Concerning bounds on the transport and mechanical properties of multicomponent composite materials

The Hashin-Shtrikman and Walpole bounds for the transport properties and bulk modulus of multicomponent composite materials are shown to be attained in a wide range of cases. Thus in these cases the bounds are the best possible bounds that can be given in terms of the properties of the components and the volume fractions. For three-component materials new bounds are conjectured. The conjectured bounds are presumed to apply in the cases where the Hashin-Shtrikman and Walpole bounds are not attained.     

Static magneto-polarizability of cylindrical nanostructures

The static polarizability of cylindrical systems is shown to have a strong dependence on a uniform magnetic field applied parallel to the tube axis. This dependence is demonstrated by performing exact numerical diagonalizations of simple cylinders (rolled square lattices), armchair and zig-zag carbon nanotubes (rolled honeycomb lattices) for different electron-fillings. At low temperature, the polarizability as function of the magnetic field has a discontinuous character where plateau-like region are separated by sudden jumps or peaks. A one to one correspondence is pointed out between each discontinuity of the polarizability and the magnetic-field induced cross-over between the ground state and the first excited state. Our results suggest the possibility to use measurements of the static polarizability under magnetic field to get important informations about excited states of cylindrical systems such as carbon nanotubes. Received 29 March 2001 and Received in final form 8 August 2001     

Magnetic field and finite barrier-height effects on the polarizability of a shallow donor in a GaAs quantum wire

The binding energy and the polarizability are estimated for a shallow donor confined to move in a GaAs quantum well wire (QWW) with a rectangular and square cross-section under the action of an axial magnetic field. In this work, the Hass variational method within the effective mass approximation is used in the case of infinite and finite barrier QWWs. We present our results as a function of the size of the wire and for several values of the magnetic field strength. It is found that the magnetic field strongly reduces the polarizability. The finite barrier-height effect is important for smaller well widths. For higher fields and large wire, the effects of the magnetic field are predominant and the barrier potential is a small perturbation.     

Dielectric behaviour of anisotropic ionic crystals

In the case of cubic ionic crystals Havinga has shown that the temperature variation of dielectric constant could be described in terms of volume and temperature effects. By extending his formalism to anisotropic, ionic crystals it has been shown that unlike in cubic ionic crystals where the volume effect consists of a change in the number per unit volume of the polarizable particles and their polarizability with volume, in the case of anisotropic ionic crystals, in addition to these, a variation in the anisotropy of polarizability due to uneven thermal expansion also has to be taken into account. This method of analysis has been examined by taking rutile as an example.     

Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings

Recently we presented a new technique for numerical simulations of colloidal hard-sphere systems and showed its high efficiency. Here, we extend our calculations to the treatment of both 2- and 3-dimensional monodisperse and 3-dimensional polydisperse systems (with sampled finite Gaussian size distribution of particle radii), focusing on equilibrium pair distribution functions and structure factors as well as volume fractions of random close packing (RCP). The latter were determined using in principle the same technique as Woodcock or Stillinger had used. Results for the monodisperse 3-dimensional system show very good agreement compared to both pair distribution and structure factor predicted by the Percus-Yevick approximation for the fluid state (volume fractions up to 0.50). We were not able to find crystalline 3d systems at volume fractions 0.50–0.58 as shown by former simulations of Reeet al. or experiments of Pusey and van Megen, due to the fact that we used random start configurations and no constraints of particle positions as in the cell model of Hoover and Ree, and effects of the overall entropy of the system, responsible for the melting and freezing phase transitions, are neglected in our calculations. Nevertheless, we obtained reasonable results concerning concentration-dependent long-time selfdiffusion coefficients (as shown before) and equilibrium structure of samples in the fluid state, and the determination of the volume fraction of random close packing (RCP, glassy state). As expected, polydispersity increases the respective volume fraction of RCP due to the decrease in free volume by the fraction of the smaller spheres which fill gaps between the larger particles.     

From colloidal aggregation to spinodal decomposition in sticky emulsions

Aggregation mechanisms of emulsions at high initial volume fractions () is studied using light scattering. We use emulsion droplets which can be made unstable towards aggregation by a temperature quench. For deep quenches and , the aggregation mechanism is identified as diffusion-limited cluster aggregation (DLCA). An ordering of the clusters, which is reflected by a peak in the scattering intensity, is shown to result from the intercluster separation, exhibiting different scaling than that observed at lower volume fractions. This manifests an increasing similarity to spinodal decomposition observed as is increased. For and shallow quenches, different mechanisms, closer to spinodal decomposition, are observed. These results allow the subtle boundaries between DLCA and spinodal decomposition to be explored. Received: 7 April 1998 / Revised: 19 August 1998 / Accepted: 21 August 1998     

Electron polarizability of crystalline solids in quantizing magnetic fields and topological gap numbers

A theory of the static electron polarizability of crystals whose energy spectrum is modified by quantizing magnetic fields is presented. The polarizability is strongly affected by nondissipative Hall currents induced by the presence of crossed electric and magnetic fields: these can even change its sign. Results are illustrated in detail for a two-dimensional square lattice. The polarizability and the Hall conductivity are, respectively, linked to the two topological quantum numbers entering the so-called Diophantine equation. These numbers could in principle be detected in actual experiments.     

Two-dimensional soot distributions in buoyant turbulent fires

Spatially resolved two-dimensional soot volume fractions were measured using laser-induced incandescence in 7.1 cm methane and ethylene turbulent buoyant flames to study the distributions of soot in vertical and horizontal planes, and to provide data for soot model validation. Factors affecting the LII signals were considered including the laser energy profile and the laser attenuation effects. The absolute soot volume fractions were obtained by comparison to existing extinction measurements. The instantaneous soot images were collected to cover the entire flame height. Statistical quantities of soot volume fractions including mean, root mean square, probability density function, and spatial correlation coefficient were calculated at five downstream locations. The results show that instantaneous distributions of soot volume fractions exhibit significant differences compared to the ensemble averages, strong fluctuation around the mean, relatively homogeneous probability density function, and highly anisotropic spatial correlation.     

Rotational-vibrational polarizability operator for nonlinear X<Subscript>2</Subscript>Y molecules: Application to the calculation of the Raman spectrum of the H<Subscript>2</Subscript>O molecule

For nonlinear X₂Y molecules, an expression for the transformed polarizability operator is obtained with an accuracy of up to the second order of the theory of perturbation. This operator is applied to the calculation of the intensities of Raman lines of the H₂O molecule. The corrections to the polarizability of the molecule associated with the vibrational-rotational interaction are shown to considerably change the integral intensity of a pure rotational band. The dependence of the average polarizability of the molecule on the vibrational quantum number V ₂, describing deformation vibrations, is estimated.     

Collision-induced light scattering in low density neon gas

Experimental data on depolarized light scattering in neon gas are presented, for densities less than 60 amagats. The line shapes are found to be exponential, and the intensity proportional to the square of the density. The results are then discussed in terms of a moment analysis of binary collisions, to show that they can be interpreted neither in the standard DID model, nor using the anisotropic pair polarizability calculated by Heller, Harris and Gelbart or by Oxtoby and Gelbart. A possible form of the pair polarizability is presented and found to yield a satisfactory correlation function of the scattered field.     

纳米流体传质扩散系数的测定

本文建立光学实验测试系统,测量了不同温度条件下罗丹明B在不同粒子体积份额的纳米流体(Cu-乙二醇和Cu-水)中的质扩散系数。实验结果表明;罗丹明B在纳米流体中的扩散系数大于其在基液中的扩散系数,且扩散系数随着粒子体积份额的增大而增大;当粒子体积份额一定时,扩散系数随着温度的升高而增大。     

Weakly nonlinear analysis of the magnetorotational instability in a model channel flow

We show by means of a perturbative weakly nonlinear analysis that the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible rotating shear flow subject to a background vertical magnetic field in a thin channel gives rise to a Ginzburg-Landau equation for the disturbance amplitude. For small magnetic Prandtl number (P(m)), the saturation amplitude is proportional square root P(m) and the resulting momentum transport scales as R(-1), where R is the hydrodynamic Reynolds number. Simplifying assumptions, such as linear shear base flow, mathematically expedient boundary conditions, and continuous spectrum of the vertical linear modes, are used to facilitate this analysis. The asymptotic results are shown to comply with numerical calculations using a spectral code. They suggest that the transport due to the nonlinearly developed MRI may be very small in experimental setups with P(m)<1.     

Diffusive liquid propagation in porous and elastic materials: the case of foams under microgravity conditions

We report the results of fluid transport experiments in aqueous foams under microgravity. Using optical and electrical methods, the capillary motion of the foam fluid and the local liquid fractions are monitored. We show that foams can be continuously wetted up to high liquid fractions ( approximately 0.3), without any bubble motion instabilities. Data are compared to drainage models: For liquid fractions above 0.2, discrepancies are found and identified. These new results on foam hydrodynamics and structure can be useful for other poroelastic materials, such as plants and biological tissues.     

Diffusion limited cluster aggregation with irreversible slippery bonds

Irreversible diffusion limited cluster aggregation (DLCA) of hard spheres was simulated using Brownian cluster dynamics. Bound spheres were allowed to move freely within a specified range, but no bond breaking was allowed. The structure and size distribution of the clusters was investigated before gelation. The pair correlation function and the static structure factor of the gels were determined as a function of the volume fraction and time. Slippery bonds led to local densification of the clusters and the gels, with a certain degree of order. At low volume fractions densification of the clusters occurred during their growth, but at higher volume fractions it occurred mainly after gelation. At very low volume fractions, the large-scale structure (fractal dimension), size distribution and growth kinetics of the clusters was found to be close to that known for DLCA with rigid bonds. Restructuring of the gels continued for long times, indicating that aging processes in systems with strong attraction do not necessarily involve bond breaking. The mean-square displacement of particles in the gels was determined. It is shown to be highly heterogeneous and to increase with decreasing volume fraction.     

On new electromagnetic waves in a multicomponent insulator

The dispersion equation for additional transverse electromagnetic waves in a multicomponent amorphous insulator is analyzed in the vicinity of a narrow absorption line. Such waves can be excited due to spatial dispersion associated with fluctuation of the polarizability of insulator molecules. The conditions under which the dispersion relation of an additional (new) wave is mainly determined by the mean square of the polarizability fluctuations are determined.     

Statistical properties of wave transport through surface-disordered waveguides

We review some general statistical properties of wave transport through surface disordered waveguides. These systems are shown to present both striking similarities and differences with respect to quasi-one-dimensional waveguides with volume disorder. The statistical properties are analysed using extensive numerical calculations and random matrix theory results. The transport properties are characterized by the statistical behaviour of different transport coefficients that can be defined for both classical (light, microwaves, sound, etc.) and quantum (electrons) waves. In analogy with bulk-disordered systems, the behaviour of the waveguide conductance/resistance (defined for both classical and quantum waves) as a function of the system length defines three different transport regimes: ballistic, diffusive and localization. However, the coupling between waveguide modes presents significant differences with respect to the coupling induced by volume defects. For any incoming mode, there is a strong preference for the forward propagation through the lowest mode. For narrow waveguides, the statistics of reflection coefficients (reflected speckle pattern) present strong finite-size effects which can be surprisingly well described by random matrix theory. Special attention is paid to the fundamental problem of the transition between different regimes. The long-standing problems of the phase randomization process between ballistic and diffusive regimes and the evolution of the conductance statistical distribution in the transition from diffusion (Gaussian statistics) to localization (log normal statistics) are also discussed.     

Pressure and temperature dependences of the dielectric constant,Raman spectra and lattice constant of SnI42

The pressure and temperature dependences of the Raman frequencies, static dielectric constant and lattice constant of the molecular crystal SnI₄, were investigated. These results are combined to evaluate the pure volume and pure temperature (i.e. volume-independent) dependences of the molecular polarizability and of the Raman-active phonon self-energies. The pressure results also allow the separation of the Raman modes into external and internal modes of the crystal; the external modes exhibit a much stronger pressure dependence, and thereby larger Grüneisen parameters, than do the internal modes. The Raman frequencies increase (decrease) with increasing pressure (temperature) whereas the dielectric constant increases with both increasing pressure and temperature, emphasizing the importance of non-volume effects. In fact, it is found that the isobaric temperature dependence of the dielectric constant is dominated by the pure temperature dependence of the molecular polarizability. The pure volume dependence of the polarizability, on the other hand, is relatively small as is perhaps typical of most molecular crystals.     

Effective dielectric constant of dilute polydisperse suspensions of spheres

We study the effective dielectric constant of a dilute, polydisperse suspension of spheres embedded in a uniform background. We consider a frequency region where the dipole polarizability of individual spheres exhibits a resonance. We evaluate the effective dielectric constant to second order in the volume fraction employing the dipole approximation, which in previous work has been shown to be applicable in resonance. We apply our results to suspensions of spheres with identical and uniform dielectric constant, assuming a log-normal distribution of sphere radii.     

Coupled wave-like and diffusive motion of excitons

Using a new formalism for exciton transport, equations for the time evolution of the average of the square of the displacement of the exciton are presented and results obtained earlier by other authors are shown to emerge as particular cases of these equations.     

Measurements of extracellular volume fraction and capillary permeability in tissues using dynamic spin-lattice relaxometry: studies in rabbit muscles

Dynamic MR longitudinal R(1) relaxometry after administration of a gadolinium contrast bolus (Gd-DTPA) has been used for in vivo measurements of the extracellular volume fraction (v) and the capillary permeability (k min(-1)) in rabbit muscles to distinguish between red slow- and white fast-twitch muscle fiber types. For this purpose a protocol imaging sequence has been used which allows fast R(1) measurements during the contrast agent uptake. Physiological tissue parameters, k and v, were obtained by computing procedures assuming a simplified monoexponential plasma model. These were shown to be about twice as large in the slow-twitch semimembranosous proprius muscle (SP), containing 100% oxidative type-I fiber, that in the fast-twitch rectus femorus muscle (RF), containing only 6% type-I fiber type. The capillary permeability has been found to be 0.25 +/- 0.02 min(-1) for the (SP) and 0.10 +/- 0.01 min(-1) for the (RF). Similarly, the extracellular volume fractions were 0.189 +/- 0.015 and 0.082 +/- 0.006 respectively, in close agreement with literature data and experimental results obtained by invasive radionuclide measurements. For the pool of the 10 studied animals, no significant variation among animals was observed in the extracellular volume fraction and the capillary permeability for the different muscle fiber types. The dynamic relaxometry method used is easy to implement on conventional MR imagers and has potential applications in muscle diseases. The method has also potential applications for tissue characterization based on extracellular volume and capillary permeability quantification. In particular, the method can be used for the evaluation of tumors and their responses to therapies.