A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

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Pattern formation outside of equilibrium

Solid lipid nanoparticles: Production, characterization and applications

Single-molecule force spectroscopy has emerged as a powerful tool to investigate the forces and motions associated with biological molecules and enzymatic activity. The most common force spectroscopy techniques are optical tweezers, magnetic tweezers and atomic force microscopy. Here we describe these techniques and illustrate them with examples highlighting current capabilities and limitations.

Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

The goal of this survey is to review recent developments in the hydro­ dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem­ onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further­ more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-

/pdf/local-and-global-instabilities-in-spatially-developing-flows-ja4x14nrk6.pdf

Local and global instabilities in spatially developing flows

We report details of experimental studies of the effect of dilute silica networks on critical phenomena for two binary fluid mixtures: lutidine-water (LW) and isobutyric acid\char21{}water (IBAW). For both mixtures, the primary effect of the silica is to induce a time-independent perturbation of the mixtures' concentration, making it spatially nonuniform. We interpret this as the static response of the critical system to the spatial nonuniformities of the silica concentration. We have measured this response by light scattering and find it is both temperature and concentration dependent, becoming strongly so in the vicinity of the consolute points of the mixtures. We observed no critical fluctuations for the LW-gel system. For the IBAW-gel system, time-dependent scattering was observed, and the temporal autocorrelation function of the scattered intensity revealed three regimes. Well away from the consolute point, the decay was exponential. By taking the effect of the time-independent response of the mixture to the silica gel into account, we found that the decay rates were comparable to those of the pure system. Correlation functions measured closer to the consolute point contained a significant nonexponential component for sufficiently large values of the scattering wave vector. This component is well fitted by either a stretched exponential or an activated form. From the amplitude of the normalized autocorrelation function we deduce that the critical fluctuations are suppressed in amplitude relative to those of the pure system as the consolute point is approached. Sufficiently near the phase boundary of the pure system, a very slowly decaying mode was also observed in the autocorrelation function. This mode died away hours after the small temperature change that induced it. A further temperature change toward the two-phase region induced it agian, while a change in the opposite direction did not. We interpret this behavior as resulting from a phase separation process. IBAW-gel samples held deep in the two-phase region of the pure system for months ordered macroscopically, proving that this system has long-range order in the presence of such silica networks.

Critical behavior in the presence of a disordered environment.

Employing a differential optical mixing spectrometer, we have determined that the translational diffusion coefficient (DT) of aspartate transcarbamylase (AT-Case) decreases by (41 plus or minus 06)% in the presence of succinate and carbamyl phosphate This result, combined with the change in the sedimentation coefficient determined by Gerhart and Schachman (1968) and repeated by us in the present work indicates that ATCase experiences an increase in frictional coefficient of approximately 4% due to succinate and carbamyl phosphate, and that any change in the enzyme's partial specific volume (v) under these conditions is less than about 03% We have also measured (DT)20,w for ATCase as (375 plus of minus 011) x 10-7 cm2/sec Combining this with our measured value of s20,2-o for ATCase of (117 plus or minus 02) x 10-13 sec and the calculated value of v of 0738 cm3/g (Rosenbusch and Weber, 1971), we have determined the molecular weight of ATCase as (29 plus of minus 01) x 10-5 We have also observed the ATCase dimer and find that at a dimer concentration of 06 mg/ml the value of s20,w for the dimer is 158 x 10-13 sec and that this value decreases by (40 plus or minus 05)% upon the addition of succinate and carbamyl phosphate, a behavior essentially identical with that of the monomer

The effect of succinate on the translational diffusion coefficient of aspartate transcarbamylase.

Accurate measurements are reported of both the correlation range and the Rayleigh linewidth of xenon near its critical point. The linewidth data agree quite well with the mode-mode coupling results, and disagree with renormalization-group dynamics calculations.

Correlation range and Rayleigh linewidth of xenon near the critical point

A general-purpose, multifunction light-scattering instrument has been
developed at the NASA Lewis Research Center for Space Shuttle and Space
Station colloid crystallization and other microgravity experiments. For a
single sample, the instrument can measure two-dimensional Bragg scattering
from 0.5° to 60°, dynamic and static light scattering from 10° to
170°, the shear modulus of samples before and after crystallization, and
digital color images of the sample. A carousel positions any one of eight 3-ml
samples into the test position for separate experiments. Program challenges
and flight results from the STS-83 Space Shuttle mission are
discussed.

Physics of Hard Spheres Experiment: a general-purpose light-scattering instrument

Richard Heinrichs, Guenter Ahlers, and David S. Cannell Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106 (Received 16 January 1986) We report measurements of the axial variation of the wave number q of Taylor-vortex flow in a system with aspect ratio 17 <. L <. 25 containing ten vortex pairs between rigid nonrotating ends. Near the critical Reynolds number Rc, qis very nonuniform when its average value ^differs significantly from its critical value qc. For sufficiently small \\q — qc\\, the finite geometry eliminates the Eckhaus instability. Our results agree quantitatively with solutions of the Ginzburg-Landau equation.

David S. Cannell

Papers

Critical behavior in the presence of a disordered environment.

The effect of succinate on the translational diffusion coefficient of aspartate transcarbamylase.

Correlation range and Rayleigh linewidth of xenon near the critical point

Physics of Hard Spheres Experiment: a general-purpose light-scattering instrument

Effects of finite geometry on the wave number of Taylor-vortex flow.