Solution of Time Dependent Joule Heat Equation for a Graphene Sheet Under Thomson Effect

We address a physics-based solution of joule heating phenomenon in a single-layer graphene (SLG) sheet under the presence of Thomson effect. We demonstrate that the temperature in an isotopically pure (containing only C-12) SLG sheet attains its saturation level quicker than when doped with its isotopes (C-13). From the solution of the joule heating equation, we find that the thermal time constant of the SLG sheet is in the order of tenths of a nanosecond for SLG dimensions of a few micrometers. These results have been formulated using the electron interactions with the inplane and flexural phonons to demonstrate a field-dependent Landauer transmission coefficient. We further develop an analytical model of the SLG specific heat using the quadratic (out of plane) phonon band structure over the room temperature. Additionally, we show that a cooling effect in the SLG sheet can be substantially enhanced with the addition of C-13. The methodologies as discussed in this paper can be put forward to analyze the graphene heat spreader theory.

Temperature dependent electrical behaviour of Cu2SnS3 films

The temperature dependent electrical properties of the dropcasted Cu2SnS3 films have been measured in the temperature range 140 K to 317 K. The log I versus root V plot shows two regions. The region at lower bias is due to electrode limited Schottky emission and the higher bias region is due to bulk limited Poole Frenkel emission. The ideality factor is calculated from the ln I versus V plot for different temperatures fitted with the thermionic emission model and is found to vary from 6.05 eV to 12.23 eV. This large value is attributed to the presence of defects or amorphous layer at the Ag / Cu2SnS3 interface. From the Richardson's plot the Richardson's constant and the barrier height were calculated. Owing to the inhomogeneity in the barrier heights, the Richardson's constant and the barrier height were also calculated from the modified Richardson's plot. The I-V-T curves were also fitted using the thermionic field emission model. The barrier heights were found to be higher than those calculated using thermionic emission model. From the fit of the I-V-T curves to the field emission model, field emission was seen to dominate in the low temperature range of 140 K to 177 K. The temperature dependent current graphs show two regions of different mechanisms. The log I versus 1000/T plot gives activation energies E-a1 = 0.367095 - 0.257682 eV and E-a2 = 0.038416 - 0.042452 eV. The log ( I/T-2) versus 1000/T graph gives trap depths Phi(o1) = 0.314159 - 0.204752 eV and Phi(o2) = 0.007425- 0.011163 eV. With increasing voltage the activation energy E-a1 and the trap depth Phi(o1) decrease. From the ln (IT1/ 2) versus 1/T-1/ 4 graph, the low temperature region is due to variable range hopping mechanism and the high temperature region is due to thermionic emission. (C) 2014 Author(s).

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.

State Vector: A New Approach to Prediction of the Failure of Brittle Heterogeneous Media and Large Earthquakes

The concept of state vector stems from statistical physics, where it is usually used to describe activity patterns of a physical field in its manner of coarsegrain. In this paper, we propose an approach by which the state vector was applied to describe quantitatively the damage evolution of the brittle heterogeneous systems, and some interesting results are presented, i.e., prior to the macro-fracture of rock specimens and occurrence of a strong earthquake, evolutions of the four relevant scalars time series derived from the state vectors changed anomalously. As retrospective studies, some prominent large earthquakes occurred in the Chinese Mainland (e.g., the M 7.4 Haicheng earthquake on February 4, 1975, and the M 7.8 Tangshan earthquake on July 28, 1976, etc) were investigated. Results show considerable promise that the time-dependent state vectors could serve as a kind of precursor to predict earthquakes.

Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium

We investigate the influence of ionization on the propagation and spectral effects of a few-cycle ultrashort laser pulse in a two-level medium. It is found that when the fractional ionization is weak, the production of higher spectral components makes no difference. However, when the two states are essentially depleted before the peak of the laser pulse, the impact of ionization on the higher spectral components is very significant.

The instability of fluids with time dependent heating

The stability of a fluid having a non-uniform temperature stratification is examined analytically for the response of infinitesimal disturbances. The growth rates of disturbances have been established for a semi-infinite fluid for Rayleigh numbers of 10³, 10⁴, and 10⁵ and for Prandtl numbers of 7.0 and 0.7.

The critical Rayleigh number for a semi-infinite fluid, based on the effective fluid depth, is found to be 32, while it is shown that for a finite fluid layer the critical Rayleigh number depends on the rate of heating. The minimum critical Rayleigh number, based on the depth of a fluid layer, is found to be 1340.

The stability of a finite fluid layer is examined for two special forms of heating. The first is constant flux heating, while in the second, the temperature of the lower surface is increased uniformly in time. In both cases, it is shown that for moderate rates of heating the critical Rayleigh number is reduced, over the value for very slow heating, while for very rapid heating the critical Rayleigh number is greatly increased. These results agree with published experimental observations.

The question of steady, non-cellular convection is given qualitative consideration. It is concluded that, although the motion may originate from infinitesimal disturbances during non-uniform heating, the final flow field is intrinsically non-linear.

DEVELOPMENT AND APPLICATIONS OF TIME-DEPENDENT DENSITY MATRIX FUNCTIONAL THEORY

En esta tesis estudiamos las teorías sobre la Matriz Densidad Reducida (MDR) como un marco prometedor. Nos enfocamos sobre esta teorías desde dos aspectos: Primero, usamos algunos modelos sencillos hechos con dos partículas las cuales estan armónicamente confinadas como una base para ilustrar la utilidad de la matriz densidad. Para tales sistemas, usamos la MDR de un cuerpo para calcular algunas cantidades de interés tales como densidad de momentum. Posteriormente obtenemos los orbitales naturales y su número de ocupación para algunos de los modelos, y en uno de los casos expresamos la MDR de dos cuerpos de manera exacta en términos de la MDR de un cuerpo. También usamos el teorema diferencial del virial para establecer una descripción unificada de la familia entera de estos sistemas modelo en términos de la densidad. En la seguna parte cambiamos a casos fuera del equilibrio y analizamos la así llamada jerarquía BBGKY de ecuaciones para describir la evolución temporal de un sistema de muchos cuerpos en términos de sus MDRs (a todos los órdenes). Proveemos un exhaustivo estudio de los desafíos y problemas abiertos ligados a la truncación de tales jerarquías de ecuaciones para hacerlas aplicables. Restringimos nuestro análisis a la evolución acoplada de la MDR de uno y dos cuerpos, donde los efectos de correlación de alto orden estan embebidos dentro de la aproximación usada para cerrar las ecuaciones. Probamos que dentro de esta aproximación, el número de electrones y la energía total se conservan, sin importar la aproximación usada. Luego, demostramos que aplicando los esquemas de truncación de estado base para llevar los electrones a comportamientos indeseables y no físicos, tales como la violación e incluso la divergencia en la densidad electrónica local, tanto en regímenes correlacionados débiles y fuertes.

Mechanical and leaching behaviour of slag-cement and lime-activated slag stabilised/solidified contaminated soil.

Stabilisation/solidification (S/S) is an effective technique for reducing the leachability of contaminants in soils. Very few studies have investigated the use of ground granulated blast furnace slag (GGBS) for S/S treatment of contaminated soils, although it has been shown to be effective in ground improvement. This study sought to investigate the potential of GGBS activated by cement and lime for S/S treatment of a mixed contaminated soil. A sandy soil spiked with 3000mg/kg each of a cocktail of heavy metals (Cd, Ni, Zn, Cu and Pb) and 10,000mg/kg of diesel was treated with binder blends of one part hydrated lime to four parts GGBS (lime-slag), and one part cement to nine parts GGBS (slag-cement). Three binder dosages, 5, 10 and 20% (m/m) were used and contaminated soil-cement samples were compacted to their optimum water contents. The effectiveness of the treatment was assessed using unconfined compressive strength (UCS), permeability and acid neutralisation capacity (ANC) tests with determination of contaminant leachability at the different acid additions. UCS values of up to 800kPa were recorded at 28days. The lowest coefficient of permeability recorded was 5×10(-9)m/s. With up to 20% binder dosage, the leachability of the contaminants was reduced to meet relevant environmental quality standards and landfill waste acceptance criteria. The pH-dependent leachability of the metals decreased over time. The results show that GGBS activated by cement and lime would be effective in reducing the leachability of contaminants in contaminated soils.