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At least 127 records · Page 7

Solving multiple scattering problems in planetary atmospheres

Definitions are provided of the basic concepts occurring in the solution of multiple scattering problems involving planetary atmospheres and attention is given to aspects of problem characterization. Approaches are considered for finding the answer to a particular problem without the performance of detailed calculations. The characteristics of albedos are investigated, taking into account semiinfinite atmospheres and finite atmospheres. Questions of surface illumination are discussed along with aspects related to energy deposition in the atmosphere, intensity, and polarization. Precise numerical methods are examined and analytical solutions are presented.

Irvine, W. M.↗

Fault Tolerance in ZigBee Wireless Sensor Networks

Wireless sensor networks (WSN) based on the IEEE 802.15.4 Personal Area Network standard are finding increasing use in the home automation and emerging smart energy markets. The network and application layers, based on the ZigBee 2007 PRO Standard, provide a convenient framework for component-based software that supports customer solutions from multiple vendors. This technology is supported by System-on-a-Chip solutions, resulting in extremely small and low-power nodes. The Wireless Connections in Space Project addresses the aerospace flight domain for both flight-critical and non-critical avionics. WSNs provide the inherent fault tolerance required for aerospace applications utilizing such technology. The team from Ames Research Center has developed techniques for assessing the fault tolerance of ZigBee WSNs challenged by radio frequency (RF) interference or WSN node failure.

Alena, Richard↗

Implementation of a fully-balanced periodic tridiagonal solver on a parallel distributed memory architecture

While parallel computers offer significant computational performance, it is generally necessary to evaluate several programming strategies. Two programming strategies for a fairly common problem - a periodic tridiagonal solver - are developed and evaluated. Simple model calculations as well as timing results are presented to evaluate the various strategies. The particular tridiagonal solver evaluated is used in many computational fluid dynamic simulation codes. The feature that makes this algorithm unique is that these simulation codes usually require simultaneous solutions for multiple right-hand-sides (RHS) of the system of equations. Each RHS solutions is independent and thus can be computed in parallel. Thus a Gaussian elimination type algorithm can be used in a parallel computation and the more complicated approaches such as cyclic reduction are not required. The two strategies are a transpose strategy and a distributed solver strategy. For the transpose strategy, the data is moved so that a subset of all the RHS problems is solved on each of the several processors. This usually requires significant data movement between processor memories across a network. The second strategy attempts to have the algorithm allow the data across processor boundaries in a chained manner. This usually requires significantly less data movement. An approach to accomplish this second strategy in a near-perfect load-balanced manner is developed. In addition, an algorithm will be shown to directly transform a sequential Gaussian elimination type algorithm into the parallel chained, load-balanced algorithm.

Eidson, T. M.↗

A multiple-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations

A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.

Atkins, Harold↗

Dynamic analysis of a magnetic bearing system with flux control

Using measured values of two-dimensional forces in a magnetic actuator, equations of motion for an active magnetic bearing are presented. The presence of geometric coupling between coordinate directions causes the equations of motion to be nonlinear. Two methods are used to examine the unbalance response of the system: simulation by direct integration in time; and determination of approximate steady state solutions by harmonic balance. For relatively large values of the derivative control coefficient, the system behaves in an essentially linear manner, but for lower values of this parameter, or for higher values of the coupling coefficient, the response shows a split of amplitudes in the two principal directions. This bifurcation is sensitive to initial conditions. The harmonic balance solution shows that the separation of amplitudes actually corresponds to a change in stability of multiple coexisting solutions.

Knight, Josiah↗

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.

42 ENGINEERING↗

Accurate orbit determination strategies for the tracking and data relay satellites

The National Aeronautics and Space Administration (NASA) has developed the Tracking and Data Relay Satellite (TDRS) System (TDRSS) for tracking and communications support of low Earth-orbiting satellites. TDRSS has the operational capability of providing 85% coverage for TDRSS-user spacecraft. TDRSS currently consists of five geosynchronous spacecraft and the White Sands Complex (WSC) at White Sands, New Mexico. The Bilateration Ranging Transponder System (BRTS) provides range and Doppler measurements for each TDRS. The ground-based BRTS transponders are tracked as if they were TDRSS-user spacecraft. Since the positions of the BRTS transponders are known, their radiometric tracking measurements can be used to provide a well-determined ephemeris for the TDRS spacecraft. For high-accuracy orbit determination of a TDRSS user, such as the Ocean Topography Experiment (TOPEX)/Poseidon spacecraft, high-accuracy TDRS orbits are required. This paper reports on successive refinements in improved techniques and procedures leading to more accurate TDRS orbit determination strategies using the Goddard Trajectory Determination System (GTDS). These strategies range from the standard operational solution using only the BRTS tracking measurements to a sophisticated iterative process involving several successive simultaneous solutions for multiple TDRSs and a TDRSS-user spacecraft. Results are presented for GTDS-generated TDRS ephemerides produced in simultaneous solutions with the TOPEX/Poseidon spacecraft. Strategies with different user spacecraft, as well as schemes for recovering accurate TDRS orbits following a TDRS maneuver, are also presented. In addition, a comprehensive assessment and evaluation of alternative strategies for TDRS orbit determination, excluding BRTS tracking measurements, are presented.

Oza, D. H.↗

Forced stationary solutions in a barotropic channel: Multiple equilibria and theory of nonlinear resonance

A barotropic flow over sinusoidal topography in a beta channel in the presence of forcing and dissipation was studied. The work is divided into two parts: (1) computation of the stationary solutions of the model, by Newton's method together with a finite difference approximation, and comparison of solutions with the solutions of the linear theory; (2) development of a nonlinear theory that reproduce the numerical solutions.

Rambaldi, S.↗

MHD intermediate shocks in coronal mass ejections

A simplified model of coronal mass ejections is considered in which at least a portion of the interaction with the background corona involves a shock wave, and the allowable shock solutions and their compressive signatures are examined. The MHD shock-jump equations have a maximum of three possible types of solutions with an entropy rise for fixed values of the physical variables (slow, intermediate, and fast shocks). However, one of the three solution classes (the intermediate shock) is widely believed to not occur in nature and is regarded as nonevolutionary or extraneous. Without the intermediate shock, there is no multiplicity of solutions in that only one shock (or none) can occur for given physical values. All three potential shock types are considered, and it is shown solely on the basis of the shock-jump equations, that intermediate shocks must exist along some segment of the shock front for certain parametric regimes and for conditions that probably occur in some coronal mass ejections.

Steinolfson, R. S.↗

Multiple steady states in atmospheric chemistry

The equations describing the distributions and concentrations of trace species are nonlinear and may thus possess more than one solution. This paper develops methods for searching for multiple physical solutions to chemical continuity equations and applies these to subsets of equations describing tropospheric chemistry. The calculations are carried out with a box model and use two basic strategies. The first strategy is a 'search' method. This involves fixing model parameters at specified values, choosing a wide range of initial guesses at a solution, and using a Newton-Raphson technique to determine if different initial points converge to different solutions. The second strategy involves a set of techniques known as homotopy methods. These do not require an initial guess, are globally convergent, and are guaranteed, in principle, to find all solutions of the continuity equations. The first method is efficient but essentially 'hit or miss' in the sense that it cannot guarantee that all solutions which may exist will be found. The second method is computationally burdensome but can, in principle, determine all the solutions of a photochemical system. Multiple solutions have been found for models that contain a basic complement of photochemical reactions involving O(x), HO(x), NO(x), and CH4. In the present calculations, transitions occur between stable branches of a multiple solution set as a control parameter is varied. These transitions are manifestations of hysteresis phenomena in the photochemical system and may be triggered by increasing the NO flux or decreasing the CH4 flux from current mean tropospheric levels.

Stewart, Richard W.↗

Natural convection in melt crystal growth - The influence of flow pattern on solute segregation

The results of two lines of research aimed at calculating the structure of the flows driven by buoyancy in small-scale crystal growth systems and at understanding the coupling between these flows, the shape of the solidification interface, and dopant segregation in the crystal are reviewed. First, finite-element methods are combined with computer-aided methods for detecting multiple steady solutions to analyze the structure of the buoyancy-driven axisymmetric flows in a vertical cylinder heated from below. This system exhibits onset of convection, multiple steady flows, and loss of the primary stable flow beyond a critical value of the Rayleigh number. Second, results are presented for calculations of convection, melt/solid interface shape, and dopant segregation within a vertical ampoule with thermal boundary conditions that represent a prototype of the vertical Bridgman growth system.

Brown, R. A.↗

H2, fixed architecture, control design for large scale systems

The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.

Mercadal, Mathieu↗

CRICKET: Cryogenic Reservoir Inventory by Cost-Effective Kinetically Enhanced Technology

NASA PROGRAMMATIC CHALLENGE: Locate hidden water ice in the darkest, coldest places on the moon using dozens of simple, autonomous robots. CONCEPTUAL SOLUTION: Use multiple small, autonomous bots to search for hidden water ice in permanently shadowed regions of the surface of the moon. Bots will locate and tag hidden water ice for follow up missions.Technical Basis for proposed solution: use of emerging and maturing technologies - MEMS, Cubesats, Sensor nets, integrated devices – will minimize cost risk and maximize return. Benefits: Cricket will enable human exploration through in-situ resource utilization: Cricket will demonstrate a distributed constellation to achieve a key NASA goal of novel uses of commercially available technologies. Cricket will reignite public interest in lunar exploration through a sustained human, and robotic, presence on the moon. Technical Approach: The cricket constellation has three members: the "queen"; the "hive" and the "cricket" foragers. The queen transports the hive an its crickets to the moon. The hive lands on the surface and disperses the crickets (there may be more than one species of cricket). The crickets then use the hive as a communications and recharging hub. Each cricket hosts algorithms that allow it to explore its surroundings and monitor its power state - something like a lunar Roomba - and return for recharging. If they are lost due to power or surface condition problems, replacements can carry out the hive tasks. The two most successful types of bio-inspired algorithms (BIAs) are evolutionary algorithms and swarm-based algorithms which are inspired by the natural evolution and collective behavior in animals.The evolution of the idea is summarized in Table 1 and Figure 1. NIAC context: This system integrates key elements from other NIAC efforts; it uses them and extends them into a meaningful whole

Cryogenics↗

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗

Chain conformations and phase separation in polymer solutions with varying solvent quality

Molecular dynamics simulations are used to investigate the conformations of a single polymer chain, represented by the Kremer-Grest bead-spring model, in a solution with a Lennard-Jones liquid as the solvent when the interaction strength between the polymer and solvent is varied. Results show that when the polymer-solvent interaction is unfavorable, the chain collapses as one would expect in a poor solvent. For more attractive polymer-solvent interactions, the solvent quality improves and the chain is increasingly solvated and exhibits ideal and then swollen conformations. However, as the polymer-solvent interaction strength is increased further to be more than about twice the strength of the polymer-polymer and solvent-solvent interactions, the chain exhibits an unexpected collapsing behavior. Correspondingly, for strong polymer-solvent attractions, phase separation is observed in the solutions of multiple chains. These results indicate that the solvent becomes effectively poor again at very attractive polymer-solvent interactions. Nonetheless, the mechanism of chain collapsing and phase separation in this limit differs from the case with a poor solvent rendered by unfavorable polymer-solvent interactions. In the latter, the solvent is excluded from the domain of the collapsed chains while in the former, the solvent is still present in the pervaded volume of a collapsed chain or in the polymer-rich domain that phase separates from the pure solvent. Finally, in the limit of strong polymer-solvent attractions, the solvent behaves as a glue to stick monomers together, causing a single chain to collapse and multiple chains to aggregate and phase separate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

OGLE-2018-BLG-1011Lb,c: Microlensing Planetary System with Two Giant Planets Orbiting a Low-mass Star

We report a multiplanetary system found from the analysis of microlensing event OGLE-2018-BLG-1011, for which the light curve exhibits a double-bump anomaly around the peak. We find that the anomaly cannot be fully explained by the binary-lens or binary-source interpretations and its description requires the introduction of an additional lens component. The 3L1S (three lens components and a single source) modeling yields three sets of solutions, in which one set of solutions indicates that the lens is a planetary system in a binary, while the other two sets imply that the lens is a multiplanetary system. By investigating the fits of the individual models to the detailed light curve structure, we find that the multiple-planet solution with planet-to-host mass ratios ∼9.5 X 10(exp −3) and ∼15 X 10(eap −3) are favored over the other solutions. From the Bayesian analysis, we find that the lens is composed of two planets with masses 1.8 (sup +3.4, sub -1.1) M(J) and 2.8 (sup +5.8, sub -1.7) M(J) around a host with a mass 0.18 (sup +0.33,sub - 0.10) M(ʘ) and located at a distance 7.1(sup +1.1, sub -1.5) kpc. The estimated distance indicates that the lens is the farthest system among the known multiplanetary systems. The projected planet–host separations are a(⊥,2) = 1.8 (sup +2.1, sub -1.5)au (0.8 (sup +0.9,sub -0.6 au) and a(⊥,3) = 0.8 (sup +0.9, sub -0.6)au , where the values of a(⊥,2) inside and outside the parenthesis are the separations corresponding to the two degenerate solutions, indicating that both planets are located beyond the snow line of the host, as with the other four multiplanetary systems previously found by microlensing.

Cheongho Han↗

Bifurcation Analysis Reveals Solution Structures of Phase Field Models

The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, in this study, we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models. Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions. To elucidate the idea, we apply this analytical approach to three representative phase field equations: the Allen-Cahn equation, the Cahn-Hilliard equation, and the Allen-Cahn-Ohta-Kawasaki system. The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.

97 MATHEMATICS AND COMPUTING↗

Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

Abstract Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction . For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.

Chen, Bin↗