Article
Mathematics, Applied
Livia Betz
Summary: In this study, a rate-independent damage model with two damage variables coupled through a penalty term in the stored energy is considered. The nonconvex energy functional leads to discontinuous solutions in time, for which suitable notions of weak solutions allowing for jumps are required. The vanishing-viscosity approach based on an L2(omega)-arclength parametrization is used to prove the existence of vanishing-viscosity solutions belonging to the class of parametrized solutions, characterized in various ways, emphasizing the influence of viscous effects at jump points.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2021)
Article
Mathematics, Applied
Jinjing Liu, Rong Pan, Lei Yao
Summary: This paper investigates the vanishing viscosity limit for rarefaction wave with vacuum in an ionized plasma. By letting the viscosity tend to zero in the Navier-Stokes-Poisson system of ions, the corresponding quasineutral Euler system can be obtained, which includes solutions with vacuum state. A sequence of solutions to the Navier-Stokes-Poisson system is constructed that converges to the rarefaction wave with vacuum as the viscosity tends to zero, and the uniform convergence rate is obtained.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Mechanics
J. Alfaiate, L. J. Sluys
Summary: Localisation of cracking in quasi-brittle materials is a challenging task, and conventional iterative methods often fail to provide convergence of the numerical solution. On the other hand, traditional total approaches cannot properly approximate the underlying material law. This study introduces the Total Iterative Approach, which updates internal damage variables iteratively, and demonstrates its robustness and ability to accurately approximate the material law in analyzing softening behavior through examples.
ENGINEERING FRACTURE MECHANICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Debdeep Bhattacharya, Robert P. Lipton
Summary: This paper investigates load controlled quasistatic evolution and establishes well-posedness results for the nonlocal continuum model related to peridynamics. The local existence and uniqueness of quasistatic evolution is demonstrated for load paths originating at stable critical points, which can be associated with local energy minima among the convex set of deformations belonging to the strength domain of the material. The load-controlled evolution is shown to exhibit energy balance.
MULTISCALE MODELING & SIMULATION
(2023)
Article
Mathematics
Lin He, Yong Wang
Summary: This article investigates the initial data of compressible Euler equations with finite energy and total mass. By constructing a sequence of solutions of one-dimensional compressible Navier-Stokes equations, which converges to a weak solution of compressible Euler equations, the validity of the inviscid limit of the compressible Navier-Stokes equations is proven. Additionally, the interesting case of the Saint-Venant model for shallow water is also covered in this study.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Zhaonan Luo, Wei Luo, Zhaoyang Yin
Summary: The paper investigates the inviscid limit for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. It provides a uniform estimate for the solution in Besov spaces using the Littlewood-Paley theory, and shows the continuity of the data-to-solution map. The convergence of the strong solution to an Euler system and a Fokker-Planck equation is proven, with convergence rates in Lebesgue spaces also obtained.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Engineering, Mechanical
Sansit Patnaik, Sai Sidhardh, Fabio Semperlotti
Summary: This study introduces a fractional-order continuum mechanics approach that can capture stiffening and softening effects in a stable manner. The method is suitable for static and free vibration analysis, able to simulate the response of Timoshenko beams or Mindlin plates.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
Wenlong Wu, Minghui Cai, Zeyu Zhang, Weigong Tian, Haijun Pan
Summary: The elevated temperature tensile behavior of a Nb-Mo microalloyed medium steel was investigated, and it was found that the ultimate tensile strength was significantly reduced with increasing deformation temperature, while the yield strength and total elongation values changed slightly. The best combination of ultimate tensile strength and total elongation was achieved at a deformation temperature of 50 degrees C.
Article
Mathematics, Applied
Gianni Dal Maso, Rodica Toader
Summary: We studied a variational model for crack growth in elasto-plastic materials with hardening in the antiplane case, and found the existence of a solution to the initial value problem with prescribed time-dependent boundary conditions.
ADVANCES IN CALCULUS OF VARIATIONS
(2022)
Article
Mathematics, Applied
James P. Kelliher
Summary: This paper applies Tosio Kato's methodology to establish necessary and sufficient conditions for the convergence of solutions to the Navier-Stokes equations to solutions of the Euler equations in the presence of a boundary. It extends the existing conditions for no-slip boundary conditions to allow for nonhomogeneous Dirichlet boundary conditions and curved boundaries, and introduces several new conditions. A brief comparison of various correctors used for similar purposes in the literature is also provided.
Article
Mathematics, Applied
Wenshu Zhou
Summary: This paper investigates the nonhomogeneous initial boundary value problem for a simplified compressible Navier-Stokes system with cylindrical symmetry and temperature-dependent viscosity, in which the acceleration effect in one direction is ignored. The article proves the global unique solvability of strong solution with large data, justifies the vanishing shear viscosity limit, and obtains the optimal L-2 convergence rate for the angular and axial velocities as well as the estimation on the boundary layer thickness.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2022)
Review
Chemistry, Multidisciplinary
Jinwoo Kim, Ji Young Kim, Eun Soo Park
Summary: Alloying, the mixing of multiple metallic elements, has been a classic method for novel materials development since ancient times. This article describes a hybrid approach combining metallurgical bottom-up and chemical top-down processes for fabricating multicomponent alloy nanostructures. The method allows for precise control of alloy composition and cooling rate to prepare precursor alloys for nanoparticles and nanofoams with varied atomic structures and sizes.
ACCOUNTS OF CHEMICAL RESEARCH
(2022)
Article
Computer Science, Interdisciplinary Applications
Ricardo A. S. Frantz, Georgios Deskos, Sylvain Laizet, Jorge H. Silvestrini
Summary: This study investigates the potential of a high-order finite-difference spectral vanishing viscosity approach to simulate gravity currents at high Reynolds numbers. The results show that the SVV model yields slightly more accurate results than the Smagorinsky model while consuming fewer computational resources. By performing large-eddy simulations and comparing with experimental data, it is found that the SVV method can accurately simulate the characteristics of gravity currents and is consistent with experimental results.
COMPUTERS & FLUIDS
(2021)
Article
Mathematics, Applied
Giuseppe Maria Coclite, Nicola De Nitti, Alexander Keimer, Lukas Pflug
Summary: A class of nonlocal conservation laws with a second-order viscous regularization term is studied, which has applications in modelling macroscopic traffic flow. The solution of the nonlocal problem converges to the entropy solution of the corresponding local conservation law as the nonlocal impact and the viscosity parameter tend to zero. The key idea of the proof is observing the behavior of the nonlocal term and deriving a suitable energy estimate on it for convergence.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
Tadeusz Antczak
Summary: In this paper, two mathematical methods are used to solve a complex multicriteria optimization problem by transforming it into a differentiable vector optimization problem with vanishing constraints. One of the methods is a linearized approach, which constructs a multiobjective programming problem to solve the original problem. The presented methods can be applied to solve differentiable vector optimization problems with vanishing constraints.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Maria Giovanna Mora, Alessandro Scagliotti
Summary: This paper characterizes the equilibrium measure for a family of nonlocal and anisotropic energies, showing that it is unaffected by anisotropy and coincides with the optimal distribution under purely Coulomb interactions. This contradicts the mechanical conjecture about the arrangement of positive edge dislocations, and represents a rare explicit characterization of equilibrium measure for nonlocal interaction energies outside radially symmetric cases.
ADVANCES IN CALCULUS OF VARIATIONS
(2022)
Article
Materials Science, Multidisciplinary
V Deshpande, A. DeSimone, R. McMeeking, P. Recho
Summary: This paper introduces a framework that combines an active gel model of cell mechanical scaffold with a complex cell metabolic system to stochastically provide the chemical energy needed for active stress. The study shows that cell shape fluctuations depend on the mechanical environment that constraints the cell.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Multidisciplinary Sciences
D. Riccobelli, G. Noselli, A. DeSimone
Summary: This study investigates the deformations of an elastic beam subjected to an axial force and constrained to slide smoothly along a rigid support, revealing transitions between helical and twisted shapes. The experimental results show good quantitative agreement with the mathematical predictions of the proposed model.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Mathematics, Applied
J. A. Carrillo, J. Mateu, M. G. Mora, L. Rondi, L. Scardia, J. Verdera
Summary: This paper characterises the minimisers of a one-parameter family of nonlocal and anisotropic energies in probability measures in Rn. It proves the uniqueness of minimisers within a certain range and demonstrates the impact of anisotropy of the interaction kernel on the shape of minimisers, highlighting a paradigmatic example in higher dimensions.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Biology
Giancarlo Cicconofri, Giovanni Noselli, Antonio DeSimone
Summary: The model for flagellar mechanics in Euglena gracilis demonstrates that the peculiar non-planar shapes of its beating flagellum, termed 'spinning lasso', arise from the mechanical interactions between the axoneme and the paraflagellar rod. The complex non-planar configurations of the system are the energetically optimal compromise between the incompatible shapes of the two components.
Article
Mathematics, Applied
Gianni Dal Maso, Rodica Toader
Summary: The properties of crack length in pressure-sensitive elasto-plastic materials in the planar case are studied, and it is proven that under suitable technical assumptions, the length is a pure jump function on the crack path.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics
Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida Zeppieri
Summary: In this paper, we investigate the deterministic and stochastic homogenisation of free-discontinuity functionals under linear growth and coercivity conditions. A novel aspect of our deterministic result is that it is based on very general assumptions on the integrands, which do not need to be periodic in the space variable. Combining this result with the pointwise Subadditive Ergodic Theorem, we establish a stochastic homogenisation result for stationary random integrands, characterising the limit integrands in terms of asymptotic cell formulas, similar to the classical periodic homogenisation case.
Article
Engineering, Biomedical
Outman Akouissi, Stephanie P. Lacour, Silvestro Micera, Antonio DeSimone
Summary: In this study, the mechanical stresses induced on the peripheral nerve by the implant's micromotion were modeled using finite element analysis. The results indicate that the material, geometry, and surface coating of the implant are crucial for its stability and durability. Specifically, implants with smooth edges, materials that are no more than three orders of magnitude stiffer than the nerve, and innovative geometries that redistribute micromotion-associated loads can improve the long-term performance of peripheral nerve implants.
JOURNAL OF NEURAL ENGINEERING
(2022)
Article
Mathematics, Applied
Gianni Dal Maso, Rodica Toader
Summary: We introduce a new space of generalised functions with bounded variation to prove the existence of a solution to a minimum problem that arises in the variational approach to fracture mechanics in elastoplastic materials. We study the fine properties of the functions belonging to this space and prove a compactness result. In order to use the Direct Method of the Calculus of Variations we prove a lower semicontinuity result for the functional occurring in this minimum problem. Moreover, we adapt a nontrivial argument introduced by Friedrich to show that every minimizing sequence can be modified to obtain a new minimizing sequence that satisfies the hypotheses of our compactness result.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Lorenzo Freddi, Peter Hornung, Maria Giovanna Mora, Roberto Paroni
Summary: This paper proves that when prescribed with affine boundary conditions on the short sides of the strip, the (extended) Sadowsky functional can still be deduced as the Gamma-limit of the Kirchhoff energy on a rectangular strip, providing a rigorous theoretical basis for Sadowsky's original argument about the equilibrium shape of a Mobius strip.
JOURNAL OF NONLINEAR SCIENCE
(2022)
Article
Mechanics
Alberto Lolli, Giovanni Corsi, Antonio DeSimone
Summary: This study addresses the navigation problems of a model bio-inspired micro-swimmer swimming at low Reynolds numbers, including predicting velocity and trajectories based on rotation rates, and finding optimal rotation rates to achieve desired translational and rotational velocities. Different designs of propulsive rotors were considered and their relative performance was evaluated.
Article
Mathematics, Applied
Maria Giovanna Mora, Filippo Riva
Summary: This paper studies the variational derivation of linear elasticity in the presence of live loads and computes its linearization for small pressure using gamma-convergence. The strong convergence of minimizers is proven.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
(2022)
Article
Mathematics, Applied
Gianni Dal Maso, Rodica Toader
Summary: We studied a variational model for crack growth in elasto-plastic materials with hardening in the antiplane case, and found the existence of a solution to the initial value problem with prescribed time-dependent boundary conditions.
ADVANCES IN CALCULUS OF VARIATIONS
(2022)
Article
Biology
ThankGod Echezona Ebenezer, Ross S. Low, Ellis Charles O'Neill, Ishuo Huang, Antonio DeSimone, Scott C. Farrow, Robert A. Field, Michael L. Ginger, Sergio Adrian Guerrero, Michael Hammond, Vladimir Hampl, Geoff Horst, Takahiro Ishikawa, Anna Karnkowska, Eric W. Linton, Peter Myler, Masami Nakazawa, Pierre Cardol, Rosina Sanchez-Thomas, Barry J. Saville, Mahfuzur R. Shah, Alastair G. B. Simpson, Aakash Sur, Kengo Suzuki, Kevin M. Tyler, Paul V. Zimba, Neil Hall, Mark C. Field
Summary: Euglenoids are unicellular flagellates with wide geographical and ecological distribution. They have biotechnological potential and show promise in fields such as biofuels, nutraceuticals, bioremediation, cancer treatments, and robotics design. However, the lack of reference genomes hinders the development of these applications. The Euglena International Network aims to overcome these challenges.
Article
Chemistry, Physical
Valentina Damioli, Erik Zorzin, Antonio DeSimone, Giovanni Noselli, Alessandro Lucantonio
Summary: This study presents a geometrical model for the transient shaping of thin hydrogel plates based on the theory of non-Euclidean plates. Experimental results show the emergence of non-axisymmetric shapes in the early stages, caused by boundary layer effects induced by solvent transport. The study highlights the limitations of purely geometrical models and emphasizes the importance of transient, reduced theories for accurately controlling the morphing dynamics of active structures.
