Memory and nonlocal effects of heat transport in a spherical nanoparticle

In this paper a mathematical model describing the heat transport in a spherical nanoparticle subject to Newton heating at its surface is presented. The governing equations involve a phonon hydrodynamic equation for the heat flux and the classical energy equation that relates the heat flux and the temperature. Assuming radial symmetry the model is reduced to two partial differential equation, one for the radial component of the flux and one for the temperature. We solve the model numerically by means of finite differences. The resulting temperature profiles show characteristic wave-like behaviour consistent with the non Fourier components in the hydrodynamic equation.

Nonlocal Hydrodynamic Models for the Optical Response of Plasmonic Nanostructures

In order to model the interaction between light and plasmonic structures at deep-nanometer scale, which is governed by non-classical effects, a nonlocal hydrodynamic approach has been extensively studied. Several hydrodynamic models have been proposed, solving the coupled equations: the linearized hydrodynamic equation of motion and the electrodynamic Maxwell’s equations, by employing additional boundary conditions. This work compares four hydrodynamic models: the hard wall hydrodynamic model (HW-HDM), the curl-free hydrodynamic model (CF-HDM), the shear forces hydrodynamic model (SF-HDM), and the quantum hydrodynamic model (Q-HDM). The analysis is conducted for a metallic spherical nanoparticle, as an example. The above hydrodynamic models are also compared with experiments available in literature. It is demonstrated that HW-HDM and QHDM outperform the other two hydrodynamic models.

Bistabilities and domain walls in weakly open quantum systems

Weakly pumped systems with approximate conservation laws can be efficiently described by (generalized) Gibbs ensembles if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the zz-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength \epsilonϵ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as \sim 1/\sqrt{\epsilon}∼1/ϵ while the density of domain walls is exponentially small in 1/\sqrt{\epsilon}1/ϵ. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.

Study on the Influence of Mesh Grouping on Numerical Simulation Results of Fish Cages

The Morison Model is widely applied in the numerical simulation for the hydrodynamics assessment of fish cage. In the Morison model, hydrodynamic forces are calculated based on twines. To reduce the computational time, mesh grouping methods (replacement of multiple meshes with less number of equivalent meshes) have been implemented widely in the calculation. However, as the hydrodynamic equation for a mesh is quite different under wave and current, it is not appropriate to use the classical mesh grouping. On the basis of basic hydrodynamic equations of the meshes with current and wave, this paper carried out the study about theoretical analysis of two methods (the equivalent area method and the equivalent volume method) of the mesh grouping, using main parameters of nets such as the diameter, solidity ratio and elastic modulus related to mesh grouping. A single-point mooring cage, of which tension and displacement could be calculated with finite element method, was selected as a case to carry out the verification of two mesh grouping methods. Flume model experiment was used to validate the accuracy of mesh grouping methods. The results indicated that, the equivalent area method has a higher accuracy in the pure current condition, while the equivalent volume method was more accurate in combined waves and current. The accuracy of results using mesh grouping to analyze hydrodynamics of nets within a certain range of grouping times could be insured with an improved calculation speed. This paper can provide practical advice on the mesh grouping process in the numerical simulation of fish cages and fishing gear.