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At least 235 records · Page 13

A General Method for Solving Systems of Non-Linear Equations

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Nachtsheim, Philip R.↗

Use of the quasilinearization algorithm for the simulation of LSS slewing

The use of the Maximum Principle for the large angle slewing of large space structures (LSS) usually results in the so-called two-point boundary-value problem, in which many requirements (e.g., minimum time, small amplitude, and limited control power, etc.) must be satisfied simultaneously. The successful solution of this problem depends largely on the use of an efficient numerical algorithm. There are many candidate algorithms available for this problem (e.g., quasilinearization, gradient, etc.). Here researchers discuss only the quasilinearization method which has been used for several cases of large angle slewing of LSS. The basic idea of this algorithm is to make a series of successive approximations of the solution from a particular solvable case (linear or nonlinear) to a more general practical case. For the rigid spacecraft slewing problem with no constraints on the controls, the solution procedure can be found in the literature. This procedure needs to be modified if a minimum time for the slewing problem is desired with control limits given. Recently, an indirect method for finding the minimum time was developed to meet all these requirements. For the general mixed (including both rigid and flexible parts) problem, an additional constraint of small vibrational amplitude on the flexible parts is imposed.

Li, Feiyue↗

A Novel Technique for Distributed Measuring of Strain in the Vadose Zone

Characterizing water content and pressure changes in the vadose zone is important to understanding a variety of geologic processes, ranging from permeability, to evapotranspiration, and aquifer recharge. Changes in water content, or pressure, cause strain in the solid porous medium of the vadose zone, and it is possible that measuring those strains could be used a characterization tool. The Coherence-length-gated Microwave Photonics Interferometry (CMPI) technique measures strain at high resolution along many intervals defined by pairs of reflectors distributed along an optical fiber. This technique has recently been developed at Clemson University, and it has the spatial, and temporal resolution to characterize the strains that are expected to occur with hydrologic changes in the vadose zone. However, the technique has never been used to measure strain in porous media, so its capabilities remain uncertain. The objective of this thesis is to evaluate the ability of using CMPI to measure strain changes in the vadose zone. The research approach consists of conducting laboratory tests using a column filled with sand that was subjected to changes in water content and pressure. An optical fiber with CMPI reflectors was deployed in a high surface area ribbon and used to measure strain along the axis of the column. The column was made from 8-inch, Schedule 40 PVC pipe (75 cm tall, 20 cm inner diameter) and filled with medium-grained sand (K = 2.5x10-6 m/s, porosity = 0.28, Coefficient of Uniformity = 2, van Genuchten (n = 4.34 and  = 0.00039 m-1), Young’s Modulus = 18 – 47 MPa). Five pressure and four temperature sensors attached to probes inserted into the wall. The optical fiber includes five reflectors spaced 10 cm apart on the inside and outside of the column along the vertical axis. Strain measurements are made between pairs of reflectors. The reflectors are created in 250-micron-diameter acrylate-coated single mode Corning SMF28e+ optical fiber using a femtosecond laser. The optical fiber was laminated between two pieces of polyester film creating a large surface area to transfer strain from the porous media to the optical fiber. The experiments were conducted by filling the column from the bottom or infiltrating water from the top. The water was allowed to equilibrate to room temperature prior to each test in order to limit thermoelastic strain. Five injection tests with a rate of 250 ml/min and three infiltration tests at varying rates were conducted, and the results show patterns of strain and pressure are generally similar. Hydrologic conditions define three zones based on the pressure magnitude and distribution. 1.) Ambient Zone where the pressure heads are quasi-static and the pressure gradient is roughly unity (head gradient of zero). This is the uppermost zone and is characterized by negative pressures. 2.) Transition Zone where the pressures increase from ambient to zero, are changing relatively rapidly and the pressure gradient is relatively steep (pressure head gradients of 2). The Transition zone is 10 to 15 cm thick. 3.) Positive Pressure Zone where the pressure is positive, the rate of change is slower than in the transition zone and the gradient is flatter (pressure head gradient 1.1 to 1.2). This is the lowest zone in the column. Injection of water causes the pressure to increase and the three zones to move upward. The Transition zone moves at a rate of approximately 0.0002 m/s +/- .00005, according to analyses of pressure profiles. This is the same as the average velocity of the water calculated as volumetric flux/effective porosity =5.4x10-5 m/s/0.28. Strain signals in the range of 10s  were observed with a noise level of generally less than 0.1  (signal to noise ratio of greater than 100) during injection and drainage. The spatial and temporal distributions of strain caused by injection depend on the location of the moving pressure zones. The locations of the different pressure zones were determined from pressure profiles at different times and these data were transferred to strain time series. This showed that strain in the Ambient pressure zone is either unchanged or slightly compressive, whereas strain in Transition zone is tensile and roughly proportional to the pressure change, and strain ranges from tensile to compressive in the Positive Pressure zone. In general, the strain is variable at the top of the Positive Pressure zone, but it appears to be consistently tensile lower in the zone. The spatial distribution of strain causes three distinct stages in the strain times series measured between pairs of CMPI reflectors. The strain is unchanged or slightly compressive during Stage 1, it increases (positive strain is tensile) approximately linearly at a rate of 0.02 to 0.03 μ/s during the Stage 2, and then flattens out in Stage 3. The strain increases again during Stage 4 of the time series. The pressure also changes in stages. It is unchanged during Stage 1 and then increases relatively rapidly at a rate of between 4 and 10 Pa/s during Stage 2 and continues to increase during Stages 3 and 4, but at a rate slightly slower than during Stage 2 (from 2.5 to 3.5 Pa/s). The rates of pressure and strain change are consistent with basic analyses. The rate of pressurization is similar to the calculated velocity of flow in the saturated zone, and this is similar to the measured velocity of the strain increase. The ratio of the pressurization rate and strain rate during Stage 2 (2.5 (Pa/s) /0.03 (μ/s)) is 80 MPa, which is approximately equal to the upper range expected considering the uniaxial compression and the Young’s Modulus of the sand. An interesting effect occurs when the upper surface of the sand becomes saturated. Significant compression (several 10s of ) occurs as the pressure and saturation increase at the upper surface. Compression occurs throughout the column, but the effect is greatest at the top of the column. The rate of compression is fastest slightly before ponding occurs, but it slows markedly and nearly stops when water starts to accumulate at the surface (ponding). This effect reverses when the surface of the sand is drained, resulting in tension throughout the column. The compression caused by this effect can be as large or larger than the tensile strain that accumulated during filling. This effect was unexpected because increasing pressure is normally associated with tensile strain. Nevertheless, this effect was observed consistently in all tests where the pressure changes at the upper surface, including tests where water was injected from below or infiltrated from above. This effect behaves as if the pore pressure at the upper surface of the sand exerts a normal force on the boundary (increasing pore pressure exerts a downward compression on the boundary). The results of these laboratory experiments indicate that CMPI can measure strain caused by fluid pressure changes in the vadose zone with a signal to noise ratio of 100 or more. Injection and drainage cause a strain signal that is complex, but repeatable. The magnitudes of the strain signal are consistent with magnitudes that are expected based on poroelastic calculations using independently measured properties of the sand. These results indicate that the CMPI technique with an optical fiber laminated in a polyester ribbon generates data that represent the strain distribution during hydrologic processes of imbibition and drainage in variably saturated sand. This suggests that distributed strain measurements using CMPI could be a viable approach for evaluating processes in the vadose zone, laying the groundwork for future field implementation.

47 OTHER INSTRUMENTATION↗

Regolith layering processes based on studies of low-temperature volatile elements in Apollo core samples

The concentrations of Hg released at at the most 130 C increase with depth in near-surface samples from cores. This is in response to a daytime thermal gradient with temperatures of approximately 400 K at the surface decreasing to approximately 250 K at greater than 10 cm depth (Keihm and Langseth, 1973). The steepness of the slopes and the depths to which the concentration gradients extend appear to be determined by the color, density and possibly the grain size of the soils. Earlier surface layers can be identified and, in general, are in agreement with other indicators of such layers. Low temperature volatilized Br exhibits trends that parallel those of Hg in a number of cases. This is also true of Br and Hg fractions released in stepwise heating experiments at higher temperatures. The coherence, especially in higher temperature fractions, between these chemically dissimilar elements implies a common physical process of entrapment; possibly one related to the presence of vapor deposits on surfaces and to opening and closing of microcracks and pores.

Jovanovic, S.↗

Similarity analysis of compressor tip clearance flow structure

A new approach is presented for analyzing compressor tip clearance flow. The basic idea is that the clearance velocity field can be (approximately) decomposed into independent throughflow and crossflow, since chordwise pressure gradients are much smaller than normal pressure gradients in the clearance region. As in the slender body approximation in external aerodynamics, this description implies that the three-dimensional steady clearance flow can be viewed as a two-dimensional, unsteady flow. Using this approach, a similarity scaling for the crossflow in the clearance region is developed and a generalized description of the clearance vortex is derived. Calculations based on the similarity scaling agree well with a wide range of experimental data in regard to flow features such as crossflow velocity field, static pressure field, and tip clearance vortex trajectory.

Chen, G. T.↗

Radiative transfer in dusty nebulae. III - The effects of dust albedo

The effects of an albedo of internal dust, such as ionization structure and temperature of dust grain, were studied by the quasi-diffusion method with an iterative technique for solving the radiative heat transfer equations. It was found that the generalized on-the-spot approximation solution is adequate for most astrophysical applications for a zero albedo; for a nonzero albedo, the Eddington approximation is more accurate. The albedo increases the average energy of the diffuse photons, increasing the ionization level of hydrogen and heavy elements if the Eddington approximation is applied; the dust thermal gradient is reduced so that the infrared spectrum approaches blackbody spectrum with an increasing albedo.

Petrosian, V.↗

Global collocation methods for approximation and the solution of partial differential equations

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

Solomonoff, A.↗

Pore Formation and Mobility Investigation (PPMI): Description and Initial Analysis of Experiments Conducted aboard the International Space Station

Flow visualization experiments during the controlled directional melt back and re-solidification of succinonitrile (SCN) and SCN-water mixtures were conducted using the Pore Formation and Mobility Investigation (PFMI) apparatus in the glovebox facility (GBX) aboard the International Space Station. The study samples were initially 'cast' on earth under 450 millibar of nitrogen into 1 cm ID glass sample tubes approximately 30 cm in length, containing 6 in situ thermocouples. During the Space experiments, the processing parameters and flow visualization settings are remotely monitored and manipulated from the ground Telescience Center (TSC). The ground solidified sample is first subjected to a unidirectional melt back, generally at 10 microns per second, with a constant temperature gradient ahead of the melting interface. Bubbles of different sizes are seen to initiate at the melt interface and, upon release from the melting solid, translate at different speeds in the temperature field ahead of them before coming to rest. Over a period of time these bubbles dissolve into the melt. The gas-laden liquid is then directionally solidified in a controlled manner, generally starting at a rate of 1 micron /sec. Observation and preliminary analysis of bubble formation and mobility in pure SCN samples during melt back and the subsequent structure resulting during gas generation upon re-solidification are presented and discussed.

Grugel, R. N.↗

Pore Formation and Mobility Investigation (PFMI): Description and Initial Analysis of Experiments Conducted aboard the International Space Station

Flow visualization experiments during the controlled directional melt back and re-solidification of succinonitrile (SCN) and SCN-water mixtures were conducted using the Pore Formation and Mobility Investigation (PFMI) apparatus in the glovebox facility (GBX) aboard the International Space Station. The study samples were initially "cast" on earth under 450 millibar of nitrogen into 1 cm ID glass sample tubes approximately 30 cm in length, containing 6 in situ thermocouples. During the Space experiments, the processing parameters and flow visualization settings are remotely monitored and manipulated from the ground Telescience Center (TSC). The ground solidified sample is first subjected to a unidirectional melt back, generally at 10 microns per second, with a constant temperature gradient ahead of the melting interface. Bubbles of different sizes are seen to initiate at the melt interface and, upon release from the melting solid, translate at different speeds in the temperature field ahead of them before coming to rest. Over a period of time these bubbles dissolve into the melt. The gas-laden liquid is then directionally solidified in a controlled manner, generally starting at a rate of 1 micron /sec. Observation and preliminary analysis of bubble formation and mobility in pure SCN samples during melt back and the subsequent structure resulting during gas generation upon re-solidification are presented and discussed.

Grugel, R. N.↗

Observations of Sk-69 deg 203 and the interstellar extinction towards SN 1987A

Optical and UV spectroscopic observations of the Large Magellanic Cloud (LMC) star Sk-69 deg 203 are discussed. The optical data reveal Sk-69 deg 203 to be a BO.7 Ia supergiant with a moderate nitrogen enhancement, and its UV spectrum is consistent with this classification. UV interstellar extinction curves were constructed for the star using, as flux standards, two lightly reddened LMS supergiants, which bracket Sk-69 deg 203's spectral type. The resultant extinction curves are consistent with the extinction law derived previously for the 30 Doradus region, and the results for Sk-69 deg 203 suggest that the general 30 Doradus extinction law is appropriate for dereddening the observed fluxes of SN 1987A. Published H I 21 observations place SN 1987A in a region with a strong E-W gradient in the total hydrogen content. Comparison with the H I column density implied by the reddening indicates that the supernova is imbedded approximately in the middle of the main H I complex.

Fitzpatrick, Edward L.↗

Effects of Adverse Pressure Gradient on the Incompressible Reattaching Flow Over a Rearward-Facing Step

The turbulent, incompressible reattaching flow over a rearward-facing step has been studied by many researchers over the years. One of the principal quantities determined in these experiments has been the distance from the step to the point (or region) where the separated shear layer reattaches to the surface (x(r)). The values for x(r)/h, where h is the step height, have covered a wider range than can reasonably be attributed to experimental technique or inaccuracy. Often the reason for a largely different value of x(r)/h can be attributed to an incompletely developed turbulent layer, or a transitional or laminar boundary layer. However, for the majority of experiments where the boundary layer is believed to be fully developed and turbulent, x(r)/h still varies several step heights; generally, 5 1/2 approximately < x(r)/h approximately < 7 1/2. This observed variation has usually been attributed to such variables as l/h (step length to height, h/delta (step height to initial boundary-layer thickness), R(e)(theta)), or the experimental technique for determining reattachment location. However, there are so many different combinations of variables in the previous experiments that it was not possible to sort out the effects of particular conditions on the location of reattachment. In the present experiment velocity profiles have been measured in and around the region of separated flow. Results show a large influence of adverse pressure gradient on the reattaching flow over a rearward-facing step that has not been reported previously. Further, the many previous experiments for fully developed, turbulent flow in parallel-walled channels have shown a range of reattachment location that has not been explained by differences in initial flow conditions. Although these initial flow conditions might contribute to the observed variation of reattachment location, it appears that the pressure gradient effect can explain most of that variation.

Kuehn, Donald M.↗

New Observations of the Heliospheric Magnetic Field from the Voyager Spacecraft

We review recent observations of variations of the heliospheric magnetic field B(t) made by Voyager 1 and 2 (V1 and V2), and we discuss the boundary conditions needed for models to explain the observations. Usually, observations from a spacecraft close to the Sun, such as ACE, WIND or Ulysses are used as input to a time-dependent model. Generally, the predicted profile B(t) can be compared directly with the observed profile only when either V1 or V2 is approximately radially aligned with a near-Sun spacecraft; this happens rarely and only for a brief time interval. The Bastille Day events illustrate this situation. In the absence of radial alignment of the spacecraft it is possible to predict the development of a global structure (a GMIR) with data from ACE or WIND, if they obtain a representative sample the flows that merge to form a GMIR. When latitudinal gradients are small and when there is statistical homogeneity in the azimuthal direction, it is possible to predict the statistical properties of the large-scale fluctuations of B(t) observed by V1 or V2 during a year or so. We illustrate this situation with observations from the recent solar maximum and the declining phase of the solar cycle. Predictions of detailed observations made by V1 and V2 under general conditions (e.g., when there is a large latitudinal gradient) require boundary conditions as a function of time on a surface, such as a Sun-centered sphere with a radius of 1 AU. These conditions can only be provided by global solar observations. We suggest the feasibility of such an approach, using V2 observations for 2005 and 2006. The prediction of observations in the heliosheath requires the solution of the 3-D boundary problem for the supersonic solar wind and propagation of solar wind through the termination shock into the heliosphere. The properties of B(t) observed in the heliosheath have not yet been predicted.

Burlaga, Leonard F.↗

Overall chilled water system energy consumption modeling and optimization

The emergence of increasingly affordable variable-speed drive technology has changed the approach used to control chilled water systems equipped with these drives. The purpose of this research was to develop an integrated chilled water modeling technique that can determine the optimal system setpoints and estimate the energy saving potential of chiller system. The chiller system equipped with Variable Frequency Drives (VFDs) on cooling tower fans and condenser water pumps. To accomplish the objective, physical component models of the centrifugal chiller, cooling tower and condenser water pump were established with the goal of incorporating the system’s condenser water flow rate and cooling tower fan speeds as optimization variables. Furthermore, a cooling load prediction algorithm was developed using a multiple non-linear regression model to approximate the building’s cooling load subject to a range of environmental conditions. The inputs and outputs of the individual component models were linked to estimate how adjusting the cooling tower fan and condenser water pump speed would influence the system’s comprehensive performance. Here, the overall system model was then optimized using a generalized reduced gradient optimization algorithm to determine the potential energy savings through speed control with VFDs and to ascertain a control logic strategy for the building automation system to operate the heating and cooling system. A case-study was performed on a single chiller system at a museum and the model was calibrated according to logged data collected over four months. Results showed that for the system analyzed, the energy saving of optimizing the cooling tower fan system was found to be 12–15%, while the energy saving potential of optimizing the condenser water pump with the cooling tower fan was negligible. Additionally, comparing different cooling tower fan control strategies showed that a wet-bulb approach-based cooling tower control strategy was shown to have the highest correlation to the optimized fan speed with an R 2 of 0.924.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Estimates of Terms in Ohm's Law During an Encounter with an Electron Diffusion Region

We present measurements from the Magnetospheric Multiscale (MMS) mission taken during a reconnection event on the dayside magnetopause which includes a passage through an electron diffusion region (EDR). The four MMS satellites were separated by about 10 km such that estimates of gradients and divergences allow a reasonable estimate of terms in the generalized Ohm's law, which is key to investigating the energy dissipation during reconnection. The strength and character of dissipation mechanisms determines how magnetic energy is released. We show that both electron pressure gradients and electron inertial effects are important, but not the only participants in reconnection near EDRs, since there are residuals of a few mVm (approximately 30-50%) of E+ U(sub e) x B (from the sum of these two terms) during the encounters. These results are compared to a simulation, which exhibits many of the observed features, but where relatively little residual is present.

Torbert, R. B.↗

Probabilistic partition of unity networks for high–dimensional regression problems

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly paralleliazable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. Here, we also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.

97 MATHEMATICS AND COMPUTING↗

Correction of Doppler-broadened Rayleigh backscattering effects in H2O dial measurements

A general method of solutions for treating effects of Doppler-broadened Rayleigh backscattering in H2O Differential Absorption Lidar (DIAL) measurements are described and discussed. Errors in vertical DIAL measuremtns caused by this laser line broadening effect can be very large and, therfore, this effect has to be accounted for accurately. To analyze and correct effects of Doppler-broadened Rayleigh backscattering in DIAL experiments, a generalized DIAL approximation was derived starting from a lidar equation, which includes Doppler broadening. To evaluate the accuracy of H2O DIAL measurements, computer simulations were performed. It was concluded that correction of Doppler broadened Rayleigh backscattering is possible with good accuracy in most cases of tropospheric H2O DIAL measurements, but great care has to be taken when layers with steep gradients of Mie backscattering like clouds or inversion layers are present.

Ansmann, A.↗

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗

The early evolution of the solar system

The problems of relating collapse conditions in an interstellar cloud to a model of the primitive solar nebula are discussed. In such a nebula there is a radial force balance between gravity, the pressure gradient, and centrifugal forces due to the rotation. Approximate values are given for the combinations of temperature and density throughout the nebula, from a maximum of about 2000 K near the center to less than 200 K in the outer portion. These conditions are based upon the compression adiabats in the terminal stages of the collapse of an interstellar cloud. One general conclusion, of great importance for accumulation of bodies within the solar system, is that interstellar grains should not be completely evaporated at distances in the nebula beyond about one or more astronomical units.

Cameron, A. G. W.↗