Kurt M. Ehlers

Kurt M. Ehlers
Truckee Meadows Community College · Department of Mathematics

PhD, UC Santa Cruz

About

26
Publications
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Introduction
My research interests are in the application of geometric methods to problems in classical mechanics, biophysics, and optics. I especially enjoy collaborating with scientists and engineers. For over 25 years I have been interested in solving the mystery of the mechanism behind the motility of the cyanobacterium Synechococcus which swims in sea water at speeds of 10 body lengths per second with no apparent moving parts such as flagella.

Publications

Publications (26)
Article
Full-text available
A nonholonomic system, for short “NH,” consists of a configuration space Q n, a Lagrangian \( L(q,\dot q,t) \), a nonintegrable constraint distribution \( \mathcal{H} \subset TQ \), with dynamics governed by Lagrange-d’Alembert’s principle. We present here two studies, both using adapted moving frames. In the first we explore the affine connection...
Article
Full-text available
Bacteria that swim without the benefit of flagella might do so by generating longitudinal or transverse surface waves. For example, swimming speeds of order 25 microns/s are expected for a spherical cell propagating longitudinal waves of 0.2 micron length, 0.02 micron amplitude, and 160 microns/s speed. This problem was solved earlier by mathematic...
Article
Full-text available
We propose a model for the self-propulsion of the marine bacterium Synechococcus utilizing a continuous looped helical track analogous to that found in Myxobacteria [1]. In our model cargo-carrying protein motors, driven by proton-motive force, move along a continuous looped helical track. The movement of the cargo creates surface distortions in th...
Article
Full-text available
The familiar yellow or orange disks of the moon and sun, especially when they are low in the sky, and brilliant red sunsets are a result of the selective extinction (scattering plus absorption) of blue light by atmospheric gas molecules and small aerosols, a phenomenon explainable using the Rayleigh scattering approximation. On rare occasions, dust...
Article
Full-text available
In a note at the 1928 International Congress of Mathematicians Cartan outlined how his ?method of equivalence? can provide the invariants of nonholonomic systems on a manifold ?? with kinetic lagrangians [29]. Cartan indicated which changes of the metric outside the constraint distribution ?? ? ???? preserve the nonholonomic connection ?????? = Pro...
Data
Stereo animation of the helical rotor. (GIF)
Data
Stereo electron microgram showing the paracrystalline structure of the S-layer. (TIF)
Article
Since a first proof-of-concept for an autonomous micro-swimming device appeared in 2005 a strong interest on the subject ensued. The most common configuration consists of a cell driven by an external propeller, bio-inspired by bacteria such as E.coli. It is natural to investigate whether micro-robots powered by internal mechanisms could be competit...
Article
Sir James Lighthill proposed in 1992 that acoustic streaming (AS) within the mammalian cochlea could play a role in the transmission of acoustic signals to the auditory sensory cells. Microelectromechanical devices for mixing and pumping, based on the acoustic streaming effect were introduced in the mid 1990s. Nature may have preceded this inventio...
Article
Full-text available
The concept of wavelength-dependent absorption Ångström coefficients (AACs) is discussed and clarified for both single and two-wavelengths AACs and guidance for their implementation with noisy absorption spectra is provided. This discussion is followed by application of the concept to models for brown carbon bulk absorption spectra including the da...
Article
Full-text available
The concept of wavelength-dependent absorption Ångström coefficients (AACs) is discussed and clarified for both single and two-wavelengths AACs and guidance for their implementation with noisy absorption spectra is provided. This discussion is followed by application of the concept to models for brown carbon bulk absorption spectra including the da...
Article
Full-text available
Micro-engineering pumping devices without mechanical parts appeared “way back” in the early 1990’s. The working principle is acoustic streaming. Has Nature “rediscovered” this invention 2.7 Gyr ago? Strands of marine cyanobacteria Synechococcus swim 25 diameters per second without any visible means of propulsion. We show that nanoscale amplitude vi...
Article
Full-text available
Certain cyanobacteria, such as open ocean strains of Synechococcus, are able to swim at speeds up to 25 diameters per second, without flagella or visible changes in shape. The means by which Synechococcus generates thrust for self-propulsion is unknown. The only mechanism that has not been ruled out employs tangential waves of surface deformations....
Article
Full-text available
“Rubber” coated bodies rolling over a surface satisfy a no-twist condition in addition to the no slip condition satisfied by “marble” coated bodies [1]. Rubber rolling has an interesting differential geometric appeal because the geodesic curvatures of the curves on the surfaces at corresponding points are equal. The associated distribution in the 5...
Article
Cartan's moving frames method is a standard tool in Riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by nonholonomic constraints.
Article
Full-text available
We apply Cartan's method of equivalence to the case of nonholonomic geometry on three-dimensional contact manifolds. Our main result is to derive the differential invariants for these structures and give geometric interpretations. We show that the symmetry group of such a structure has dimension at most four. Our motivation is to study the geometry...
Article
A geometrical approach for low Reynolds number swimming was introduced by Shapere and Wilczek1. Here we pursue some developments for the two dimensional theory. The outer membrane or the ciliary envelope of the planar organism is represented by the conformal image of the unit circle. Power expenditures and velocities can be computed using complex v...
Chapter
Stokesian swimming is a geometric exercise, a collective game. In Part I, we review Shapere and Wilczek’s gauge-theoretical approach for a single organism. We estimate the speeds of organisms moving by propagating small amplitude waves, and we make a conjecture regarding a new inequality for the Stokes’ curvature. In Part II, we extend the gauge th...
Article
According to a modern formulation of the classic result of H. Lorentz (1907), the propulsion operator P Σ (U →)=F →, which maps the velocity U → along a C 2 surface Σ to the surface force field F →, is selfadjoint and positive. Using the boundary integral representation, we show that P has a discrete set of eigenvalues tending to infinity, and that...
Article
Stokesian swimming is a geometric exercise, a collective game. In Part I, we review Shapere and Wilczek's gauge-theoretical approach for a single organism. We estimate the speeds of organisms moving by propagating small amplitude waves, and we make a conjecture regarding a new inequality for the Stokes' curvature. In Part II, we extend the gauge th...
Article
Stokesian swimming is a geometric exercise, a collective game. In Part I, we review Shapere and Wilczek's gauge-theoretical approach for a single organism. We estimate the speeds of organisms moving by propagating small amplitude waves, and we make a conjecture regarding a new inequality for the Stokes' curvature. In Part II, we extend the gauge th...
Article
According to a classic result of H.Lorentz, the propulsion opera- tor P�( ~ U) = ~ F, which maps the velocity boundary condition along a C 2 surfaceto the surface force field, is self-adjoint and positive. Using the boundary integral representation, we show that P has a dis- crete set of eigenvalues tending to infinity, and that the eigenbasis is L...
Chapter
We address two research lines, continuing our work in [11]. The first uses the affine connection introduced by Cartan at the 1928 International Congress of Mathematicians. We classify here the 2-3-5 nonholonomic geometries. The maximum symmetry case, 6-dimensional, has two branches. We describe the most interesting and quite surprising one, that oc...
Article
Typescript. Thesis (Ph. D.)--University of California, Santa Cruz, 1995. Includes bibliographical references (55-58).

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