces is proposed, allowing for different responses in loading and unloading processes. Motivated by a variational approximation with damage models, its applicability to constructing quasi-static evolution in a simple one-dimensional model is investigated. The cohesive fracture model arises naturally via Gamma-convergence from a phase-field model of the generalized Ambrosio-Tortorelli type, which can be used as regularization for numerical simulations.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2021)
Article
Engineering, Geological
Mincai Jia, Bo Liu, Jianfeng Xue, Guoqing Ma
Summary: The paper introduces a three-dimensional discrete element-finite difference coupling method and validates its effectiveness in dynamic compaction tests. It is found that dynamic stress propagation and tamper penetration play different roles in soil deformations, and allocating more tamping energy to the bearing capacity mechanism can improve the efficiency of dynamic compaction.
Article
Computer Science, Interdisciplinary Applications
Na Zhang, Ahmad S. Abushaikha
Summary: This paper presents a fully implicit mimetic finite difference method (MFD) for general fractured reservoir simulation, extending this novel numerical discretization scheme to discrete fracture models. The MFD scheme supports general polyhedral meshes and full tensor properties, improving modeling and simulation of subsurface reservoirs. The paper also describes the principle of the MFD approach and presents numerical formulations of the discrete fracture model, demonstrating accuracy and robustness through case studies.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Geological
Yousef Navidtehrani, Covadonga Betegon, Robert W. Zimmerman, Emilio Martinez-Paneda
Summary: This study uses the Griffith criterion and finite element analysis to evaluate the conditions and validity of the Brazilian test. It finds that the range of conditions where the Brazilian test is valid is narrower than previously assumed, and current practices and standards are inappropriate for many rock-like materials. The study also proposes a test protocol and showcases its validity through case studies and a MATLAB App.
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
(2022)
Article
Optics
Jaesun Park, Kyung-Young Jung
Summary: The FDTD method is widely used for analyzing electromagnetic wave propagation in complex dispersive media, with mLor FDTD method showing potential to unify other dispersion models. Research found that numerical stability of mLor FDTD method is equivalent to its original model-based FDTD counterparts.
Article
Mathematics
Angel Garcia, Mihaela Negreanu, Francisco Urena, Antonio M. Vargas
Summary: The study demonstrates the existence and uniqueness of discrete solutions of a porous medium equation with diffusion, using the generalized finite difference method to achieve convergence of the numerical solution. This method allows for the use of meshes with complicated geometry or irregular node distributions, providing more accurate solutions when dealing with sufficiently smooth and bounded nonnegative initial data.
Article
Energy & Fuels
Marcin Jaraczewski, Tadeusz J. Sobczyk, Adam Warzecha
Summary: This article introduces an algorithm that directly provides a steady state solution by representing the predicted periodic time and space function with appropriate Fourier series. The algorithm uses discrete partial differential operators for time and space derivatives and allows for the derivation of finite difference equations directly from the field and circuit equations. The effectiveness of the proposed approach is confirmed through testing on a simple case of a solenoid coil with a ferromagnetic and conductive cylindrical core, both qualitatively in terms of physical phenomena and quantitatively in comparison with results from specialized commercial software.
Article
Physics, Multidisciplinary
A. M. S. Macedo, L. D. da Silva, L. G. B. Souza, C. A. Batista, W. R. de Oliveira
Summary: This paper introduces an integral transform technique that maps differential equations and special functions of standard continuous calculus onto finite difference equations and deformed special functions of mimetic discrete calculus. The technique has insightful applications in mathematics and physics, particularly in solving finite difference equations, applying discrete versions of integral transforms, solving master equations of stochastic physics, developing a discrete version of H theory, and finding lattice Green's functions for quantum charge transport.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Chemistry, Physical
Ivan P. Bosko, Viktor N. Staroverov
Summary: The Fermi-Amaldi correction is a semi-classical exchange functional that is exact for one- and closed-shell two-electron systems. We demonstrate that this functional is exact for any number of fermions or bosons of arbitrary spin as long as the particles occupy the same spatial orbital. The Fermi-Amaldi functional is also size-consistent for such systems.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Frederic Marazzato, Alexandre Ern, Laurent Monasse
Summary: The variational discrete element method is used to simulate quasi-static crack propagation by considering cracks to propagate between mesh cells through mesh facets. The elastic behavior is parameterized by continuous mechanical parameters and guided by a discrete energetic cracking criterion coupled with a discrete kinking criterion. Two-dimensional numerical examples are presented to demonstrate the robustness and versatility of the method.
COMPUTATIONAL MECHANICS
(2022)
Article
Mathematics, Applied
Guanyu Zhou
Summary: In this study, we analyze two finite volume schemes for the chemotaxis system in a two-dimensional domain, demonstrating mass conservation, positivity, and well-posedness without the need for the CFL condition. We investigate the stability of equilibrium and local stability, and apply discrete semigroup theory for error analysis, achieving a convergence rate O(tau+h) in Lp norm. The theoretical results are validated through numerical experiments.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Interdisciplinary Applications
Zareen A. Khan, Hijaz Ahmad
Summary: Discrete fractional calculus is utilized to interpret neural schemes with memory impacts. This study formulates discrete fractional nonlinear inequalities for numerical solutions of discrete fractional differential equations and discusses aspects such as boundedness, uniqueness, and continuous dependency. The methodology employed proves the leading consequences for solutions of discrete fractional difference equations.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Computer Science, Interdisciplinary Applications
Davide Dapelo, Stephan Simonis, Mathias J. Krause, John Bridgeman
Summary: The research proposes two 3D models to overcome numerical instability issues in high-Peclet flows, coupling a Lattice-Boltzmann Navier-Stokes solver with an advection-diffusion model or a finite-difference algorithm. Through improving numerical diffusivity and validation tests, it is shown that the coupled finite-difference/Lattice-Boltzmann model provides stable solutions in the case of infinite Pe and Pe(g).
JOURNAL OF COMPUTATIONAL SCIENCE
(2021)
Article
Computer Science, Interdisciplinary Applications
Jeffrey D. Hyman, Matthew R. Sweeney, Carl W. Gable, Daniil Svyatsky, Konstantin Lipnikov, David Moulton
Summary: This paper presents a comprehensive workflow for simulating single-phase flow and transport in fractured porous media. The workflow includes mesh generation, discretization of governing equations, and implementation of numerical methods for high-performance computing. The paper also provides methods to improve mesh quality and verification tests based on analytic solutions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Giacomo Albi, Stefano Almi, Marco Morandotti, Francesco Solombrino
Summary: This paper studies a mean-field selective optimal control problem of multipopulation dynamics via transient leadership. The problem considers the spatial position and probability of belonging to a certain population for the agents, and introduces an activation function to tune the control on each agent. By using Gamma-convergence, the mean-field limit of the finite-particle control problem is identified, ensuring the convergence of optimal controls. Specific applications in the context of opinion dynamics are discussed.
APPLIED MATHEMATICS AND OPTIMIZATION
(2022)
Article
Mathematics, Applied
Giuliano Lazzaroni, Riccardo Molinarolo, Francesco Solombrino
Summary: This paper deals with a debonding model for a thin film in two-dimensional space, involving the wave equation and a flow rule for the evolution of the domain. A general definition of energy release rate is proposed and well posed for radial solutions, allowing for the use of representation formulas typical of one-dimensional models.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Filippo Riva, Giovanni Scilla, Francesco Solombrino
Summary: The notion of inertial balanced viscosity (IBV) solution is introduced to describe rate-independent evolutionary processes. It is proved that these solutions converge in finite dimension and can be obtained via a natural extension of the minimizing movements algorithm. In the case of a nontrivial kernel, the weaker notion of inertial virtual viscosity (IVV) solution is introduced, and the analogous convergence result holds.
ADVANCES IN CALCULUS OF VARIATIONS
(2023)
Article
Automation & Control Systems
Virginia De Cicco, Giovanni Scilla
Summary: We establish a sufficient condition for the lower semicontinuity of nonautonomous noncoercive surface energies on GSBD(p) functions. The condition extends the definition of nonautonomous symmetric joint convexity, previously introduced for autonomous integrands. We also extend a nonautonomous chain formula in SBV and utilize it to prove the lower semicontinuity result. This work has practical significance in evaluating surface energies arising from variational models of fractures in inhomogeneous materials.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2023)
Article
Mathematics, Applied
Giuliano Lazzaroni, Riccardo Molinarolo, Filippo Riva, Francesco Solombrino
Summary: This article revisits the issues of existence and regularity for the wave equation in non-cylindrical domains. Using diffeomorphisms, the authors demonstrate how weak solutions can be derived by increasing regularity assumptions and improving their regularity, while maintaining an energy balance. They also provide a rigorous definition of dynamic energy release rate density for debonding problems and formulate a proper notion of solutions for such problems. The consistency of this formulation is compared with previous ones found in the literature.
INTERFACES AND FREE BOUNDARIES
(2022)
Article
Mathematics, Applied
Stefano Almi, Claudio D'Eramo, Marco Morandotti, Francesco Solombrino
Summary: This paper proves the well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation, under a general set of assumptions. The case of different time scales between the agents' locations and labels dynamics is considered, with further assumptions on the evolution of the labels. The limit system couples a mean-field-type evolution in the space of positions and an instantaneous optimization of the payoff functional in the space of labels.
MILAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Roberta Marziani, Francesco Solombrino
Summary: We investigated the G-convergence of general non-local convolution type functionals with varying densities dependent on the space variable and symmetrized gradient. The limit is a local free-discontinuity functional, characterized by an asymptotic cell formula for the bulk term. This leads to a homogenization result in the stochastic setting.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
(2023)
Article
Mathematics, Applied
Stefano Almi, Dario Reggiani, Francesco Solombrino
Summary: This work focuses on deriving a simplified model for brittle membranes in finite elasticity through variational methods. The main mathematical tools used in this analysis include: (i) a new density result in GSBV(P) for functions that satisfy a maximal-rank constraint on the subgradients, which can be approximated by C-1-local immersions on regular subdomains of the cracked set, and (ii) the construction of recovery sequences using suitable W-1, W-infinity diffeomorphisms that map the regular subdomains onto the fractured configuration.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Mathematics, Applied
Giovanni Scilla, Francesco Solombrino, Bianca Stroffolini
Summary: An integral representation result for free-discontinuity energies on the space GSBV(p(.)) with variable exponent p(x) under the assumption of log-Hölder continuity is proved. The analysis is based on a variable exponent version of the global method for relaxation devised by Bouchitté et al. (Arch Ration Mech Anal 165:187-242, 2002) for a constant exponent. G-convergence of sequences of energies of the same type is proven, limit integrands are identified using asymptotic cell formulas, and a non-interaction property between bulk and surface contributions is proved.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Automation & Control Systems
Chiara Leone, Giovanni Scilla, Francesco Solombrino, Anna Verde
Summary: This study proves a regularity result for free-discontinuity energies defined on the space SBVp() of special functions of bounded variation with variable exponent, assuming a log-Holder continuity for the variable exponent p(x). The analysis expands on the regularity theory for minimizers of a class of free-discontinuity problems in the nonstandard growth case.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2023)
Article
Mathematics
Stefano Almi, Marco Morandotti, Francesco Solombrino
Summary: Motivated by leader-follower multi-agent dynamics, this study investigates a class of optimal control problems aiming to influence the behavior of a given population through another controlled one interacting with the first. The system's evolution follows a non-linear Fokker-Planck-type equation accounting for randomness. The study develops a well-posedness theory for control vector fields with very low regularity, as well as a rigorous mean-field limit based on stochastic particle approximation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Vito Crismale, Manuel Friedrich, Francesco Solombrino
Summary: This paper proves an integral representation formula for a class of energies defined on the space of generalized special functions of bounded deformation (GSBDP) in arbitrary space dimensions. These functionals are relevant in modeling linear elastic solids with surface discontinuities, such as fracture, damage, surface tension between different elastic phases, or material voids. The approach is based on the global method for relaxation and a recent Korn-type inequality in GSBD(p). Furthermore, the general strategy allows for the generalization of integral representation results in SBDp to higher dimensions and revisiting results in the framework of generalized special functions of bounded variation (GSBV(p)).
ADVANCES IN CALCULUS OF VARIATIONS
(2022)
Article
Mathematics, Applied
Jihoon Ok, Giovanni Scilla, Bianca Stroffolini
Summary: This passage discusses the issue of partial Holder continuity for the boundary points of minimizers of quasiconvex non-degenerate functionals.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
(2022)
Article
Mathematics, Interdisciplinary Applications
Fernando Farroni, Giovanni Scilla, Francesco Solombrino
Summary: The paper analyzes the approximation in the sense of Gamma-convergence of nonisotropic Griffith-type functionals with p-growth (p > 1) in the symmetrized gradient, using a suitable sequence of non-local convolution type functionals defined on Sobolev spaces.
MATHEMATICS IN ENGINEERING
(2022)
