相关论文: Onsager coefficients in periodically driven system…
Using a Lagrangian mechanics approach, we construct a framework to study the dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. We have shown in our previous work that for…
We investigate magnetic-field asymmetries in the linear transport of a mesoscopic conductor interacting with its environment. Interestingly, we find that the interaction between the two systems causes an asymmetry only when the environment…
Methods based on "(Jacobian) matrix measure" to show the convergence of a dynamical system to a limit cycle (LC), generally assume that the measure is negative everywhere on the LC. We relax this assumption by assuming that the matrix…
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and…
Periodically driven flows are fundamental models of chaotic behavior and the study of their transport properties is an active area of research. A well-known analytic construction is the augmentation of phase space with an additional time…
This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial…
In this paper we compare three frameworks for modeling flows of complex fluids: (i) local conservations of mass, momentum and energy, (ii) GENERIC, and (iii) Onsager principle. The first is based on the mass, momentum, and energy…
Governing equations for evolution of concentration and temperature in three-component systems were derived in the framework of classical irreversible thermodynamics using Onsager variational principle and were presented for…
We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time \pi on…
We study the anisotropic linear Maxwell system on a bounded domain $\Omega$ with perfectly conducting boundary conditions. It is damped via a conductivity $\sigma$ which is strictly positive on a collar at the boundary. We prove that…
The static second hyperpolarizability is derived from the space-fractional Schr\"{o}dinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second…
Thermoelectricity is traditionally explained via Onsager's irreversible, flux-force framework. The coupled flows of heat and electric charge are modelled as steady-state flows, driven by the thermodynamic forces defined in terms of the…
We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying index, along with a new {\em Regularized…
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…
We show that for any $\gamma < \frac{1}{3}$ there exist H\"{o}lder continuous weak solutions $v \in C^{\gamma}([0,T] \times \mathbb{T}^2)$ of the two-dimensional incompressible Euler equations that strictly dissipate the total kinetic…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
Coherent sets are time-dependent regions in the physical space of nonautonomous flows that exhibit little mixing with their neighborhoods, robustly under small random perturbations of the flow. They thus characterize the global long-term…
How does the arrow of time (dissipative, irreversible behavior) emerge from time-reversible Hamiltonian mechanics? Two ingredients are needed: the underlying system must be ergodic or phase-mixing, and our knowledge of the system must be…
We propose a simple model of coupled heat and particle transport based on a zero-dimensional classical deterministic dynamics which is reminiscent of a railway switch whose action is only a function of the particle's energy. It is shown…