Kinesin's biased stepping mechanism: amplification of neck linker zippering.

A physically motivated model of kinesin's motor function is developed within the framework of rectified Brownian motion. The model explains how the amplification of neck linker zippering arises naturally through well-known formulae for overdamped dynamics, thereby providing a means to understand how weakly-favorable zippering leads to strongly favorable plus-directed binding of a free kinesin head to microtubule. Additional aspects of kinesin's motion, such as head coordination and rate-limiting steps, are directly related to the force-dependent inhibition of ATP binding to a microtubule bound head. The model of rectified Brownian motion is presented as an alternative to power stroke models and provides an alternative interpretation for the significance of ATP hydrolysis in the kinesin stepping cycle.

Quasiadiabatic analysis for ionization of a particle in a periodically perturbed delta(x) potential.

We study an ionization process for a particle bound by an attractive delta(x) potential of a certain depth defined on a finite lattice under an external periodic force. Ionization coincides with the time when first two time dependent energy eigenvalues get close to each other. We use a slow driving force away from the resonance frequency. We also observe intermittent high frequency oscillation which can be analyzed with two level approximation.

Evolution of escape processes with a time-varying load.

We study an escape process of a noisy particle with a time varying load. We present an effective nonperturbative method which works even when the time varying load amplitude is comparable to other parameters. It is based on the idea that for every instant of time, we know the quasiadiabatic eigenspectrum and the quasiadiabatic eigenfunctions of the instantaneous system. We show that when two time-varying quasiadiabatic eigenvalues in the spectrum get close to each other, the amplitudes of the quasiadiabatic eigenfuntions show an abrupt change; therefore, the escape rate is highly affected.

Entropy evolution for the Baker map.

Gibbs entropy is invariant for the Baker map. A Jordan basis spectral decomposition of the Baker Frobenius-Perron operator suggests that any initial density evolves to the stationary density that has maximal entropy. This entropy conundrum is resolved by considering the difference between weak and strong convergence. A binary representation is used to make these points transparent. (c) 1998 American Institute of Physics.

Construction of the Jordan basis for the Baker map.

The Jordan canonical form basis states for an invertible chaotic map, the Baker map, are constructed. A straightforwardly obtained recursion formula is presented for construction of the Jordan states and of the spectral decomposition of the Frobenius-Perron evolution operator. Comparison of this method with earlier, subdynamics techniques demonstrates that it is much more direct and simpler. The physical significance of the Jordan states is approached from the point of view of an entropy evolution equation. The method is also applied to the Bernoulli map, yielding its eigenstates more straightforwardly than done previously. (c) 1997 American Institute of Physics.

Unstable evolution of pointwise trajectory solutions to chaotic maps.

Simple chaotic maps are used to illustrate the inherent instability of trajectory solutions to the Frobenius-Perron equation. This is demonstrated by the difference in the behavior of delta-function solutions and of extended densities. Extended densities evolve asymptotically and irreversibly into invariant measures on stationary attractors. Pointwise trajectories chaotically roam over these attractors forever. Periodic Gaussian distributions on the unit interval are used to provide insight. Viewing evolving densities as ensembles of unstable pointwise trajectories gives densities a stochastic interpretation. (c) 1995 American Institute of Physics.

Enhanced quantum fluctuations in a chaotic single mode ammonia laser.

A detailed study of the effects of quantum fluctuations in a chaotic single mode laser is presented. It has been well established that the linear noise approximation eventually becomes invalid for the case of chaotic dynamics. A more accurate description of the laser is achieved through use of nonlinear Langevin equations. Simple expressions for the time evolution of the phases of the electric field and polarization are derived. These expressions predict that chaotic dynamics will greatly enhance phase diffusion. This prediction is verified through numerical simulations. A quantitative method, for determining the amount of amplification of quantum noise by chaos is discussed. This method makes use of a metric introduced in symbolic dynamics. The fluctuations are shown to have been amplified by over two orders of magnitude, making them macroscopically visible.

Amplification of intrinsic fluctuations by the Lorenz equations.

Macroscopic systems (e.g., hydrodynamics, chemical reactions, electrical circuits, etc.) manifest intrinsic fluctuations of molecular and thermal origin. When the macroscopic dynamics is deterministically chaotic, the intrinsic fluctuations may become amplified by several orders of magnitude. Numerical studies of this phenomenon are presented in detail for the Lorenz model. Amplification to macroscopic scales is exhibited, and quantitative methods (binning and a difference-norm) are presented for measuring macroscopically subliminal amplification effects. In order to test the quality of the numerical results, noise induced chaos is studied around a deterministically nonchaotic state, where the scaling law relating the Lyapunov exponent to noise strength obtained for maps is confirmed for the Lorenz model, a system of ordinary differential equations.