Oscillation-free method for semilinear diffusion equations under noisy initial conditions

Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a local linearization. The accuracy of our oscillation-free method is proved and its usefulness is further verified through solving a Fisher-type equation where oscillation-free solutions are successfully produced in spite of random errors in the initial conditions.Comment: 19 pages, 9 figure

The impact of a young radio galaxy : Clues from the cosmic ray electron population

In the framework of hierarchical structure formation, active galactic nuclei (AGN) feedback shapes the galaxy luminosity function. Low luminosity, galaxy-scale double radio sources are ideal targets to investigate the interplay between AGN feedback and star formation. We use Very Large Array and BIMA millimetre-wave array observations to study the radio continuum emission of NGC 3801 between 1.4 and 112.4 GHz. We find a prominent spectral break at 10 GHz, where the spectrum steepens as expected from cosmic ray electron (CRe) ageing. Using the equipartition magnetic field and fitting JP models locally, we create a spatially resolved map of the spectral age of the CRe population. The spectral age of τint =2.0±0.2Myr agrees within a factor of 2 with the dynamical age of the expanding X-ray emitting shells. The spectral age varies only little across the lobes, requiring an effective mixing process of the CRe such as a convective backflow of magnetized plasma. The jet termination points have a slightly younger CRe spectral age, hinting at in situ CRe re-acceleration. Our findings support the scenario where the supersonically expanding radio lobes heat the interstellar medium (ISM) of NGC 3801 via shock waves, and, as their energy is comparable to the energy of the ISM, are clearly able to influence the galaxy's further evolution.Peer reviewe

Robot acting on moving bodies (RAMBO): Preliminary results

A robot system called RAMBO is being developed. It is equipped with a camera, which, given a sequence of simple tasks, can perform these tasks on a moving object. RAMBO is given a complete geometric model of the object. A low level vision module extracts and groups characteristic features in images of the object. The positions of the object are determined in a sequence of images, and a motion estimate of the object is obtained. This motion estimate is used to plan trajectories of the robot tool to relative locations nearby the object sufficient for achieving the tasks. More specifically, low level vision uses parallel algorithms for image enchancement by symmetric nearest neighbor filtering, edge detection by local gradient operators, and corner extraction by sector filtering. The object pose estimation is a Hough transform method accumulating position hypotheses obtained by matching triples of image features (corners) to triples of model features. To maximize computing speed, the estimate of the position in space of a triple of features is obtained by decomposing its perspective view into a product of rotations and a scaled orthographic projection. This allows the use of 2-D lookup tables at each stage of the decomposition. The position hypotheses for each possible match of model feature triples and image feature triples are calculated in parallel. Trajectory planning combines heuristic and dynamic programming techniques. Then trajectories are created using parametric cubic splines between initial and goal trajectories. All the parallel algorithms run on a Connection Machine CM-2 with 16K processors

Robot Acting on Moving Bodies (RAMBO): Interaction with tumbling objects

Interaction with tumbling objects will become more common as human activities in space expand. Attempting to interact with a large complex object translating and rotating in space, a human operator using only his visual and mental capacities may not be able to estimate the object motion, plan actions or control those actions. A robot system (RAMBO) equipped with a camera, which, given a sequence of simple tasks, can perform these tasks on a tumbling object, is being developed. RAMBO is given a complete geometric model of the object. A low level vision module extracts and groups characteristic features in images of the object. The positions of the object are determined in a sequence of images, and a motion estimate of the object is obtained. This motion estimate is used to plan trajectories of the robot tool to relative locations rearby the object sufficient for achieving the tasks. More specifically, low level vision uses parallel algorithms for image enhancement by symmetric nearest neighbor filtering, edge detection by local gradient operators, and corner extraction by sector filtering. The object pose estimation is a Hough transform method accumulating position hypotheses obtained by matching triples of image features (corners) to triples of model features. To maximize computing speed, the estimate of the position in space of a triple of features is obtained by decomposing its perspective view into a product of rotations and a scaled orthographic projection. This allows use of 2-D lookup tables at each stage of the decomposition. The position hypotheses for each possible match of model feature triples and image feature triples are calculated in parallel. Trajectory planning combines heuristic and dynamic programming techniques. Then trajectories are created using dynamic interpolations between initial and goal trajectories. All the parallel algorithms run on a Connection Machine CM-2 with 16K processors

Geology of the Lower Paleozoic Rocks in the Boundary Mountain Anticlinorium

Guidebook for field trips in the Rangeley Lakes - Dead River Basin region, western Maine: 62nd annual meeting October 2, 3, and 4, 1970: Trip A-

Use of breath hydrogen and methane as markers of colonic fermentation in epidemiologic studies: circadian patterns of excretion.

Fermentation in the large bowel has been postulated to play a protective role against colon cancer. Hydrogen and methane are end products of this fermentation process and are absorbed into the bloodstream and excreted via expired air in the breath. Breath levels of hydrogen and, to a lesser extent, methane correlate strongly with colonic fermentation and may serve as useful biomarkers for this process. In a preliminary study to assess the usefulness of these two markers in epidemiologic studies, we followed the hourly excretion of the two gases in expired alveolar air for 48 hr in 20 healthy subjects, using a Quintron gas chromatograph equipped with a solid-state detector specific for reducing gases. All subjects excreted hydrogen, but 71% did not excrete methane. Possible atmospheric contamination of the samples was corrected for on the basis of breath carbon dioxide levels. A clear circadian pattern of excretion was observed for breath hydrogen, with a decrease during the early morning followed by a progressive increase during the rest of the day. Methane excretion was constant throughout the day. This study shows that four samples collected at convenient times (0600, 1300, 1800, and 2200 hr) are optimal to characterize individuals by their breath excretions of hydrogen and methane during a 24-hr period

Measurement of complex fragments and clues to the entropy production from 42-137-MeV/nucleon Ar + Au

Intermediate-rapidity fragments with A=1-14 emitted from 42-137-MeV/nucleon Ar + Au have been measured. Evidence is presented that these fragments arise from a common moving source. Entropy values are extracted from the mass distributions by use of quantum statistical and Hauser-Feshbach theories. The extracted entropy values of S/A≈2-2.4 are much smaller than the values expected from measured deuteron-to-proton ratios, but are still considerably higher than theoretically predicted values