A comparative review of peridynamics and phase-field models for engineering fracture mechanics
Computational modeling of the initiation and propagation of complex fracture is central to the
discipline of engineering fracture mechanics. This review focuses on two promising …
discipline of engineering fracture mechanics. This review focuses on two promising …
Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision
This paper proposes a review focused on exotic chemotaxis and cross-diffusion models in
complex environments. The term exotic is used to denote the dynamics of models interacting …
complex environments. The term exotic is used to denote the dynamics of models interacting …
Mean-field limits: from particle descriptions to macroscopic equations
JA Carrillo, YP Choi - Archive for Rational Mechanics and Analysis, 2021 - Springer
We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in
velocity and aggregation equations with nonlocal velocity fields from Newton-type particle …
velocity and aggregation equations with nonlocal velocity fields from Newton-type particle …
[图书][B] Dynamics and analysis of alignment models of collective behavior
R Shvydkoy - 2021 - Springer
Collective phenomena occur in nature, technology, and social behavior in a vast variety of
contexts. For example, birds and fish use their sensory abilities to communicate and align …
contexts. For example, birds and fish use their sensory abilities to communicate and align …
On the mathematics of swarming: emergent behavior in alignment dynamics
E Tadmor - arXiv preprint arXiv:2102.09134, 2021 - ams.org
. System 1 is a canonical model for alignment dynamics in which pairwise interactions steer
towards average heading. Alignment originated in pioneering works Rey87 VCBCS95 …
towards average heading. Alignment originated in pioneering works Rey87 VCBCS95 …
Sticky particle Cucker–Smale dynamics and the entropic selection principle for the 1D Euler-alignment system
We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment
system with measure-valued density, bounded velocity, and locally integrable …
system with measure-valued density, bounded velocity, and locally integrable …
Swarming: hydrodynamic alignment with pressure
E Tadmor - Bulletin of the American Mathematical Society, 2023 - ams.org
We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering
toward a weighted average heading. We consider the class of so-called $ p $-alignment …
toward a weighted average heading. We consider the class of so-called $ p $-alignment …
On hydrodynamic limits of the Vlasov-Navier-Stokes system
D Han-Kwan, D Michel - arXiv preprint arXiv:2103.06668, 2021 - arxiv.org
We introduce a framework to justify hydrodynamic limits of the Vlasov-Navier-Stokes system.
We specifically study high friction regimes, which take into account the fact that particles of …
We specifically study high friction regimes, which take into account the fact that particles of …
From microscopic to macroscopic scale equations: mean field, hydrodynamic and graph limits
T Paul, E Trélat - arXiv preprint arXiv:2209.08832, 2022 - arxiv.org
We elaborate on various ways to pass to the limit a given family of finite-dimensional particle
systems, either by mean field limit, deriving the Vlasov equation, or by hydrodynamic or …
systems, either by mean field limit, deriving the Vlasov equation, or by hydrodynamic or …
Anticipation breeds alignment
R Shu, E Tadmor - Archive for Rational Mechanics and Analysis, 2021 - Springer
We study the large-time behavior of systems driven by radial potentials, which react to
anticipated positions, x^ τ (t)= x (t)+ τ v (t) x τ (t)= x (t)+ τ v (t), with anticipation increment τ> 0 …
anticipated positions, x^ τ (t)= x (t)+ τ v (t) x τ (t)= x (t)+ τ v (t), with anticipation increment τ> 0 …