Generalized Semimagic Squares for Digital Halftoning

Completing Aronov et al.'s study on zero-discrepancy matrices for digital halftoning, we determine all (m, n, k, l) for which it is possible to put mn consecutive integers on an m-by-n board (with wrap-around) so that each k-by-l region holds the same sum. For one of the cases where this is impossible, we give a heuristic method to find a matrix with small discrepancy.Comment: 6 pages, 6 figure

Symmetry as a sufficient condition for a finite flex

We show that if the joints of a bar and joint framework $(G,p)$ are positioned as `generically' as possible subject to given symmetry constraints and $(G,p)$ possesses a `fully-symmetric' infinitesimal flex (i.e., the velocity vectors of the infinitesimal flex remain unaltered under all symmetry operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which preserves the symmetry of $(G,p)$ throughout the path. This and other related results are obtained by symmetrizing techniques described by L. Asimov and B. Roth in their paper `The Rigidity Of Graphs' from 1978 and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes that can be detected with these symmetry-based methods can in general not be found with the analogous non-symmetric methods.Comment: 26 pages, 10 figure

Catalysis of the Thermal Decomposition of Transition Metal Nitrate Hydrates by Poly(vinylidene difluoride)

Poly(vinylidene difluoride) (PVDF) doped with transition metal nitrate hydrates are cast into thin films giving a high β-phase content. Analysis of the thermal behavior of the doped PVDF shows that the decomposition of the metal (II) nitrate hydrates to metal (II) oxides is catalyzed by the PVDF, as evidenced by reduction in the decomposition temperature by as much as 170 °C compared to the pure metal salts. In contrast, there is little to no apparent catalysis for the decomposition of the metal (III) nitrate hydrates. The FTIR spectra of the gas phase decomposition products show H2O and NO2 are the major components for both PVDF-doped material and the pure metal nitrate hydrates. A mechanism for the role of PVDF is proposed that uses the internal electric field of the ferroelectric phase to orient the nitrate ions and polarize the N-O bonds

A Nonliearly Dispersive Fifth Order Integrable Equation and its Hierarchy

In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and two hierarchies of equations that share the same conserved charges. We construct two compatible Hamiltonian structures as well as their Casimir functionals. One of the structures has a single Casimir functional while the other has two. This allows us to extend the flows into negative order and clarifies the meaning of two different hierarchies of positive flows. We study the behavior of these systems under a hodograph transformation and show that they are related to the Kaup-Kupershmidt and the Sawada-Kotera equations under appropriate Miura transformations. We also discuss briefly some properties associated with the generalization of second, third and fourth order Lax operators.Comment: 11 pages, LaTex, version to be published in Journal of Nonlinear Mathematical Physics, has expanded discussio

The Puzzle of the Flyby Anomaly

Close planetary flybys are frequently employed as a technique to place spacecraft on extreme solar system trajectories that would otherwise require much larger booster vehicles or may not even be feasible when relying solely on chemical propulsion. The theoretical description of the flybys, referred to as gravity assists, is well established. However, there seems to be a lack of understanding of the physical processes occurring during these dynamical events. Radio-metric tracking data received from a number of spacecraft that experienced an Earth gravity assist indicate the presence of an unexpected energy change that happened during the flyby and cannot be explained by the standard methods of modern astrodynamics. This puzzling behavior of several spacecraft has become known as the flyby anomaly. We present the summary of the recent anomalous observations and discuss possible ways to resolve this puzzle.Comment: 6 pages, 1 figure. Accepted for publication by Space Science Review

Synchronization Transition in the Kuramoto Model with Colored Noise

We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and analytically solvable cases of white noise and quenched random frequencies.Comment: 4 pages, 2 figure

Influence of Solvent and Molecular Weight in Wrinkle Formation in Spin-cast Polystyrene Thin Films

The surface morphology of polystyrene thin films formed from various molecular weight polystyrene and solvent conditions is studied. When spin-cast from tetrahydrofuran (THF) wrinkles are formed at the extremities that have periodicity with wavelengths in the μm range and amplitudes in the nm range but varies with molecular weight. A mixed solvent system consisting of THF and dimethylformamide (DMF) leads to periodic structures only with THF-rich compositions. THF and DMF have similar properties relevant to spin-casting: density, surface tension, molecular weight, and viscosity but different boiling points and room temperature vapor pressures, demonstrating that formation periodicity requires a volatile solvent. The formation of the surface structures is attributed to the Marangoni effect and the film thicknesses and wave parameters are shown to be consistent with literature models

Evolution of Surface Morphology of Spin-Coated Poly(methylmethacrylate) Thin Films

The morphology of sub-micron poly(methyl methacrylate) films coated to glass supports by spin coating from toluene is examined using surface profilometry. Wrinkled surfaces with local quasi-sinusoidal periodicity were seen on the surfaces of films with thicknesses of larger than 75 nm. The surface wrinkles had large aspect ratios with wavelengths in the tens of microns and amplitudes in the tens of nanometers. Wrinkles that formed during spin-coating are attributed to surface perturbations caused by Rayleigh–Bénard–Marangoni convective instabilities. The effects of film thickness, coating solution concentration, and drying rate on the thin film surface morphology are investigated. The results can be used to prepare surfaces with controlled morphology, either smooth or with periodic wrinkles

Modeling of Poly(methylmethacrylate) Viscous Thin Films by Spin-coating

A predictive film thickness model based on an accepted equation of state is applied to the spin-coating of sub-micron poly(methylmethacrylate) viscous thin films from toluene. Concentration effects on density and dynamic viscosity of the spin-coating solution are closely examined. The film thickness model is calibrated with a system-specific film drying rate and was observed to scale with the square root of spin speed. Process mapping is used to generate a three-dimensional design space for the control of film thickness

Robotic control of the seven-degree-of-freedom NASA laboratory telerobotic manipulator

A computationally efficient robotic control scheme for the NASA Laboratory Telerobotic Manipulator (LTM) is presented. This scheme utilizes the redundancy of the seven-degree-of-freedom LTM to avoid joint limits and singularities. An analysis to determine singular configurations is presented. Performance criteria are determined based on the joint limits and singularity analysis. The control scheme is developed in the framework of resolved rate control using the gradient projection method, and it does not require the generalized inverse of the Jacobian. An efficient formulation for determining the joint velocities of the LTM is obtained. This control scheme is well suited for real-time implementation, which is essential if the end-effector trajectory is continuously modified based on sensory feedback. Implementation of this scheme on a Motorola 68020 VME bus-based controller of the LTM is in progress. Simulation results demonstrating the redundancy utilization in the robotic mode are presented