A multiresolution wavelet representation in two or more dimensions

In the multiresolution approximation, a signal is examined on a hierarchy of resolution scales by projection onto sets of smoothing functions. Wavelets are used to carry the detail information connecting adjacent sets in the resolution hierarchy. An algorithm has been implemented to perform a multiresolution decomposition in n greater than or equal to 2 dimensions based on wavelets generated from products of 1-D wavelets and smoothing functions. The functions are chosen so that an n-D wavelet may be associated with a single resolution scale and orientation. The algorithm enables complete reconstruction of a high resolution signal from decomposition coefficients. The signal may be oversampled to accommodate non-orthogonal wavelet systems, or to provide approximate translational invariance in the decomposition arrays

Kinematics of the swimming of Spiroplasma

\emph{Spiroplasma} swimming is studied with a simple model based on resistive-force theory. Specifically, we consider a bacterium shaped in the form of a helix that propagates traveling-wave distortions which flip the handedness of the helical cell body. We treat cell length, pitch angle, kink velocity, and distance between kinks as parameters and calculate the swimming velocity that arises due to the distortions. We find that, for a fixed pitch angle, scaling collapses the swimming velocity (and the swimming efficiency) to a universal curve that depends only on the ratio of the distance between kinks to the cell length. Simultaneously optimizing the swimming efficiency with respect to inter-kink length and pitch angle, we find that the optimal pitch angle is 35.5$^\circ$ and the optimal inter-kink length ratio is 0.338, values in good agreement with experimental observations.Comment: 4 pages, 5 figure

Models of helically symmetric binary systems

Results from helically symmetric scalar field models and first results from a convergent helically symmetric binary neutron star code are reported here; these are models stationary in the rotating frame of a source with constant angular velocity omega. In the scalar field models and the neutron star code, helical symmetry leads to a system of mixed elliptic-hyperbolic character. The scalar field models involve nonlinear terms that mimic nonlinear terms of the Einstein equation. Convergence is strikingly different for different signs of each nonlinear term; it is typically insensitive to the iterative method used; and it improves with an outer boundary in the near zone. In the neutron star code, one has no control on the sign of the source, and convergence has been achieved only for an outer boundary less than approximately 1 wavelength from the source or for a code that imposes helical symmetry only inside a near zone of that size. The inaccuracy of helically symmetric solutions with appropriate boundary conditions should be comparable to the inaccuracy of a waveless formalism that neglects gravitational waves; and the (near zone) solutions we obtain for waveless and helically symmetric BNS codes with the same boundary conditions nearly coincide.Comment: 19 pages, 7 figures. Expanded version of article to be published in Class. Quantum Grav. special issue on Numerical Relativit