Search results for " non-equilibrium"

Derivation of a Homogenized Two-Temperature Model from the Heat Equation

2014

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat: Coll\`ege de France Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pitman, Boston, London, 1982.]

Thermal solitons in nanotubes

2022

Starting from a recent proposal of a nonlinear Maxwell-Cattaneo equation for the heat transport with relaxational effects at nanoscale, in a special case of thermal-wave propagation we derive a nonlinear Schrodinger equation for the amplitudes of the heatflux perturbation. The complete integrability of the obtained equation is investigated in order to prove the existence of infinite conservation laws, as well as the existence of infinite exact solutions. In this regards, we have considered the simplest nontrivial solutions, namely, the bright and dark (thermal) solitons, which may be interesting for energy transport and for information transmission in phononic circuits. (c) 2022 Elsevier B.…

Local thermal non-equilibrium effects in the Darcy–Bénard instability of a porous layer heated from below by a uniform flux

2013

Abstract The influence of the lack of thermal equilibrium between the solid phase and the fluid phase on the convective instability in a porous medium is studied. A horizontal layer with parallel and impermeable bounding walls is considered. The lower wall is assumed to be isoflux, and the upper wall isothermal. The basic motionless state is perturbed with small-amplitude disturbances, so that a linear analysis of the instability is carried out with a streamfunction-temperature formulation of the local balance equations. Then, the governing equations are solved for the normal modes, leading to an eigenvalue problem for the neutral stability. This eigenvalue problem is solved analytically, t…

Effective temperature and scaling laws of polarized quantum vortex bundles

2011

Abstract An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In the quadratic approximation of the excitation energy in terms of the wave amplitude A, a previously known scaling relation between amplitude and wavelength k of Kelvin waves in polarized bundles, namely A ∝ k − 1 / 2 , follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.

Effects of Lévy noise on the dynamics of sine-Gordon solitons in long Josephson junctions

2015

We numerically investigate the generation of solitons in current-biased long Josephson junctions in relation to the superconducting lifetime and the voltage drop across the device. The dynamics of the junction is modelled with a sine-Gordon equation driven by an oscillating field and subject to an external non-Gaussian noise. A wide range of $\alpha$-stable L\'evy distributions is considered as noise source, with varying stability index $\alpha$ and asymmetry parameter $\beta$. In junctions longer than a critical length, the mean switching time (MST) from superconductive to the resistive state assumes a values independent of the device length. Here, we demonstrate that such a value is direc…

GEOMETRY OF DISSIPATIVE PHASE TRANSITIONS

The main objective of this thesis is the development of geometrical methods for the investigation of critical phenomena. In particular, a novel approach based on the Uhlmann curvature is introduced for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions. NESS-QPTs offer a unique arena where such a distinction fades off. We propose a method to reveal and quantitatively assess the quantum character of such critical phenomena. We apply this tool to a paradigmatic class of lattice fermion systems with local res…

Self-organization and nanostructural control in thin film heterojunctions.

2013

In spite of more than two-decades of studies of molecular self-assembly, the achievement of low cost, easy-to-implement and multi-parameter bottom-up approaches to address the supramolecular morphology in three-dimensional (3D) systems is still missing. In the particular case of molecular thin films, the 3D nanoscale morphology and function are crucial for both fundamental and applied research. Here we show how it is possible to tune the 3D film structure (domain size, branching, etc.) of thin film heterojunctions with nanoscale accuracy together with the modulation of their optoelectronic properties by employing an easy two-step approach. At first we prepared multi-planar heterojunctions w…

Thermoconvective instability and local thermal non-equilibrium in a porous layer with isoflux-isothermal boundary conditions

2014

The effects of lack of local thermal equilibrium between the solid phase and the fluid phase are taken into account for the convective stability analysis of a horizontal porous layer. The layer is bounded by a pair of plane parallel walls which are impermeable and such that the lower wall is subject to a uniform flux heating, while the upper wall is isothermal. The local thermal non-equilibrium is modelled through a two-temperature formulation of the energy exchange between the phases, resulting in a pair of local energy balance equations: one for each phase. Small-amplitude disturbances of the basic rest state are envisaged to test the stability. Then, the standard normal mode procedure is…

Many-particle theory for time-dependent quantum transport in nanostructures

2012

During the recent decades, molecular electronics has established its place as one of the promising fields in the nanoscience. The possibility to manufacture and control molecular junctions where single molecules are squeezed between the conducing electrodes has opened up new possibilities to develop nanoscale devices which could be employed as building blocks for future nanoelectronic applications. The driving force for this new branch of physics has been the experimental advances but also theoretical methods have been under intensive study and many theoretical tools have been developed to understand the electron transport processes in the nanoscale systems. This thesis focuses on developin…