Heating the Solar Atmosphere by the Self-Enhanced Thermal Waves Caused by the Dynamo Processes

We discuss a possible mechanism for heating the solar atmosphere by the ensemble of thermal waves, generated by the photospheric dynamo and propagating upwards with increasing magnitudes. These waves are self-sustained and amplified due to the specific dependence of the efficiency of heat release by Ohmic dissipation on the ratio of the collisional to gyro- frequencies, which in its turn is determined by the temperature profile formed in the wave. In the case of sufficiently strong driving, such a mechanism can increase the plasma temperature by a few times, i.e. it may be responsible for heating the chromosphere and the base of the transition region.Comment: v2: A number of minor corrections and additional explanations. AASTeX, 5 pages, 2 EPS figures, submitted to The Astrophysical Journa

An ADM 3+1 formulation for Smooth Lattice General Relativity

A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equations to evolve the lattice. Each time step will involve three basic steps. First, the coordinate quantities such as the Riemann and extrinsic curvatures are extracted from the lattice. Second, the 3+1 ADM equations are used to evolve the coordinate data, and finally, the coordinate data is used to update the scalar data on the lattice (such as the leg lengths). The scheme will be presented only for the case of vacuum spacetime though there is no reason why it could not be extended to non-vacuum spacetimes. The scheme allows any choice for the lapse function and shift vectors. An example for the Kasner $T^3$ cosmology will be presented and it will be shown that the method has, for this simple example, zero discretisation error.Comment: 18 pages, plain TeX, 5 epsf figues, gzipped ps file also available at http://newton.maths.monash.edu.au:8000/preprints/3+1-slgr.ps.g

Experimental Studies of the Aerothermal Characteristics of the Project Orion CEV heat Shield in High Speed Transitional and Turbulent Flows

An experimental program has been completed by CUBRC exploring laminar, transitional, and turbulent flows over a 7.0% scale model of the Project ORION CEV geometry. This program was executed primarily to answer questions concerning the increase in heat transfer on the windward, or "hot shoulder" of the CEV heat shield from laminar to turbulent flow. To answer these questions CUBRC constructed and instrumented a 14.0 inch diameter Project ORION CEV model and ran a range of Reynolds numbers based on diameter from 1.0 to over 40 million at a Mach number of 8.0. These Reynolds numbers were selected to cover laminar to turbulent heating data on the "hot shoulder". Data obtained during these runs will be used to guide design decisions as they apply to heat shield thickness and extent. Several experiments at higher enthalpies were achieved to obtain data for code validation with real gas effects and transition. CUBRC also performed computation studies of these experiments to aid in the data reduction process and study turbulence modeling

A Numerical Scheme for Invariant Distributions of Constrained Diffusions

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the corresponding stochastic networks and thus it is important to develop reliable and efficient algorithms for numerical computation of such distributions. In this work we propose and analyze a Monte-Carlo scheme based on an Euler type discretization of the reflected stochastic differential equation using a single sequence of time discretization steps which decrease to zero as time approaches infinity. Appropriately weighted empirical measures constructed from the simulated discretized reflected diffusion are proposed as approximations for the invariant probability measure of the true diffusion model. Almost sure consistency results are established that in particular show that weighted averages of polynomially growing continuous functionals evaluated on the discretized simulated system converge a.s. to the corresponding integrals with respect to the invariant measure. Proofs rely on constructing suitable Lyapunov functions for tightness and uniform integrability and characterizing almost sure limit points through an extension of Echeverria's criteria for reflected diffusions. Regularity properties of the underlying Skorohod problems play a key role in the proofs. Rates of convergence for suitable families of test functions are also obtained. A key advantage of Monte-Carlo methods is the ease of implementation, particularly for high dimensional problems. A numerical example of a eight dimensional Skorohod problem is presented to illustrate the applicability of the approach

Analysis of Alignment Algorithms with Mixed Dimensions for Dimensionality Reduction

SUMMARY We consider an alignment algorithm for reconstructing global coordinates of a given data set from coordinates constructed for data points in small local neighborhoods through computing a spectral subspace of an alignment matrix. We show that, under certain conditions, the null space of the alignment matrix recovers global coordinates even when local point sets have different dimensions. This result generalizes a previous analysis to allow alignment of local coordinates of mixed dimensions. We also extend this result to the setting of a semi-supervised learning problem and we present several examples to illustrate our results

Proceedings of the International Workshop on Numerical Modeling for Underground Mine Excavation Design

"Numerical models play a significant role in the design of safe underground mining excavations and support systems. Advances in the capabilities of numerical modeling software, together with ever increasing computational speeds, have made it possible to investigate the very nature of the large-scale rock mass and its response to mining excavations. The improved understanding of the rock response obtained from modeling enhances our designs, resulting in greater stability and safety of the mining excavations. To help advance the state of the art in this field, the National Institute for Occupational Safety and Health organized the International Workshop on Numerical Modeling for Underground Mine Excavation Design. The workshop was held in Asheville, NC, on June 28, 2009, in association with the 43rd U.S. Rock Mechanics Symposium. The proceedings include 10 papers from leading rock mechanics and numerical modeling experts in the United States, Canada, Australia, and Germany. The papers address a wide range of issues, including various numerical modeling approaches, rock mass modeling, and applications in coal and metal mines." - NIOSHTIC-2An efficient approach to numerical simulation of coal mine-related -- geotechnical issues / D. P. Adhikary and H. Guo -- A review of recent experience in modeling of caving / M. Board and M. E. Pierce -- Characterization of natural fragmentation using a discrete fracture network approach and implications for current rock mass classification systems / D. Elmo, S. Rogers, and D. Kennard -- Three-dimensional modeling of large arrays of pillars for coal mine design / G.S. Esterhuizen, and C. Mark -- Numerical model evaluation of floor-bearing capacity in coal mines / M. M. Gadde -- It is better to be approximately right than precisely wrong: why simple models work in mining geomechanics / R. E. Hammah and J. H. Curran -- An overview of calibrating and using the LaModel program for coal mine design / K. A. Heasley -- Deep coal longwall panel design for strong strata: the influence of software choice on results / M. K. Larson and J. K. Whyatt -- Practical application of numerical modeling for the study of sudden floor heave failure mechanisms / H. Maleki, C. Stewart, R. Stone, and J. Abshire -- Advanced numerical solutions for strata control in mining / A. Studeny and C. Scioredited by Gabriel S. Esterhuizen, Christopher Mark, Ted M. Klemetti, and Robert J. Tuchman."June 2009."Includes bibliographical references

Storm-water infiltration and focused recharge modeling with finite-volume two-dimensional Richards equation: application to an experimental rain garden

Rain gardens are infiltration systems that provide volume and water quality control, recharge enhancement, as well as landscape, ecological, and economic benefits. A model for application to rain gardens based on Richards equation coupled to a surface water balance was developed, using a two-dimensional finite-volume code. It allows for alternating upper boundary conditions, including ponding and overflow, and can simulate heterogeneous soil-layering or more complex geometries to estimate infiltration and recharge. The algorithm is conservative, and exhibits good performance compared to standard models for several test cases (less than 0.1% absolute mass balance error); simulations were also performed for an experimental rain garden and comparisons to collected data are presented. The model accurately simulated the matrix flow, soil water distribution, as well as deep percolation (potential recharge) for a natural rainfall event in the controlled experimental setup. Read More: http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29HY.1943-7900.0000111?prevSearch=authors%3A%28Dussaillant%2C%29&searchHistoryKey

Stress Rupture Life Reliability Measures for Composite Overwrapped Pressure Vessels

Composite Overwrapped Pressure Vessels (COPVs) are often used for storing pressurant gases onboard spacecraft. Kevlar (DuPont), glass, carbon and other more recent fibers have all been used as overwraps. Due to the fact that overwraps are subjected to sustained loads for an extended period during a mission, stress rupture failure is a major concern. It is therefore important to ascertain the reliability of these vessels by analysis, since the testing of each flight design cannot be completed on a practical time scale. The present paper examines specifically a Weibull statistics based stress rupture model and considers the various uncertainties associated with the model parameters. The paper also examines several reliability estimate measures that would be of use for the purpose of recertification and for qualifying flight worthiness of these vessels. Specifically, deterministic values for a point estimate, mean estimate and 90/95 percent confidence estimates of the reliability are all examined for a typical flight quality vessel under constant stress. The mean and the 90/95 percent confidence estimates are computed using Monte-Carlo simulation techniques by assuming distribution statistics of model parameters based also on simulation and on the available data, especially the sample sizes represented in the data. The data for the stress rupture model are obtained from the Lawrence Livermore National Laboratories (LLNL) stress rupture testing program, carried out for the past 35 years. Deterministic as well as probabilistic sensitivities are examined