Structural transitions and dynamical regimes for directional locking of vortices and colloids driven over periodic substrates

We examine collective dynamical locking effects for superconducting vortices and colloids interacting with square and triangular substrate arrays under a slowly rotated dc drive. A rich variety of lattice configurations associated with a series of steps in the velocity-force curves occur during the locking transitions. These include triangular, square, smectic, and disordered particle arrangements that can be identified using the structure factor. We show that the step widths vary with the ratio of the number of particles to the number of pinning sites. Unlike a static system, where matching effects occur at simple integer commensuration ratios, we find dynamical commensuration effects that arise when an integer number of particle chains flow between rows of pins. We identify two distinct types of locking as a function of substrate strength, distinguished by whether the particles flow along or between the pinning rows.     

Dynamics of step bunching in heteroepitaxial growth on vicinal substrates

When a heteroepitaxial film is grown on a vicinal substrate, the terrace steps at the growth front may bunch together to relieve strain, resulting in a rough surface. On the other hand, proper manipulation of the growth kinetics may suppress the inherent bunching instability, thus preserving step-flow growth. Here we show that the step dynamics in the early stages of growth can already determine whether the bunching instability is truly suppressed, prior to bunching actually taking place in the unstable regime. We determine the critical film thickness above which steps will bunch and exploit its scaling properties and usefulness for extracting intrinsic energy parameters. Experimental studies of SrRuO(3) films grown on vicinal SrTiO(3) substrates clearly establish the existence of the critical film thickness in step bunching.     

Virial expansion for charged colloids and electrolytes

Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (“virial”) expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters d₊ and d_- and charge valences q₊ and q_- of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically d ₊∼d _- and q ₊∼q _-, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient. Received 6 September 2001 / Received in final form 20 May 2002 Published online 24 September 2002     

Dynamics and hysteresis of the contact line between liquid hydrogen and cesium substrates

We have measured both the hysteresis and the dynamics of the edge of a liquid hydrogen meniscus on several solid cesium substrates. We find that the dynamics of the contact line is thermally activated. For all substrates, we find that the activation energy is of the order of the hysteresis. We show that the pinning of the contact line on mesoscopic defects of the Cs substrate is likely to control both the hysteresis and the dynamics of the contact line at low velocity, close to the depinning threshold. Such a mechanism could be relevant also for simple room-temperature systems.     

Weak and strong coupling theories for polarizable colloids and nanoparticles

A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nanoparticles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far field. All the results are compared with the Monte?Carlo simulations, showing an excellent agreement between the theory and the simulations.     

Nonequilibrium Linear Response for Markov Dynamics,II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle.     

Nematic-wetted colloids in the isotropic phase: pairwise interaction, biaxiality, and defects

We calculate the interaction between two spherical colloidal particles embedded in the isotropic phase of a nematogenic liquid. The surface of the particles induces wetting nematic coronas that mediate an elastic interaction. In the weak wetting regime, we obtain exact results for the interaction energy and the texture, showing that defects and biaxiality arise, although they are not topologically required. We evidence rich behaviors, including the possibility of reversible colloidal aggregation and dispersion. Complex anisotropic self-assembled phases might be formed in dense suspensions.     

The unbearable heaviness of colloids: facts, surprises, and puzzles in sedimentation

Sedimentation has played a key role in the development of colloid science. In fact, it is because of the celebrated experiments by Perrin, yielding a concrete demonstration of molecular reality and giving strong support to Einstein's theory of Brownian motion, that colloids enter the realm of basic physics. Subsequent investigations have shown that a lot more can be learnt both from sedimentation equilibrium and from particle settling dynamics. These advances, together with new experimental approaches, will be reviewed in this paper. Yet, we shall also show that inquiring about gravity settling is far from being a closed matter: for instance, the concept of buoyancy for a settling colloidal mixture is far from being obvious. Moreover, sedimentation holds novel surprises, such as colloidal inflations and settling disasters, showing that a simple external field like gravity may induce mind-boggling, and theoretically challenging effects.     

Photocurrent, rectification, and magnetic field symmetry of induced current through quantum dots

We report mesoscopic dc current generation in an open chaotic quantum dot with ac excitation applied to one of the shape-defining gates. For excitation frequencies large compared to the inverse dwell time of electrons in the dot (i.e., GHz), we find mesoscopic fluctuations of induced current that are fully asymmetric in the applied perpendicular magnetic field, as predicted by recent theory. Conductance, measured simultaneously, is found to be symmetric in field. In the adiabatic (i.e., MHz) regime, in contrast, the induced current is always symmetric in field, suggesting its origin is mesoscopic rectification.     

Precise full-field distortion rectification and evaluation method for a digital projector

Digital projectors have been widely used in many accuracy-sensitive fields. Although some calibration methods have been proposed to obtain the intrinsic parameters for a digital projector, especially the radial and tangential distortion, there are few studies on how to rectify the projected image to obtain an ideal projection pattern and further evaluate the results. In this paper, a precise full-field image rectification technique is proposed based on the principle of projector calibration. The pixel remapping and interpolation techniques are detailed step by step. All of the method’s steps maintain subpixel accuracy. Moreover, a full-field verification method is presented to evaluate the effectiveness of the projector distortion procedure using a full-field phase map. A full-field non-linear distortion distribution map can be generated to represent distortion characteristics of nearly all the pixels of a projector in a very intuitive way. The experimental results validate and show the effectiveness of the proposed full-field rectification technique and evaluation method.     

Phase diagram of a polydisperse soft-spheres model for liquids and colloids

The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon.     

Mixtures of anisotropic and spherical colloids: Phase behavior, confinement, percolation phenomena and kinetics

Purely entropic systems such as suspensions of hard rods, platelets and spheres show rich phase behavior. Rods and platelets have successfully been used as models to predict the equilibrium properties of liquid crystals for several decades. Over the past years hard particle models have also been studied in the context of non-equilibrium statistical mechanics, in particular regarding the glass transition, jamming, sedimentation and crystallization. Recently suspensions of hard anisotropic particles also moved into the focus of materials scientists who work on conducting soft matter composites. An insulating polymer resin that is mixed with conductive filler particles becomes conductive when the filler percolates. In this context the mathematical topic of connectivity percolation finds an application in modern nano-technology. In this article, we briefly review recent work on the phase behavior, confinement effects, percolation transition and phase transition kinetics in hard particle models. In the first part, we discuss the effects that particle anisotropy and depletion have on the percolation transition. In the second part, we present results on the kinetics of the liquid-to-crystal transition in suspensions of spheres and of ellipsoids.     

Self-Similarity,Operators and Dynamics

We construct a large class of infinite self-similar (fractal, hierarchical or substitution) graphs and show, under a certain strong symmetry assumption, that the spectrum of the Laplacian can be described in terms of iterations of an associated rational function (so-called 'spectral decimation'). We prove that the spectrum consists of the Julia set of the rational function and a (possibly empty) set of isolated eigenvalues which accumulate to the Julia set. In order to obtain our results, we start with investigation of abstract spectral self-similarity of operators.     

Diffusing wave spectroscopy of dense colloids: Liquid,crystal and glassy states

Using intensity autocorrelation of multiply scattered light, we show that the increase in interparticle interaction in dense, binary colloidal fluid mixtures of particle diameters 0.115μm and 0.089μm results in freezing into a crystalline phase at volume fractionφ of 0.1 and into a glassy state atφ=0.2. The functional form of the field autocorrelation functiong ⁽¹⁾(t) for the binary fluid phase is fitted to exp[−γ(6k ₀ ² D _eff t)^1/2] wherek ₀ is the magnitude of the incident light wavevector andγ is a parameter inversely proportional to the photon transport mean free pathl*. TheD _eff is thel* weighted average of the individual diffusion coefficients of the pure species. Thel* used in calculatingD _eff was computed using the Mie theory. In the solid (crystal or glass) phase, theg ⁽¹⁾(t) is fitted (only with a moderate success) to exp[−γ(6k ₀ ² W(t))^1/2] where the mean-squared displacementW(t) is evaluated for a harmonically bound overdamped Brownian oscillator. It is found that the fitted parameterγ for both the binary and monodisperse suspensions decreases significantly with the increase of interparticle interactions. This has been justified by showing that the calculated values ofl* in a monodisperse suspension using Mie theory increase very significantly with the interactions incorporated inl* via the static structure factor.     

Stilbazolium merocyanine dye determination in different solutions,concentrations and colloids using SERS

Surface‐enhanced Raman scattering (SERS) measurements were carried out on stilbazolium merocyanine dye in methanol and pyridine solvents. Both solutions were measured in a series of concentrations covering a range of 5 × 10⁻⁵ M to 5 × 10⁻⁸ M . In these measurements, Ag and Au colloids were used, and the results have shown that Ag colloids yield better enhancement in the Raman spectra of this dye. Moreover, the effect of adding NaCl solution to the SERS samples was also studied. All measurements were carried out using the state‐of‐the‐art ChiralRaman instrument, which utilizes a 532 nm laser source. We report here on the success of using SERS to obtain Raman spectra of merocyanine dye at very low concentrations in an attempt to find a new approach that can be used for further investigations of the dye. The SERS spectra are reported here, and the results from different solutions, colloids, concentrations and pH values are compared. Copyright © 2006 John Wiley & Sons, Ltd.     

Light scattering computational methods for particles on substrates

Four theoretical and computational methods to describe the scattering from simple particles on substrates are presented and discussed. These methods are based on the extinction theorem, image theory, the double-interaction model, and geometrical optics (ray-tracing). We compare the four methods with measurements of scattered light from gold metallic cylinders resting on a gold metallic substrate. In particular, we analyze the co-polarized (s and p polarization) full-scan and back-scattering intensities in the far field within the plane of incidence. Advantages and disadvantages of each method as a computational and reliable tool are discussed.     

Pseudo-random number generation for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU devices

Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton’s equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.     

Inertial effects, mass separation and rectification power in Lévy ratchets

We study the dynamics of particles in an external anisotropic periodic potential under the influence of additive white Lévy noise, in a general not overdamped situation. Different quantities characterizing directionality, coherence and dispersion are analyzed as functions of the mass and other systems parameters. We show that, while the current decreases monotonously with the stability index of the Lévy noise, there exists a particular intermediate value of such parameter (slightly dependent on the mass) that minimizes the time required to form a coherent particle package advancing in the preferred direction. Moreover, we show the possibility of observing mass separation. This means that particles of different masses may advance in opposite directions when influenced by the same ratchet potential and the same Lévy noise. Finally, we show that the ratio of the advanced distance to the total distance travelled constitutes a relevant measure for the rectification power, useful not only for Lévy ratchets but also for general ratchets systems. In particular, we find that it behaves quite similar to the rectification efficiency for standard models of rocking and flashing ratchets found in the literature.