Related papers: Elastic bending energy: a variational approach
A class of variational schemes for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasineutral background is developed for high-quality simulations of surface plasmon polaritons. The Lagrangian density of lossless…
Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…
We discuss a 1D variational problem modeling an elastic sheet on water, lifted at one end. Its terms include the membrane and bending energy of the sheet as well as terms due to gravity and surface tension. By studying a suitable…
In [12], the authors studied a particular class of equilibrium solutions of the Helfrich energy which satisfy a second order condition called the reduced membrane equation. In this paper we develop and apply a second variation formula for…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
Elastodynamic equations have been formulated with either Newton's second law of motion, Lagrange's equation, or Hamilton's principle for over 150 years. In this work, contrary to classical continuum mechanics, a novel strategic methodology…
In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elas- ticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is…
We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic…
Variational principle is the main approach to obtain complete and self-consistent field equations in gravitational theories. This method works well in pure field cases such as $f(R)$ and Horndeski gravities. However, debates exist in the…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $\rho$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational…
When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a…
The early Dirac proposal to model the electron as a charged membrane is reviewed. A rigidity term, instead of the natural membrane tension, involving linearly the extrinsic curvature of the worldvolume swept out by the membrane is…
We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction is the definition of discrete deformation gradients and discrete Cauchy-Green deformation…
Metric independent $\sigma$ models are constructed. These are field theories which generalise the membrane idea to situations where the target space has fewer dimensions than the base manifold. Instead of reparametrisation invariance of the…
We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the…
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially…
We address the geometric Cauchy problem for surfaces associated to the membrane shape equation describing equilibrium configurations of vesicles formed by lipid bilayers. This is the Euler-Lagrange equation of the Canham-Helfrich-Evans…