In recent years many experimentalists have reported an anomalously enhanced thermal conductivity in liquid suspensions of nanoparticles. Despite the importance of this effect for heat transfer applications, no agreement has emerged about the mechanism of this phenomenon, or even about the experimentally observed magnitude of the enhancement. To address these issues, this paper presents a combined experimental and theoretical study of heat conduction and particle agglomeration in nanofluids. On the experimental side, nanofluids of alumina particles in water and ethylene glycol are characterized using thermal conductivity measurements, viscosity measurements, dynamic light scattering, and other techniques. The results show that the particles are agglomerated, with an agglomeration state that evolves in time. The data also show that the thermal conductivity enhancement is within the range predicted by effective medium theory. On the theoretical side, a model is developed for heat conduction through a fluid containing nanoparticles and agglomerates of various geometries. The calculations show that elongated and dendritic structures are more efficient in enhancing the thermal conductivity than compact spherical structures of the same volume fraction, and that surface (Kapitza) resistance is the major factor resulting in the lower than effective medium conductivities measured in our experiments. Together, these results imply that the geometry, agglomeration state, and surface resistance of nanoparticles are the main variables controlling thermal conductivity enhancement in nanofluids.

We report a hydrodynamic analysis of the long-time behavior of the linear and angular velocity autocorrelation functions of an isolated colloid particle constrained to have quasi-two-dimensional motion, and compare the predicted behavior with the results of lattice-Boltzmann simulations. Our analysis uses the singularity method to characterize unsteady linear motion of an incompressible fluid. For bounded fluids we construct an image system with a discrete set of fundamental solutions of the Stokes equation from which we extract the long-time decay of the velocity. For the case that there are free slip boundary conditions at walls separated by $H$ particle diameters, the time evolution of the parallel linear velocity and the perpendicular rotational velocity following impulsive excitation both correspond to the time evolution of a two-dimensional (2D) fluid with effective density ${\rho }_{2D}=\rho H$. For the case that there are no slip boundary conditions at the walls, the same types of motion correspond to 2D fluid motions with a coefficient of friction $\xi ={\pi }^2\nu /H^2$ modulo a prefactor of order 1, with $\nu$ the kinematic viscosity. The linear particle motion perpendicular to the walls also experiences an effective frictional force, but the time dependence is proportional to $t^{-2}$, which cannot be related to either pure 3D or pure 2D fluid motion. Our incompressible fluid model predicts correct self-diffusion constants but it does not capture all of the effects of the fluid confinement on the particle motion. In particular, the linear motion of a particle perpendicular to the walls is influenced by coupling between the density flux and the velocity field, which leads to damped velocity oscillations whose frequency is proportional to $c_s/H$, with $c_s$ the velocity of sound. For particle motion parallel to no slip walls there is a slowing down of a density flux that spreads diffusively, which generates a long-time decay proportional to $t^{-1}$.

We present the results of a theoretical study of internal microstructures in two-dimensional ferrofluids without an external magnetic field. Recent experiments with these systems demonstrate the appearance of linear chains and ringlike and various branched clusters. We consider linear chains, rings, and branched Y-like “forks.” In the model of an ideal gas of noninteracting clusters, taking into account interactions only between nearest particles, we estimate the equilibrium distribution functions of the chains, forks, and rings over a number of particles in them. Our results show that for experimentally realistic situations the majority of particles are united into chains and forks, the number of particles in the rings being relatively small. The results of calculations are in qualitative agreement with experiments.

Axial trapping through a dielectric interface is investigated in the framework of the angular spectrum representation and of the generalized Lorenz-Mie theory. We determine the optical force for an arbitrarily polarized non-paraxial, strongly aberrated, axially symmetric focusing beam and apply this description to the case of an arbitrarily positioned dielectric microsphere, commonly employed in optical tweezers, not taking into account the contribution of evanescent waves at the interface. We derive the analytical expression of the force profile, finding that the incident polarization does not affect the axial optical force. In addition, we derive an approximated expression for the axial force as a function of beam displacement just outside the microsphere and we show how the information provided by the ripple structure of the optical trapping efficiency versus sphere displacement curve, due to the aberration effect, could be exploited to calibrate the bead axial position versus the experimental beam positioning controls.

In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of noninteracting particles through a small hole due to the integrable structure of the phase space of the system. Furthermore, for a certain hole position, a saturation value in the decay that can be tuned arbitrarily by varying the eccentricity of the ellipse is observed and explained. When harmonic boundary oscillations are applied, this saturation value, caused by librator-type orbits, is gradually destroyed via two fundamental processes which are discussed in detail. As a result, an amplitude-dependent emission rate is obtained in the long-time behavior of the decay, suggesting that the driven elliptical billiard can be used as a controllable source of particles.

Motivated by stochastic models of climate phenomena, the steady state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady states provide a constraint on the character of these fluctuations. The properties of the fluctuations which are unconstrained by the fluctuation theorem are investigated and related to the model parameters. The irreversibility of trajectory segments, which satisfies a fluctuation theorem, is used as a measure of nonequilibrium fluctuations. The moments of the irreversibility probability density function (pdf) are found and the pdf is seen to be non-Gaussian. The average irreversibility goes to zero for short and long trajectory segments and has a maximum for some finite segment length, which defines a characteristic time scale of the fluctuations. The initial average irreversibility growth rate is equal to the average entropy production and is related to noise amplification. For systems with a separation of deterministic time scales, modes with time scales much shorter than the trajectory time span and whose noise amplitudes are not asymptotically large, do not, to first order, contribute to the irreversibility statistics, providing a potential basis for dimensional reduction.

The applicability of constitutive models based on kinetic theory for dense granular flows is examined. First, we calculate the average coordination number of a particle in a dense flow down an inclined plane using discrete element simulations that employ a linear spring-dashpot model for particle interactions. It is found that the average coordination number decreases as the spring constant increases at constant coefficient of restitution, and is less than 1 for the values of spring constant corresponding to materials such as sand and glass beads. The Bagnold coefficients, which are the ratios of the different components of the stress and the square of the strain rate, are calculated using both discrete element (DE) simulations and event driven (ED) simulations; collisions are considered to be instantaneous in the latter simulations. It is found that the theoretical predictions of the Bagnold coefficients are in quantitative agreement with both DE and ED simulations provided the pair distribution function obtained from the simulations is inserted into the theory. However, it is found that the pair distribution function in a sheared granular flow is significantly larger than that in an equilibrium fluid of elastic particles.

A random matrix model to describe the coupling of $m$-fold symmetry is constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that such an experimental and theoretical study may supply a powerful means to discern the intrinsic symmetry of physical systems.

We examine one- and two-dimensional models of linearly coupled lattices of the discrete-nonlinear-Schrödinger type. Analyzing ground states of the system with equal powers (norms) in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the total power. Asymmetric states, with unequal powers in their components, emerge through a subcritical pitchfork bifurcation, which, for very weakly coupled lattices, changes into a supercritical one. We identify the stability of various solution branches. Dynamical manifestations of the symmetry breaking are studied by simulating the evolution of the unstable branches. The results present the first example of spontaneous symmetry breaking in two-dimensional lattice solitons. This feature has no counterpart in the continuum limit because of the collapse instability in the latter case.

Towards getting the full-scale solutions to particle-laden flows, a multidirect forcing technique and immersed boundary method are proposed in the present work. The immersed solid boundary is represented by Lagrangian points and the no-slip condition is efficiently satisfied by exerting multidirect forcing. The hydrodynamic interactions between the stationary or moving solid boundary and the Newtonian fluid are able to be accurately described. This method is simple but efficient which is validated by simulating the flows around a stationary circular disc at different Reynolds numbers and the free sedimentation of a particle. The predicted results agree well with previous experimental and numerical data. When applying this method to study particle sedimentation near a vertical wall, the rotation shifting phenomenon is observed besides the anomalous rolling and the lateral migration.

Morphological differences in semicrystalline polymers due to different crystallization conditions have implications for the chain motion. The local dynamics in the noncrystalline regions of solution-crystallized linear polyethylene is lower than in a melt-crystallized sample, but the opposite is observed for chain diffusion between noncrystalline and crystalline regions. The activation enthalpy for chain diffusion, however, is the same, indicating that entropic differences in the noncrystalline regions strongly influence the chain diffusion of the same polymer in different morphologies.

We present a general theory of thermoacoustic phenomena in one phase states of one-component fluids. Singular behavior is predicted in supercritical fluids near the critical point. In a one-dimensional geometry we start with linearized hydrodynamic equations taking into account the effects of heat conduction in the boundary walls and the bulk viscosity. We introduce a coefficient $Z\left(\omega \right)$ characterizing reflection of sound with frequency $\omega$ at the boundary in a rigid cell. As applications, we examine acoustic eigenmodes, response to time-dependent perturbations, and sound emission and reflection. Resonance and rapid adiabatic changes are noteworthy. In these processes, the role of the thermal diffusion layers is enhanced near the critical point because of the strong critical divergence of the thermal expansion.

We study the level statistics of an interacting multiqubit system, namely the kicked Ising spin chain, in the regime of quantum chaos. Long range quasienergy level statistics show effects analogous to the ones observed in semiclassical systems due to the presence of short classical periodic orbits, while short range level statistics display perfect statistical agreement with random matrix theory. Even though our system possesses no classical limit, our results suggest existence of an important nonuniversal system specific behavior at short time scale, which clearly goes beyond finite size effects in random matrix theory.

We use a continuous acquisition, high-speed camera with integrated centroid tracking to simultaneously measure the positions of a ring of micron-sized particles held in holographic optical tweezers. Hydrodynamic coupling between the particles gives a set of eigenmodes, each one independently relaxing with a characteristic decay rate (eigenvalue) that can be measured using our positional data. Despite the finite particle size, we find an excellent agreement between the measured eigenvalues and those numerically predicted by Oseen theory applied to the two-dimensional (2D) ring geometry. Particle motions are also analyzed in terms of the alternative eigenmode set obtained by wrapping onto the ring the eigenmodes of a 1D periodic chain. We identify the modes for which the periodic chain is a good approximation to the ring and those for which it is not.

Charged colloidal particles whose interacting potential is governed by a short-range attraction and a long-range screened electrostatic repulsion contributions form aggregates whose shape, size, and overall charge are sensitively dependent on the balance between attraction and repulsion. In some cases, this class of colloidal systems shows an equilibrium cluster phase, where particles associate and dissociate reversibly into clusters. When the aggregation of the charged particles is induced by adding an oppositely charged polyion, very close to the isoelectric condition, the interaggregate interactions become very strong and a dynamical arrested state seems to occur. We provide some experimental evidences of this structural arrest in a colloid system composed by vesicles built up by a cationic lipid stuck together by an oppositely charged linear polyion, by means of the combined use of static and dynamic light scattering technique complemented by laser Doppler electrophoretic measurements. Our results show that the second virial coefficient, which is related to the potential of mean force between two adjacent aggregates, markedly increases in the vicinity of the isoelectric point. We interpret this increase as a print of strong interparticle interactions, yielding to a dynamical arrested state via cluster growth.

Soft x-ray spectromicroscopy has been used to investigate the degree of the molecular alignment of sulfonated benzo[de]benzo[4.5]imidazo[2,1-a]isoquinoline[7,1], a lyotropic chromonic liquid crystal (LCLC). LCLC thin films cast from concentrated aqua solution $(20\%\mathrm{wt.})$, aligned by shear flow and dried, show strong linear dichroism in their C-, N-, O-, S-$K$ edge near edge x-ray spectra (NEXAFS). The carbon $K$ edge has been used for quantitative evaluation of the orientational texture of the films at a submicron spatial scale. This has verified there is predominantly in-plane alignment of the LC director. To highlight the role of hydrophobic-hydrophilic interactions, two stereoisomers of the same dye has been synthesized with different positioning of terminal sulfonate groups, in the form of a mixture of isomers with sulfonate groups in 2,10 and 2,11 positions (Y104 compound) and in a 5,10-disulfo arrangement (Y105). Both compounds develop characteristic herringbone-type texture with similar domain sizes. Polarized optical microscopy and higher resolution x-ray microscopy show sinusoidal-like undulations of the molecular director, with occasional crisscross appearance. Such behavior is found to be consistent with earlier observation of striations, characteristic of the columnar phase. The drastic difference in the degree of undulation ($\pm 15°$ in Y104 and $\pm 7°$ in Y105 films) and long period of undulation (approaching the film thickness) requires further analysis. It was also found that the degree of in-plane order within domains changes from 0.8 for Y104 to $>0.9$ in Y105 films.

It is demonstrated in electro-optic experiments that an external electric field of the order of ${10}^5\text{V}/\text{m}$ induces persisting texture transitions in a nematic phase formed by bent-core mesogens. The field-induced metastable state is identified by its optical and electric properties. After the field is switched off, the original and induced states can coexist in domains for about one hour in planar sandwich cells. During this time, the induced domains gradually shrink but they can be stabilized in moderate electric fields. The occurrence of similar domains in homeotropic cells suggests that the transition into a metastable biaxial state is observed. In the field-free planar ground state, the formation of inversion walls is observed inside the metastable domains.

Recent work has shown that the resistive force arising from viscous effects within the pore region could explain observed translocation times in certain experiments involving voltage-driven translocations of DNA through nanopores [Ghosal, Phys. Rev. E 71, 051904 (2006); Phys. Rev. Lett. 98, 238104 (2007)]. The electrokinetic flow inside the pore and the accompanying viscous effects also play a crucial role in the interpretation of experiments where the DNA is immobilized inside a nanopore [Keyser et al., Nat. Phys. 2, 473 (2006)]. In this paper the viscous force is explicitly calculated for a nanopore of cylindrical geometry. It is found that the reductions of the tether force due to viscous drag and due to charge reduction by Manning condensation are of similar size. The result is of importance in the interpretation of experimental data on tethered DNA.

We analyze the behavior of an ensemble of inertial particles in a one-dimensional smooth Gaussian velocity field, in the limit of large inertia, but considering a finite correlation time for the random field. The amplitude of the concentration fluctuations is characterized by slow decay at large inertia and a much larger correlation length than that of the random field. The fluctuation structure in velocity space is very different from predictions from short-time correlated random velocity fields, with only few particle pairs crossing at sufficiently small relative velocity to produce correlations. Concentration fluctuations are associated with depletion of the relative velocity variance of colliding particles.

Subdiffusion in the presence of an external force field can be described in phase space by the fractional Klein-Kramers equation. In this paper, we explore the stochastic structure of this equation. Using a subordination method, we define a random process whose probability density function is a solution of the fractional Klein-Kramers equation. The structure of the introduced process agrees with the two-stage scenario underlying the anomalous diffusion mechanism, in which trapping events are superimposed on the Langevin dynamics. We develop an efficient computer algorithm for visualization of fractional Klein-Kramers dynamics and present some simulation results based on Monte Carlo techniques.