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We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local…

Mathematical Physics · Physics 2015-06-18 Sebastian Aland , Sabine Egerer , John Lowengrub , Axel Voigt

A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our $p$-energy is defined through a relaxation process, where a suitable $p$-rotation of inscribed polygonals is adopted.…

Differential Geometry · Mathematics 2023-01-02 Domenico Mucci , Alberto Saracco

We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order temporal discretizations are proposed based on this new…

Numerical Analysis · Mathematics 2024-08-27 Harald Garcke , Wei Jiang , Chunmei Su , Ganghui Zhang

We establish local existence and a quasi-optimal error estimate for piecewise cubic minimizers to the bending energy under a discretized inextensibility constraint. In previous research a discretization is used where the inextensibility…

Numerical Analysis · Mathematics 2025-09-03 Sören Bartels , Balázs Kovács , Dominik Schneider

We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual…

Mathematical Finance · Quantitative Finance 2025-06-13 Dongmei Zhu , Ashley Davey , Harry Zheng

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Statistical Mechanics · Physics 2011-09-09 Guy Fayolle , Cyril Furtlehner

We consider a mixed formulation of parametrized elasticity problems in terms of stress, displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce conservation of linear and angular momentum. Due to the…

Numerical Analysis · Mathematics 2024-10-10 Wietse M. Boon , Nicola R. Franco , Alessio Fumagalli

We investigate non-convex optimization problems in $BV(\Omega)$ with two-sided pointwise inequality constraints. We propose a regularization and penalization method to numerically solve the problem. Under certain conditions, weak limit…

Optimization and Control · Mathematics 2021-10-06 Carolin Natemeyer , Daniel Wachsmuth

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by…

Statistical Mechanics · Physics 2010-09-08 Martial Mazars

In this paper we will review recent advances in the application of the augmented Lagrange multiplier method as a general approach for generating multiplier--free stabilised methods. We first show how the method generates Galerkin/Least…

Numerical Analysis · Mathematics 2022-07-04 Erik Burman , Peter Hansbo , Mats G. Larson

This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly…

Mathematical Physics · Physics 2012-06-11 Jonathan Soto , Jean-Jacques E. Slotine

Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues -- just to mention a few…

Numerical Analysis · Mathematics 2024-01-02 Luca Heltai , Paolo Zunino

We propose a model for the coupling between free fluid and a linearized poro-hyperelastic body. In this model, the Brinkman equation is employed for fluid flow in the porous medium, incorporating inertial effects into the fluid dynamics. A…

Numerical Analysis · Mathematics 2024-07-19 Aparna Bansal , Nicolás A. Barnafi , Dwijendra Narain Pandey , Ricardo Ruiz-Baier

Aiming at simulating elastic rods, we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods. After reviewing this model and discussing topological effects of periodic rods, we prove…

Numerical Analysis · Mathematics 2019-11-19 Sören Bartels , Philipp Reiter

We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence…

Numerical Analysis · Mathematics 2024-12-20 Masato Kimura , Atsushi Suzuki

In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…

Optimization and Control · Mathematics 2018-10-25 Veronika Karl , Ira Neitzel , Daniel Wachsmuth

We study an obstacle problem for the length-penalized elastic bending energy for open planar curves pinned at the boundary. We first consider the case without length penalization and investigate the role of global minimizers among graph…

Analysis of PDEs · Mathematics 2025-11-03 Marius Müller , Kensuke Yoshizawa

Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients. Its applications span various fields, including mathematics, physics,…

Optimization and Control · Mathematics 2024-01-18 Gianluca Giacchi , Bastien Milani , Benedetta Franchieschiello

We consider models for elastic liquids, such as solutions of flexible polymers. They introduce a relaxation time $\lambda$ into the system, over which stresses relax. We study the kinematics of the problem, and clarify the relationship…

Fluid Dynamics · Physics 2021-03-17 J. H. Snoeijer , A. Pandey , M. A. Herrada , J. Eggers

We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…

Dynamical Systems · Mathematics 2015-08-11 Ivan Polekhin