相关论文: Onsager's variational principle in active soft mat…
We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…
The variational principle of the Onsager-Machlup integral is used to describe the stochastic dynamics of a micromachine, such as an enzyme, characterized by odd elasticity. The obtained most probable path is found to become non-reciprocal…
We present a general, constructive method to derive thermodynamically consistent models and consistent dynamic boundary conditions hierarchically following the generalized Onsager principle. The method consists of two steps in tandem: the…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
Hydrodynamic equations for a one-component plasma are derived as a generalization of the Euler equations to include the effects of the long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify…
We derive the virial theorem appropriate to two-dimensional point vortices at statistical equilibrium in the microcanonical and canonical ensembles. In an unbounded domain, it relates the angular velocity to the angular momentum and the…
Existing operator learning methods rely on supervised training with high-fidelity simulation data, introducing significant computational cost. In this work, we propose the deep Onsager operator learning (DOOL) method, a novel unsupervised…
Theories of self-organized active fluid surfaces have emerged as an important class of minimal models for the shape dynamics of biological membranes, cells and tissues. However, due to their inherent geometric nonlinearities and the absence…
A dynamic wetting problem is studied for a moving thin fiber inserted in fluid and with a chemically inhomogeneous surface. A reduced model is derived for contact angle hysteresis by using the Onsager principle as an approximation tool. The…
In this note we propose a basic $L^2$-based approach for studying the global and local energy equalities of the incompressible 3D Navier-Stokes equations in the standard energy class on $\mathbb{T}^3 \times (0,T]$. Motivated by L. Onsager's…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…
We establish an implicit variational principle for the equations of the contact flow generated by the Hamiltonian $H(x,u,p)$ with respect to the contact 1-form $\alpha=du-pdx$ under Tonelli and Osgood growth assumptions. It is the first…
Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
Inertial effects affecting both the translational and rotational dynamics are inherent to a broad range of active systems at the macroscopic scale. Thus, there is a pivotal need for proper models in the framework of active matter to…
The Onsager linear relations between macroscopic flows and thermodynamics forces are derived from the point of view of large deviation theory. For a given set of macroscopic variables, we consider the short-time evolution of…
We present a natural framework for constructing energy-stable time discretization schemes. By leveraging the Onsager principle, we demonstrate its efficacy in formulating partial differential equation models for diverse gradient flow…
A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by…