Identifying diffusion processes in one-dimensional lattices in thermal equilibrium

In this Letter, I propose that a properly rescaled spatiotemporal correlation function of the energy density fluctuations may be applied to characterize the equilibrium diffusion processes in lattice systems with finite temperature. Applying this function, the diffusion processes in three one-dimensional nonlinear lattices are studied. The diffusion exponent is shown to be related to the diverging exponent of the thermal conductivity of a lattice through the relation , as has been proved based on the Lévy walk assumption. The diffusion behavior is explained in terms of solitons and phonons.     

Field-dependent conductivity and diffusion in a two-dimensional Lorentz gas

The conductivity and diffusion of a color-charged two-dimensional thermostatted Lorentz gas in a color field is studied by a variety of methods. In this gas, point particles move through a regular triangular array of soft scatterers, where, in the presence of a field, a nonequilibrium stationary state is reached by coupling to a Gaussian thermostat. The zero-field conductivity and diffusion coefficient are computed with equilibrium molecular dynamics dynamics from the Green-Kubo formula and the Einstein relation. Their values are consistent and approach those obtained by Machta and Zwanzig in the limit of hard (disk) scatterers. The field-dependent conductivity is obtained from its constitutive relation, from the coupling constant to the thermostat, and by using the recently derived conjugate pairing rule of Evans, Cohen, and Morriss, from the two maximal Lyapunov exponents of the Lorentz gas in the stationary state. All these methods give consistent results. Finally, elements of the field-dependent diffusion tensor have been computed. At zero field, they are consistent with the zero-field conductivity, but they vanish beyond a critical field strength, suggesting a dynamical phase transition at the critical field; the conductivity appears to remain finite, approaching a constant value for large field strengths.     

Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures

A novel theoretical basis for the evaluation of the thermal conductivity and the thermal diffusion ratios of dilute polyatomic gas mixtures is derived within the semi-classical isotropic kinetic theory. New expressions for species diffusion coefficients, thermal diffusion coefficients, and thermal diffusion ratios are also obtained by using an expansion vector based upon the total energy of the molecules. Finally, practical and accurate expressions for the thermal conductivity and the thermal diffusion ratios are derived by using the recent theory of iterative transport algorithms, as developed by the authors. The resulting expressions can be used in either theoretical calculations or computational models of multicomponent flows.     

Electrical conductivity and diffusion coefficient of electrons in a graphene bilayer

The electron diffusion coefficient and the electrical conductivity of a graphene bilayer in an external electric field with a strength vector directed along the graphene sheet are calculated theoretically. The evolution of the electron system is simulated using the Boltzmann kinetic equation in the relaxation-time semi-classical approximation. Analytic expressions are obtained for the electron diffusion coefficient and the electrical conductivity, and the nonlinear dependences of these quantities on the electric field are established. The dependences of these quantities on the control electrostatic potential between graphene layers are analyzed.     

Velocity of water diffusion through germanium oxide

The diffusion of water through an oxide film on germanium was investigated by measurement of the surface conductivity, and a relation was found between the coefficient of diffusion and the humidity of the ambient medium.     

Anomalous heat conduction and anomalous diffusion in one-dimensional systems

We establish a connection between anomalous heat conduction and anomalous diffusion in one-dimensional systems. It is shown that if the mean square of the displacement of the particle is =2Dt(alpha)(01) implies anomalous heat conduction with a divergent thermal conductivity (beta>0). More interestingly, subdiffusion (alpha<1) implies anomalous heat conduction with a convergent thermal conductivity (beta<0), and, consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our results.     

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.     

Study of a generalized thermoelastic diffusion bi-layered structures with variable thermal conductivity and mass diffusivity

Physical properties may change with temperature and concentration, especially in high temperature and concentration. In this work, the dynamical treatment of a bi-layered structure is implemented under the generalized thermoelastic diffusion theory. To distinguish from existed works, variable thermal conductivity and mass diffusivity of both media are considered. The model is subjected to a sudden thermal shock and a chemical shock, respectively. An analytical technique based on Laplace transform is adopted. Numerical results are evaluated and represented graphically, from which the effects of thermal conductivity and mass diffusivity of both media on the responses are discussed. And finally, some concluding remarks are summarized, based upon which the structure may be optimized by adopting suitable material parameter in both thermal and diffusive sense.     

Computed values of rotational collision number and diffusion coefficients for oxygen

Recent experimental data on thermal conductivity and viscosity are used to calculate values of rotational collision numbers and diffusion coefficients for oxygen in the temperature range 400–1600 K.     

On the behaviour of organic gel multi-size spray diffusion flames

The recently reported, experimentally observed, unusual behaviour of organic gellant-based fuel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion is incorporated in a phenomenological manner in a model of a two-dimensional arbitrary multi-size spray diffusion flame. Non-unity Lewis numbers are permitted for the fuel vapour and oxidant. A combined analytical/numerical solution of the governing equations is presented and used to investigate how a spray's initial polydispersity and the frequency of oscillatory evaporation influence the combustion field. It is demonstrated that the initial droplet size distribution and the frequency of evaporation of the burning gel droplets can have an acute impact both on the homogeneous diffusion flame shape, height and width and on the thermal field downstream of the flame front. Hot spots of individual (or clusters of) burning droplets can be created and under certain operating conditions can lead to hotter temperatures than experienced in the main homogeneous flame. The intensity of these hotspots, their number and location are sensitive to spray related parameters. In realistic combustion chambers there is a danger inherent in the existence of hotspots in undesirable regions as they can damage the structural integrity. Other computed results demonstrate that, in relation to the spray diffusion flames obtained using an equivalent purely liquid fuel spray, the use of a gel fuel spray can lead, under certain operating conditions, to a reduction in flame height and temperature. The latter effect is critical when considering flame extinction.     

AC-driven anomalous stochastic diffusion and chaotic transport in magnetic superlattices

We study regular and chaotic motion of the charge carriers in a two-dimensional electron gas subject to a spatially periodic magnetic field and to an AC electric field. We show how the interplay between the time-periodic electric and the spatially-periodic magnetic field leads to dynamical chaos and to fast stochastic diffusion of the electrons. The cases of a one-dimensional magnetic modulation with AC pumping and of a pure two-dimensional magnetic modulation are compared. We find the direct effect of anomalous diffusion and Lévy flights on the conductivity of a sample.     

Density and current response functions in strongly disordered electron systems: diffusion,electrical conductivity and Einstein relation

We study noninteracting quantum charged particles (electron gas) subject to a strong random potential and perturbed by a weak classical electromagnetic field. We examine consequences of gauge invariance and charge conservation in the space of Bloch waves. We use two specific forms of the Ward identity between the one- and two-particle averaged Green functions to establish exact relations between the density and current response functions. In particular, we find precise conditions under which we can extract the current-current from the density-density correlation functions and vice versa. We use these results to prove a formula relating the density response and the electrical conductivity in strongly disordered systems. We introduce quantum diffusion as a response function that reduces to the diffusion constant in the static limit. We then derive Ficks law, a quantum version of the Einstein relation and prove the existence of the diffusion pole in the quasistatic limit of the zero-temperature electron-hole correlation function. We show that the electrical conductivity controls the long-range spatial fluctuations of the electron-hole correlation function only in the static limit.Received: 10 June 2003, Published online: 22 September 2003PACS: 72.10.Bg General formulation of transport theory - 72.15.Eb Electrical and thermal conduction in crystalline metals and alloys - 72.15.Qm Scattering mechanisms and Kondo effect     

Lateral heat diffusion in layered structures: Theory and photothermal experiments

It is very important to understand how the heat diffuses in the case of nano objects and of layered structures. We will demonstrate that the lateral diffusion could be very different in the case of a good conductor layer deposited on a bad one and for the reverse (bad one on good substrate). Moreover, we will show how a thermoreflectance experiment can reveal both the thermal conductivity and the thermal diffusivity of thin layers deposited on substrates.     

Sodium diffusion in cryolite at elevated temperatures studied by quasielastic neutron scattering

Quasielastic neutron scattering (QENS) has been applied to study the sodium mobility on nanosecond time scales in the perovskite fluoride cryolite, Na₃AlF₆, at high temperatures. Up to T = 1153 K the diffusion of Na ions is well described by a diffusion process of jumps between six and eight-fold coordinated sites. Above this temperature, where a step-like increase in the electrical conductivity occurs, the jump length increases, which indicates additional jumps over larger distances. The electrical conductivity derived from the self-diffusion coefficient via the Nernst–Einstein relation and the corresponding activation energy are in excellent agreement with the previous conductivity measurements. We conclude that the jump diffusion of sodium ions is the dominant mechanism for the electrical conductivity in cryolite at high temperatures up to T = 1153 K.     

Influence of charge carrier diffusion on the stability of a charged drop of a finite-conductivity liquid

A dispersion relation for the capillary oscillations of a spherical drop of a viscous incompressible liquid with a charge transfer finite rate is derived and analyzed with emphasis on the role of diffusion. It is shown that diffusion has the strongest influence on the stability of rapidly damped quasi-periodic motions of a low-conductivity liquid. The instability growth rate of capillary oscillations grows with the charge diffusion coefficient and decreases with rising conductivity of the liquid.     

Effective thermal conductivity of condensed polymeric nanofluids (nanosolids) controlled by diffusion and interfacial scattering

Thermal properties of polymeric nanosolids, obtained by condensing the corresponding nanofluids, are investigated using photothermal techniques. The heat transport properties of two sets of polyvinyl alcohol (PVA) based nanosolids, TiO₂/PVA and Cu/PVA, prepared by condensing the respective nanofluids, which are prepared by dispersing nanoparticles of TiO₂ and metallic copper in liquid PVA, are reported. Two photothermal techniques, the photoacoustic and the photopyroelectric techniques, have been employed for measuring thermal diffusivity, thermal conductivity and specific heat capacity of these nanosolids. The experimental results indicate that thermal conduction in these polymer composites is controlled by heat diffusion through the embedded particles and interfacial scattering at matrix–particle boundaries. These two mechanisms are combined to arrive at an expression for their effective thermal conductivity. Analysis of the results reveals the possibility to tune the thermal conductivity of such nanosolids over a wide range using the right types of nanoparticles and right concentration.     

Effects of Metal Absorber Thermal Conductivity on Clear Plastic Laser Transmission Welding

In our previous study, metals have been used as absorbers in the clear plastic laser transmission welding. The effects of metal thermal conductivity on the welding quality are investigated in the present work. Four metals with distinctly different thermal conductivities, i.e., titanium, nickel, molybdenum, and copper, are selected as light absorbers. The lap welding is conducted with an 808 nm diode laser and simulation experiments are also conducted. Nickel electroplating test is carried out to minimize the side-effects from different light absorptivities of different metals. The results show that the welding with an absorber of higher thermal conductivity can accommodate higher laser input power before smoking, which produces a wider and stronger welding seam.The positive role of the higher thermal conductivity can be attributed to the fact that a desirable thermal field distribution for the molecular diffusion and entanglement is produced from the case with a high thermal conductivity.     

Electron diffusion and the Einstein relation in high-density gases

A model which used multiple-scattering theory to derive the density dependence of thermal electron mobilities, is employed to do the same for the diffusion coefficient. A surprising consequence of this is that the thermal Einstein relation is not the simple expression that is generally written and never verified, but rather one that depends on the density.     

Thermal conductivity and diffusion behaviour of lauric acid confined in carbon nanotubes as heat storage materials

The thermal conductivity and diffusion behaviour of lauric acid (LA) confined in single-walled carbon nanotube (CNT) with the filling ratio of 80% are investigated by molecular dynamics (MD) simulations. It is found that the concentric multilayer LA tubes are clearly observed under the interaction of CNT and LA and the hydrogen bonds (HB) among LA molecules in a confined environment. Due to the phonon scattering in low-frequency and the high-thermal conductivity characteristics of CNT, the axial thermal conductivity of CNT/LA is 49–57% lower than that of empty CNT and 115–188 times higher than that of crystal LA at the temperature range of 280 and 360?K. The confined LA molecules move as a whole cluster due to the long-lasting HB action and travel much faster than the bulk.     

Collective and single particle diffusion on surfaces

We review in this article the current theoretical understanding of collective and single particle diffusion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diffusion coefficients. This is followed by a section on the basic concepts involved in this field. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diffusion coefficients which can be defined properly only in the long length and time scales. The central role in this is played by the memory effects. We also discuss the concept of diffusion under nonequilibrium conditions. In the third section, a variety of different theoretical approaches that have been employed in studying surface diffusion such as first principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism are presented. These first three sections form an introduction to the field of surface diffusion. Section 4 contains subsections that discuss surface diffusion for various systems which have been investigated both experimentally and theoretically. The focus here is not so much on specific systems but rather on important issues concerning diffusion measurements or calculations. Examples include the influence of steps, diffusion in systems undergoing phase transitions, and the role of correlation and memory effects. Obviously, the choice of topics here reflects the interest and expertise of the authors and is by no means exhaustive. Nevertheless, these topics form a collection of issues that are under active investigation, with many important open questions remaining.