David S. Cannell

Bio: David S. Cannell is an academic researcher from University of California, Santa Barbara. The author has contributed to research in topics: Convection & Light scattering. The author has an hindex of 40, co-authored 128 publications receiving 5921 citations. Previous affiliations of David S. Cannell include Memorial University of Newfoundland.

Critical dynamics in the presence of a silica gel.

Abstract: Dynamic and static light scattering results are reported for isobutyric acid and water in a 4 wt.% silica network with a crossover length of 300 A. In the one-phase region, well away from the critical point, the decay rate for order parameter fluctuations is unaffected by the network. Near the critical point, the order-parameter correlation function is well fitted by the sum of an exponential with decay rate Γ 1 and a term of the form exp{ln(τ/t 0 )/ln(Γ 2 t 0 )] 3 , with Γ 2 ≃Γ 1

Structure of silica gels.

Abstract: The structure of silica hydrogels has been studied by elastic light scattering. Like colloidal silica gels and neutrally catalyzed aerogels, these gels show mass fractal behavior at length scales below a crossover length \ensuremath{\xi} and scatter like a spatially random distribution of fractal objects for length scales g\ensuremath{\xi}. Their fractal dimension D depends on \ensuremath{\xi} and, unlike the other gels for which \ensuremath{\xi}\ensuremath{\propto}${\mathrm{\ensuremath{\varphi}}}^{1/(\mathit{D}\mathrm{\ensuremath{-}}3)}$, \ensuremath{\xi} depends on both silica volume fraction \ensuremath{\varphi} and gelation conditions. However, all our data are consistent with the correlation function 〈\ensuremath{\delta}\ensuremath{\varphi}(0)\ensuremath{\delta}\ensuremath{\varphi}(r)〉=A${\mathrm{\ensuremath{\varphi}}}^{2}$${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{r}/\ensuremath{\xi}}$/(r/\ensuremath{\xi}${)}^{3\mathrm{\ensuremath{-}}\mathit{D}}$, with A=1.8\ifmmode\pm\else\textpm\fi{}0.13.

Practical method for calculation of multiple light scattering.

Abstract: We present a method for directly simulating multiple light scattering to all orders. This method is quite general and should be adaptable for use with any optical geometry. It has been tested by using the simulation to calculate the amount of multiple scattering and to correct light scattering data for a critical binary fluid mixture near its consolute point in a standard scattering geometry that rejects most multiple scattering. Such geometries make simulation difficult since very few simulated scattering events are accepted by the optics. We also present, as an example of the flexibility of the method, an analysis of multiple scattering from a critical binary fluid mixture undergoing phase separation in a very different optical geometry which does not reject multiple scattering.

Stochastic influences on pattern formation in Rayleigh-Bénard convection: Ramping experiments.

Abstract: We report on computer-enhanced shadowgraph flow-visualization and heat-flux measurements of pattern formation in convective flows in a thin fluid layer of depth {ital d} that is heated from below Most of the experiments were conducted in a cylindrical container of radius {ital r} and aspect ratio {Gamma}=={ital r}/{ital d}=10 The temperature of the top plate of the container was held constant while the heat current through the fluid was linearly ramped in time, resulting in a temperature difference {Delta}{ital T} between the bottom and top plates After initial transients ended, the reduced Rayleigh number {epsilon}=={Delta}{ital T}/{Delta}{ital T}{sub {ital c}}{minus}1, where {Delta}{ital T}{sub {ital c}} is the critical temperature difference for the onset of convection, increased linearly with ramp rate {beta} such that {epsilon}({ital t})={beta}{ital t} When time was scaled by the vertical thermal diffusion time, our ramp rates were in the range 001{le}{beta}{le}030 When the sidewalls of the cell were made of conventional plastic materials, a concentric pattern of convection rolls was always induced by dynamic sidewall forcing When sidewalls were made of a gel that had virtually the same thermal diffusivity as the fluid, pattern formation occurred independent of cell geometry In the earliest stages the patterns were thenmore » composed of irregularly arranged cells and varied randomly between experimental runs The same random cellular flow was also observed in samples of square horizontal cross section The results demonstrate the importance of stochastic effects on pattern formation in this system However, an explanation of the measured convective heat current in terms of theoretical models requires that the noise source in these models have an intensity that is four orders of magnitude larger than that of thermal noise« less

Pattern formation outside of equilibrium

Abstract: 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.

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

Abstract: 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.

On the theory of superconductivity

Abstract: 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.

Local and global instabilities in spatially developing flows

Abstract: 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-