A stiff one-armed swimmer in glycerine goes nowhere. However, if its arm is elastic, the swimmer can go on its way. Quantifying this observation, we study a hyperdiffusion equation for the shape of the elastica in a v...
A stiff one-armed swimmer in glycerine goes nowhere. However, if its arm is elastic, the swimmer can go on its way. Quantifying this observation, we study a hyperdiffusion equation for the shape of the elastica in a viscous fluid, find solutions for impulsive or oscillatory forcing, and elucidate relevant aspects of propulsion. These results have application in a variety of physical and biological contexts, from dynamic experiments measuring biopolymer bending moduli to instabilities of twisted elastic filaments.
Exploiting the “natural” frame of space curves, we formulate an intrinsic dynamics of a twisted elastic filament in a viscous fluid. Coupled nonlinear equations describing the temporal evolution of the filament'...
Exploiting the “natural” frame of space curves, we formulate an intrinsic dynamics of a twisted elastic filament in a viscous fluid. Coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density capture the dynamic interplay of twist and writhe. These equations are used to illustrate a remarkable nonlinear phenomenon: geometric untwisting of open filaments, whereby twisting strains relax through a transient writhing instability without axial rotation. Experimentally observed writhing motions of fibers of the bacterium B. subtilis [N. H. Mendelson et al., J. Bacteriol. 177, 7060 (1995)] may be examples of this untwisting process.
The results for a height and flow-dependent model for turbulent viscosity are reported. This model is developed to explain the generation of sand waves in tidal seas and resolves the problem of excitation of very long...
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The results for a height and flow-dependent model for turbulent viscosity are reported. This model is developed to explain the generation of sand waves in tidal seas and resolves the problem of excitation of very long waves in sand wave formation, because it leads to damping of the long waves and gives a finite separation between the most excited mode and the zero mode. For parameter settings within a physically realistic range, a linear analysis of the resulting system yields a first excited mode whose wavelength is similar to the characteristic wavelength of sand waves observed in nature. This result can be the starting point for a nonlinear analysis of the system.
The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to be...
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The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive a point approximation to density values of the conditional distribution of such estimates. In an example problem, this approximate distribution captures the essential features of the distribution of ML estimates in the presence of Gaussian-distributed noise.
The image segmentation problem in computer vision is considered. Given a two-dimensional domain D and a function defined on it (the original image), the problem is to obtain a ‘cartoon’ associated with this function...
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A formulation for selecting operator and control inputs to a high fidelity dynamics model, governed by differential-algebraic equations, is presented to minimize deviation in its response relative to that of a lower f...
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A formulation for selecting operator and control inputs to a high fidelity dynamics model, governed by differential-algebraic equations, is presented to minimize deviation in its response relative to that of a lower fidelity model that is also governed by differential-algebraic equations of motion. An adjoint variable method for computing sensitivity of the error measure defined is derived and implemented in a nonlinear programming formulation that is suitable for iterative minimization of the error functional. A numerical example using a multibody mechanism is presented to demonstrate effectiveness of the method and provide insights into means for effectively formulating problems of model correlation and strategies for their solution.
A new class of propagating fronts is proposed in which a spreading instability evolves through a singular configuration before saturating. As an example, we examine the viscous Rayleigh instability of a stationary flu...
A new class of propagating fronts is proposed in which a spreading instability evolves through a singular configuration before saturating. As an example, we examine the viscous Rayleigh instability of a stationary fluid column, using the marginal stability criterion to estimate the front velocity, front width, and the selected wavelength in terms of the surface tension and viscosity contrast. Systems that may display this phenomenon include droplets elongated in extensional flows, capillary bridges, liquid crystal tethers, and viscoelastic jets. The related problem of propagation in Rayleigh-like systems that do not fission is also considered.
We present an ultrafast nonlinear optical loop mirror (NOLM) switch based on multiple collisions between orthogonally polarized signal and control solitons in highly birefringent optical fiber. The 8-m circumference s...
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