Showing papers by "David A. Kessler published in 2003"

Stretching instability of helical springs.

Abstract: We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to steplike contraction, and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the region of parameters in which the deformation is continuous from that in which stretching instabilities occur.

Does the continuum theory of dynamic fracture work

Abstract: We investigate the validity of the linear elastic fracture mechanics approach to dynamic fracture. We first test the predictions in a lattice simulation, using a formula of Eshelby for the time-dependent stress intensity factor. Excellent agreement with the theory is found. We then use the same method to analyze the experiment of Sharon and Fineberg. The data here are not consistent with the theoretical expectation.

Effect of curvature and twist on the conformations of a fluctuating ribbon

Abstract: We study the effects of asymmetric bending and twist rigidities and of spontaneous curvature and twist, on the statistical mechanics of fluctuating ribbons. Using a combination of Monte Carlo and differential geometry methods we perform computer simulations and calculate the probability density of the end-to-end distance of a ribbon. We find that for rectilinear ribbons of asymmetric cross section and for spontaneously curved rods with circular cross section, the distribution of end-to-end distance (but not its mean square) is affected by twist rigidity and by spontaneous twist. Possible relevance of these effects to the physics of DNA is discussed.

Equilibrium state of molecular breeding

Abstract: We investigate the equilibrium state of the model of Peng, \textit{et al.} for molecular breeding. In the model, a population of DNA sequences is successively culled by removing the sequences with the lowest binding affinity to a particular target sequence. The remaining sequences are then amplified to restore the original population size, undergoing some degree of point-substitution of nucleotides in the process. Working in the infinite population size limit, we derive an equation for the equilibrium distribution of binding affinity, here modeled by the number of matches to the target sequence. The equation is then solved approximately in the limit of large sequence length, in the three regimes of strong, intermediate and weak selection. The approximate solutions are verified via comparison to exact numerical results.

Fluctuating Filaments Under Tension - From Flexible Chains to Rigid Rods

Abstract: We develop a novel biased Monte-Carlo simulation technique to measure the force-extension curves and the distribution function of the extension of fluctuating filaments stretched by external force The method is applicable for arbitrary ratio of the persistence length to the contour length and for arbitrary forces The simulation results agree with analytic expressions for the force-extension curves and for the renormalized length-scale-dependent elastic moduli, derived in the rigid rod and in the strong force limits We find that orientational fluctuations and wall effects produce non-Gaussian distributions for nearly rigid filaments in the small to intermediate force regime We compare our results to the predictions of previous investigators and propose new experiments on nearly rigid rods such as actin filaments