Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction

The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys., 90 (1) : 463-473, 1989] to account for the influence of fluctuations in hydrodynamic interactions in Rouse chains, is adapted here to derive a new mean-field approximation for the FENE spring force. This "FENE-PG" force law approximately accounts for spring-force fluctuations, which are neglected in the widely used FENE-P approximation. The Gaussian Approximation for hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force approximations to obtain approximate models for finitely-extensible bead-spring chains with hydrodynamic interactions. The closed set of ODE's governing the evolution of the second-moments of the configurational probability distribution in the approximate models are used to generate predictions of rheological properties in steady and unsteady shear and uniaxial extensional flows, which are found to be in good agreement with the exact results obtained with Brownian dynamics simulations. In particular, predictions of coil-stretch hysteresis are in quantitative agreement with simulations' results. Additional simplifying diagonalization-of-normal-modes assumptions are found to lead to considerable savings in computation time, without significant loss in accuracy.Comment: 26 pages, 17 figures, 2 tables, 75 numbered equations, 1 appendix with 10 numbered equations Submitted to J. Chem. Phys. on 6 February 200

Auroral thermosphere temperatures from observations of 6300 A emissions

Doppler temperatures determined from observations of the atomic oxygen OI 6300 A line during March 1984 at the University of Alaska/Fairbanks are presented. Temperatures are obtained from Fabry-Perot Interferometer pressure scans using a Fourier transform smoothing and fitting technique; this technique is presented in detail. The temperatures and the spread in the temperatures are consistent from day to day. On the clear nights of March 10 to 13, the temperatures were 800, 750, 750 and 800 K, respectively, with a spread of + or - 100 K. These temperatures are compared to the MSIS (84) model atmosphere for similar geomagnetic conditions and found to be in general agreement; they are also consistent with results obtained by other investigators

Two-dimensional turbulence of dilute polymer solutions

We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that at vanishingly small concentrations, such that the polymers are passively transported, the probability distribution of polymer elongation has a power law tail: its slope is related to the statistics of finite-time Lyapunov exponents of the flow, in quantitative agreement with theoretical predictions. We show that at finite concentrations and sufficiently large elasticity the polymers react on the flow with manifold consequences: velocity fluctuations are drastically depleted, as observed in soap film experiments; the velocity statistics becomes strongly intermittent; the distribution of finite-time Lyapunov exponents shifts to lower values, signalling the reduction of Lagrangian chaos.Comment: 4 pages, 5 figure

Supersymmetry solution for finitely extensible dumbbell model

Exact relaxation times and eigenfunctions for a simple mechanical model of polymer dynamics are obtained using supersymmetry methods of quantum mechanics. The model includes the finite extensibility of the molecule and does not make use of the self-consistently averaging approximation. The finite extensibility reduces the relaxation times when compared to a linear force. The linear viscoelastic behaviour is obtained in the form of the ``generalized Maxwell model''. Using these results, a numerical integration scheme is proposed in the presence of a given flow kinematics.Comment: 5 pages, 2 figure

Microrheological Characterisation of Anisotropic Materials

We describe the measurement of anisotropic viscoelastic moduli in complex soft materials, such as biopolymer gels, via video particle tracking microrheology of colloid tracer particles. The use of a correlation tensor to find the axes of maximum anisotropy, and hence the mechanical director, is described. The moduli of an aligned DNA gel are reported, as a test of the technique; this may have implications for high DNA concentrations in vivo. We also discuss the errors in microrheological measurement, and describe the use of frequency space filtering to improve displacement resolution, and hence probe these typically high modulus materials.Comment: 5 pages, 5 figures. Replaced after refereeing/ improvement. Main results are the same. The final, published version of the paper is here http://link.aps.org/abstract/PRE/v73/e03190

Practical Broad-Band Tuning of Dye Lasers by Solvent Shifting

We have operated a dye laser over a broad wavelength range (593.8-667.0nm) by shifting the dye emission profile with incremental changes of solvent composition. This was accomplished with the laser operating continuously, and only minor adjustment of the laser optics was required. Solvent tuning was facilitated by the critical dependence of the optimum laser wavelength on concentration of the second solvent. Using the known solvent-sensitive laser dye 9-diethylaminobenzo[a]phenoxaz-5-one (DBP), 87% of the tuning range from pure xylenes to pure methanol was covered by cumulative addition of 24 vol. % methanol to the starting xylenes solution. The optimum dye concentration was found to be independent of solvent composition, so that maximum laser power could be maintained by mixing equimolar dye solutions in the two solvents. These results establish the practicality of solvent-tuning as a method of conducting laser experiments over a broad wavelength range

Evaluating the Applicability of the Fokker-Planck Equation in Polymer Translocation: A Brownian Dynamics Study

Brownian dynamics (BD) simulations are used to study the translocation dynamics of a coarse-grained polymer through a cylindrical nanopore. We consider the case of short polymers, with a polymer length, N, in the range N=21-61. The rate of translocation is controlled by a tunable friction coefficient, gamma_{0p}, for monomers inside the nanopore. In the case of unforced translocation, the mean translocation time scales with polymer length N as ~ (N-N_p)^alpha, where N_p is the average number of monomers in the nanopore. The exponent approaches the value alpha=2 when the pore friction is sufficiently high, in accord with the prediction for the case of the quasi-static regime where pore friction dominates. In the case of forced translocation, the polymer chain is stretched and compressed on the cis and trans sides, respectively, for low gamma_{0p}. However, the chain approaches conformational quasi-equilibrium for sufficiently large gamma_{0p}. In this limit the observed scaling of with driving force and chain length supports the FP prediction that is proportional to N/f_d for sufficiently strong driving force. Monte Carlo simulations are used to calculate translocation free energy functions for the system. The free energies are used with the Fokker-Planck equation to calculate translocation time distributions. At sufficiently high gamma_{0p}, the predicted distributions are in excellent agreement with those calculated from the BD simulations. Thus, the FP equation provides a valid description of translocation dynamics for sufficiently high pore friction for the range of polymer lengths considered here. Increasing N will require a corresponding increase in pore friction to maintain the validity of the FP approach. Outside the regime of low N and high pore friction, the polymer is out of equilibrium, and the FP approach is not valid.Comment: 13 pages, 11 figure

Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity

Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unlike the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used delta-function repulsive potential in the limit of a width parameter "d" going to zero, enables the performance of Brownian dynamics simulations. The simulations results, which describe the exact behavior of the model, indicate that for chains of arbitrary but finite length, a delta-function potential leads to equilibrium and zero shear rate properties which are identical to the predictions of the Rouse model. On the other hand, a non-zero value of "d" gives rise to a prediction of swelling at equilibrium, and an increase in zero shear rate properties relative to their Rouse model values. The use of a delta-function potential appears to be justified in the limit of infinite chain length. The exact simulation results are compared with those obtained with an approximate solution which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian. The Gaussian approximation is shown to be exact to first order in the strength of excluded volume interaction, and is found to be accurate above a threshold value of "d", for given values of chain length and strength of excluded volume interaction.Comment: Revised version. Long chain limit analysis has been deleted. An improved and corrected examination of the long chain limit will appear as a separate posting. 32 pages, 9 postscript figures, LaTe