NASA Astrophysics Data System (ADS)
Awaluddin, Moehammad; Yuwono, Bambang Darmo; Puspita, Yolanda Adya
2016-05-01
Continuous Global Positioning System (GPS) observations showed significant crustal displacements as a result of the 2010 Mentawai earthquake. The Least Square Inversion method of Mentawai earthquake slip distribution from SuGAR observations yielded in an optimum value of slip distribution by giving a weight of smoothing constraint and a weight of slip value constraint = 0 at the edge of the earthquake rupture area. A maximum coseismic slip of the inversion calculation was 1.997 m and concentrated around stations PRKB (Pagai Island). In addition, the values of dip-slip direction tend to be more dominant. The seismic moment calculated from the slip distribution was 6.89 × 10E+20 Nm, which is equivalent to a magnitude of 7.8.
If Coulomb's law were not inverse square: The charge distribution inside a solid conducting sphere
NASA Astrophysics Data System (ADS)
Spencer, Ross L.
1990-04-01
The distribution of charge between concentric conducting shells has been at the heart of the most sensitive tests of the exponent in Coulomb's law since the days of Henry Cavendish. But it appears that no one has ever answered the question of how an excess of charge would distribute itself throughout the interior of a solid conductor if Coulomb's law were other than inverse square. Spherically symmetric solutions to this problem have been found under the assumption that the potential of a point charge varies either as e-kr/r or as 1/rn.
On the Magic Square and Inverse
ERIC Educational Resources Information Center
Elzaidi, S. M.
2005-01-01
In this note, we give a method for finding the inverse of a three by three magic square matrix without using the usual methods for finding the inverse of a matrix. Also we give a method for finding the inverse of a three by three magic square matrix whose entries are also matrices. By using these ideas, we can construct large matrices whose…
Inverse-Square Orbits: A Geometric Approach.
ERIC Educational Resources Information Center
Rainwater, James C.; Weinstock, Robert
1979-01-01
Presents a derivation of Kepler's first law of planetary motion from Newtonian principles. Analogus derivations of the hyperbolic and parabolic orbits of nonreturning comets and the hyperbolic orbit for a particle in a repulsive inverse-square field are also presented. (HM)
Optical inverse-square displacement sensor
Howe, Robert D.; Kychakoff, George
1989-01-01
This invention comprises an optical displacement sensor that uses the inverse-square attenuation of light reflected from a diffused surface to calculate the distance from the sensor to the reflecting surface. Light emerging from an optical fiber or the like is directed onto the surface whose distance is to be measured. The intensity I of reflected light is angle dependent, but within a sufficiently small solid angle it falls off as the inverse square of the distance from the surface. At least a pair of optical detectors are mounted to detect the reflected light within the small solid angle, their ends being at different distances R and R+.DELTA.R from the surface. The distance R can then be found in terms of the ratio of the intensity measurements and the separation length as ##EQU1##
Optical inverse-square displacement sensor
Howe, R.D.; Kychakoff, G.
1989-09-12
This invention comprises an optical displacement sensor that uses the inverse-square attenuation of light reflected from a diffused surface to calculate the distance from the sensor to the reflecting surface. Light emerging from an optical fiber or the like is directed onto the surface whose distance is to be measured. The intensity I of reflected light is angle dependent, but within a sufficiently small solid angle it falls off as the inverse square of the distance from the surface. At least a pair of optical detectors are mounted to detect the reflected light within the small solid angle, their ends being at different distances R and R + [Delta]R from the surface. The distance R can then be found in terms of the ratio of the intensity measurements and the separation length as given in an equation. 10 figs.
Testing Newton's Gravitational Inverse-Square Law
NASA Astrophysics Data System (ADS)
Hagedorn, Charles
2015-04-01
Newton's inverse-square law of gravitation is the oldest standing mathematical description of a fundamental interaction. Experimental tests of gravity's distance-dependence define a frontier between our understanding of gravity and many proposed forms of new physics. These experiments constrain the size of possible extra dimensions, bound attempted resolution of the cosmological-constant problem, search for self-interacting chameleons, make direct measurements at the dark-energy length-scale, and more. As gravity is ~1040 times weaker than electromagnetism, gravity remains hidden by experimental backgrounds at distances smaller than the diameter of a fine human hair. This talk will survey the past, present, and near-future of the experimental field, with substantial emphasis on precision sub-millimeter laboratory experiments.
Models with inverse-square exchange
NASA Astrophysics Data System (ADS)
Ha, Z. N. C.; Haldane, F. D. M.
1992-10-01
A one-dimensional quantum N-body system of either fermions or bosons with SU(n) ``spins'' (or colors in particle physics language) interacting via inverse-square exchange is presented in this paper. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product-type wave function. The class of states we construct in this paper corresponds to the ground state and the low-energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state we find the harmonic fluid parameters (i.e., the charge, spin velocities, etc.) explicitly. The correlation exponent and the compressibility are also found. As expected, the general harmonic relation [i.e., vS=(vNvJ)1/2] is satisfied among the charge and spin velocities.
Laboratory Tests of the Inverse Square Law of Gravity
NASA Astrophysics Data System (ADS)
Schlamminger, Stephan
2010-02-01
Newton's inverse square force law of gravity follows directly from the fact that we live in a 3-dimensional world. For sub-millimeter length scales there may be undiscovered, extra dimensions. Such extra dimensions can be detected with inverse square law tests accessible to torsion balances. I will present an overview of two experiments that are being conducted at the University of Washington to search for gravitational-strength deviations from the inverse square law for extra dimension length scales smaller than 50 micrometers. One experiment is designed to measure the distance dependent force between closely spaced masses, whereas the second experiment is a null experiment and is only sensitive to a deviation from the inverse square law of gravity. The first experiment consists of a torsion pendulum that is suspended above a continuously rotating attractor. The attractor and the pendulum are disks with azimuthal sectors of alternating high and a low density. The torque on the pendulum disk varies as a function of the attractor angle with a 3 degree period. The amplitude of the torque signal is analyzed as a function of the separation between the pendulum and the attractor. The second experiment consists of a plate pendulum that is suspended parallel to a larger vertical plate attractor. The pendulum plate has an internal density asymmetry with a dense inlay on one half facing the attractor and another inlay on the other half on the side away from the attractor. If the inverse square law holds, the gravitational field of the attractor is uniform and the torque on the pendulum is independent of the gap between pendulum and attractor. The attractor position is modulated between a near and far position and the torque difference on the pendulum is recorded and analyzed for a possible inverse square law violation. )
Solving the Inverse-Square Problem with Complex Variables
ERIC Educational Resources Information Center
Gauthier, N.
2005-01-01
The equation of motion for a mass that moves under the influence of a central, inverse-square force is formulated and solved as a problem in complex variables. To find the solution, the constancy of angular momentum is first established using complex variables. Next, the complex position coordinate and complex velocity of the particle are assumed…
From Moon-Fall to Motions under Inverse Square Laws
ERIC Educational Resources Information Center
Foong, S. K.
2008-01-01
The motion of two bodies, along a straight line, under the inverse square law of gravity is considered in detail, progressing from simpler cases to more complex ones: (1) one body fixed and one free; (2) both bodies free and identical mass; (3) both bodies free and different masses; and (4) the inclusion of electrostatic forces for both bodies'…
The Inverse-Square Law with Data Loggers
ERIC Educational Resources Information Center
Bates, Alan
2013-01-01
The inverse-square law for the intensity of light received at a distance from a light source has been verified using various experimental techniques. Typical measurements involve a manual variation of the distance between a light source and a light sensor, usually by sliding the sensor or source along a bench, measuring the source-sensor distance…
A Data Analysis for the Inverse Square Law
ERIC Educational Resources Information Center
Downie, Russell
2007-01-01
When first encountered, inverse square laws can damage the confidence of beginning physics students whose maths skills are uncertain. Engaging in practical exercises that help them work with the idea can be a great help. We have used the following apparatus for a number of years and our students understand and enjoy the exercise.
The Confirmation of the Inverse Square Law Using Diffraction Gratings
ERIC Educational Resources Information Center
Papacosta, Pangratios; Linscheid, Nathan
2014-01-01
Understanding the inverse square law, how for example the intensity of light or sound varies with distance, presents conceptual and mathematical challenges. Students know intuitively that intensity decreases with distance. A light source appears dimmer and sound gets fainter as the distance from the source increases. The difficulty is in…
Robust inverse kinematics using damped least squares with dynamic weighting
NASA Technical Reports Server (NTRS)
Schinstock, D. E.; Faddis, T. N.; Greenway, R. B.
1994-01-01
This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.
Sub-Millimeter Tests of the Newtonian Inverse Square Law
Adelberger, Eric
2005-11-09
It is remarkable that small-scale experiments can address important open issues in fundamental science such as: 'why is gravity so weak compared to the other interactions?' and 'why is the cosmological constant so small compared to the predictions of quantum mechanics?' String theory ideas (new scalar particles and extra dimensions) and other notions hint that Newton's Inverse-Square Law could break down at distances less than 1 mm. I will review some motivations for testing the Inverse-Square Law, and discuss recent mechanical experiments with torsion balances, small-scillators, micro-cantilevers, and ultra-cold neutrons. Our torsion-balance experiments have probed for gravitational-strength interactions with length scales down to 70 micrometers, which is approximately the diameter of a human hair.
Short-range inverse-square law experiment in space
NASA Technical Reports Server (NTRS)
Paik, H. J.; Moody, M. V.
2002-01-01
Newton's inverse-square law is a cornerstone of General Relativity. Its validity has been demonstrated to better than one part in thousand in ranges greater than 1 cm. The range below 1 mm has been left largely unexplored, due to the difficulties associated with designing sensitive short-range experiments. However, the theoretical rationale for testing Newton's law at ranges below 1 mm has become very strong recently.
Short-range inverse-square law experiment in space
NASA Technical Reports Server (NTRS)
Strayer, D.; Paik, H. J.; Moody, M. V.
2002-01-01
The objective of ISLES (Inverse-Square Law Experiment in Space) is to perform a null test ofNewton's law on the ISS with a resolution of one part in lo5 at ranges from 100 pm to 1 mm. ISLES will be sensitive enough to detect axions with the strongest allowed coupling and to test the string-theory prediction with R z 5 pm.
Classical and quantum dynamics in an inverse square potential
NASA Astrophysics Data System (ADS)
Guillaumín-España, Elisa; Núñez-Yépez, H. N.; Salas-Brito, A. L.
2014-10-01
The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete "fall-to-the-center" with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence of bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.
Classical and quantum dynamics in an inverse square potential
Guillaumín-España, Elisa; Núñez-Yépez, H. N.; Salas-Brito, A. L.
2014-10-15
The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence of bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.
Attractive inverse square potential, U(1) gauge, and winding transitions.
Nisoli, Cristiano; Bishop, A R
2014-02-21
The inverse square potential arises in a variety of different quantum phenomena, yet notoriously it must be handled with care: it suffers from pathologies rooted in the mathematical foundations of quantum mechanics. We show that its recently studied conformality breaking corresponds to an infinitely smooth winding-unwinding topological transition for the classical statistical mechanics of a one-dimensional system: this describes the tangling or untangling of floppy polymers under a biasing torque. When the ratio between torque and temperature exceeds a critical value the polymer undergoes tangled oscillations, with an extensive winding number. At lower torque or higher temperature the winding number per unit length is zero. Approaching criticality, the correlation length of the order parameter-the extensive winding number-follows a Kosterlitz-Thouless-type law. The model is described by the Wilson line of a (0+1) U(1) gauge theory, and applies to the tangling or untangling of floppy polymers and to the winding or diffusing kinetics in diffusion-convection reactions. PMID:24579570
Attractive Inverse Square Potential, U(1) Gauge, and Winding Transitions
NASA Astrophysics Data System (ADS)
Nisoli, Cristiano; Bishop, A. R.
2014-02-01
The inverse square potential arises in a variety of different quantum phenomena, yet notoriously it must be handled with care: it suffers from pathologies rooted in the mathematical foundations of quantum mechanics. We show that its recently studied conformality breaking corresponds to an infinitely smooth winding-unwinding topological transition for the classical statistical mechanics of a one-dimensional system: this describes the tangling or untangling of floppy polymers under a biasing torque. When the ratio between torque and temperature exceeds a critical value the polymer undergoes tangled oscillations, with an extensive winding number. At lower torque or higher temperature the winding number per unit length is zero. Approaching criticality, the correlation length of the order parameter—the extensive winding number—follows a Kosterlitz-Thouless-type law. The model is described by the Wilson line of a (0+1) U(1) gauge theory, and applies to the tangling or untangling of floppy polymers and to the winding or diffusing kinetics in diffusion-convection reactions.
Superconducting gravity gradiometer and a test of inverse square law
NASA Technical Reports Server (NTRS)
Moody, M. V.; Paik, Ho Jung
1989-01-01
The equivalence principle prohibits the distinction of gravity from acceleration by a local measurement. However, by making a differential measurement of acceleration over a baseline, platform accelerations can be cancelled and gravity gradients detected. In an in-line superconducting gravity gradiometer, this differencing is accomplished with two spring-mass accelerometers in which the proof masses are confined to motion in a single degree of freedom and are coupled together by superconducting circuits. Platform motions appear as common mode accelerations and are cancelled by adjusting the ratio of two persistent currents in the sensing circuit. The sensing circuit is connected to a commercial SQUID amplifier to sense changes in the persistent currents generated by differential accelerations, i.e., gravity gradients. A three-axis gravity gradiometer is formed by mounting six accelerometers on the faces of a precision cube, with the accelerometers on opposite faces of the cube forming one of three in-line gradiometers. A dedicated satellite mission for mapping the earth's gravity field is an important one. Additional scientific goals are a test of the inverse square law to a part in 10(exp 10) at 100 km, and a test of the Lense-Thirring effect by detecting the relativistic gravity magnetic terms in the gravity gradient tensor for the earth.
On the pole of non-square transfer function matrix Moore-Penrose pseudo-inverses
NASA Astrophysics Data System (ADS)
Zhang, Wei; Ou, Linlin; He, Xing; Zhang, Weidong
2015-10-01
An essential step in many controller design approaches is computing the inverse of the plant. For a square plant, its inverse is stable if the plant is minimum phase (MP). Nevertheless, this conclusion does not hold for a non-square plant. In this paper, the pole feature of the Moore-Penrose pseudo-inverse of a non-square transfer function matrix is analysed. Instead of complicated advanced mathematical tools, only basic results of polynomial theory and the Binet-Cauchy theorem are used in the analysing procedure. The condition for testing the stability of the Moore-Penrose pseudo-inverse of an MP non-square transfer function matrix is given. This condition implies that the Moore-Penrose pseudo-inverse of a non-square transfer function matrix cannot be directly used as the optimal controller. Numerical examples are provided to illustrate the correctness of the condition.
Most-Perfect Pandiagonal Magic Squares and Their Moore-Penrose Inverse
ERIC Educational Resources Information Center
Trenkler, Dietrich; Trenkler, Gotz
2004-01-01
In this note 4 x 4 most-perfect pandiagonal magic squares are considered in which rows, columns and the two main, along with the broken, diagonals add up to the same sum. It is shown that the Moore-Penrose inverse of these squares has the same magic property.
Application of the least-squares inversion method: Fourier series versus waveform inversion
NASA Astrophysics Data System (ADS)
Min, Dong-Joo; Shin, Jungkyun; Shin, Changsoo
2015-11-01
We describe an implicit link between waveform inversion and Fourier series based on inversion methods such as gradient, Gauss-Newton, and full Newton methods. Fourier series have been widely used as a basic concept in studies on seismic data interpretation, and their coefficients are obtained in the classical Fourier analysis. We show that Fourier coefficients can also be obtained by inversion algorithms, and compare the method to seismic waveform inversion algorithms. In that case, Fourier coefficients correspond to model parameters (velocities, density or elastic constants), whereas cosine and sine functions correspond to components of the Jacobian matrix, that is, partial derivative wavefields in seismic inversion. In the classical Fourier analysis, optimal coefficients are determined by the sensitivity of a given function to sine and cosine functions. In the inversion method for Fourier series, Fourier coefficients are obtained by measuring the sensitivity of residuals between given functions and test functions (defined as the sum of weighted cosine and sine functions) to cosine and sine functions. The orthogonal property of cosine and sine functions makes the full or approximate Hessian matrix become a diagonal matrix in the inversion for Fourier series. In seismic waveform inversion, the Hessian matrix may or may not be a diagonal matrix, because partial derivative wavefields correlate with each other to some extent, making them semi-orthogonal. At the high-frequency limits, however, the Hessian matrix can be approximated by either a diagonal matrix or a diagonally-dominant matrix. Since we usually deal with relatively low frequencies in seismic waveform inversion, it is not diagonally dominant and thus it is prohibitively expensive to compute the full or approximate Hessian matrix. By interpreting Fourier series with the inversion algorithms, we note that the Fourier series can be computed at an iteration step using any inversion algorithms such as the
High Accuracy Optical Inverse Square Law Experiment Using Inexpensive Light to Frequency Converters
ERIC Educational Resources Information Center
Wanser, Keith H.; Mahrley, Steve; Tanner, Joshua
2012-01-01
In this paper we report on the use of two different light to frequency converters, four different light sources, three of which are novel and inexpensive, and a hand held digital multimeter with a frequency counter, suitable for making accurate and rapid determination of the optical inverse square law exponent of -2 to better than [plus or…
Analysis of Temperature Distributions in Nighttime Inversions
NASA Astrophysics Data System (ADS)
Telyak, Oksana; Krasouski, Aliaksandr; Svetashev, Alexander; Turishev, Leonid; Barodka, Siarhei
2015-04-01
Adequate prediction of temperature inversion in the atmospheric boundary layer is one of prerequisites for successful forecasting of meteorological parameters and severe weather events. Examples include surface air temperature and precipitation forecasting as well as prediction of fog, frosts and smog with hazardous levels of atmospheric pollution. At the same time, reliable forecasting of temperature inversions remains an unsolved problem. For prediction of nighttime inversions over some specific territory, it is important to study characteristic features of local circulation cells formation and to properly take local factors into account to develop custom modeling techniques for operational use. The present study aims to investigate and analyze vertical temperature distributions in tropospheric inversions (isotherms) over the territory of Belarus. We study several specific cases of formation, evolution and decay of deep nighttime temperature inversions in Belarus by means of mesoscale numerical simulations with WRF model, considering basic mechanisms of isothermal and inverse temperature layers formation in the troposphere and impact of these layers on local circulation cells. Our primary goal is to assess the feasibility of advance prediction of inversions formation with WRF. Modeling results reveal that all cases under consideration have characteristic features of radiative inversions (e.g., their formation times, development phases, inversion intensities, etc). Regions of "blocking" layers formation are extensive and often spread over the entire territory of Belarus. Inversions decay starts from the lowermost (near surface) layer (altitudes of 5 to 50 m). In all cases, one can observe formation of temperature gradients that substantially differ from the basic inversion gradient, i.e. the layer splits into smaller layers, each having a different temperature stratification (isothermal, adiabatic, etc). As opposed to various empirical techniques as well as
Renormalization of the Strongly Attractive Inverse Square Potential: Taming the Singularity
NASA Astrophysics Data System (ADS)
Alhaidari, A. D.
2014-10-01
Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle's state as it approaches the origin when the attractive coupling parameter is greater than the critical value of 1/4. Due to this unphysical divergence in oscillations, we are proposing that the interaction gets screened at short distances making the coupling parameter acquire an effective (renormalized) value that falls within the weak range 0 to 1/4. This prevents the oscillations form growing without limit giving a lower bound to the energy spectrum and forcing the Hamiltonian of the system to be self-adjoint. Technically, this translates into a regularization scheme whereby the inverse square potential is replaced near the origin by another that has the same singularity but with a weak coupling strength. Here, we take the Eckart as the regularizing potential and obtain the corresponding solutions (discrete bound states and continuum scattering states).
A novel study on Kepler’s law and inverse square law of gravitation
NASA Astrophysics Data System (ADS)
Zhang, Bingzhan; Zhen, Shengchao; Zhao, Han; Huang, Kang; Deng, Bin; Chen, Ye-Hwa
2015-05-01
The Udwadia-Kalaba equation is a simple, aesthetic, and thought-provoking description of the world at a very fundamental level. It is about the way systems move. In this paper, we creatively apply the Udwadia-Kalaba approach to study heavenly bodies’ movements (especially on Kepler’s law and the inverse square law of gravitation). In an alternative way, we show that a heavenly body’s motion orbit can be an ellipse, a circle, a hyperbola, or a parabola and show the conservation of angular momentum. Furthermore, by applying the Udwadia-Kalaba approach, we use the constraint of motion orbit (ellipse, circle, hyperbola, or parabola) and the conservation of angular momentum constraint (or energy conservation constraint) and easily verify that any heavenly body’s motion complies with the inverse square law of gravitation. That is, we study Kepler’s law and Newton’s inverse square law in an analytical way, which makes the dynamicist more clear about the way heavenly bodies move and also makes the celestial mechanician more clear about the analytical mechanics (the Udwadia-Kalaba approach). Furthermore, for the students of dynamics and celestial physics, a different unique perspective is provided for them to study. At the end, we present the detailed process of applying the Udwadia-Kalaba approach to two imaginary cases to show its simplicity and efficiency.
2013-01-01
Background A comparative study of the use of mean centering of ratio spectra and inverse least squares for the resolution of paracetamol, methylparaben, propylparaben, chlorpheniramine maleate and pseudoephedrine hydrochloride has been achieved showing that the two chemometric methods provide a good example of the high resolving power of these techniques. Method (I) is the mean centering of ratio spectra which depends on using the mean centered ratio spectra in four successive steps that eliminates the derivative steps and therefore the signal to noise ratio is improved. The absorption spectra of prepared solutions were measured in the range of 220–280 nm. Method (II) is based on the inverse least squares that depend on updating developed multivariate calibration model. The absorption spectra of the prepared mixtures in the range 230–270 nm were recorded. Results The linear concentration ranges were 0–25.6, 0–15.0, 0–15.0, 0–45.0 and 0–100.0 μg mL-1 for paracetamol, methylparaben, propylparaben, chlorpheniramine maleate and pseudoephedrine hydrochloride, respectively. The mean recoveries for simultaneous determination were between 99.9-101.3% for the two methods. The two developed methods have been successfully used for prediction of five-component mixture in Decamol Flu syrup with good selectivity, high sensitivity and extremely low detection limit. Conclusion No published method has been reported for simultaneous determination of the five components of this mixture so that the results of the mean centering of ratio spectra method were compared with those of the proposed inverse least squares method. Statistical comparison was performed using t-test and F-ratio at P = 0.05. There was no significant difference between the results. PMID:24028626
A least-squares estimation approach to improving the precision of inverse dynamics computations.
Kuo, A D
1998-02-01
A least-squares approach to computing inverse dynamics is proposed. The method utilizes equations of motion for a multi-segment body, incorporating terms for ground reaction forces and torques. The resulting system is overdetermined at each point in time, because kinematic and force measurements outnumber unknown torques, and may be solved using weighted least squares to yield estimates of the joint torques and joint angular accelerations that best match measured data. An error analysis makes it possible to predict error magnitudes for both conventional and least-squares methods. A modification of the method also makes it possible to reject constant biases such as those arising from misalignment of force plate and kinematic measurement reference frames. A benchmark case is presented, which demonstrates reductions in joint torque errors on the order of 30 percent compared to the conventional Newton-Euler method, for a wide range of noise levels on measured data. The advantages over the Newton-Euler method include making best use of all available measurements, ability to function when less than a full complement of ground reaction forces is measured, suppression of residual torques acting on the top-most body segment, and the rejection of constant biases in data.
Null Test of the Gravitational Inverse Square Law with a Superconducting Gravity Gradiometer.
NASA Astrophysics Data System (ADS)
Chan, Hinghung Anthony
The goal of this research was to develop a cryogenic gravitational null detector and to carry out a prototype test of the inverse square law with the new instrument on a laboratory scale of 1 - 10 m. The Laplacian of the Newtonian gravitational potential (DEL)('2)(phi), is source independent and is a null quantity in vacuum. It has, therefore, been proposed to perform a null test of the inverse square law by using a three-axis gravity gradiometer as a null detector. We have analyzed such a null experiment in detail using gravity sources of various kinds. Errors in the null detector such as misalignment between two differencing component accelerometers, orthogonality errors among three gradiometer axes, and a finite baseline effect have been analyzed. Various orientations and configurations of the detector and the source are suggested to suppress these errors. The single-axis portion of a three-axis superconducting gravity gradiometer has been completed in the course of this research. The theory of the superconducting gravity gradiometer has been generalized and put into a Lagrangian formulation. A condition for frequency-independent common mode balance is derived and verified in the experiment. This balance combined with a multi-stage vibration isolation scheme has enabled a stable operation of the gradiometer for prolonged periods. In a preliminary test, the gradiometer has exhibited a noise level of 1 - 2 E Hz('- 1/2) below 1 Hz, limited by seismic noise, where 1 E (TBOND) 10(' -9) m s('-2) m('-1). To perform a test of the inverse square law, the single-axis gradiometer is mounted with its axis tilted from the vertial by an angle tan('-1(' ))SQRT.(2. The device is then turned incrementally by 120(DEGREES) around the vertical to carry the gradiometer from one axis to the other two axes of an orthogonal coordinate system. A lead pendulum weighing 1,600 kg forms a periodic monopole source of gravity. The gradiometer outputs are individually time-averaged over 2
NASA Astrophysics Data System (ADS)
Jardani, A.; Revil, A.; Akoa, F.; Schmutz, M.; Florsch, N.; Dupont, J. P.
2006-10-01
We propose a least squares inversion algorithm to determine the spatially variable depth of the water table in shallow unconfined aquifers using self-potential signals measured on the ground surface. Traditionally, the water table is determined only at few locations using piezometers. Our approach relates its shape with the distribution of the self-potential signals according to a Fredholm equation of the first kind. The latter is discretized to obtain a linear matrix formulation of the forward problem. This new formulation is very general and can account for the resistivity distribution of the vadose zone. It is used to setup the inverse problem using the approach of Tarantola (1987) for a test site located in Normandy (France) where 225 self-potential measurements were performed over an area of 15,400 m2. Ground water flows through the loess overlying a low permeability clay-with-flint weathered chalk, at a depth between 1 to 7 meters, into sinkholes in chalk bedrock. The method determines the water table with a precision of 0.4 m.
[A hyperspectral subpixel target detection method based on inverse least squares method].
Li, Qing-Bo; Nie, Xin; Zhang, Guang-Jun
2009-01-01
In the present paper, an inverse least square (ILS) method combined with the Mahalanobis distance outlier detection method is discussed to detect the subpixel target from the hyperspectral image. Firstly, the inverse model for the target spectrum and all the pixel spectra was established, in which the accurate target spectrum was obtained previously, and then the SNV algorithm was employed to preprocess each original pixel spectra separately. After the pretreatment, the regressive coefficient of ILS was calculated with partial least square (PLS) algorithm. Each point in the vector of regressive coefficient corresponds to a pixel in the image. The Mahalanobis distance was calculated with each point in the regressive coefficient vector. Because Mahalanobis distance stands for the extent to which samples deviate from the total population, the point with Mahalanobis distance larger than the 3sigma was regarded as the subpixel target. In this algorithm, no other prior information such as representative background spectrum or modeling of background is required, and only the target spectrum is needed. In addition, the result of the detection is insensitive to the complexity of background. This method was applied to AVIRIS remote sensing data. For this simulation experiment, AVIRIS remote sensing data was free downloaded from the NASA official websit, the spectrum of a ground object in the AVIRIS hyperspectral image was picked up as the target spectrum, and the subpixel target was simulated though a linear mixed method. The comparison of the subpixel detection result of the method mentioned above with that of orthogonal subspace projection method (OSP) was performed. The result shows that the performance of the ILS method is better than the traditional OSP method. The ROC (receive operating characteristic curve) and SNR were calculated, which indicates that the ILS method possesses higher detection accuracy and less computing time than the OSP algorithm. PMID:19385196
Sensitivity analysis of distributed volcanic source inversion
NASA Astrophysics Data System (ADS)
Cannavo', Flavio; Camacho, Antonio G.; González, Pablo J.; Puglisi, Giuseppe; Fernández, José
2016-04-01
A recently proposed algorithm (Camacho et al., 2011) claims to rapidly estimate magmatic sources from surface geodetic data without any a priori assumption about source geometry. The algorithm takes the advantages of fast calculation from the analytical models and adds the capability to model free-shape distributed sources. Assuming homogenous elastic conditions, the approach can determine general geometrical configurations of pressured and/or density source and/or sliding structures corresponding to prescribed values of anomalous density, pressure and slip. These source bodies are described as aggregation of elemental point sources for pressure, density and slip, and they fit the whole data (keeping some 3D regularity conditions). Although some examples and applications have been already presented to demonstrate the ability of the algorithm in reconstructing a magma pressure source (e.g. Camacho et al., 2011,Cannavò et al., 2015), a systematic analysis of sensitivity and reliability of the algorithm is still lacking. In this explorative work we present results from a large statistical test designed to evaluate the advantages and limitations of the methodology by assessing its sensitivity to the free and constrained parameters involved in inversions. In particular, besides the source parameters, we focused on the ground deformation network topology, and noise in measurements. The proposed analysis can be used for a better interpretation of the algorithm results in real-case applications. Camacho, A. G., González, P. J., Fernández, J. & Berrino, G. (2011) Simultaneous inversion of surface deformation and gravity changes by means of extended bodies with a free geometry: Application to deforming calderas. J. Geophys. Res. 116. Cannavò F., Camacho A.G., González P.J., Mattia M., Puglisi G., Fernández J. (2015) Real Time Tracking of Magmatic Intrusions by means of Ground Deformation Modeling during Volcanic Crises, Scientific Reports, 5 (10970) doi:10.1038/srep
Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions
NASA Technical Reports Server (NTRS)
Rubinstein, R.; Greenberg, P. S.
1994-01-01
Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation
Long-buried dismantling of a centuries-old myth: Newton's Principia and inverse-square orbits
NASA Astrophysics Data System (ADS)
Weinstock, Robert
1989-09-01
The author's 1982 report of the fallacy inherent in Newton's treatment of inverse-square orbits in the Principia was anticipated by Ferdinand Rosenberger in his 1895 book-length study of Newton's life and work [Isaac Newton und Seine Physikalischen Principien (Barth, Leipzig, 1895)]. A new alternative formulation of the case against the Principia treatment is offered as surpassing in effectiveness that of Rosenberger and the essentially equivalent 1982 formulation by the author. Also offered is exposure of a long-enduring misrepresentation of a portion of the Principia that deals with inverse-square orbits.
Yoshida, A; Hiraki, Y; Ohkawa, Y; Yamada, T; Hashimoto, K; Aono, K
1986-02-01
To determine the characteristic curve of the radiographic screen/film systems in a short focal spot-film distance, the inverse square sensitometric method was modified by changing the radiation intensity with two kinds of filters. The characteristic curves obtained in the two exposure series with these two kinds of filters were overlapped to obtain a complete one. The characteristic curve thus obtained was almost the same as the one obtained by the original inverse square sensitometric method. The accuracy of the characteristic curves obtained by the modified method was well-reflected in the clinical radiographs. PMID:3962729
Finding a Minimally Informative Dirichlet Prior Distribution Using Least Squares
Dana Kelly; Corwin Atwood
2011-03-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straight-forward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in closed form, and so an approximate beta distribution is used in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial aleatory model for common-cause failure, must be estimated from data that is often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
ERIC Educational Resources Information Center
Whyntie, T.; Parker, B.
2013-01-01
The Timepix hybrid silicon pixel detector has been used to investigate the inverse square law of radiation from a point source as a demonstration of the CERN [at] school detector kit capabilities. The experiment described uses a Timepix detector to detect the gamma rays emitted by an [superscript 241]Am radioactive source at a number of different…
NASA Astrophysics Data System (ADS)
Choi, S.; Kim, C.; Kim, H. R.; Park, C.; Park, H. Y.
2015-12-01
We performed the marine magnetic and the bathymetry survey in the Lau basin for finding the submarine hydrothermal deposits in October 2009. We acquired magnetic and bathymetry datasets by using Overhouser Proton Magnetometer SeaSPY(Marine Magnetics Co.) and Multi-Beam Echo Sounder EM120(Kongsberg Co.). We conducted the data processing to obtain detailed seabed topography, magnetic anomaly and reduction to the pole(RTP). The Lau basin is one of the youngest back-arc basins in the Southwest Pacific. This region was a lot of hydrothermal activities and hydrothermal deposits. In particular, Tofua Arc(TA) in the Lau basin consists of various and complex stratovolcanos(from Massoth et al., 2007).), We calculated the magnetic susceptibility distribution of the TA19-1 seamount(longitude:176°23.5'W, latitude: 22°42.5'W)area using the RTP data by 3-D magnetic inversion from Jung's previous study(2013). Based on 2D 'compact gravity inversion' by Last & Kubik(1983), we expend it to the 3D algorithm using iterative reweighted least squares method with some weight matrices. The used weight matrices are two types: 1) the minimum gradient support(MGS) that controls the spatial distribution of the solution from Porniaguine and Zhdanov(1999); 2) the depth weight that are used according to the shape of subsurface structures. From the modeling, we derived the appropriate scale factor for the use of depth weight and setting magnetic susceptibility. Furthermore, we have to enter a very small error value to control the computation of the singular point of the inversion model that was able to be easily calculated for modeling. In addition, we applied separately weighted value for the correct shape and depth of the magnetic source. We selected the best results model by change to converge of RMS. Compared between the final modeled result and RTP values in this study, they are generally similar to the each other. But the input values and the modeled values have slightly little difference
Cold Fermi gas with inverse square interaction in a harmonic trap
NASA Astrophysics Data System (ADS)
Kulkarni, Manas; Abanov, Alexander G.
2011-05-01
We study equilibrium density and spin density profiles for a model of cold one-dimensional spin 1/2 fermions interacting via inverse square interaction and exchange in an external harmonic trap. This model is the well-known spin-Calogero model (sCM) and its fully nonlinear collective field theory description is known. We extend the field theory description to the presence of an external harmonic trap and obtain analytic results for statics and dynamics of the system. For instance, we find how the equilibrium density profile changes upon tuning the interaction strength. The results we obtain for equilibrium configurations are very similar to the ones obtained recently by Ma and Yang (2010) [1] for a model of fermions with short ranged interactions. Our main approximation is the neglect of the terms of higher order in spatial derivatives in equations of motion - gradientless approximation (Kulkarni et al., 2009) [2]. Within this approximation the hydrodynamic equations of motion can be written as a set of decoupled forced Riemann-Hopf equations for the dressed Fermi momenta of the model. This enables us to write analytical solutions for the dynamics of spin and charge. We describe the time evolution of the charge density when an initial non-equilibrium profile is created by cooling the gas with an additional potential in place and then suddenly removing the potential. We present our results as a simple "single-particle" evolution in the phase space reminiscing a similar description of the dynamics of noninteracting one-dimensional fermions.
A finite class of q-orthogonal polynomials corresponding to inverse gamma distribution
NASA Astrophysics Data System (ADS)
Soleyman, F.; Masjed-Jamei, M.; Area, I.
2016-09-01
In this paper, a class of finite q-orthogonal polynomials is studied whose weight function corresponds to the inverse gamma distribution as q → 1 . Via Sturm-Liouville theory in q-difference spaces, the orthogonality of this class is proved and its norm square value is computed. Also, its general properties such as q-weight function, q-difference equation and the basic hypergeometric representation are recovered in the continuous case.
Tan, Wen-Hai; Yang, Shan-Qing; Shao, Cheng-Gang; Li, Jia; Du, An-Bin; Zhan, Bi-Fu; Wang, Qing-Lan; Luo, Peng-Shun; Tu, Liang-Cheng; Luo, Jun
2016-04-01
By using a torsion pendulum and a rotating eightfold symmetric attractor with dual modulation of both the interested signal and the gravitational calibration signal, a new test of the gravitational inverse-square law at separations down to 295 μm is presented. A dual-compensation design by adding masses on both the pendulum and the attractor was adopted to realize a null experiment. The experimental result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=59 μm. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 70-300 μm, and improves the previous bounds by up to a factor of 2 at the length scale λ≈160 μm. PMID:27081964
NASA Astrophysics Data System (ADS)
Tan, Wen-Hai; Yang, Shan-Qing; Shao, Cheng-Gang; Li, Jia; Du, An-Bin; Zhan, Bi-Fu; Wang, Qing-Lan; Luo, Peng-Shun; Tu, Liang-Cheng; Luo, Jun
2016-04-01
By using a torsion pendulum and a rotating eightfold symmetric attractor with dual modulation of both the interested signal and the gravitational calibration signal, a new test of the gravitational inverse-square law at separations down to 295 μ m is presented. A dual-compensation design by adding masses on both the pendulum and the attractor was adopted to realize a null experiment. The experimental result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α |≤1 ) down to a length scale λ =59 μ m . This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 70 - 300 μ m , and improves the previous bounds by up to a factor of 2 at the length scale λ ≈160 μ m .
Fair and Square Computation of Inverse "Z"-Transforms of Rational Functions
ERIC Educational Resources Information Center
Moreira, M. V.; Basilio, J. C.
2012-01-01
All methods presented in textbooks for computing inverse "Z"-transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence "x"("k") whose "Z"-transform is "X"("z"); 2) computation using the inversion integral…
NASA Astrophysics Data System (ADS)
Singh, Sarvesh Kumar; Rani, Raj
2014-08-01
Identification of a point release is a parametric estimation problem associated with the estimation of its parameters namely, location and strength. A least-squares inversion algorithm, free from initial guess of release parameters, is utilized here for the source identification in eleven trials of single continuous point releases conducted during Fusion Field Trials 2007. The source locations are retrieved within an average error of 23 m from their true locations. The maximum and minimum errors in the retrieval of the source location are obtained as 57.3 m and 3 m respectively. The source strength is retrieved within a factor of 1.6 in all the trials. The sensitivity of the source estimation is analysed with respect to (i) variation of grid sizes in discretized space, (ii) inclusion of zero measurements and (iii) addition of new measurements. Posterior uncertainty is mentioned in terms of variance of the source parameters, approximated by using the Hessian of the cost function. In addition, an attempt is made to obtain the minimum number of measurements for a successful source inversion. The study explores the future applicability of this least-squares inversion technique for point source identification.
Inverse distributed hydrological modelling of alpine catchments
NASA Astrophysics Data System (ADS)
Kunstmann, H.; Krause, J.; Mayr, S.
2005-12-01
Even in physically based distributed hydrological models, various remaining parameters must be estimated for each sub-catchment. This can involve tremendous effort, especially when the number of sub-catchments is large and the applied hydrological model is computationally expensive. Automatic parameter estimation tools can significantly facilitate the calibration process. Hence, we combined the nonlinear parameter estimation tool PEST with the distributed hydrological model WaSiM. PEST is based on the Gauss-Marquardt-Levenberg method, a gradient-based nonlinear parameter estimation algorithm. WaSiM is a fully distributed hydrological model using physically based algorithms for most of the process descriptions. WaSiM was applied to the alpine/prealpine Ammer River catchment (southern Germany, 710 km2) in a 100×100 m2 horizontal resolution. The catchment is heterogeneous in terms of geology, pedology and land use and shows a complex orography (the difference of elevation is around 1600 m). Using the developed PEST-WaSiM interface, the hydrological model was calibrated by comparing simulated and observed runoff at eight gauges for the hydrologic year 1997 and validated for the hydrologic year 1993. For each sub-catchment four parameters had to be calibrated: the recession constants of direct runoff and interflow, the drainage density, and the hydraulic conductivity of the uppermost aquifer. Additionally, five snowmelt specific parameters were adjusted for the entire catchment. Altogether, 37 parameters had to be calibrated. Additional a priori information (e.g. from flood hydrograph analysis) narrowed the parameter space of the solutions and improved the non-uniqueness of the fitted values. A reasonable quality of fit was achieved. Discrepancies between modelled and observed runoff were also due to the small number of meteorological stations and corresponding interpolation artefacts in the orographically complex terrain. A detailed covariance analysis was performed
Inverse distributed hydrological modelling of Alpine catchments
NASA Astrophysics Data System (ADS)
Kunstmann, H.; Krause, J.; Mayr, S.
2006-06-01
Even in physically based distributed hydrological models, various remaining parameters must be estimated for each sub-catchment. This can involve tremendous effort, especially when the number of sub-catchments is large and the applied hydrological model is computationally expensive. Automatic parameter estimation tools can significantly facilitate the calibration process. Hence, we combined the nonlinear parameter estimation tool PEST with the distributed hydrological model WaSiM. PEST is based on the Gauss-Marquardt-Levenberg method, a gradient-based nonlinear parameter estimation algorithm. WaSiM is a fully distributed hydrological model using physically based algorithms for most of the process descriptions. WaSiM was applied to the alpine/prealpine Ammer River catchment (southern Germany, 710 km2 in a 100×100 m2 horizontal resolution. The catchment is heterogeneous in terms of geology, pedology and land use and shows a complex orography (the difference of elevation is around 1600 m). Using the developed PEST-WaSiM interface, the hydrological model was calibrated by comparing simulated and observed runoff at eight gauges for the hydrologic year 1997 and validated for the hydrologic year 1993. For each sub-catchment four parameters had to be calibrated: the recession constants of direct runoff and interflow, the drainage density, and the hydraulic conductivity of the uppermost aquifer. Additionally, five snowmelt specific parameters were adjusted for the entire catchment. Altogether, 37 parameters had to be calibrated. Additional a priori information (e.g. from flood hydrograph analysis) narrowed the parameter space of the solutions and improved the non-uniqueness of the fitted values. A reasonable quality of fit was achieved. Discrepancies between modelled and observed runoff were also due to the small number of meteorological stations and corresponding interpolation artefacts in the orographically complex terrain. Application of a 2-dimensional numerical
Lo, Yen-Li; Pan, Wen-Harn; Hsu, Wan-Lun; Chien, Yin-Chu; Chen, Jen-Yang; Hsu, Mow-Ming; Lou, Pei-Jen; Chen, I-How; Hildesheim, Allan; Chen, Chien-Jen
2016-01-01
Evidence on the association between dietary component, dietary pattern and nasopharyngeal carcinoma (NPC) is scarce. A major challenge is the high degree of correlation among dietary constituents. We aimed to identify dietary pattern associated with NPC and to illustrate the dose-response relationship between the identified dietary pattern scores and the risk of NPC. Taking advantage of a matched NPC case–control study, data from a total of 319 incident cases and 319 matched controls were analyzed. Dietary pattern was derived employing partial least square discriminant analysis (PLS-DA) performed on energy-adjusted food frequencies derived from a 66-item food-frequency questionnaire. Odds ratios (ORs) and 95% confidence intervals (CIs) were estimated with multiple conditional logistic regression models, linking pattern scores and NPC risk. A high score of the PLS-DA derived pattern was characterized by high intakes of fruits, milk, fresh fish, vegetables, tea, and eggs ordered by loading values. We observed that one unit increase in the scores was associated with a significantly lower risk of NPC (ORadj = 0.73, 95% CI = 0.60–0.88) after controlling for potential confounders. Similar results were observed among Epstein-Barr virus seropositive subjects. An NPC protective diet is indicated with more phytonutrient-rich plant foods (fruits, vegetables), milk, other protein-rich foods (in particular fresh fish and eggs), and tea. This information may be used to design potential dietary regimen for NPC prevention. PMID:27249558
A spatiotemporal dynamic distributed solution to the MEG inverse problem
Lamus, Camilo; Hämäläinen, Matti S.; Temereanca, Simona; Brown, Emery N.; Purdon, Patrick L.
2012-01-01
MEG/EEG are non-invasive imaging techniques that record brain activity with high temporal resolution. However, estimation of brain source currents from surface recordings requires solving an ill-conditioned inverse problem. Converging lines of evidence in neuroscience, from neuronal network models to resting-state imaging and neurophysiology, suggest that cortical activation is a distributed spatiotemporal dynamic process, supported by both local and long-distance neuroanatomic connections. Because spatiotemporal dynamics of this kind are central to brain physiology, inverse solutions could be improved by incorporating models of these dynamics. In this article, we present a model for cortical activity based on nearest-neighbor autoregression that incorporates local spatiotemporal interactions between distributed sources in a manner consistent with neurophysiology and neuroanatomy. We develop a dynamic Maximum a Posteriori Expectation-Maximization (dMAP-EM) source localization algorithm for estimation of cortical sources and model parameters based on the Kalman Filter, the Fixed Interval Smoother, and the EM algorithms. We apply the dMAP-EM algorithm to simulated experiments as well as to human experimental data. Furthermore, we derive expressions to relate our dynamic estimation formulas to those of standard static models, and show how dynamic methods optimally assimilate past and future data. Our results establish the feasibility of spatiotemporal dynamic estimation in large-scale distributed source spaces with several thousand source locations and hundreds of sensors, with resulting inverse solutions that provide substantial performance improvements over static methods. PMID:22155043
Inversion of generalized relaxation time distributions with optimized damping parameter
NASA Astrophysics Data System (ADS)
Florsch, Nicolas; Revil, André; Camerlynck, Christian
2014-10-01
Retrieving the Relaxation Time Distribution (RDT), the Grains Size Distribution (GSD) or the Pore Size Distribution (PSD) from low-frequency impedance spectra is a major goal in geophysics. The “Generalized RTD” generalizes parametric models like Cole-Cole and many others, but remains tricky to invert since this inverse problem is ill-posed. We propose to use generalized relaxation basis function (for instance by decomposing the spectra on basis of generalized Cole-Cole relaxation elements instead of the classical Debye basis) and to use the L-curve approach to optimize the damping parameter required to get smooth and realistic inverse solutions. We apply our algorithm to three examples, one synthetic and two real data sets, and the program includes the possibility of converting the RTD into GSD or PSD by choosing the value of the constant connecting the relaxation time to the characteristic polarization size of interest. A high frequencies (typically above 1 kHz), a dielectric term in taken into account in the model. The code is provided as an open Matlab source as a supplementary file associated with this paper.
ERIC Educational Resources Information Center
Sein, Lawrence T., Jr.
2006-01-01
The isotopic distribution in mass spectroscopy is described for identifying pure compounds, being able to distinguish molecular fragments by masses. Punnett squares are familiar, easy to compute, and often graphical which makes helpful to students and the relative distribution of isotopic combination is easily generated for even isotopic…
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
NASA Astrophysics Data System (ADS)
Ikot, Akpan N.; Maghsoodi, Elham; Zarrinkamar, Saber; Hassanabadi, Hassan
2013-11-01
The Dirac equation for the combined Mobius square and inversely quadratic Yukawa potentials including a Coulomb-like interaction term has been investigated in the presence of spin and pseudospin symmetries with arbitrary spin-orbit quantum number κ .We have obtained the explicit energy eigenvalues and the corresponding eigenfunctions by the framework of Nikiforov-Uvarov method.
Passive acoustic inversion to estimate bedload size distribution in rivers
NASA Astrophysics Data System (ADS)
Petrut, Teodor; Geay, Thomas; Belleudy, Philippe; Gervaise, Cédric
2016-04-01
The knowledge of sediment transport rate in rivers is related to issues like changes in channel forms, inundation risks and river's ecological functions. The passive acoustic method introduced here measures the bedload processes by recording the noise generated by the inter-particle collisions. In this research, an acoustic inversion is proposed to estimate the size distribution of mobile particles. The theoretical framework of Hertz's impact between two solids rigid is used to model the sediment-generated noise. This model combined with the acoustical power spectrum density gives the information on the particle sizes. The sensitivity of the method is performed and finally the experimental validation is done through a series of tests in the laboratory as well in a natural stream. The limitations of the proposed inversion method are drawn assuming the wave propagation effects in the channel. It is stated that propagation effects limit the applicability of the method to large rivers, like fluvial channels, in the detriment of mountain torrents.
ERIC Educational Resources Information Center
Brown, Malcolm
2009-01-01
Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…
In this article, we consider the least-squares approach for estimating parameters of a spatial variogram and establish consistency and asymptotic normality of these estimators under general conditions. Large-sample distributions are also established under a sp...
The probability distribution function for the sum of squares of independent random variables
NASA Astrophysics Data System (ADS)
Fateev, Yury; Dmitriev, Dmitry; Tyapkin, Valery; Kremez, Nikolai; Shaidurov, Vladimir
2016-08-01
In the present paper, the probability distribution function is derived for the sum of squares of random variables for nonzero expectations. This distribution function enables one to develop an efficient one-step algorithm for phase ambiguity resolution when determining the spatial orientation from signals of satellite radio-navigation systems. Threshold values for rejecting false solutions and statistical properties of the algorithm are obtained.
Inversion for slip distribution for the 2012 Costa Rica earthquake
NASA Astrophysics Data System (ADS)
McCormack, K. A.; Hesse, M. A.; Stadler, G.
2014-12-01
On 5 September 2012, a major megathrust earthquake (Mw=7.6) ruptured the plate interface beneath the Nicoya Peninsula, Costa Rica. This event was centered 12 km offshore of the central Nicoya coast, at a depth of 18 km. The maximum slip exceeded 2 meters, and the rupture spread outward along the plate interface to encompass 3000 km2 of the Nicoya seismogenic zone. More than 1700 aftershocks were recorded within the first 5 days. These aftershocks outlined two distinct rupture patches; one centered on the central coast and the other beneath the southern tip of the peninsula. We formulate a Bayesian inverse problem to infer the coseismic slip on the fault plane based on instantaneous surface displacements and changes in well heads in order to image the remaining "locked" patch that has been inferred previously. We compute the maximum a posteriori (MAP) estimate of the posterior slip distribution on the fault, and use a local Gaussian approximation around the MAP point to characterize the uncertainty. The elastic deformation is computed using a finite element method that allows for the spatial variation of elastic properties that has been observed in the crust overlying the seismogenic zone. We solve the optimization problem using gradients obtained from adjoints. The linearity of the inverse problem allows for the efficient solution of the optimal experimental design problem for the placement of the GPS stations to monitor the remaining locked patch. In the future, the results obtained here will provide the initial condition for a time-dependent poroelastic model for fault slip and fluid migration due to overpressure caused by a megathrust earthquake. This will provide constraints on the crustal permeability structure in a tectonically active region.
Mean square displacement evaluation by elastic neutron scattering self-distribution function.
Magazù, Salvatore; Maisano, Giacomo; Migliardo, Federica; Benedetto, Antonio
2008-06-01
In the present work an operational recipe for the mean square displacement (MSD) determination, highlighting the connection between elastic incoherent neutron scattering (EINS) intensity profiles and the associated self-distribution function, is presented. The determination of the thermal behavior of the total MSD and of its partial contributions is tested on EINS data collected by the backscattering spectrometer IN13 (ILL, Grenoble) on a model system such as PolyEthylene Glycol with a mean molecular weight of 400 Dalton (PEG 400).
A Bayesian inversion for slip distribution of 1 Apr 2007 Mw8.1 Solomon Islands Earthquake
NASA Astrophysics Data System (ADS)
Chen, T.; Luo, H.
2013-12-01
On 1 Apr 2007 the megathrust Mw8.1 Solomon Islands earthquake occurred in the southeast pacific along the New Britain subduction zone. 102 vertical displacement measurements over the southeastern end of the rupture zone from two field surveys after this event provide a unique constraint for slip distribution inversion. In conventional inversion method (such as bounded variable least squares) the smoothing parameter that determines the relative weight placed on fitting the data versus smoothing the slip distribution is often subjectively selected at the bend of the trade-off curve. Here a fully probabilistic inversion method[Fukuda,2008] is applied to estimate distributed slip and smoothing parameter objectively. The joint posterior probability density function of distributed slip and the smoothing parameter is formulated under a Bayesian framework and sampled with Markov chain Monte Carlo method. We estimate the spatial distribution of dip slip associated with the 1 Apr 2007 Solomon Islands earthquake with this method. Early results show a shallower dip angle than previous study and highly variable dip slip both along-strike and down-dip.
Suitability of Gamma, Chi-square, Weibull, and Beta distributions as synthetic unit hydrographs
NASA Astrophysics Data System (ADS)
Bhunya, P. K.; Berndtsson, R.; Ojha, C. S. P.; Mishra, S. K.
2007-02-01
SummaryMost available methods for synthetic unit hydrograph (SUH) derivation involve manual, subjective fitting of a hydrograph through a few data points. Because of this tedious procedure, the generated unit hydrograph is often left unadjusted for unit runoff volume. During recent decades, use of probability distribution functions (pdfs) in developing SUH has received much attention because of its similarity with unit hydrograph properties. In this study, the potential of four popular pdfs, i.e., two-parameter Gamma, three-parameter Beta, two-parameter Weibull, and one-parameter Chi-square distribution to derive SUH have been explored. Simple formulae are derived using analytical and numerical schemes to compute the distribution parameters, and their validity is checked with simulation of field data. The Gamma and Chi-square distributions behave analogously, and the Beta distribution approximates a Gamma distribution in a limiting case. Application to field data shows that the Beta and Weibull distributions are more flexible in hydrograph prediction than the Gamma, Chi-square, Gray [Gray, D.M., 1961. Synthetic hydrographs for small drainage areas. In: Proceedings of the ASCE, 87, HY4, pp. 33-54], SCS [SCS, 1957. Use of Storm and Watershed Characteristics in Synthetic Hydrograph Analysis and Application: V. Mockus. US Dept. of Agriculture, Soil Conservation Service, Washington, DC], and Snyder [Synder, F.F., 1938. Synthetic unit hydrographs. Trans. Am. Geophys. Union 19, 447-454] methods. A sensitivity analysis of pdf parameters on peak flow estimates of an UH indicated that Gamma and Chi-square distributions overestimate the peak flow value, for any overestimation in its parameter estimates. However, for the Beta and Weibull distributions a reverse trend was observed. Both were found to behave similarly at higher α (ratio of time to base and time to peak of UH) values. Further, an analogous triangular hydrograph approach was used to express the mean and variance
NASA Technical Reports Server (NTRS)
Devasia, Santosh; Bayo, Eduardo
1993-01-01
This paper addresses the problem of inverse dynamics for articulated flexible structures with both lumped and distributed actuators. This problem arises, for example, in the combined vibration minimization and trajectory control of space robots and structures. A new inverse dynamics scheme for computing the nominal lumped and distributed inputs for tracking a prescribed trajectory is given.
Expected distributions of root-mean-square positional deviations in proteins.
Pitera, Jed W
2014-06-19
The atom positional root-mean-square deviation (RMSD) is a standard tool for comparing the similarity of two molecular structures. It is used to characterize the quality of biomolecular simulations, to cluster conformations, and as a reaction coordinate for conformational changes. This work presents an approximate analytic form for the expected distribution of RMSD values for a protein or polymer fluctuating about a stable native structure. The mean and maximum of the expected distribution are independent of chain length for long chains and linearly proportional to the average atom positional root-mean-square fluctuations (RMSF). To approximate the RMSD distribution for random-coil or unfolded ensembles, numerical distributions of RMSD were generated for ensembles of self-avoiding and non-self-avoiding random walks. In both cases, for all reference structures tested for chains more than three monomers long, the distributions have a maximum distant from the origin with a power-law dependence on chain length. The purely entropic nature of this result implies that care must be taken when interpreting stable high-RMSD regions of the free-energy landscape as "intermediates" or well-defined stable states.
A variational Bayesian approach for inverse problems with skew-t error distributions
NASA Astrophysics Data System (ADS)
Guha, Nilabja; Wu, Xiaoqing; Efendiev, Yalchin; Jin, Bangti; Mallick, Bani K.
2015-11-01
In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-t distribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback-Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g. Cauchy problem and permeability estimation problem.
Muralisankar, S; Manivannan, A; Balasubramaniam, P
2015-09-01
The aim of this manuscript is to investigate the mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks with time-delays. The time-delays are assumed to be interval time-varying and randomly occurring. Based on the new Lyapunov-Krasovskii functional and stochastic analysis approach, a novel sufficient condition is obtained in the form of linear matrix inequality such that the delayed stochastic neural networks are globally robustly asymptotically stable in the mean-square sense for all admissible uncertainties. Finally, the derived theoretical results are validated through numerical examples in which maximum allowable upper bounds are calculated for different lower bounds of time-delay.
The origin, global distribution, and functional impact of the human 8p23 inversion polymorphism.
Salm, Maximilian P A; Horswell, Stuart D; Hutchison, Claire E; Speedy, Helen E; Yang, Xia; Liang, Liming; Schadt, Eric E; Cookson, William O; Wierzbicki, Anthony S; Naoumova, Rossi P; Shoulders, Carol C
2012-06-01
Genomic inversions are an increasingly recognized source of genetic variation. However, a lack of reliable high-throughput genotyping assays for these structures has precluded a full understanding of an inversion's phylogenetic, phenotypic, and population genetic properties. We characterize these properties for one of the largest polymorphic inversions in man (the ∼4.5-Mb 8p23.1 inversion), a structure that encompasses numerous signals of natural selection and disease association. We developed and validated a flexible bioinformatics tool that utilizes SNP data to enable accurate, high-throughput genotyping of the 8p23.1 inversion. This tool was applied retrospectively to diverse genome-wide data sets, revealing significant population stratification that largely follows a clinal "serial founder effect" distribution model. Phylogenetic analyses establish the inversion's ancestral origin within the Homo lineage, indicating that 8p23.1 inversion has occurred independently in the Pan lineage. The human inversion breakpoint was localized to an inverted pair of human endogenous retrovirus elements within the large, flanking low-copy repeats; experimental validation of this breakpoint confirmed these elements as the likely intermediary substrates that sponsored inversion formation. In five data sets, mRNA levels of disease-associated genes were robustly associated with inversion genotype. Moreover, a haplotype associated with systemic lupus erythematosus was restricted to the derived inversion state. We conclude that the 8p23.1 inversion is an evolutionarily dynamic structure that can now be accommodated into the understanding of human genetic and phenotypic diversity.
NASA Technical Reports Server (NTRS)
Rummel, R.; Sjoeberg, L.; Rapp, R. H.
1978-01-01
A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.
NASA Technical Reports Server (NTRS)
Miller, C. D.
1972-01-01
Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.
Hartzell, S.; Mendoza, C.
1991-01-01
An iterative least-squares technique is used to simultaneously invert the strong-motion records and teleseismic P waveforms for the 1978 Tabas, Iran, earthquake to deduce the rupture history. The effects of using different data sets and different parametrizations of the problem (linear versus nonlinear) are considered. A consensus of all the inversion runs indicates a complex, multiple source for the Tabas earthquake, with four main source regions over a fault length of 90 km and an average rupture velocity of 2.5 km/sec. -from Authors
Bietenholz, Wolfgang Chryssomalakos, Chryssomalis Salgado, Marcelo
2015-10-15
We comment on a fatal flaw in the analysis contained in the work of Martínez-y-Romero et al., [J. Math. Phys. 54, 053509 (2013)], which concerns the motion of a point particle in an inverse square potential, and show that most conclusions reached there are wrong. In particular, the manifestly senseless claim that, in the attractive potential case, no bounded orbits exist for negative energies, is traced to a sign error. Several more mistakes, both in the classical and the quantum cases, are pointed out.
NASA Astrophysics Data System (ADS)
Bietenholz, Wolfgang; Chryssomalakos, Chryssomalis; Salgado, Marcelo
2015-10-01
We comment on a fatal flaw in the analysis contained in the work of Martínez-y-Romero et al., [J. Math. Phys. 54, 053509 (2013)], which concerns the motion of a point particle in an inverse square potential, and show that most conclusions reached there are wrong. In particular, the manifestly senseless claim that, in the attractive potential case, no bounded orbits exist for negative energies, is traced to a sign error. Several more mistakes, both in the classical and the quantum cases, are pointed out.
NASA Astrophysics Data System (ADS)
Zhu, Liang; Hu, Penghao; Yang, Wenguo; Dang, Xueming; Zhang, Lisong
2016-01-01
The reasonable permanent magnetic field distribution has an important influence on improving the measuring accuracy in intelligent ball joint. In view of the defects on the ring permanent magnet in the previous experiment scheme, a new method on Square Pane Permanent Magnet (SPPM) is put forward. It possesses distinct advantages on orientation identification and model simplification. This paper proposes an optimized theory model of the magnetic field distribution of SPPM and gives the magnetic field theoretical expressions. The experiments have shown that the experimental data basically agreed with the theory value which is less than 4.3% error in full scale. This result verified the correctness of the analytic work and paves the way for improving the measurement accuracy in intelligent ball joint.
ERIC Educational Resources Information Center
Sichel, H. S.
1992-01-01
Discusses the use of the generalized inverse Gaussian-Poisson (GIGP) distribution in bibliometric studies. The main types of size-frequency distributions are described, bibliometric distributions in logarithms are examined; parameter estimation is discussed; and goodness-of-fit tests are considered. Examples of applications are included. (17…
NASA Astrophysics Data System (ADS)
Schuster, David M.
1993-04-01
An inverse method has been developed to compute the structural stiffness properties of wings given a specified wing loading and aeroelastic twist distribution. The method directly solves for the bending and torsional stiffness distribution of the wing using a modal representation of these properties. An aeroelastic design problem involving the use of a computational aerodynamics method to optimize the aeroelastic twist distribution of a tighter wing operating at maneuver flight conditions is used to demonstrate the application of the method. This exercise verifies the ability of the inverse scheme to accurately compute the structural stiffness distribution required to generate a specific aeroelastic twist under a specified aeroelastic load.
Distributed weighted least-squares estimation with fast convergence for large-scale systems☆
Marelli, Damián Edgardo; Fu, Minyue
2015-01-01
In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods. PMID:25641976
Wave Packet Dynamics in the Infinite Square Well with the Wigner Quasi-probability Distribution
NASA Astrophysics Data System (ADS)
Belloni, Mario; Doncheski, Michael; Robinett, Richard
2004-05-01
Over the past few years a number of authors have been interested in the time evolution and revivals of Gaussian wave packets in one-dimensional infinite wells and in two-dimensional infinite wells of various geometries. In all of these circumstances, the wave function is guaranteed to revive at a time related to the inverse of the system's ground state energy, if not sooner. To better visualize these revivals we have calculated the time-dependent Wigner quasi-probability distribution for position and momentum, P_W(x; p), for Gaussian wave packet solutions of this system. The Wigner quasi-probability distribution clearly demonstrates the short-term semi-classical time dependence, as well as longer-term revival behavior and the structure during the collapsed state. This tool also provides an excellent way of demonstrating the patterns of highly-correlated Schrödinger-cat-like `mini-packets' which appear at fractional multiples of the exact revival time. This research is supported in part by a Research Corporation Cottrell College Science Award (CC5470) and the National Science Foundation under contracts DUE-0126439 and DUE-9950702.
Inversion techniques for determining the droplet size distribution in clouds: numerical examination.
Chow, L C; Tien, C L
1976-02-01
The Phillips-Twomey and Backus-Gilbert inversion techniques are applied to determine the size distribution of water droplets in clouds from light scattering data at backward angles. The data are generated numerically from the Mie scattering functions and an assumed cloud model. The size distribution is recovered from these data using the two inversion techniques and is compared with the assumed model. It is found that the Phillips-Twomey technique gives better agreement between the assumed and recovered size distributions than the Backus-Gilbert technique. Also, it is more stable to random errors artificially introduced into the scattering data.
ERIC Educational Resources Information Center
Yuan, Ke-Hai
2008-01-01
In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the…
Developing a Near Real-time System for Earthquake Slip Distribution Inversion
NASA Astrophysics Data System (ADS)
Zhao, Li; Hsieh, Ming-Che; Luo, Yan; Ji, Chen
2016-04-01
Advances in observational and computational seismology in the past two decades have enabled completely automatic and real-time determinations of the focal mechanisms of earthquake point sources. However, seismic radiations from moderate and large earthquakes often exhibit strong finite-source directivity effect, which is critically important for accurate ground motion estimations and earthquake damage assessments. Therefore, an effective procedure to determine earthquake rupture processes in near real-time is in high demand for hazard mitigation and risk assessment purposes. In this study, we develop an efficient waveform inversion approach for the purpose of solving for finite-fault models in 3D structure. Full slip distribution inversions are carried out based on the identified fault planes in the point-source solutions. To ensure efficiency in calculating 3D synthetics during slip distribution inversions, a database of strain Green tensors (SGT) is established for 3D structural model with realistic surface topography. The SGT database enables rapid calculations of accurate synthetic seismograms for waveform inversion on a regular desktop or even a laptop PC. We demonstrate our source inversion approach using two moderate earthquakes (Mw~6.0) in Taiwan and in mainland China. Our results show that 3D velocity model provides better waveform fitting with more spatially concentrated slip distributions. Our source inversion technique based on the SGT database is effective for semi-automatic, near real-time determinations of finite-source solutions for seismic hazard mitigation purposes.
NASA Astrophysics Data System (ADS)
Biccari, Umberto; Zuazua, Enrique
2016-09-01
This article is devoted to the analysis of control properties for a heat equation with a singular potential μ /δ2, defined on a bounded C2 domain Ω ⊂RN, where δ is the distance to the boundary function. More precisely, we show that for any μ ≤ 1 / 4 the system is exactly null controllable using a distributed control located in any open subset of Ω, while for μ > 1 / 4 there is no way of preventing the solutions of the equation from blowing-up. The result is obtained applying a new Carleman estimate.
NASA Technical Reports Server (NTRS)
Rutledge, Charles K.
1988-01-01
The validity of applying chi-square based confidence intervals to far-field acoustic flyover spectral estimates was investigated. Simulated data, using a Kendall series and experimental acoustic data from the NASA/McDonnell Douglas 500E acoustics test, were analyzed. Statistical significance tests to determine the equality of distributions of the simulated and experimental data relative to theoretical chi-square distributions were performed. Bias and uncertainty errors associated with the spectral estimates were easily identified from the data sets. A model relating the uncertainty and bias errors to the estimates resulted, which aided in determining the appropriateness of the chi-square distribution based confidence intervals. Such confidence intervals were appropriate for nontonally associated frequencies of the experimental data but were inappropriate for tonally associated estimate distributions. The appropriateness at the tonally associated frequencies was indicated by the presence of bias error and noncomformity of the distributions to the theoretical chi-square distribution. A technique for determining appropriate confidence intervals at the tonally associated frequencies was suggested.
NASA Astrophysics Data System (ADS)
Benedetto, A.; Magazù, S.; Migliardo, F.; Mondelli, C.; Gonzalez, M. A.
2012-02-01
In the present contribution, a procedure for molecular motion characterization based on the evaluation of the Mean Square Displacement (MSD), through the Self-Distribution Function (SDF), is presented. It is shown how MSD, which represents an important observable for the characterization of dynamical properties, can be decomposed into different partial contributions associated to system dynamical processes within a specific spatial scale. It is also shown how the SDF procedure allows us to evaluate both total MSD and partial MSDs through total and partial SDFs. As a result, total MSD is the weighed sum of partial MSDs in which the weights are obtained by the fitting procedure of measured Elastic Incoherent Neutron Scattering (EINS) intensity. We apply SDF procedure to data collected,by IN13, IN10 and IN4 spectrometers (Institute Laue Langevin), on aqueous mixtures of two homologous disaccharides (sucrose and trehalose) and on dry and hydrated (H2O and D2O) lysozyme with and without disaccharides. It emerges that the hydrogen bond imposed network of the water-trehalose mixture appears to be stronger with respect to that of the water-sucrose mixture. This result can justify the higher bioprotectant effectiveness of trehalose. Furthermore, it emerges that partial MSDs of sucrose and trehalose are equivalent in the low Q domain (0÷1.7) Å-1 whereas they are different in the high Q domain (1.7÷4) Å-1. This suggests that the higher structure sensitivity of sucrose should be related to the small spatial observation windows. Moreover, the role of the instrumental resolution in EINS is considered. The nature of the dynamical transition is highlighted and it is shown that it occurs when the system relaxation time becomes shorter than the instrumental energy time. Finally, the bioprotectants effect on protein dynamics and the amplitude of vibrations in lysozyme are presented.
Wang, Jing; Guan, Huaiqun; Solberg, Timothy
2011-07-15
Purpose: A statistical projection restoration algorithm based on the penalized weighted least-squares (PWLS) criterion can substantially improve the image quality of low-dose CBCT images. The performance of PWLS is largely dependent on the choice of the penalty parameter. Previously, the penalty parameter was chosen empirically by trial and error. In this work, the authors developed an inverse technique to calculate the penalty parameter in PWLS for noise suppression of low-dose CBCT in image guided radiotherapy (IGRT). Methods: In IGRT, a daily CBCT is acquired for the same patient during a treatment course. In this work, the authors acquired the CBCT with a high-mAs protocol for the first session and then a lower mAs protocol for the subsequent sessions. The high-mAs projections served as the goal (ideal) toward, which the low-mAs projections were to be smoothed by minimizing the PWLS objective function. The penalty parameter was determined through an inverse calculation of the derivative of the objective function incorporating both the high and low-mAs projections. Then the parameter obtained can be used for PWLS to smooth the noise in low-dose projections. CBCT projections for a CatPhan 600 and an anthropomorphic head phantom, as well as for a brain patient, were used to evaluate the performance of the proposed technique. Results: The penalty parameter in PWLS was obtained for each CBCT projection using the proposed strategy. The noise in the low-dose CBCT images reconstructed from the smoothed projections was greatly suppressed. Image quality in PWLS-processed low-dose CBCT was comparable to its corresponding high-dose CBCT. Conclusions: A technique was proposed to estimate the penalty parameter for PWLS algorithm. It provides an objective and efficient way to obtain the penalty parameter for image restoration algorithms that require predefined smoothing parameters.
Age distribution curve in psychiatric admissions inversely correlates with Life Satisfaction.
Le Bon, Olivier; Le Bon, Serge-Daniel
2014-09-30
A strong inverse correlation was found between the age-distribution curve of psychiatric admissions and the U-bend Life Satisfaction curve. It may indicate that the peak of mental disorders at midlife reflects a less satisfactory period of life or, conversely, that the mental health load burdens of Life Satisfaction.
Grechin, S G; Nikolaev, P P; Sharandin, E A
2014-10-31
The functional possibilities of diode-side-pumped laser heads of solid-state lasers for forming inverse population distributions of different types are analysed. The invariants determining the relationship between the laser head parameters upon scaling are found. The results of comparative experimental studies are presented. (lasers)
NASA Astrophysics Data System (ADS)
Chen, T.; Gong, X.
2011-12-01
In inversion of geodetic data for distribution of fault slip minimizing the first or second order derivatives of slip across fault plane is generally employed to smooth slips of neighboring patches.Smoothing parameter is subjective selected to determine the relative weight placed on fitting data versus smoothing the slip distribution.We use the Fully Bayesian Inversion method(Fukuda,2008)to simultaneously estimate the slip distribution and smoothing parameter objectively in a Bayesian framework. The distributed slips,the posterior probability density function and the smoothing parameter is formulated with Bayes' theorem and sampled with a Markov chain Monte Carlo method. Here We will apply this method to Coseismic and Postseismic displacement data from the 2007 Solomon Islands Earthquake and compare the results of this method with generally favored method.
Vugrinovich, R.G.
1981-01-01
A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated Sm and is given by the median of the set of n(n - 1)/2 slope estimators, which may be calculated by inserting pairs of points (Xi, Yi)and (Xj, Yj)into the slope formula Si = (Yi - Yj)/(Xi - Xj), 1 ??? i k (median {|Ri - Rm|}). If no outliers are found, the Y-intercept is given by Rm. Confidence limits on Rm and Sm can be found from the sets of Ri and Si, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques. ?? 1981 Plenum Publishing Corporation.
Universal inverse power-law distribution for temperature and rainfall in the UK region
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2014-06-01
Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.
Gu, Y D; Ren, X J; Li, J S; Lake, M J; Zhang, Q Y; Zeng, Y J
2010-06-01
Metatarsal fracture is one of the most common foot injuries, particularly in athletes and soldiers, and is often associated with landing in inversion. An improved understanding of deformation of the metatarsals under inversion landing conditions is essential in the diagnosis and prevention of metatarsal injuries. In this work, a detailed three-dimensional (3D) finite element foot model was developed to investigate the effect of inversion positions on stress distribution and concentration within the metatarsals. The predicted plantar pressure distribution showed good agreement with data from controlled biomechanical tests. The deformation and stresses of the metatarsals during landing at different inversion angles (normal landing, 10 degree inversion and 20 degree inversion angles) were comparatively studied. The results showed that in the lateral metatarsals stress increased while in the medial metatarsals stress decreased with the angle of inversion. The peak stress point was found to be near the proximal part of the fifth metatarsal, which corresponds with reported clinical observations of metatarsal injuries.
NASA Astrophysics Data System (ADS)
Hori, T.; Nakata, R.; Kuwatani, T.; Okada, M.
2014-12-01
A Trial for Improvement in Reproducibility of Spatial Distribution of Afterslip in Geodetic Data InversionAfterslips of plate boundary earthquakes in subduction zones sometimes show doughnut-shaped slip distribution. For example, little afterslip occurred in the coseismic slip area of the 2003 Tokachi-oki earthquake of magnitude (M) 8.0 while large slip occurred in its surrounding area (ex. Miyazaki et al., 2004). However, it is difficult to resolve such heterogeneous distribution for M7 class earthquakes especially in offshore region. We demonstrated the reproducibility of spatial distribution of afterslip following a M7 class earthquake through numerical experiments to estimate slip distribution on the plate interface beneath the Hyuga-nada offshore region, southwest Japan (Nakata et al., 2013). We calculated synthetic displacement data from the result of numerical simulation conducted for the afterslip following a M 6.8 earthquake, for existing global navigation satellite system stations on land and planned ocean floor pressure gauge network stations. The spatial distribution of fault slip is estimated using a Kalman filter-based inversion. The slip distribution estimated by using ocean floor stations demonstrates that the heterogeneity of plate coupling, which roughly corresponds to the coseismic area of the M 6.8 earthquake with a radius of 10 km. The estimated slip amount in the coseismic area is nearly half of the peak one around it, although no slip is the true answer. This discrepancy is caused by the smoothness constraint in the inversion. To improve the reproducibility of the slip distribution, it is necessary to introduce different type of constraints. Based on a Bayesian approach, we introduce an evaluation function that can treat both discontinuity and smoothness in slip distribution.
A new stochastic algorithm for inversion of dust aerosol size distribution
NASA Astrophysics Data System (ADS)
Wang, Li; Li, Feng; Yang, Ma-ying
2015-08-01
Dust aerosol size distribution is an important source of information about atmospheric aerosols, and it can be determined from multiwavelength extinction measurements. This paper describes a stochastic inverse technique based on artificial bee colony (ABC) algorithm to invert the dust aerosol size distribution by light extinction method. The direct problems for the size distribution of water drop and dust particle, which are the main elements of atmospheric aerosols, are solved by the Mie theory and the Lambert-Beer Law in multispectral region. And then, the parameters of three widely used functions, i.e. the log normal distribution (L-N), the Junge distribution (J-J), and the normal distribution (N-N), which can provide the most useful representation of aerosol size distributions, are inversed by the ABC algorithm in the dependent model. Numerical results show that the ABC algorithm can be successfully applied to recover the aerosol size distribution with high feasibility and reliability even in the presence of random noise.
NASA Astrophysics Data System (ADS)
Michalak, Anna M.; Kitanidis, Peter K.
2004-08-01
As the incidence of groundwater contamination continues to grow, a number of inverse modeling methods have been developed to address forensic groundwater problems. In this work the geostatistical approach to inverse modeling is extended to allow for the recovery of the antecedent distribution of a contaminant at a given point back in time, which is critical to the assessment of historical exposure to contamination. Such problems are typically strongly underdetermined, with a large number of points at which the distribution is to be estimated. To address this challenge, the computational efficiency of the new method is increased through the application of the adjoint state method. In addition, the adjoint problem is presented in a format that allows for the reuse of existing groundwater flow and transport codes as modules in the inverse modeling algorithm. As demonstrated in the presented applications, the geostatistical approach combined with the adjoint state method allow for a historical multidimensional contaminant distribution to be recovered even in heterogeneous media, where a numerical solution is required for the forward problem.
NASA Astrophysics Data System (ADS)
Kato, Takeyoshi; Sugimoto, Hiroyuki; Suzuoki, Yasuo
We established a procedure for estimating regional electricity demand and regional potential capacity of distributed generators (DGs) by using a grid square statistics data set. A photovoltaic power system (PV system) for residential use and a co-generation system (CGS) for both residential and commercial use were taken into account. As an example, the result regarding Aichi prefecture was presented in this paper. The statistical data of the number of households by family-type and the number of employees by business category for about 4000 grid-square with 1km × 1km area was used to estimate the floor space or the electricity demand distribution. The rooftop area available for installing PV systems was also estimated with the grid-square statistics data set. Considering the relation between a capacity of existing CGS and a scale-index of building where CGS is installed, the potential capacity of CGS was estimated for three business categories, i.e. hotel, hospital, store. In some regions, the potential capacity of PV systems was estimated to be about 10,000kW/km2, which corresponds to the density of the existing area with intensive installation of PV systems. Finally, we discussed the ratio of regional potential capacity of DGs to regional maximum electricity demand for deducing the appropriate capacity of DGs in the model of future electricity distribution system.
Magazù, Salvatore; Maisano, Giacomo; Migliardo, Federica; Benedetto, Antonio
2008-07-31
In the present work an operational recipe for the mean square displacement (MSD) determination, highlighting the connection between the self-distribution function and average statistical values, is presented. The determination of the MSD and of its contributions associated with different mechanisms, together with their thermal behavior, is performed by evaluating the self-distribution function derived by elastic incoherent neutron scattering (EINS). The approach is tested on EINS data collected by the backscattering spectrometer IN13 (ILL, Grenoble, France) on two model systems such as dry myoglobin in trehalose and poly(ethylene glycol) with mean molecular weight M(w) = 400 (PEG 400).
NASA Astrophysics Data System (ADS)
Aitala, E. M.; Amato, S.; Anjos, J. C.; Appel, J. A.; Ashery, D.; Banerjee, S.; Bediaga, I.; Blaylock, G.; Bracker, S. B.; Burchat, P. R.; Burnstein, R. A.; Carter, T.; Carvalho, H. S.; Copty, N. K.; Cremaldi, L. M.; Darling, C.; Denisenko, K.; Deval, S.; Fernandez, A.; Fox, G. F.; Gagnon, P.; Gerzon, S.; Gobel, C.; Gounder, K.; Halling, A. M.; Herrera, G.; Hurvits, G.; James, C.; Kasper, P. A.; Kwan, S.; Langs, D. C.; Leslie, J.; Lichtenstadt, J.; Lundberg, B.; Maytal-Beck, S.; Meadows, B.; de Mello Neto, J. R.; Mihalcea, D.; Milburn, R. H.; de Miranda, J. M.; Napier, A.; Nguyen, A.; D'Oliveira, A. B.; O'Shaughnessy, K.; Peng, K. C.; Perera, L. P.; Purohit, M. V.; Quinn, B.; Radeztsky, S.; Rafatian, A.; Reay, N. W.; Reidy, J. J.; Dos Reis, A. C.; Rubin, H. A.; Sanders, D. A.; Santha, A. K.; Santoro, A. F.; Schwartz, A. J.; Sheaff, M.; Sidwell, R. A.; Slaughter, A. J.; Sokoloff, M. D.; Solano, J.; Stanton, N. R.; Stefanski, R. J.; Stenson, K.; Summers, D. J.; Takach, S.; Thorne, K.; Tripathi, A. K.; Watanabe, S.; Weiss-Babai, R.; Wiener, J.; Witchey, N.; Wolin, E.; Yang, S. M.; Yi, D.; Yoshida, S.; Zaliznyak, R.; Zhang, C.
2001-05-01
We present the first direct measurements of the pion valence-quark momentum distribution which is related to the square of the pion light-cone wave function. The measurements were carried out using data on diffractive dissociation of 500 GeV/c π- into dijets from a platinum target at Fermilab experiment E791. The results show that the \\|qq¯> light-cone asymptotic wave function describes the data well for Q2~10 \\(GeV/c\\)2 or more. We also measured the transverse momentum distribution of the diffractive dijets.
NASA Astrophysics Data System (ADS)
Kusznir, N. J.; Alvey, A.; Roberts, A. M.
2013-12-01
Mapping crustal thickness, continental lithosphere thinning and oceanic lithosphere distribution represents a substantial challenge for the Polar Regions. Using gravity anomaly inversion, we have produced the first comprehensive maps of crustal thickness and oceanic lithosphere distribution for the Arctic. The Arctic region formed as a series of small distinct ocean basins leading to a complex distribution of oceanic crust, thinned continental crust, possible micro-continents and rifted continental margins. Mapping of continental lithosphere thinning factor and crustal thickness from gravity inversion provide predictions of ocean-continent transition structure and magmatic type and continent ocean boundary location independent of magnetic isochrons. Restoration of crustal thickness and continent-ocean boundary location from gravity inversion may be used to test plate tectonic reconstructions. Using crustal thickness and continental lithosphere thinning factor maps with superimposed shaded-relief free-air gravity anomaly, we improve the determination of pre-breakup rifted margin conjugacy and sea-floor spreading trajectory within the Arctic basins. By restoring crustal thickness & continental lithosphere thinning maps of the Eurasia Basin & NE Atlantic to their initial post-breakup configuration we show the geometry and segmentation of the rifted continental margins at their time of breakup, together with the location of highly-stretched failed breakup basins and rifted micro-continents. Our gravity inversion predicts thin crust and high continental lithosphere thinning factors in the Makarov, Podvodnikov, Nautilus and Canada Basins consistent with these basins being underlain by oceanic or highly thinned continental crust. Larger crustal thicknesses, in the range 20 - 30 km, are predicted for the Lomonosov, Alpha and Mendeleev Ridges. Moho depths predicted compare well with seismic estimates. Predicted very thin continental or oceanic crust under the North Chuchki
Chen, Yanming; Zhao, Qingjie
2015-01-01
This paper deals with the problem of multi-target tracking in a distributed camera network using the square-root cubature information filter (SCIF). SCIF is an efficient and robust nonlinear filter for multi-sensor data fusion. In camera networks, multiple cameras are arranged in a dispersed manner to cover a large area, and the target may appear in the blind area due to the limited field of view (FOV). Besides, each camera might receive noisy measurements. To overcome these problems, this paper proposes a novel multi-target square-root cubature information weighted consensus filter (MTSCF), which reduces the effect of clutter or spurious measurements using joint probabilistic data association (JPDA) and proper weights on the information matrix and information vector. The simulation results show that the proposed algorithm can efficiently track multiple targets in camera networks and is obviously better in terms of accuracy and stability than conventional multi-target tracking algorithms. PMID:25951338
Chen, Yanming; Zhao, Qingjie
2015-05-05
This paper deals with the problem of multi-target tracking in a distributed camera network using the square-root cubature information filter (SCIF). SCIF is an efficient and robust nonlinear filter for multi-sensor data fusion. In camera networks, multiple cameras are arranged in a dispersed manner to cover a large area, and the target may appear in the blind area due to the limited field of view (FOV). Besides, each camera might receive noisy measurements. To overcome these problems, this paper proposes a novel multi-target square-root cubature information weighted consensus filter (MTSCF), which reduces the effect of clutter or spurious measurements using joint probabilistic data association (JPDA) and proper weights on the information matrix and information vector. The simulation results show that the proposed algorithm can efficiently track multiple targets in camera networks and is obviously better in terms of accuracy and stability than conventional multi-target tracking algorithms.
Chen, Yanming; Zhao, Qingjie
2015-01-01
This paper deals with the problem of multi-target tracking in a distributed camera network using the square-root cubature information filter (SCIF). SCIF is an efficient and robust nonlinear filter for multi-sensor data fusion. In camera networks, multiple cameras are arranged in a dispersed manner to cover a large area, and the target may appear in the blind area due to the limited field of view (FOV). Besides, each camera might receive noisy measurements. To overcome these problems, this paper proposes a novel multi-target square-root cubature information weighted consensus filter (MTSCF), which reduces the effect of clutter or spurious measurements using joint probabilistic data association (JPDA) and proper weights on the information matrix and information vector. The simulation results show that the proposed algorithm can efficiently track multiple targets in camera networks and is obviously better in terms of accuracy and stability than conventional multi-target tracking algorithms. PMID:25951338
Inverse analysis of non-uniform temperature distributions using multispectral pyrometry
NASA Astrophysics Data System (ADS)
Fu, Tairan; Duan, Minghao; Tian, Jibin; Shi, Congling
2016-05-01
Optical diagnostics can be used to obtain sub-pixel temperature information in remote sensing. A multispectral pyrometry method was developed using multiple spectral radiation intensities to deduce the temperature area distribution in the measurement region. The method transforms a spot multispectral pyrometer with a fixed field of view into a pyrometer with enhanced spatial resolution that can give sub-pixel temperature information from a "one pixel" measurement region. A temperature area fraction function was defined to represent the spatial temperature distribution in the measurement region. The method is illustrated by simulations of a multispectral pyrometer with a spectral range of 8.0-13.0 μm measuring a non-isothermal region with a temperature range of 500-800 K in the spot pyrometer field of view. The inverse algorithm for the sub-pixel temperature distribution (temperature area fractions) in the "one pixel" verifies this multispectral pyrometry method. The results show that an improved Levenberg-Marquardt algorithm is effective for this ill-posed inverse problem with relative errors in the temperature area fractions of (-3%, 3%) for most of the temperatures. The analysis provides a valuable reference for the use of spot multispectral pyrometers for sub-pixel temperature distributions in remote sensing measurements.
Arctic and N Atlantic Crustal Thickness and Oceanic Lithosphere Distribution from Gravity Inversion
NASA Astrophysics Data System (ADS)
Kusznir, Nick; Alvey, Andy
2014-05-01
The ocean basins of the Arctic and N. Atlantic formed during the Mesozoic and Cenozoic as a series of distinct ocean basins, both small and large, leading to a complex distribution of oceanic crust, thinned continental crust and rifted continental margins. The plate tectonic framework of this region was demonstrated by the pioneering work of Peter Ziegler in AAPG Memoir 43 " Evolution of the Arctic-North Atlantic and the Western Tethys" published in 1988. The spatial evolution of Arctic Ocean and N Atlantic ocean basin geometry and bathymetry are critical not only for hydrocarbon exploration but also for understanding regional palaeo-oceanography and ocean gateway connectivity, and its influence on global climate. Mapping crustal thickness and oceanic lithosphere distribution represents a substantial challenge for the Polar Regions. Using gravity anomaly inversion we have produced comprehensive maps of crustal thickness and oceanic lithosphere distribution for the Arctic and N Atlantic region, We determine Moho depth, crustal basement thickness, continental lithosphere thinning and ocean-continent transition location using a 3D spectral domain gravity inversion method, which incorporates a lithosphere thermal gravity anomaly correction (Chappell & Kusznir 2008). Gravity anomaly and bathymetry data used in the gravity inversion are from the NGA (U) Arctic Gravity Project and IBCAO respectively; sediment thickness is from a new regional compilation. The resulting maps of crustal thickness and continental lithosphere thinning factor are used to determine continent-ocean boundary location and the distribution of oceanic lithosphere. Crustal cross-sections using Moho depth from the gravity inversion allow continent-ocean transition structure to be determined and magmatic type (magma poor, "normal" or magma rich). Our gravity inversion predicts thin crust and high continental lithosphere thinning factors in the Eurasia, Canada, Makarov, Podvodnikov and Baffin Basins
Budic, Lara; Didenko, Gregor; Dormann, Carsten F
2016-01-01
In species distribution analyses, environmental predictors and distribution data for large spatial extents are often available in long-lat format, such as degree raster grids. Long-lat projections suffer from unequal cell sizes, as a degree of longitude decreases in length from approximately 110 km at the equator to 0 km at the poles. Here we investigate whether long-lat and equal-area projections yield similar model parameter estimates, or result in a consistent bias. We analyzed the environmental effects on the distribution of 12 ungulate species with a northern distribution, as models for these species should display the strongest effect of projectional distortion. Additionally we choose four species with entirely continental distributions to investigate the effect of incomplete cell coverage at the coast. We expected that including model weights proportional to the actual cell area should compensate for the observed bias in model coefficients, and similarly that using land coverage of a cell should decrease bias in species with coastal distribution. As anticipated, model coefficients were different between long-lat and equal-area projections. Having progressively smaller and a higher number of cells with increasing latitude influenced the importance of parameters in models, increased the sample size for the northernmost parts of species ranges, and reduced the subcell variability of those areas. However, this bias could be largely removed by weighting long-lat cells by the area they cover, and marginally by correcting for land coverage. Overall we found little effect of using long-lat rather than equal-area projections in our analysis. The fitted relationship between environmental parameters and occurrence probability differed only very little between the two projection types. We still recommend using equal-area projections to avoid possible bias. More importantly, our results suggest that the cell area and the proportion of a cell covered by land should be
Budic, Lara; Didenko, Gregor; Dormann, Carsten F
2016-01-01
In species distribution analyses, environmental predictors and distribution data for large spatial extents are often available in long-lat format, such as degree raster grids. Long-lat projections suffer from unequal cell sizes, as a degree of longitude decreases in length from approximately 110 km at the equator to 0 km at the poles. Here we investigate whether long-lat and equal-area projections yield similar model parameter estimates, or result in a consistent bias. We analyzed the environmental effects on the distribution of 12 ungulate species with a northern distribution, as models for these species should display the strongest effect of projectional distortion. Additionally we choose four species with entirely continental distributions to investigate the effect of incomplete cell coverage at the coast. We expected that including model weights proportional to the actual cell area should compensate for the observed bias in model coefficients, and similarly that using land coverage of a cell should decrease bias in species with coastal distribution. As anticipated, model coefficients were different between long-lat and equal-area projections. Having progressively smaller and a higher number of cells with increasing latitude influenced the importance of parameters in models, increased the sample size for the northernmost parts of species ranges, and reduced the subcell variability of those areas. However, this bias could be largely removed by weighting long-lat cells by the area they cover, and marginally by correcting for land coverage. Overall we found little effect of using long-lat rather than equal-area projections in our analysis. The fitted relationship between environmental parameters and occurrence probability differed only very little between the two projection types. We still recommend using equal-area projections to avoid possible bias. More importantly, our results suggest that the cell area and the proportion of a cell covered by land should be
NASA Astrophysics Data System (ADS)
Tomaschitz, Roman
2013-12-01
Bessel integrals of type {int_0^infty {k^{μ+2}{e}^{-ak2-(b+{i} ω)k}j_l^{2} (pk)dk}} are studied, where the squared spherical Bessel function j {/l 2} is averaged with a modulated Gaussian power-law density. These integrals define the multipole moments of Gaussian random fields on the unit sphere, arising in multipole fits of temperature and polarization power spectra of the cosmic microwave background. The averages can be calculated in closed form as finite Hankel series, which allow high-precision evaluation. In the case of integer power-law exponents μ, singularities emerge in the series coefficients, which requires ɛ expansion. The pole extraction and regularization of singular Hankel series is performed, for integer Gaussian power-law densities as well as for the special case of Kummer averages (a = 0 in the exponential of the integrand). The singular ɛ residuals are used to derive combinatorial identities (sum rules) for the rational Hankel coefficients, which serve as consistency checks in precision calculations of the integrals. Numerical examples are given, and the Hankel evaluation of Gaussian and Kummer averages is compared with their high-index Airy approximation over a wide range of integer Bessel indices l.
Technology Transfer Automated Retrieval System (TEKTRAN)
The beard testing method for measuring cotton fiber length is based on the fibrogram theory. However, in the instrumental implementations, the engineering complexity alters the original fiber length distribution observed by the instrument. This causes challenges in obtaining the entire original le...
Mendoza, C.; Hartzell, S.H.
1988-01-01
We have inverted the teleseismic P waveforms recorded by stations of the Global Digital Seismograph Network for the 8 July 1986 North Palm Springs, California, the 28 October 1983 Borah Peak, Idaho, and the 19 September 1985 Michoacan, Mexico, earthquakes to recover the distribution of slip on each of the faults using a point-by-point inversion method with smoothing and positivity constraints. Results of the inversion indicate that the Global digital Seismograph Network data are useful for deriving fault dislocation models for moderate to large events. However, a wide range of frequencies is necessary to infer the distribution of slip on the earthquake fault. Although the long-period waveforms define the size (dimensions and seismic moment) of the earthquake, data at shorter period provide additional constraints on the variation of slip on the fault. Dislocation models obtained for all three earthquakes are consistent with a heterogeneous rupture process where failure is controlled largely by the size and location of high-strength asperity regions. -from Authors
An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions
Li, Weixuan; Lin, Guang
2015-03-21
Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.
An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions
Li, Weixuan; Lin, Guang
2015-08-01
Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.
An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions
Li, Weixuan; Lin, Guang
2015-03-21
Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle thesemore » challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.« less
Pore Size Distributions Inferred from Modified Inversion Percolation Modeling of Drainage Curves
NASA Astrophysics Data System (ADS)
Dralus, D. E.; Wang, H. F.; Strand, T. E.; Glass, R. J.; Detwiler, R. L.
2005-12-01
Experiments have been conducted of drainage in sand packs. At equilibrium, the interface between the fluids forms a saturation transition fringe where the saturation decreases monotonically with height. This behavior was observed in a 1-inch thick pack of 20-30 sand contained front and back within two thin, 12-inch-by-24-inch glass plates. The translucent chamber was illuminated from behind by a bank of fluorescent bulbs. Acquired data were in the form of images captured by a CCD camera with resolution on the grain scale. The measured intensity of the transmitted light was used to calculate the average saturation at each point in the chamber. This study used a modified invasion percolation (MIP) model to simulate the drainage experiments to evaluate the relationship between the saturation-versus-height curve at equilibrium and the pore size distribution associated with the granular medium. The simplest interpretation of a drainage curve is in terms of a distribution of capillary tubes whose radii reproduce the the observed distribution of rise heights. However, this apparent radius distribution obtained from direct inversion of the saturation profile did not yield the assumed radius distribution. Further investigation demonstrated that the equilibrium height distribution is controlled primarily by the Bond number (ratio of gravity to capillary forces) with some influence from the width of the pore radius distribution. The width of the equilibrium fringe is quantified in terms of the ratio of Bond number to the standard deviation of the pore throat distribution. The normalized saturation-vs-height curves exhibit a power-law scaling behavior consistent with both Brooks-Corey and Van Genuchten type curves. Fundamental tenets of percolation theory were used to quantify the relationship between the apparent and actual radius distributions as a function of the mean coordination number and of the ratio of Bond number to standard deviation, which was supported by both MIP
Inverse-cubic law of index fluctuation distribution in Indian markets
NASA Astrophysics Data System (ADS)
Pan, Raj Kumar; Sinha, Sitabhra
2008-03-01
One of the principal statistical features characterizing the activity in financial markets is the distribution of fluctuations in market indicators such as the index. While the developed stock markets, e.g., the New York Stock Exchange (NYSE) have been found to show heavy-tailed return distribution with a characteristic power-law exponent, the universality of such behavior has been debated, particularly in regard to emerging markets. Here we investigate the distribution of several indices from the Indian financial market, one of the largest emerging markets in the world. We have used tick-by-tick data from the National Stock Exchange (NSE), as well as, daily closing data from both the NSE and Bombay Stock Exchange (BSE). We find that the cumulative distributions of index returns have long tails consistent with a power law having exponent α ≈ 3, at time scales of both 1 min and 1 day. This "inverse-cubic law" is quantitatively similar to what has been observed in developed markets, thereby providing strong evidence of universality in the behavior of market fluctuations.
Gu, Y. D.; Ren, X. J.; Li, J. S.; Lake, M. J.; Zhang, Q. Y.
2009-01-01
Metatarsal fracture is one of the most common foot injuries, particularly in athletes and soldiers, and is often associated with landing in inversion. An improved understanding of deformation of the metatarsals under inversion landing conditions is essential in the diagnosis and prevention of metatarsal injuries. In this work, a detailed three-dimensional (3D) finite element foot model was developed to investigate the effect of inversion positions on stress distribution and concentration within the metatarsals. The predicted plantar pressure distribution showed good agreement with data from controlled biomechanical tests. The deformation and stresses of the metatarsals during landing at different inversion angles (normal landing, 10 degree inversion and 20 degree inversion angles) were comparatively studied. The results showed that in the lateral metatarsals stress increased while in the medial metatarsals stress decreased with the angle of inversion. The peak stress point was found to be near the proximal part of the fifth metatarsal, which corresponds with reported clinical observations of metatarsal injuries. PMID:19685241
Layer 1 VPN services in distributed next-generation SONET/SDH networks with inverse multiplexing
NASA Astrophysics Data System (ADS)
Ghani, N.; Muthalaly, M. V.; Benhaddou, D.; Alanqar, W.
2006-05-01
Advances in next-generation SONET/SDH along with GMPLS control architectures have enabled many new service provisioning capabilities. In particular, a key services paradigm is the emergent Layer 1 virtual private network (L1 VPN) framework, which allows multiple clients to utilize a common physical infrastructure and provision their own 'virtualized' circuit-switched networks. This precludes expensive infrastructure builds and increases resource utilization for carriers. Along these lines, a novel L1 VPN services resource management scheme for next-generation SONET/SDH networks is proposed that fully leverages advanced virtual concatenation and inverse multiplexing features. Additionally, both centralized and distributed GMPLS-based implementations are also tabled to support the proposed L1 VPN services model. Detailed performance analysis results are presented along with avenues for future research.
Hirao, S; Hayashi, R; Moriizumi, J; Yamazawa, H; Tohjima, Y; Mukai, H
2015-11-01
In this study, the (222)Rn flux density distribution at surface was estimated in East Asia with the Bayesian synthesis inversion using measurement data and a long-range atmospheric (222)Rn transport model. Surface atmospheric (222)Rn concentrations measured at Hateruma Island in January 2008 were used. The estimated (222)Rn flux densities were generally higher than the prior ones. The area-weighted mean (222)Rn flux density for East Asia in January 2008 was estimated to be 44.0 mBq m(-2) s(-1). The use of the estimated (222)Rn flux density improved the discrepancy of the model-calculated concentrations with the measurements at Hateruma Island.
Topological variations of the inverse dual converter for high-power dc-dc distribution systems
NASA Astrophysics Data System (ADS)
Ehsani, Mehrdad; Laskai, Laszlo
New dc-to-dc converter topologies are presented which are suitable for high density high power supplies. Topological variations of the basic inverse dual converter (IDC) circuit such as the transformer coupled, the multiphase and the multipulse derivation of the single phase IDC have been analyzed and some simulation results have been presented. The single phase IDC offers a buck-boost operation over wide range without transformer, bidirectional power flow, and complementary commutation of the switches. The topologies examined in this paper have additional features such as lower device and component stresses, and smaller filter requirements, resulting in smaller size and weight. Some performance and possible applications are also examined. IDCs for serial and parallel power distribution, and ac tapping of the IDC are discussed.
Lee, Chien-Wei; Hwu, Jenn-Gwo
2013-10-15
We derive a statistical physics model of two-dimensional electron gas (2DEG) and propose an accurate approximation method for calculating the quantum-mechanical effects of metal-oxide-semiconductor (MOS) structure in accumulation and strong inversion regions. We use an exponential surface potential approximation in solving the quantization energy levels and derive the function of density of states in 2D to 3D transition region by applying uncertainty principle and Schrödinger equation in k-space. The simulation results show that our approximation method and theory of density of states solve the two major problems of previous researches: the non-negligible error caused by the linear potential approximation and the inconsistency of density of states and carrier distribution in 2D to 3D transition region.
Xia, J.; Miller, R.D.; Xu, Y.
2008-01-01
Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (>2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data. ?? Birkhaueser 2008.
Inverse modeling of InSAR and ground leveling data for 3D volumetric strain distribution
NASA Astrophysics Data System (ADS)
Gallardo, L. A.; Glowacka, E.; Sarychikhina, O.
2015-12-01
Wide availability of modern Interferometric Synthetic aperture Radar (InSAR) data have made possible the extensive observation of differential surface displacements and are becoming an efficient tool for the detailed monitoring of terrain subsidence associated to reservoir dynamics, volcanic deformation and active tectonism. Unfortunately, this increasing popularity has not been matched by the availability of automated codes to estimate underground deformation, since many of them still rely on trial-error subsurface model building strategies. We posit that an efficient algorithm for the volumetric modeling of differential surface displacements should match the availability of current leveling and InSAR data and have developed an algorithm for the joint inversion of ground leveling and dInSAR data in 3D. We assume the ground displacements are originated by a stress free-volume strain distribution in a homogeneous elastic media and determined the displacement field associated to an ensemble of rectangular prisms. This formulation is then used to develop a 3D conjugate gradient inversion code that searches for the three-dimensional distribution of the volumetric strains that predict InSAR and leveling surface displacements simultaneously. The algorithm is regularized applying discontinuos first and zero order Thikonov constraints. For efficiency, the resulting computational code takes advantage of the resulting convolution integral associated to the deformation field and some basic tools for multithreading parallelization. We extensively test our algorithm on leveling and InSAR test and field data of the Northwest of Mexico and compare to some feasible geological scenarios of underground deformation.
NASA Astrophysics Data System (ADS)
Baer, P.; Mastrandrea, M.
2006-12-01
Simple probabilistic models which attempt to estimate likely transient temperature change from specified CO2 emissions scenarios must make assumptions about at least six uncertain aspects of the causal chain between emissions and temperature: current radiative forcing (including but not limited to aerosols), current land use emissions, carbon sinks, future non-CO2 forcing, ocean heat uptake, and climate sensitivity. Of these, multiple PDFs (probability density functions) have been published for the climate sensitivity, a couple for current forcing and ocean heat uptake, one for future non-CO2 forcing, and none for current land use emissions or carbon cycle uncertainty (which are interdependent). Different assumptions about these parameters, as well as different model structures, will lead to different estimates of likely temperature increase from the same emissions pathway. Thus policymakers will be faced with a range of temperature probability distributions for the same emissions scenarios, each described by a central tendency and spread. Because our conventional understanding of uncertainty and probability requires that a probabilistically defined variable of interest have only a single mean (or median, or modal) value and a well-defined spread, this "multidimensional" uncertainty defies straightforward utilization in policymaking. We suggest that there are no simple solutions to the questions raised. Crucially, we must dispel the notion that there is a "true" probability probabilities of this type are necessarily subjective, and reasonable people may disagree. Indeed, we suggest that what is at stake is precisely the question, what is it reasonable to believe, and to act as if we believe? As a preliminary suggestion, we demonstrate how the output of a simple probabilistic climate model might be evaluated regarding the reasonableness of the outputs it calculates with different input PDFs. We suggest further that where there is insufficient evidence to clearly
Cao, Meng-Li; Meng, Qing-Hao; Zeng, Ming; Sun, Biao; Li, Wei; Ding, Cheng-Jun
2014-01-01
This paper investigates the problem of locating a continuous chemical source using the concentration measurements provided by a wireless sensor network (WSN). Such a problem exists in various applications: eliminating explosives or drugs, detecting the leakage of noxious chemicals, etc. The limited power and bandwidth of WSNs have motivated collaborative in-network processing which is the focus of this paper. We propose a novel distributed least-squares estimation (DLSE) method to solve the chemical source localization (CSL) problem using a WSN. The DLSE method is realized by iteratively conducting convex combination of the locally estimated chemical source locations in a distributed manner. Performance assessments of our method are conducted using both simulations and real experiments. In the experiments, we propose a fitting method to identify both the release rate and the eddy diffusivity. The results show that the proposed DLSE method can overcome the negative interference of local minima and saddle points of the objective function, which would hinder the convergence of local search methods, especially in the case of locating a remote chemical source. PMID:24977387
Cao, Meng-Li; Meng, Qing-Hao; Zeng, Ming; Sun, Biao; Li, Wei; Ding, Cheng-Jun
2014-01-01
This paper investigates the problem of locating a continuous chemical source using the concentration measurements provided by a wireless sensor network (WSN). Such a problem exists in various applications: eliminating explosives or drugs, detecting the leakage of noxious chemicals, etc. The limited power and bandwidth of WSNs have motivated collaborative in-network processing which is the focus of this paper. We propose a novel distributed least-squares estimation (DLSE) method to solve the chemical source localization (CSL) problem using a WSN. The DLSE method is realized by iteratively conducting convex combination of the locally estimated chemical source locations in a distributed manner. Performance assessments of our method are conducted using both simulations and real experiments. In the experiments, we propose a fitting method to identify both the release rate and the eddy diffusivity. The results show that the proposed DLSE method can overcome the negative interference of local minima and saddle points of the objective function, which would hinder the convergence of local search methods, especially in the case of locating a remote chemical source. PMID:24977387
Cao, Meng-Li; Meng, Qing-Hao; Zeng, Ming; Sun, Biao; Li, Wei; Ding, Cheng-Jun
2014-06-27
This paper investigates the problem of locating a continuous chemical source using the concentration measurements provided by a wireless sensor network (WSN). Such a problem exists in various applications: eliminating explosives or drugs, detecting the leakage of noxious chemicals, etc. The limited power and bandwidth of WSNs have motivated collaborative in-network processing which is the focus of this paper. We propose a novel distributed least-squares estimation (DLSE) method to solve the chemical source localization (CSL) problem using a WSN. The DLSE method is realized by iteratively conducting convex combination of the locally estimated chemical source locations in a distributed manner. Performance assessments of our method are conducted using both simulations and real experiments. In the experiments, we propose a fitting method to identify both the release rate and the eddy diffusivity. The results show that the proposed DLSE method can overcome the negative interference of local minima and saddle points of the objective function, which would hinder the convergence of local search methods, especially in the case of locating a remote chemical source.
Pan, Feifei; Peters-lidard, Christa D.; King, Anthony Wayne
2010-11-01
Soil particle size distribution (PSD) (i.e., clay, silt, sand, and rock contents) information is one of critical factors for understanding water cycle since it affects almost all of water cycle processes, e.g., drainage, runoff, soil moisture, evaporation, and evapotranspiration. With information about soil PSD, we can estimate almost all soil hydraulic properties (e.g., saturated soil moisture, field capacity, wilting point, residual soil moisture, saturated hydraulic conductivity, pore-size distribution index, and bubbling capillary pressure) based on published empirical relationships. Therefore, a regional or global soil PSD database is essential for studying water cycle regionally or globally. At the present stage, three soil geographic databases are commonly used, i.e., the Soil Survey Geographic database, the State Soil Geographic database, and the National Soil Geographic database. Those soil data are map unit based and associated with great uncertainty. Ground soil surveys are a way to reduce this uncertainty. However, ground surveys are time consuming and labor intensive. In this study, an inverse method for estimating mean and standard deviation of soil PSD from observed soil moisture is proposed and applied to Throughfall Displacement Experiment sites in Walker Branch Watershed in eastern Tennessee. This method is based on the relationship between spatial mean and standard deviation of soil moisture. The results indicate that the suggested method is feasible and has potential for retrieving soil PSD information globally from remotely sensed soil moisture data.
NASA Astrophysics Data System (ADS)
Kelbert, A.; Schultz, A.
2004-12-01
The case for substantial heterogeneity in mantle conductivity has stimulated the development of methods for solving Maxwell's equations in a heterogeneous conducting sphere. A global 3-D frequency domain forward solver has been devised (Uyeshima & Schultz, 2000), accurate and efficient enough to be an attractive kernel of a practical inverse method. The solver employs a staggered-grid finite difference formulation in spherical coordinates. The induced fields are found as a solution to the integral form of Maxwell's equations, while the system is solved using stabilised biconjugate gradient methods. A single, accurate forward solution takes approx. 4 minutes on 5 GFLOP (peak) processor. The aim of our present research is to produce an inverse solver, to be applied to the Fujii & Schultz (2002) data set of globally-distributed EM response functions, which would reconstruct the 3-D electrical conductivity distribution in the upper to mid-mantle. Geophysical inversion is an ill-posed problem, therefore the aim is to apply suitable parameter constraints and a nonlinear search algorithm to identify candidate minima, then to apply local gradient methods around those minima. Our specific target involves designing a fast enough global optimisation routine that would allow us to produce at least one fully 3-D starting model, optimal with respect to the RMS misfit between the data and the forward solutions. A new and very flexible inverse solver has been developed utilizing parallel optimisation routines to obtain a starting model that satisfies the data. 3-D simulations have been run, the parametrization based on a spherical harmonic representation of a chess board model of varying degree and order. The inversion has demonstrated accurate fidelity in reproducing resolvable features of the test model. A study has been made of the reduction in fidelity as the number and distribution of observatory sites on the Earth's surface is degraded. An inversion of the Fujii & Schultz
NASA Technical Reports Server (NTRS)
Zhang, Y. C.; Zhang, J. Z. H.; Kouri, D. J.; Haug, K.; Schwenke, D. W.
1988-01-01
Numerically exact, fully three-dimensional quantum mechanicl reactive scattering calculations are reported for the H2Br system. Both the exchange (H + H-prime Br to H-prime + HBr) and abstraction (H + HBR to H2 + Br) reaction channels are included in the calculations. The present results are the first completely converged three-dimensional quantum calculations for a system involving a highly exoergic reaction channel (the abstraction process). It is found that the production of vibrationally hot H2 in the abstraction reaction, and hence the extent of population inversion in the products, is a sensitive function of initial HBr rotational state and collision energy.
NASA Technical Reports Server (NTRS)
Mcdade, Ian. C.; Llewellyn, Edward J.
1991-01-01
This paper demonstrates how the spatial distribution of optical emission rates within an auroral arc may be recovered from rocket photometer measurements made in a tomographic spin scan mode. The tomographic inversion procedures required to recover this information and the implementation of two inversion algorithms that are particularly well suited for dealing with the problem of noise in the observational data are described. The performance of the inversion algorithms and the limitations of the rocket tomography technique are assessed using various sets of simulated rocket measurements that were generated from 'known' auroral emission-rate distributions. The simulations are used to investigate how the quality of the tomographic recovery may be influenced by various factors such as noise in the data, rocket penetration of the auroral form, background sources of emission, smearing due to the photometer field of view, and temporal variations in the auroral form.
NASA Astrophysics Data System (ADS)
Wang, Shihong; Liu, Zhiliang; Pang, Chongguang
2015-07-01
The geographic character of the inverse cascade is analyzed based on the spectral kinetic energy flux calculated in the global ocean, using sea surface height (SSH) data from satellites, reanalysis data, and model outputs. It is shown that the strongest inverse cascade occurs mostly in high-energy eastward-flowing currents, such as the Antarctic Circumpolar Current (ACC), the Kuroshio Extension, and the Gulf Stream, which matches the global distribution pattern of the eddy kinetic energy (EKE). Hence, the eddy scales predicted by the local linear baroclinic instability Lbci and from the altimeter observation Leddy are mapped out and compared with the energy injection scale Linj and the arrest-start scale Larrest-start of the inverse cascade, respectively. Generally, Lbci agrees well with Linj in the midlatitude and high-latitude oceans, especially in the Northern Hemisphere. Leddy falls within the arrest ranges of the inverse cascade and is quite close to Larrest-start. Finally, the depth dependence and the anisotropy of the inverse kinetic energy cascade are also diagnosed in the global ocean. We have found that the strength of the inverse cascades decreases with increasing depth, but the global pattern of the strength is nearly invariable. Meanwhile, the variations in depth hardly affect the Linj and Larrest-start. After considering the anisotropy in the spectral flux calculation, a possible inertial range for the zonal spectral kinetic energy flux is expected, where the cascade magnitude will keep a nearly constant negative value associated with the oceanic zonal jets.
Zhou, C.; Liu, L.; Lane, J.W.
2001-01-01
A nonlinear tomographic inversion method that uses first-arrival travel-time and amplitude-spectra information from cross-hole radar measurements was developed to simultaneously reconstruct electromagnetic velocity and attenuation distribution in earth materials. Inversion methods were developed to analyze single cross-hole tomography surveys and differential tomography surveys. Assuming the earth behaves as a linear system, the inversion methods do not require estimation of source radiation pattern, receiver coupling, or geometrical spreading. The data analysis and tomographic inversion algorithm were applied to synthetic test data and to cross-hole radar field data provided by the US Geological Survey (USGS). The cross-hole radar field data were acquired at the USGS fractured-rock field research site at Mirror Lake near Thornton, New Hampshire, before and after injection of a saline tracer, to monitor the transport of electrically conductive fluids in the image plane. Results from the synthetic data test demonstrate the algorithm computational efficiency and indicate that the method robustly can reconstruct electromagnetic (EM) wave velocity and attenuation distribution in earth materials. The field test results outline zones of velocity and attenuation anomalies consistent with the finding of previous investigators; however, the tomograms appear to be quite smooth. Further work is needed to effectively find the optimal smoothness criterion in applying the Tikhonov regularization in the nonlinear inversion algorithms for cross-hole radar tomography. ?? 2001 Elsevier Science B.V. All rights reserved.
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2016-09-01
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference
NASA Astrophysics Data System (ADS)
Baba, T.; Takagawa, T.; Tsushima, H.; Hayashi, Y.; Tomita, T.; Gómez, C.; Catalan, P. A.
2014-12-01
A major earthquake occurred on the plate boundary between the Nazca plate and the South American plate on April 1, 2014 in northern Chile associated with a tsunami that was recorded at the offshore DART buoys and the coastal tide gauges. The epicenter was located in a seismic gap called "Iquique gap", but the moment magnitude was estimated to be 8.2 from the seismic wave analysis which was much smaller than the size of seismic gap. It is important to reveal the slip distribution of this earthquake in order to assess remaining tsunami risk in the region. We therefore carried out a tsunami inversion analysis for this earthquake. We used tsunami waveform data recorded at both of the offshore and coastal gauges, and 30 arc-sec interval bathymetric grid complied by the Hydrographic and Oceanographic Service of the Chilean Navy. We also examined effect of tsunami governing equations used in creating Green's functions. One solution was obtained with the linear long-wave equations; the other was obtained with the linear dispersive equations. The effect of dispersive equations was found in tsunami waveforms in the open ocean. But that was not apparent in near-field records and the estimated slip distribution itself. The observed tsunami waveforms were retrieved well in the analysis except at Tocopilla where a large delay of tsunami arrival of about 10 minutes was seen in the observed data. Features of the estimated slip are 1) the slip extent was approximately 120km x 80km, 2) the major slip area was located to the south of the epicenter, a region off between Pisagua and Iquique, 3) the maximum slip was about 5m, 4) the seismic moment was calculated to be 1.28x10^21Nm (Mw 8.0).
ERIC Educational Resources Information Center
Curran, Patrick J.; Bollen, Kenneth A.; Paxton, Pamela; Kirby, James; Chen, Feinian
2002-01-01
Examined several hypotheses about the suitability of the noncentral chi square in applied research using Monte Carlo simulation experiments with seven sample sizes and three distinct model types, each with five specifications. Results show that, in general, for models with small to moderate misspecification, the noncentral chi-square is well…
Piskozub, J.
1994-12-31
The multifrequency lidar inverse problem discussed consists of calculating the size distribution of sol particles from backscattered lidar data. Sea-water (marine) aerosol is particularly well suited for this kind of study as its scattering characteristics can be accurately represented by Mie theory as its particles are almost spherical and their complex index of refraction is well known. Here, a solution of the inverse problem concerning finding aerosol size distribution for a multifrequency lidar system working on a small number of wavelengths is proposed. The solution involves a best-fit method of finding parameters in a pre-set formula of particle size distribution. A comparison of results calculated with the algorithm from experimental lidar profiles with PMS data collected in Baltic Sea coastal zone is given.
Square dielectric THz waveguides.
Aflakian, N; Yang, N; LaFave, T; Henderson, R M; O, K K; MacFarlane, D L
2016-06-27
A holey cladding dielectric waveguide with square cross section is designed, simulated, fabricated and characterized. The TOPAS waveguide is designed to be single mode across the broad frequency range of 180 GHz to 360 GHz as shown by finite-difference time domain simulation and to robustly support simultaneous TE and TM mode propagation. The square fiber geometry is realized by pulling through a heat distribution made square by appropriate furnace design. The transmitted mode profile is imaged using a vector network analyzer with a pinhole at the receiver module. Good agreement between the measured mode distribution and the calculated mode distribution is demonstrated. PMID:27410645
NASA Astrophysics Data System (ADS)
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
ERIC Educational Resources Information Center
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
NASA Astrophysics Data System (ADS)
Tarmizi, S. N. M.; Asmat, A.; Sumari, S. M.
2014-02-01
PM10 is one of the air contaminants that can be harmful to human health. Meteorological factors and changes of monsoon season may affect the distribution of these particles. The objective of this study is to determine the temporal and spatial particulate matter (PM10) concentration distribution in Klang Valley, Malaysia by using the Inverse Distance Weighted (IDW) method at different monsoon season and meteorological conditions. PM10 and meteorological data were obtained from the Malaysian Department of Environment (DOE). Particles distribution data were added to the geographic database on a seasonal basis. Temporal and spatial patterns of PM10 concentration distribution were determined by using ArcGIS 9.3. The higher PM10 concentrations are observed during Southwest monsoon season. The values are lower during the Northeast monsoon season. Different monsoon seasons show different meteorological conditions that effect PM10 distribution.
ERIC Educational Resources Information Center
Hubbard, Guy
2003-01-01
Discusses the role of the square in art and explains that students can study modern art. Includes background information and artwork by four artists: (1) Richard Anuszkiewicz; (2) Victor Vasarely; (3) Frank Stella; and (4) Bridget Riley. (CMK)
ERIC Educational Resources Information Center
Holton, Derek; Knights, Carol
2008-01-01
Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n [congruent to] i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also…
Edwards, A W F
2012-03-01
The origin and development of Punnett's Square for the enumeration and display of genotypes arising in a cross in Mendelian genetics is described. Due to R. C. Punnett, the idea evolved through the work of the 'Cambridge geneticists', including Punnett's colleagues William Bateson, E. R. Saunders and R. H. Lock, soon after the rediscovery of Mendel's paper in 1900. These geneticists were thoroughly familiar with Mendel's paper, which itself contained a similar square diagram. A previously-unpublished three-factor diagram by Sir Francis Galton existing in the Bateson correspondence in Cambridge University Library is then described. Finally the connection between Punnett's Square and Venn Diagrams is emphasized, and it is pointed out that Punnett, Lock and John Venn overlapped as Fellows of Gonville and Caius College, Cambridge. Copious illustrations are given. PMID:22326091
Edwards, A W F
2012-03-01
The origin and development of Punnett's Square for the enumeration and display of genotypes arising in a cross in Mendelian genetics is described. Due to R. C. Punnett, the idea evolved through the work of the 'Cambridge geneticists', including Punnett's colleagues William Bateson, E. R. Saunders and R. H. Lock, soon after the rediscovery of Mendel's paper in 1900. These geneticists were thoroughly familiar with Mendel's paper, which itself contained a similar square diagram. A previously-unpublished three-factor diagram by Sir Francis Galton existing in the Bateson correspondence in Cambridge University Library is then described. Finally the connection between Punnett's Square and Venn Diagrams is emphasized, and it is pointed out that Punnett, Lock and John Venn overlapped as Fellows of Gonville and Caius College, Cambridge. Copious illustrations are given.
Chen, J. M.; Fung, J. W.; Mo, G.; Deng, F.; West, Tristram O.
2015-01-01
In order to improve quantification of the spatial distribution of carbon sinks and sources in the conterminous USA, we conduct a nested global atmospheric inversion with consideration of the spatial information of crop production and consumption. Spatially distributed 5 county-level cropland net primary productivity, harvested biomass, soil carbon change, and human and livestock consumption data over the conterminous USA are used for this purpose. Time-dependent Bayesian synthesis inversions are conducted based on CO₂ observations at 210 stations to infer CO₂ fluxes globally at monthly time steps with a nested focus on 30 regions in North America. Prior land surface carbon 10 fluxes are first generated using a biospheric model, and the inversions are constrained using prior fluxes with and without adjustments for crop production and consumption over the 2002–2007 period. After these adjustments, the inverted regional carbon sink in the US Midwest increases from 0.25 ± 0.03 Pg C yr⁻¹ to 0.42 ± 0.13 Pg C yr⁻¹, whereas the large sink in the US Southeast forest region is weakened from 0.41±0.12 Pg C yr⁻¹ 15 to 0.29 ±0.12 Pg C yr⁻¹. These adjustments also reduce the inverted sink in the West region from 0.066 ± 0.04 Pg C yr⁻¹ to 0.040 ± 0.02 Pg C yr⁻1 because of high crop consumption and respiration by humans and livestock. The general pattern of sink increase in crop production areas and sink decreases (or source increases) in crop consumption areas highlights the importance of considering the lateral carbon transfer in crop 20 products in atmospheric inverse modeling, which provides an atmospheric perspective of the overall carbon balance of a region.
NASA Astrophysics Data System (ADS)
He, Zhenzong; Qi, Hong; Wang, Yuqing; Ruan, Liming
2014-10-01
Four improved Ant Colony Optimization (ACO) algorithms, i.e. the probability density function based ACO (PDF-ACO) algorithm, the Region ACO (RACO) algorithm, Stochastic ACO (SACO) algorithm and Homogeneous ACO (HACO) algorithm, are employed to estimate the particle size distribution (PSD) of the spheroidal particles. The direct problems are solved by the extended Anomalous Diffraction Approximation (ADA) and the Lambert-Beer law. Three commonly used monomodal distribution functions i.e. the Rosin-Rammer (R-R) distribution function, the normal (N-N) distribution function, and the logarithmic normal (L-N) distribution function are estimated under dependent model. The influence of random measurement errors on the inverse results is also investigated. All the results reveal that the PDF-ACO algorithm is more accurate than the other three ACO algorithms and can be used as an effective technique to investigate the PSD of the spheroidal particles. Furthermore, the Johnson's SB (J-SB) function and the modified beta (M-β) function are employed as the general distribution functions to retrieve the PSD of spheroidal particles using PDF-ACO algorithm. The investigation shows a reasonable agreement between the original distribution function and the general distribution function when only considering the variety of the length of the rotational semi-axis.
NASA Astrophysics Data System (ADS)
Fakhreddine, Sarah; Lee, Jonghyun; Kitanidis, Peter K.; Fendorf, Scott; Rolle, Massimo
2016-02-01
The spatial distribution of reactive minerals in the subsurface is often a primary factor controlling the fate and transport of contaminants in groundwater systems. However, direct measurement and estimation of heterogeneously distributed minerals are often costly and difficult to obtain. While previous studies have shown the utility of using hydrologic measurements combined with inverse modeling techniques for tomography of physical properties including hydraulic conductivity, these methods have seldom been used to image reactive geochemical heterogeneities. In this study, we focus on As-bearing reactive minerals as aquifer contaminants. We use synthetic applications to demonstrate the ability of inverse modeling techniques combined with mechanistic reactive transport models to image reactive mineral lenses in the subsurface and quantify estimation error using indirect, commonly measured groundwater parameters. Specifically, we simulate the mobilization of arsenic via kinetic oxidative dissolution of As-bearing pyrite due to dissolved oxygen in the ambient groundwater, which is an important mechanism for arsenic release in groundwater both under natural conditions and engineering applications such as managed aquifer recharge and recovery operations. The modeling investigation is carried out at various scales and considers different flow-through domains including (i) a 1D lab-scale column (80 cm), (ii) a 2D lab-scale setup (60 cm × 30 cm) and (iii) a 2D field-scale domain (20 m × 4 m). In these setups, synthetic dissolved oxygen data and forward reactive transport simulations are used to image the spatial distribution of As-bearing pyrite using the Principal Component Geostatistical Approach (PCGA) for inverse modeling.
Chen, J. M.; Fung, J. W.; Mo, G.; Deng, F.; West, T. O.
2015-01-19
In order to improve quantification of the spatial distribution of carbon sinks and sources in the conterminous US, we conduct a nested global atmospheric inversion with detailed spatial information on crop production and consumption. County-level cropland net primary productivity, harvested biomass, soil carbon change, and human and livestock consumption data over the conterminous US are used for this purpose. Time-dependent Bayesian synthesis inversions are conducted based on CO₂ observations at 210 stations to infer CO₂ fluxes globally at monthly time steps with a nested focus on 30 regions in North America. Prior land surface carbon fluxes are first generated usingmore » a biospheric model, and the inversions are constrained using prior fluxes with and without adjustments for crop production and consumption over the 2002–2007 period. After these adjustments, the inverted regional carbon sink in the US Midwest increases from 0.25 ± 0.03 to 0.42 ± 0.13 Pg C yr⁻¹, whereas the large sink in the US southeast forest region is weakened from 0.41 ± 0.12 to 0.29 ± 0.12 Pg C yr⁻¹. These adjustments also reduce the inverted sink in the west region from 0.066 ± 0.04 to 0.040 ± 0.02 Pg C yr⁻¹ because of high crop consumption and respiration by humans and livestock. The general pattern of sink increases in crop production areas and sink decreases (or source increases) in crop consumption areas highlights the importance of considering the lateral carbon transfer in crop products in atmospheric inverse modeling, which provides a reliable atmospheric perspective of the overall carbon balance at the continental scale but is unreliable for separating fluxes from different ecosystems.« less
Chen, J. M.; Fung, J. W.; Mo, G.; Deng, F.; West, T. O.
2015-01-19
In order to improve quantification of the spatial distribution of carbon sinks and sources in the conterminous US, we conduct a nested global atmospheric inversion with detailed spatial information on crop production and consumption. County-level cropland net primary productivity, harvested biomass, soil carbon change, and human and livestock consumption data over the conterminous US are used for this purpose. Time-dependent Bayesian synthesis inversions are conducted based on CO₂ observations at 210 stations to infer CO₂ fluxes globally at monthly time steps with a nested focus on 30 regions in North America. Prior land surface carbon fluxes are first generated using a biospheric model, and the inversions are constrained using prior fluxes with and without adjustments for crop production and consumption over the 2002–2007 period. After these adjustments, the inverted regional carbon sink in the US Midwest increases from 0.25 ± 0.03 to 0.42 ± 0.13 Pg C yr⁻¹, whereas the large sink in the US southeast forest region is weakened from 0.41 ± 0.12 to 0.29 ± 0.12 Pg C yr⁻¹. These adjustments also reduce the inverted sink in the west region from 0.066 ± 0.04 to 0.040 ± 0.02 Pg C yr⁻¹ because of high crop consumption and respiration by humans and livestock. The general pattern of sink increases in crop production areas and sink decreases (or source increases) in crop consumption areas highlights the importance of considering the lateral carbon transfer in crop products in atmospheric inverse modeling, which provides a reliable atmospheric perspective of the overall carbon balance at the continental scale but is unreliable for separating fluxes from different ecosystems.
Adler, C; Ahammed, Z; Allgower, C; Amonett, J; Anderson, B D; Anderson, M; Averichev, G S; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Bekele, S; Belaga, V V; Bellwied, R; Berger, J; Bichsel, H; Bland, L C; Blyth, C O; Bonner, B E; Bossingham, R; Boucham, A; Brandin, A; Caines, H; Calderón De La Barca Sánchez, M; Cardenas, A; Carroll, J; Castillo, J; Castro, M; Cebra, D; Chattopadhyay, S; Chen, M L; Chen, Y; Chernenko, S P; Cherney, M; Chikanian, A; Choi, B; Christie, W; Coffin, J P; Conin, L; Cormier, T M; Cramer, J G; Crawford, H J; DeMello, M; Deng, W S; Derevschikov, A A; Didenko, L; Draper, J E; Dunin, V B; Dunlop, J C; Eckardt, V; Efimov, L G; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Fachini, P; Finch, E; Fisyak, Y; Flierl, D; Foley, K J; Fu, J; Gagunashvili, N; Gans, J; Gaudichet, L; Germain, M; Geurts, F; Ghazikhanian, V; Grabski, J; Grachov, O; Greiner, D; Grigoriev, V; Guedon, M; Gushin, E; Hallman, T J; Hardtke, D; Harris, J W; Heffner, M; Heppelmann, S; Herston, T; Hippolyte, B; Hirsch, A; Hjort, E; Hoffmann, G W; Horsley, M; Huang, H Z; Humanic, T J; Hümmler, H; Igo, G; Ishihara, A; Ivanshin, Y I; Jacobs, P; Jacobs, W W; Janik, M; Johnson, I; Jones, P G; Judd, E; Kaneta, M; Kaplan, M; Keane, D; Kisiel, A; Klay, J; Klein, S R; Klyachko, A; Konstantinov, A S; Kotchenda, L; Kovalenko, A D; Kramer, M; Kravtsov, P; Krueger, K; Kuhn, C; Kulikov, A I; Kunde, G J; Kunz, C L; Kutuev, R K; Kuznetsov, A A; Lakehal-Ayat, L; Lamas-Valverde, J; Lamont, M A; Landgraf, J M; Lange, S; Lansdell, C P; Lasiuk, B; Laue, F; Lebedev, A; LeCompte, T; Lednický, R; Leontiev, V M; Leszczynski, P; LeVine, M J; Li, Q; Li, Q; Lindenbaum, S J; Lisa, M A; Ljubicic, T; Llope, W J; LoCurto, G; Long, H; Longacre, R S; Lopez-Noriega, M; Love, W A; Lynn, D; Majka, R; Maliszewski, A; Margetis, S; Martin, L; Marx, J; Matis, H S; Matulenko, Y A; McShane, T S; Meissner, F; Melnick, Y; Meschanin, A; Messer, M; Miller, M L; Milosevich, Z; Minaev, N G; Mitchell, J; Moiseenko, V A; Moltz, D; Moore, C F; Morozov, V; de Moura, M M; Munhoz, M G; Mutchler, G S; Nelson, J M; Nevski, P; Nikitin, V A; Nogach, L V; Norman, B; Nurushev, S B; Odyniec, G; Ogawa, A; Okorokov, V; Oldenburg, M; Olson, D; Paic, G; Pandey, S U; Panebratsev, Y; Panitkin, S Y; Pavlinov, A I; Pawlak, T; Perevoztchikov, V; Peryt, W; Petrov, V A; Pinganaud, W; Platner, E; Pluta, J; Porile, N; Porter, J; Poskanzer, A M; Potrebenikova, E; Prindle, D; Pruneau, C; Radomski, S; Rai, G; Ravel, O; Ray, R L; Razin, S V; Reichhold, D; Reid, J G; Retiere, F; Ridiger, A; Ritter, H G; Roberts, J B; Rogachevski, O V; Romero, J L; Roy, C; Russ, D; Rykov, V; Sakrejda, I; Sandweiss, J; Saulys, A C; Savin, I; Schambach, J; Scharenberg, R P; Schweda, K; Schmitz, N; Schroeder, L S; Schüttauf, A; Seger, J; Seliverstov, D; Seyboth, P; Shahaliev, E; Shestermanov, K E; Shimanskii, S S; Shvetcov, V S; Skoro, G; Smirnov, N; Snellings, R; Sowinski, J; Spinka, H M; Srivastava, B; Stephenson, E J; Stock, R; Stolpovsky, A; Strikhanov, M; Stringfellow, B; Stroebele, H; Struck, C; Suaide, A A; Sugarbaker, E; Suire, C; Sumbera, M; Symons, T J; Szanto De Toledo, A; Szarwas, P; Takahashi, J; Tang, A H; Thomas, J H; Tikhomirov, V; Trainor, T A; Trentalange, S; Tokarev, M; Tonjes, M B; Trofimov, V; Tsai, O; Turner, K; Ullrich, T; Underwood, D G; Van Buren, G; VanderMolen, A M; Vanyashin, A; Vasilevski, I M; Vasiliev, A N; Vigdor, S E; Voloshin, S A; Wang, F; Ward, H; Watson, J W; Wells, R; Wenaus, T; Westfall, G D; Whitten, C; Wieman, H; Willson, R; Wissink, S W; Witt, R; Xu, N; Xu, Z; Yakutin, A E; Yamamoto, E; Yang, J; Yepes, P; Yokosawa, A; Yurevich, V I; Zanevski, Y V; Zborovský, I; Zhang, W M; Zoulkarneev, R; Zubarev, A N
2001-09-10
The minimum-bias multiplicity distribution and the transverse momentum and pseudorapidity distributions for central collisions have been measured for negative hadrons ( h(-)) in Au+Au interactions at square root of ([s(NN)]) = 130 GeV. The multiplicity density at midrapidity for the 5% most central interactions is dN(h(-))/d(eta)/(eta = 0) = 280+/-1(stat)+/-20(syst), an increase per participant of 38% relative to pp collisions at the same energy. The mean transverse momentum is 0.508+/-0.012 GeV/c and is larger than in central Pb+Pb collisions at lower energies. The scaling of the h(-) yield per participant is a strong function of p( perpendicular). The pseudorapidity distribution is almost constant within /eta/<1. PMID:11531517
NASA Astrophysics Data System (ADS)
Convers, Jaime; Custodio, Susana
2016-04-01
Rapid assessment of seismological parameters pertinent to the nucleation and rupture of earthquakes are now routinely calculated by local and regional seismic networks. With the increasing number of stations, fast data transmission, and advanced computer power, we can now go beyond accurate magnitude and epicentral locations, to rapid estimations of other higher-order earthquake parameters such as seismic moment tensor. Although an increased number of stations can minimize azimuthal gaps, it also increases computation time, and potentially introduces poor quality data that often leads to a lower the stability of automated inversions. In this presentation, we focus on moment tensor calculations for earthquakes occurring offshore the southwestern Iberian peninsula. The available regional seismic data in this region has a significant azimuthal gap that results from the geographical setting. In this case, increasing the number of data from stations spanning a small area (and at a small azimuthal angle) increases the calculation time without necessarily improving the accuracy of the inversion. Additionally, limited regional data coverage makes it imperative to exclude poor-quality data, as their negative effect on moment tensor inversions is often significant. In our work, we analyze methods to minimize the effects of large azimuthal gaps in a regional station coverage, of potential bias by uneven station distribution, and of poor data quality in moment tensor inversions obtained for earthquakes offshore the southwestern Iberian peninsula. We calculate moment tensors using the KIWI tools, and we implement different configurations of station-weighing, and cross-correlation of neighboring stations, with the aim of automatically estimating and selecting high-quality data, improving the accuracy of results, and reducing the computation time of moment tensor inversions. As the available recent intermediate-size events offshore the Iberian peninsula is limited due to the long
Böckmann, C
2001-03-20
A specially developed method is proposed to retrieve the particle volume distribution, the mean refractive index, and other important physical parameters, e.g., the effective radius, volume, surface area, and number concentrations of tropospheric and stratospheric aerosols, from optical data by use of multiple wavelengths. This algorithm requires neither a priori knowledge of the analytical shape of the distribution nor an initial guess of the distribution. As a result, even bimodal and multimodal distributions can be retrieved without any advance knowledge of the number of modes. The nonlinear ill-posed inversion is achieved by means of a hybrid method combining regularization by discretization, variable higher-order B-spline functions and a truncated singular-value decomposition. The method can be used to handle different lidar devices that work with various values and numbers of wavelengths. It is shown, to my knowledge for the first time, that only one extinction and three backscatter coefficients are sufficient for the solution. Moreover, measurement errors up to 20% are allowed. This result could be achieved by a judicious fusion of different properties of three suitable regularization parameters. Finally, numerical results with an additional unknown refractive index show the possibility of successfully recovering both unknowns simultaneously from the lidar data: the aerosol volume distribution and the refractive index.
Identified particle distributions in pp and Au+Au collisions at square root of (sNN)=200 GeV.
Adams, J; Adler, C; Aggarwal, M M; Ahammed, Z; Amonett, J; Anderson, B D; Anderson, M; Arkhipkin, D; Averichev, G S; Badyal, S K; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Bekele, S; Belaga, V V; Bellwied, R; Berger, J; Bezverkhny, B I; Bhardwaj, S; Bhaskar, P; Bhati, A K; Bichsel, H; Billmeier, A; Bland, L C; Blyth, C O; Bonner, B E; Botje, M; Boucham, A; Brandin, A; Bravar, A; Cadman, R V; Cai, X Z; Caines, H; Calderón de la Barca Sánchez, M; Carroll, J; Castillo, J; Castro, M; Cebra, D; Chaloupka, P; Chattopadhyay, S; Chen, H F; Chen, Y; Chernenko, S P; Cherney, M; Chikanian, A; Choi, B; Christie, W; Coffin, J P; Cormier, T M; Cramer, J G; Crawford, H J; Das, D; Das, S; Derevschikov, A A; Didenko, L; Dietel, T; Dong, X; Draper, J E; Du, F; Dubey, A K; Dunin, V B; Dunlop, J C; Dutta Majumdar, M R; Eckardt, V; Efimov, L G; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Estienne, M; Fachini, P; Faine, V; Faivre, J; Fatemi, R; Filimonov, K; Filip, P; Finch, E; Fisyak, Y; Flierl, D; Foley, K J; Fu, J; Gagliardi, C A; Ganti, M S; Gutierrez, T D; Gagunashvili, N; Gans, J; Gaudichet, L; Germain, M; Geurts, F; Ghazikhanian, V; Ghosh, P; Gonzalez, J E; Grachov, O; Grigoriev, V; Gronstal, S; Grosnick, D; Guedon, M; Guertin, S M; Gupta, A; Gushin, E; Hallman, T J; Hardtke, D; Harris, J W; Heinz, M; Henry, T W; Heppelmann, S; Herston, T; Hippolyte, B; Hirsch, A; Hjort, E; Hoffmann, G W; Horsley, M; Huang, H Z; Huang, S L; Humanic, T J; Igo, G; Ishihara, A; Jacobs, P; Jacobs, W W; Janik, M; Johnson, I; Jones, P G; Judd, E G; Kabana, S; Kaneta, M; Kaplan, M; Keane, D; Kiryluk, J; Kisiel, A; Klay, J; Klein, S R; Klyachko, A; Koetke, D D; Kollegger, T; Konstantinov, A S; Kopytine, M; Kotchenda, L; Kovalenko, A D; Kramer, M; Kravtsov, P; Krueger, K; Kuhn, C; Kulikov, A I; Kumar, A; Kunde, G J; Kunz, C L; Kutuev, R Kh; Kuznetsov, A A; Lamont, M A C; Landgraf, J M; Lange, S; Lansdell, C P; Lasiuk, B; Laue, F; Lauret, J; Lebedev, A; Lednický, R; Leontiev, V M; LeVine, M J; Li, C; Li, Q; Lindenbaum, S J; Lisa, M A; Liu, F; Liu, L; Liu, Z; Liu, Q J; Ljubicic, T; Llope, W J; Long, H; Longacre, R S; Lopez-Noriega, M; Love, W A; Ludlam, T; Lynn, D; Ma, J; Ma, Y G; Magestro, D; Mahajan, S; Mangotra, L K; Mahapatra, D P; Majka, R; Manweiler, R; Margetis, S; Markert, C; Martin, L; Marx, J; Matis, H S; Matulenko, Yu A; McShane, T S; Meissner, F; Melnick, Yu; Meschanin, A; Messer, M; Miller, M L; Milosevich, Z; Minaev, N G; Mironov, C; Mishra, D; Mitchell, J; Mohanty, B; Molnar, L; Moore, C F; Mora-Corral, M J; Morozov, V; de Moura, M M; Munhoz, M G; Nandi, B K; Nayak, S K; Nayak, T K; Nelson, J M; Nevski, P; Nikitin, V A; Nogach, L V; Norman, B; Nurushev, S B; Odyniec, G; Ogawa, A; Okorokov, V; Oldenburg, M; Olson, D; Paic, G; Pandey, S U; Pal, S K; Panebratsev, Y; Panitkin, S Y; Pavlinov, A I; Pawlak, T; Perevoztchikov, V; Peryt, W; Petrov, V A; Phatak, S C; Picha, R; Planinic, M; Pluta, J; Porile, N; Porter, J; Poskanzer, A M; Potekhin, M; Potrebenikova, E; Potukuchi, B V K S; Prindle, D; Pruneau, C; Putschke, J; Rai, G; Rakness, G; Raniwala, R; Raniwala, S; Ravel, O; Ray, R L; Razin, S V; Reichhold, D; Reid, J G; Renault, G; Retiere, F; Ridiger, A; Ritter, H G; Roberts, J B; Rogachevski, O V; Romero, J L; Rose, A; Roy, C; Ruan, L J; Sahoo, R; Sakrejda, I; Salur, S; Sandweiss, J; Savin, I; Schambach, J; Scharenberg, R P; Schmitz, N; Schroeder, L S; Schweda, K; Seger, J; Seliverstov, D; Seyboth, P; Shahaliev, E; Shao, M; Sharma, M; Shestermanov, K E; Shimanskii, S S; Singaraju, R N; Simon, F; Skoro, G; Smirnov, N; Snellings, R; Sood, G; Sorensen, P; Sowinski, J; Spinka, H M; Srivastava, B; Stanislaus, S; Stock, R; Stolpovsky, A; Strikhanov, M; Stringfellow, B; Struck, C; Suaide, A A P; Sugarbaker, E; Suire, C; Sumbera, M; Surrow, B; Symons, T J M; de Toledo, A Szanto; Szarwas, P; Tai, A; Takahashi, J; Tang, A H; Thein, D; Thomas, J H; Tikhomirov, V; Tokarev, M; Tonjes, M B; Trainor, T A; Trentalange, S; Tribble, R E; Trivedi, M D; Trofimov, V; Tsai, O; Ullrich, T; Underwood, D G; Van Buren, G; VanderMolen, A M; Vasiliev, A N; Vasiliev, M; Vigdor, S E; Viyogi, Y P; Voloshin, S A; Waggoner, W; Wang, F; Wang, G; Wang, X L; Wang, Z M; Ward, H; Watson, J W; Wells, R; Westfall, G D; Whitten, C; Wieman, H; Willson, R; Wissink, S W; Witt, R; Wood, J; Wu, J; Xu, N; Xu, Z; Xu, Z Z; Yakutin, A E; Yamamoto, E; Yang, J; Yepes, P; Yurevich, V I; Zanevski, Y V; Zborovský, I; Zhang, H; Zhang, H Y; Zhang, W M; Zhang, Z P; Zołnierczuk, P A; Zoulkarneev, R; Zoulkarneeva, J; Zubarev, A N
2004-03-19
Transverse mass and rapidity distributions for charged pions, charged kaons, protons, and antiprotons are reported for square root of [sNN]=200 GeV pp and Au+Au collisions at Relativistic Heary Ion Collider (RHIC). Chemical and kinetic equilibrium model fits to our data reveal strong radial flow and long duration from chemical to kinetic freeze-out in central Au+Au collisions. The chemical freeze-out temperature appears to be independent of initial conditions at RHIC energies. PMID:15089125
Vargas-Ubera, Javier; Aguilar, J Félix; Gale, David Michel
2007-01-01
By means of a numerical study we show particle-size distributions retrieved with the Chin-Shifrin, Phillips-Twomey, and singular value decomposition methods. Synthesized intensity data are generated using Mie theory, corresponding to unimodal normal, gamma, and lognormal distributions of spherical particles, covering the size parameter range from 1 to 250. Our results show the advantages and disadvantages of each method, as well as the range of applicability for the Fraunhofer approximation as compared to rigorous Mie theory.
NASA Astrophysics Data System (ADS)
Agata, R.; Ichimura, T.; Hirahara, K.; Hori, T.; Hyodo, M.; Hori, M.
2013-12-01
Many studies have focused on geodetic inversion analysis method of coseismic slip distribution with combination of observation data of coseismic crustal deformation on the ground and simplified crustal models such like analytical solution in elastic half-space (Okada, 1985). On the other hand, displacements on the seafloor or near trench axes due to actual earthquakes has been observed by seafloor observatories (e.g. the 2011 Tohoku-oki Earthquake (Tohoku Earthquake) (Sato et. al. 2011) (Kido et. al. 2011)). Also, some studies on tsunamis due to the Tohoku Earthquake indicate that large fault slips near the trench axis may have occurred. Those facts suggest that crustal models considering complex geometry and heterogeneity of the material property near the trench axis should be used for geodetic inversion analysis. Therefore, our group has developed a mesh generation method for finite element models of the Japanese Islands of higher fidelity and a fast crustal deformation analysis method for the models. Degree-of-freedom of the models generated by this method is about 150 million. In this research, the method is extended for inversion analyses of coseismic slip distribution. Since inversion analyses need computation of hundreds of slip response functions due to a unit fault slip assigned for respective divided cells on the fault, parallel computing environment is used. Plural crustal deformation analyses are simultaneously run in a Message Passing Interface (MPI) job. In the job, dynamic load balancing is implemented so that a better parallel efficiency is obtained. Submitting the necessary number of serial job of our previous method is also possible, but the proposed method needs less computation time, places less stress on file systems, and allows simpler job management. A method for considering the fault slip right near the trench axis is also developed. As the displacement distribution of unit fault slip for computing response function, 3rd order B
Abazov, V M; Abbott, B; Abolins, M; Acharya, B S; Adams, M; Adams, T; Aguilo, E; Ahsan, M; Alexeev, G D; Alkhazov, G; Alton, A; Alverson, G; Alves, G A; Ancu, L S; Andeen, T; Anzelc, M S; Aoki, M; Arnoud, Y; Arov, M; Arthaud, M; Askew, A; Asman, B; Atramentov, O; Avila, C; BackusMayes, J; Badaud, F; Bagby, L; Baldin, B; Bandurin, D V; Banerjee, S; Barberis, E; Barfuss, A-F; Bargassa, P; Baringer, P; Barreto, J; Bartlett, J F; Bassler, U; Bauer, D; Beale, S; Bean, A; Begalli, M; Begel, M; Belanger-Champagne, C; Bellantoni, L; Bellavance, A; Benitez, J A; Beri, S B; Bernardi, G; Bernhard, R; Bertram, I; Besançon, M; Beuselinck, R; Bezzubov, V A; Bhat, P C; Bhatnagar, V; Blazey, G; Blessing, S; Bloom, K; Boehnlein, A; Boline, D; Bolton, T A; Boos, E E; Borissov, G; Bose, T; Brandt, A; Brock, R; Brooijmans, G; Bross, A; Brown, D; Bu, X B; Buchholz, D; Buehler, M; Buescher, V; Bunichev, V; Burdin, S; Burnett, T H; Buszello, C P; Calfayan, P; Calpas, B; Calvet, S; Cammin, J; Carrasco-Lizarraga, M A; Carrera, E; Carvalho, W; Casey, B C K; Castilla-Valdez, H; Chakrabarti, S; Chakraborty, D; Chan, K M; Chandra, A; Cheu, E; Cho, D K; Choi, S; Choudhary, B; Christoudias, T; Cihangir, S; Claes, D; Clutter, J; Cooke, M; Cooper, W E; Corcoran, M; Couderc, F; Cousinou, M-C; Crépé-Renaudin, S; Cutts, D; Cwiok, M; Das, A; Davies, G; De, K; de Jong, S J; De la Cruz-Burelo, E; DeVaughan, K; Déliot, F; Demarteau, M; Demina, R; Denisov, D; Denisov, S P; Desai, S; Diehl, H T; Diesburg, M; Dominguez, A; Dorland, T; Dubey, A; Dudko, L V; Duflot, L; Duggan, D; Duperrin, A; Dutt, S; Dyshkant, A; Eads, M; Edmunds, D; Ellison, J; Elvira, V D; Enari, Y; Eno, S; Escalier, M; Evans, H; Evdokimov, A; Evdokimov, V N; Facini, G; Ferapontov, A V; Ferbel, T; Fiedler, F; Filthaut, F; Fisher, W; Fisk, H E; Fortner, M; Fox, H; Fu, S; Fuess, S; Gadfort, T; Galea, C F; Garcia-Bellido, A; Gavrilov, V; Gay, P; Geist, W; Geng, W; Gerber, C E; Gershtein, Y; Gillberg, D; Ginther, G; Gómez, B; Goussiou, A; Grannis, P D; 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Spurlock, B; Stark, J; Stolin, V; Stoyanova, D A; Strandberg, J; Strang, M A; Strauss, E; Strauss, M; Ströhmer, R; Strom, D; Stutte, L; Sumowidagdo, S; Svoisky, P; Takahashi, M; Tanasijczuk, A; Taylor, W; Tiller, B; Titov, M; Tokmenin, V V; Torchiani, I; Tsybychev, D; Tuchming, B; Tully, C; Tuts, P M; Unalan, R; Uvarov, L; Uvarov, S; Uzunyan, S; van den Berg, P J; Van Kooten, R; van Leeuwen, W M; Varelas, N; Varnes, E W; Vasilyev, I A; Verdier, P; Vertogradov, L S; Verzocchi, M; Vilanova, D; Vint, P; Vokac, P; Voutilainen, M; Wagner, R; Wahl, H D; Wang, M H L S; Warchol, J; Watts, G; Wayne, M; Weber, G; Weber, M; Welty-Rieger, L; Wenger, A; Wetstein, M; White, A; Wicke, D; Williams, M R J; Wilson, G W; Wimpenny, S J; Wobisch, M; Wood, D R; Wyatt, T R; Xie, Y; Xu, C; Yacoob, S; Yamada, R; Yang, W-C; Yasuda, T; Yatsunenko, Y A; Ye, Z; Yin, H; Yip, K; Yoo, H D; Youn, S W; Yu, J; Zeitnitz, C; Zelitch, S; Zhao, T; Zhou, B; Zhu, J; Zielinski, M; Zieminska, D; Zivkovic, L; Zutshi, V; Zverev, E G
2009-11-01
We present the first measurement of dijet angular distributions in pp collisions at square root(s) = 1.96 TeV at the Fermilab Tevatron Collider. The measurement is based on a dataset corresponding to an integrated luminosity of 0.7 fb(-1) collected with the D0 detector. Dijet angular distributions have been measured over a range of dijet masses, from 0.25 TeV to above 1.1 TeV. The data are in good agreement with the predictions of perturbative QCD and are used to constrain new physics models including quark compositeness, large extra dimensions, and TeV(-1) scale extra dimensions. For all models considered, we set the most stringent direct limits to date. PMID:20365918
Adams, J; Aggarwal, M M; Ahammed, Z; Amonett, J; Anderson, B D; Arkhipkin, D; Averichev, G S; Badyal, S K; Bai, Y; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Bekele, S; Belaga, V V; Bellingeri-Laurikainen, A; Bellwied, R; Berger, J; Bezverkhny, B I; Bhardwaj, S; Bhasin, A; Bhati, A K; Bichsel, H; Bielcik, J; Bielcikova, J; Billmeier, A; Bland, L C; Blyth, C O; Blyth, S; Bonner, B E; Botje, M; Boucham, A; Bouchet, J; Brandin, A V; Bravar, A; Bystersky, M; Cadman, R V; Cai, X Z; Caines, H; de la Barca Sánchez, M Calderón; Castillo, J; Catu, O; Cebra, D; Chajecki, Z; Chaloupka, P; Chattopadhyay, S; Chen, H F; Chen, Y; Cheng, J; Cherney, M; Chikanian, A; Christie, W; Coffin, J P; Cormier, T M; Cosentino, M R; Cramer, J G; Crawford, H J; Das, D; Das, S; de Moura, M M; Dedovich, T G; Derevschikov, A A; Didenko, L; Dietel, T; Dogra, S M; Dong, W J; Dong, X; Draper, J E; Du, F; Dubey, A K; Dunin, V B; Dunlop, J C; Mazumdar, M R Dutta; Eckardt, V; Edwards, W R; Efimov, L G; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Estienne, M; Fachini, P; Faivre, J; Fatemi, R; Fedorisin, J; Filimonov, K; Filip, P; Finch, E; Fine, V; Fisyak, Y; Fornazier, K S F; Fu, J; Gagliardi, C A; Gaillard, L; Gans, J; Ganti, M S; Geurts, F; Ghazikhanian, V; Ghosh, P; Gonzalez, J E; Gos, H; Grachov, O; Grebenyuk, O; Grosnick, D; Guertin, S M; Guo, Y; Gupta, A; Gutierrez, T D; Hallman, T J; Hamed, A; Hardtke, D; Harris, J W; Heinz, M; Henry, T W; Hepplemann, S; Hippolyte, B; Hirsch, A; Hjort, E; Hoffmann, G W; Horner, M; Huang, H Z; Huang, S L; Hughes, E W; Humanic, T J; Igo, G; Ishihara, A; Jacobs, P; Jacobs, W W; Jedynak, M; Jiang, H; Jones, P G; Judd, E G; Kabana, S; Kang, K; Kaplan, M; Keane, D; Kechechyan, A; Khodyrev, V Yu; Kiryluk, J; Kisiel, A; Kislov, E M; Klay, J; Klein, S R; Koetke, D D; Kollegger, T; Kopytine, M; Kotchenda, L; Kowalik, K L; Kramer, M; Kravtsov, P; Kravtsov, V I; Krueger, K; Kuhn, C; Kulikov, A I; Kumar, A; Kutuev, R Kh; Kuznetsov, A A; Lamont, M A C; Landgraf, J M; Lange, S; Laue, F; Lauret, J; Lebedev, A; Lednicky, R; Lehocka, S; Levine, M J; Li, C; Li, Q; Li, Y; Lin, G; Lindenbaum, S J; Lisa, M A; Liu, F; Liu, H; Liu, J; Liu, L; Liu, Q J; Liu, Z; Ljubicic, T; Llope, W J; Long, H; Longacre, R S; Lopez-Noriega, M; Love, W A; Lu, Y; Ludlam, T; Lynn, D; Ma, G L; Ma, J G; Ma, Y G; Magestro, D; Mahajan, S; Mahapatra, D P; Majka, R; Mangotra, L K; Manweiler, R; Margetis, S; Markert, C; Martin, L; Marx, J N; Matis, H S; Matulenko, Yu A; McClain, C J; McShane, T S; Meissner, F; Melnick, Yu; Meschanin, A; Miller, M L; Minaev, N G; Mironov, C; Mischke, A; Mishra, D K; Mitchell, J; Mohanty, B; Molnar, L; Moore, C F; Morozov, D A; Munhoz, M G; Nandi, B K; Nayak, S K; Nayak, T K; Nelson, J M; Netrakanti, P K; Nikitin, V A; Nogach, L V; Nurushev, S B; Odyniec, G; Ogawa, A; Okorokov, V; Oldenburg, M; Olson, D; Pal, S K; Panebratsev, Y; Panitkin, S Y; Pavlinov, A I; Pawlak, T; Peitzmann, T; Perevoztchikov, V; Perkins, C; Peryt, W; Petrov, V A; Phatak, S C; Picha, R; Planinic, M; Pluta, J; Porile, N; Porter, J; Poskanzer, A M; Potekhin, M; Potrebenikova, E; Potukuchi, B V K S; Prindle, D; Pruneau, C; Putschke, J; Rakness, G; Raniwala, R; Raniwala, S; Ravel, O; Ray, R L; Razin, S V; Reichhold, D; Reid, J G; Reinnarth, J; Renault, G; Retiere, F; Ridiger, A; Ritter, H G; Roberts, J B; Rogachevskiy, O V; Romero, J L; Rose, A; Roy, C; Ruan, L; Russcher, M J; Sahoo, R; Sakrejda, I; Salur, S; Sandweiss, J; Sarsour, M; Savin, I; Sazhin, P S; Schambach, J; Scharenberg, R P; Schmitz, N; Schweda, K; Seger, J; Seyboth, P; Shahaliev, E; Shao, M; Shao, W; Sharma, M; Shen, W Q; Shestermanov, K E; Shimanskiy, S S; Sichtermann, E; Simon, F; Singaraju, R N; Smirnov, N; Snellings, R; Sood, G; Sorensen, P; Sowinski, J; Speltz, J; Spinka, H M; Srivastava, B; Stadnik, A; Stanislaus, T D S; Stock, R; Stolpovsky, A; Strikhanov, M; Stringfellow, B; Suaide, A A P; Sugarbaker, E; Suire, C; Sumbera, M; Surrow, B; Swanger, M; Symons, T J M; de Toledo, A Szanto; Tai, A; Takahashi, J; Tang, A H; Tarnowsky, T; Thein, D; Thomas, J H; Timoshenko, S; Tokarev, M; Trainor, T A; Trentalange, S; Tribble, R E; Tsai, O D; Ulery, J; Ullrich, T; Underwood, D G; Buren, G Van; van Leeuwen, M; Molen, A M Vander; Varma, R; Vasilevski, I M; Vasiliev, A N; Vernet, R; Vigdor, S E; Viyogi, Y P; Vokal, S; Voloshin, S A; Waggoner, W T; Wang, F; Wang, G; Wang, G; Wang, X L; Wang, Y; Wang, Y; Wang, Z M; Ward, H; Watson, J W; Webb, J C; Westfall, G D; Wetzler, A; Whitten, C; Wieman, H; Wissink, S W; Witt, R; Wood, J; Wu, J; Xu, N; Xu, Z; Xu, Z Z; Yamamoto, E; Yepes, P; Yurevich, V I; Zborovsky, I; Zhang, H; Zhang, W M; Zhang, Y; Zhang, Z P; Zoulkarneev, R; Zoulkarneeva, Y; Zubarev, A N
2005-08-01
We present the first measurement of pseudorapidity distribution of photons in the region 2.3 < or = eta < or = 3.7 for different centralities in Au+Au collisions at square root of (S(NN)) = 62.4 GeV. We find that the photon yield scales with the number of participating nucleons at all collision centralities studied. The pseudorapidity distribution of photons, dominated by pi0 decays, has been compared to those of charged pions, photons, and inclusive charged particles from heavy-ion and nucleon-nucleon collisions at various energies. The photon production has been shown to be consistent with the energy and centrality independent limiting fragmentation scenario. PMID:16090941
Boudjema, A.; Tremolieres, P.
1988-01-01
Fieldwork and subsurface studies (350 bore holes and more than 100 seismic profiles) show the structural evolution of the Triassic Saharian basin. This evolution is controlled by the successive motions of ancient faults of the Paleozoic basement during the different compressional and distensional tectonic phases. These movements led to some tectonic inversions. Depending on the strike of the faults, the present results correspond to normal throw or reverse throw at the level of hydrocarbon reservoirs. These tectonic phases clearly result from relative motions between African, American, and European lithospheric plates. The Triassic basin, a mobile zone between two rigid shields, constitutes a very good indication of the successive motions. The distribution and the nature of hydrocarbon fields are clearly related to the proximity of the faults, the post-tectonic erosion of a part of the source rocks, the burial and maturation of the organic matter, and the age of structural traps.
Electromagnetic Response Inversion for a 3D Distribution of Conductivity/Dielect
2001-10-24
NLCGCS inverts electromagnetic responses for a 3D distribution of electrical conductivity and dielectric permittivity within the earth for geophysical applications using single processor computers. The software comes bundled with a graphical user interface to aid in model construction and analysis and viewing of earth images. The solution employs both dipole and finite size source configurations for harmonic oscillatory sources. A new nonlinear preconditioner is included in the solution to speed up solution convergence.
NASA Astrophysics Data System (ADS)
He, Zhenzong; Qi, Hong; Yao, Yuchen; Ruan, Liming
2014-12-01
The Ant Colony Optimization algorithm based on the probability density function (PDF-ACO) is applied to estimate the bimodal aerosol particle size distribution (PSD). The direct problem is solved by the modified Anomalous Diffraction Approximation (ADA, as an approximation for optically large and soft spheres, i.e., χ≫1 and |m-1|≪1) and the Beer-Lambert law. First, a popular bimodal aerosol PSD and three other bimodal PSDs are retrieved in the dependent model by the multi-wavelength extinction technique. All the results reveal that the PDF-ACO algorithm can be used as an effective technique to investigate the bimodal PSD. Then, the Johnson's SB (J-SB) function and the modified beta (M-β) function are employed as the general distribution function to retrieve the bimodal PSDs under the independent model. Finally, the J-SB and M-β functions are applied to recover actual measurement aerosol PSDs over Beijing and Shanghai obtained from the aerosol robotic network (AERONET). The numerical simulation and experimental results demonstrate that these two general functions, especially the J-SB function, can be used as a versatile distribution function to retrieve the bimodal aerosol PSD when no priori information about the PSD is available.
Long, A.J.; Putnam, L.D.
2009-01-01
Convolution modeling is useful for investigating the temporal distribution of groundwater age based on environmental tracers. The framework of a quasi-transient convolution model that is applicable to two-domain flow in karst aquifers is presented. The model was designed to provide an acceptable level of statistical confidence in parameter estimates when only chlorofluorocarbon (CFC) and tritium (3H) data are available. We show how inverse modeling and uncertainty assessment can be used to constrain model parameterization to a level warranted by available data while allowing major aspects of the flow system to be examined. As an example, the model was applied to water from a pumped well open to the Madison aquifer in central USA with input functions of CFC-11, CFC-12, CFC-113, and 3H, and was calibrated to several samples collected during a 16-year period. A bimodal age distribution was modeled to represent quick and slow flow less than 50 years old. The effects of pumping and hydraulic head on the relative volumetric fractions of these domains were found to be influential factors for transient flow. Quick flow and slow flow were estimated to be distributed mainly within the age ranges of 0-2 and 26-41 years, respectively. The fraction of long-term flow (>50 years) was estimated but was not dateable. The different tracers had different degrees of influence on parameter estimation and uncertainty assessments, where 3H was the most critical, and CFC-113 was least influential.
NASA Astrophysics Data System (ADS)
Long, Andrew J.; Putnam, Larry D.
2009-10-01
SummaryConvolution modeling is useful for investigating the temporal distribution of groundwater age based on environmental tracers. The framework of a quasi-transient convolution model that is applicable to two-domain flow in karst aquifers is presented. The model was designed to provide an acceptable level of statistical confidence in parameter estimates when only chlorofluorocarbon (CFC) and tritium ( 3H) data are available. We show how inverse modeling and uncertainty assessment can be used to constrain model parameterization to a level warranted by available data while allowing major aspects of the flow system to be examined. As an example, the model was applied to water from a pumped well open to the Madison aquifer in central USA with input functions of CFC-11, CFC-12, CFC-113, and 3H, and was calibrated to several samples collected during a 16-year period. A bimodal age distribution was modeled to represent quick and slow flow less than 50 years old. The effects of pumping and hydraulic head on the relative volumetric fractions of these domains were found to be influential factors for transient flow. Quick flow and slow flow were estimated to be distributed mainly within the age ranges of 0-2 and 26-41 years, respectively. The fraction of long-term flow (>50 years) was estimated but was not dateable. The different tracers had different degrees of influence on parameter estimation and uncertainty assessments, where 3H was the most critical, and CFC-113 was least influential.
NASA Astrophysics Data System (ADS)
Kusumoto, Shigekazu; Geshi, Nobuo; Gudmundsson, Agust
2010-05-01
We derived a solution for the overpressure distribution acting on the walls (surfaces) of an extension fracture (a hydrofracture) with an arbitrary opening-displacement (or aperture) variation. In the proposed model, we assume that the overpressure distribution can be described by Fourier cosine series. We at first present a solution for the forward model giving the fracture aperture when it is opened by an irregular overpressure variation obtained using the Fourier cosine series. Next, by changing the form of the solution for the forward model, we obtain a matrix equation that can be used to estimate the Fourier coefficients to obtain the overpressure distribution from the fracture aperture variation. As simple examples of this inverse analysis, we estimate the overpressure conditions from crack apertures given analytically for two cases, namely, 1) the overpressure in the crack is constant, and 2) the overpressure variation in the crack varies linearly from its center. The estimated overpressure distributions were found to be correct, although a small 'noise' was present. Since the method presented here gives the overpressure distribution as a Fourier series by the aperture data measured at a finite number of points, the overpressure conditions for forming the fracture can be determined for each wavelength. The Fourier coefficient of n = 0 is an important coefficient that gives the average value of the overpressure acting inside the crack. With the exception of n = 0, the Fourier coefficient of n = 1 expresses the longest wavelength component of the irregular overpressure. Thus, because this coefficient including the coefficient of n = 0 gives the longest wavelength component in the irregular overpressure, the component may be an important indicator of the overpressure condition that decides the basic form of the crack. We applied the solution for the inverse analysis to the thickness data of 19 non-feeder dikes exposed in the caldera wall of the Miyake
Illuminati, S; Annibaldi, A; Truzzi, C; Scarponi, G
2016-10-15
May sponge spicules represent a "tank" to accumulate heavy metals? In this study we test this hypothesis determining the distribution of Cd, Pb and Cu concentrations between organic and siliceous tissues in Antarctic Demospongia (Sphaerotylus antarcticus, Kirkpatrikia coulmani and Haliclona sp.) and in the Mediterranean species Petrosia ficiformis. Results show that although, in these sponges, spicules represent about 80% of the mass content, the accumulation of pollutant is lower in the spicules than in the corresponding organic fraction. The contribution of tissues to the total sponge content of Cd, Pb and Cu is respectively 99%, 82% and 97% for Antarctic sponges and 96%, 95% and 96% for P. ficiformis, similar in polar and temperate organisms. These results pave the way to a better understanding of the role of marine sponges in uptaking heavy metals and to their possible use as monitor of marine ecosystems, recommend by the Water Framework Directive.
Illuminati, S; Annibaldi, A; Truzzi, C; Scarponi, G
2016-10-15
May sponge spicules represent a "tank" to accumulate heavy metals? In this study we test this hypothesis determining the distribution of Cd, Pb and Cu concentrations between organic and siliceous tissues in Antarctic Demospongia (Sphaerotylus antarcticus, Kirkpatrikia coulmani and Haliclona sp.) and in the Mediterranean species Petrosia ficiformis. Results show that although, in these sponges, spicules represent about 80% of the mass content, the accumulation of pollutant is lower in the spicules than in the corresponding organic fraction. The contribution of tissues to the total sponge content of Cd, Pb and Cu is respectively 99%, 82% and 97% for Antarctic sponges and 96%, 95% and 96% for P. ficiformis, similar in polar and temperate organisms. These results pave the way to a better understanding of the role of marine sponges in uptaking heavy metals and to their possible use as monitor of marine ecosystems, recommend by the Water Framework Directive. PMID:27389453
A unified framework for approximation in inverse problems for distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Ito, K.
1988-01-01
A theoretical framework is presented that can be used to treat approximation techniques for very general classes of parameter estimation problems involving distributed systems that are either first or second order in time. Using the approach developed, one can obtain both convergence and stability (continuous dependence of parameter estimates with respect to the observations) under very weak regularity and compactness assumptions on the set of admissible parameters. This unified theory can be used for many problems found in the recent literature and in many cases offers significant improvements to existing results.
Anisotropic electron-distribution function in inverse-bremsstrahlung-heated plasmas.
Bendib, A; Bendib-Kalache, K; Cros, B; Maynard, G
2016-04-01
The electron-distribution function in homogeneous plasmas heated by a high-frequency laser field is calculated in velocity space from the Vlasov-Landau equation. The kinetic model is valid for moderate laser intensity defined by the relevant parameter α=v_{0}^{2}/v_{t}^{2}<0.5 where v_{0} and v_{t} are the peak velocity of oscillation in the high-frequency electric field and the thermal velocity, respectively. The results obtained constitute an improvement of the results reported in the literature devoted to weak electric field intensities. The electron-distribution function is calculated solving the kinetic equation with the use of the Legendre polynomial expansion within the laser field dipole approximation. It results in an infinite set of equations for the isotropic component f_{0}(v) and the anisotropic components f_{n≥1}(v) that we have solved numerically with appropriate truncation. For the second anisotropy f_{2}(v), we found that its maximum increases from the weak electric field intensity (α<0.01) to a moderate one (α=0.5) by a factor f_{2max}(α=0.5)/f_{2max}(α=0.01)≈48. Applications to the radiation pressure, electromagnetic instabilities, and photoabsorption are also considered.
Anisotropic electron-distribution function in inverse-bremsstrahlung-heated plasmas.
Bendib, A; Bendib-Kalache, K; Cros, B; Maynard, G
2016-04-01
The electron-distribution function in homogeneous plasmas heated by a high-frequency laser field is calculated in velocity space from the Vlasov-Landau equation. The kinetic model is valid for moderate laser intensity defined by the relevant parameter α=v_{0}^{2}/v_{t}^{2}<0.5 where v_{0} and v_{t} are the peak velocity of oscillation in the high-frequency electric field and the thermal velocity, respectively. The results obtained constitute an improvement of the results reported in the literature devoted to weak electric field intensities. The electron-distribution function is calculated solving the kinetic equation with the use of the Legendre polynomial expansion within the laser field dipole approximation. It results in an infinite set of equations for the isotropic component f_{0}(v) and the anisotropic components f_{n≥1}(v) that we have solved numerically with appropriate truncation. For the second anisotropy f_{2}(v), we found that its maximum increases from the weak electric field intensity (α<0.01) to a moderate one (α=0.5) by a factor f_{2max}(α=0.5)/f_{2max}(α=0.01)≈48. Applications to the radiation pressure, electromagnetic instabilities, and photoabsorption are also considered. PMID:27176419
Rajeev, K; Parameswaran, K
1998-07-20
Two iterative methods of inverting lidar backscatter signals to determine altitude profiles of aerosol extinction and altitude-resolved aerosol size distribution (ASD) are presented. The first method is for inverting two-wavelength lidar signals in which the shape of the ASD is assumed to be of power-law type, and the second method is for inverting multiwavelength lidar signals without assuming any a priori analytical form of ASD. An arbitrary value of the aerosol extinction-to-backscatter ratio (S(1)) is assumed initially to invert the lidar signals, and the ASD determined by use of the spectral dependence of the retrieved aerosol extinction coefficients is used to improve the value of S(1) iteratively. The methods are tested for different forms of altitude-dependent ASD's by use of simulated lidar-backscatter-signal profiles. The effect of random noise on the lidar backscatter signals is also studied.
Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design.
Li, Peng; Edo, Tega B; Rodenburg, John M
2014-12-01
We reconsider the closed form solution of the ptychographic phase problem called the Wigner Distribution Deconvolution Method (WDDM), which has remained discarded for twenty years. Ptychographic reconstruction is nowadays always undertaken by iterative algorithms. WDDM gives rise to a 4 dimensional data cube of all the relative phases between points in the diffraction plane. Here we demonstrate a novel method to use all this information, instead of just the small subset used in the original 'stepping out' procedure developed in the 1990s, thus greatly suppressing noise. We further develop a method for designing an improved probe (illumination function) to further decrease noise effects during the deconvolution division. Combining these two with an iterative procedure for the deconvolution, which avoids the usual difficulty of a divide by a small number, we show in model calculations that WDDM competes well with the modern conventional iterative methods like ePIE (the extended Ptychographical Iterative Engine). PMID:25068588
NASA Astrophysics Data System (ADS)
Shiraki, Yoshifumi; Kabashima, Yoshiyuki
2016-06-01
A signal model called joint sparse model 2 (JSM-2) or the multiple measurement vector problem, in which all sparse signals share their support, is important for dealing with practical signal processing problems. In this paper, we investigate the typical reconstruction performance of noisy measurement JSM-2 problems for {{\\ell}2,1} -norm regularized least square reconstruction and the Bayesian optimal reconstruction scheme in terms of mean square error. Employing the replica method, we show that these schemes, which exploit the knowledge of the sharing of the signal support, can recover the signals more precisely as the number of channels increases. In addition, we compare the reconstruction performance of two different ensembles of observation matrices: one is composed of independent and identically distributed random Gaussian entries and the other is designed so that row vectors are orthogonal to one another. As reported for the single-channel case in earlier studies, our analysis indicates that the latter ensemble offers better performance than the former ones for the noisy JSM-2 problem. The results of numerical experiments with a computationally feasible approximation algorithm we developed for this study agree with the theoretical estimation.
Khachatryan, V; Sirunyan, A M; Tumasyan, A; Adam, W; Bergauer, T; Dragicevic, M; Erö, J; Fabjan, C; Friedl, M; Frühwirth, R; Ghete, V M; Hammer, J; Hänsel, S; Hoch, M; Hörmann, N; Hrubec, J; Jeitler, M; Kasieczka, G; Kiesenhofer, W; Krammer, M; Liko, D; Mikulec, I; Pernicka, M; Rohringer, H; Schöfbeck, R; Strauss, J; Taurok, A; Teischinger, F; Waltenberger, W; Walzel, G; Widl, E; Wulz, C-E; Mossolov, V; Shumeiko, N; Suarez Gonzalez, J; Benucci, L; Ceard, L; De Wolf, E A; Hashemi, M; Janssen, X; Maes, T; Mucibello, L; Ochesanu, S; Roland, B; Rougny, R; Selvaggi, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Adler, V; Beauceron, S; Blyweert, S; D'Hondt, J; Devroede, O; Kalogeropoulos, A; Maes, J; Maes, M; Tavernier, S; Van Doninck, W; Van Mulders, P; Villella, I; Chabert, E C; Charaf, O; Clerbaux, B; De Lentdecker, G; Dero, V; Gay, A P R; Hammad, G H; Marage, P E; Vander Velde, C; Vanlaer, P; Wickens, J; Costantini, S; Grunewald, M; Klein, B; Marinov, A; Ryckbosch, D; Thyssen, F; Tytgat, M; Vanelderen, L; Verwilligen, P; Walsh, S; Zaganidis, N; Basegmez, S; Bruno, G; Caudron, J; De Favereau De Jeneret, J; Delaere, C; Demin, P; Favart, D; Giammanco, A; Grégoire, G; Hollar, J; Lemaitre, V; Militaru, O; Ovyn, S; Pagano, D; Pin, A; Piotrzkowski, K; Quertenmont, L; Schul, N; Beliy, N; Caebergs, T; Daubie, E; Alves, G A; Pol, M E; Souza, M H G; Carvalho, W; Da Costa, E M; De Jesus Damiao, D; De Oliveira Martins, C; Fonseca De Souza, S; Mundim, L; Oguri, V; Santoro, A; Silva Do Amaral, S M; Sznajder, A; Torres Da Silva De Araujo, F; Dias, F A; Dias, M A F; Fernandez Perez Tomei, T R; Gregores, E M; Marinho, F; Novaes, S F; Padula, Sandra S; Darmenov, N; Dimitrov, L; Genchev, V; Iaydjiev, P; Piperov, S; Stoykova, S; Sultanov, G; Trayanov, R; Vankov, I; Dyulendarova, M; Hadjiiska, R; Kozhuharov, V; Litov, L; Marinova, E; Mateev, M; Pavlov, B; Petkov, P; Bian, J G; Chen, G M; Chen, H S; Jiang, C H; Liang, D; Liang, S; Wang, J; Wang, J; Wang, X; Wang, Z; Yang, M; Zang, J; Zhang, Z; Ban, Y; Guo, S; Hu, Z; Mao, Y; Qian, S J; Teng, H; Zhu, B; Cabrera, A; Carrillo Montoya, C A; Gomez Moreno, B; Ocampo Rios, A A; Osorio Oliveros, A F; Sanabria, J C; Godinovic, N; Lelas, D; Lelas, K; Plestina, R; Polic, D; Puljak, I; Antunovic, Z; Dzelalija, M; Brigljevic, V; Duric, S; Kadija, K; Morovic, S; Attikis, A; Fereos, R; Galanti, M; Mousa, J; Nicolaou, C; Papadakis, A; Ptochos, F; Razis, P A; Rykaczewski, H; Tsiakkouri, D; Zinonos, Z; Mahmoud, M; Hektor, A; Kadastik, M; Kannike, K; Müntel, M; Raidal, M; Rebane, L; Azzolini, V; Eerola, P; Czellar, S; Härkönen, J; Heikkinen, A; Karimäki, V; Kinnunen, R; Klem, J; Kortelainen, M J; Lampén, T; Lassila-Perini, K; Lehti, S; Lindén, T; Luukka, P; Mäenpää, T; Tuominen, E; Tuominiemi, J; Tuovinen, E; Ungaro, D; Wendland, L; Banzuzi, K; Korpela, A; Tuuva, T; Sillou, D; Besancon, M; Dejardin, M; Denegri, D; Descamps, J; Fabbro, B; Faure, J L; Ferri, F; Ganjour, S; Gentit, F X; Givernaud, A; Gras, P; Hamel de Monchenault, G; Jarry, P; 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Kaufman, G Nicolas; Patterson, J R; Puigh, D; Riley, D; Ryd, A; Shi, X; Sun, W; Teo, W D; Thom, J; Thompson, J; Vaughan, J; Weng, Y; Wittich, P; Biselli, A; Cirino, G; Winn, D; Abdullin, S; Albrow, M; Anderson, J; Apollinari, G; Atac, M; Bakken, J A; Banerjee, S; Bauerdick, L A T; Beretvas, A; Berryhill, J; Bhat, P C; Bloch, I; Borcherding, F; Burkett, K; Butler, J N; Chetluru, V; Cheung, H W K; Chlebana, F; Cihangir, S; Demarteau, M; Eartly, D P; Elvira, V D; Fisk, I; Freeman, J; Gao, Y; Gottschalk, E; Green, D; Gutsche, O; Hahn, A; Hanlon, J; Harris, R M; James, E; Jensen, H; Johnson, M; Joshi, U; Khatiwada, R; Kilminster, B; Klima, B; Kousouris, K; Kunori, S; Kwan, S; Limon, P; Lipton, R; Lykken, J; Maeshima, K; Marraffino, J M; Mason, D; McBride, P; McCauley, T; Miao, T; Mishra, K; Mrenna, S; Musienko, Y; Newman-Holmes, C; O'Dell, V; Popescu, S; Pordes, R; Prokofyev, O; Saoulidou, N; Sexton-Kennedy, E; Sharma, S; Smith, R P; Soha, A; Spalding, W J; Spiegel, L; Tan, P; Taylor, L; Tkaczyk, S; Uplegger, L; Vaandering, E W; Vidal, R; Whitmore, J; Wu, W; Yumiceva, F; Yun, J C; Acosta, D; Avery, P; Bourilkov, D; Chen, M; Di Giovanni, G P; Dobur, D; Drozdetskiy, A; Field, R D; Fu, Y; Furic, I K; Gartner, J; Kim, B; Klimenko, S; Konigsberg, J; Korytov, A; Kotov, K; Kropivnitskaya, A; Kypreos, T; Matchev, K; Mitselmakher, G; Pakhotin, Y; Piedra Gomez, J; Prescott, C; Remington, R; Schmitt, M; Scurlock, B; Sellers, P; Wang, D; Yelton, J; Zakaria, M; Ceron, C; Gaultney, V; Kramer, L; Lebolo, L M; Linn, S; Markowitz, P; Martinez, G; Mesa, D; Rodriguez, J L; Adams, T; Askew, A; Chen, J; Diamond, B; Gleyzer, S V; Haas, J; Hagopian, S; Hagopian, V; Jenkins, M; Johnson, K F; Prosper, H; Sekmen, S; Veeraraghavan, V; Baarmand, M M; Guragain, S; Hohlmann, M; Kalakhety, H; Mermerkaya, H; Ralich, R; Vodopiyanov, I; Adams, M R; Anghel, I M; Apanasevich, L; Bazterra, V E; Betts, R R; Callner, J; Cavanaugh, R; Dragoiu, C; Garcia-Solis, E J; Gerber, C E; Hofman, D J; Khalatian, S; Lacroix, F; Shabalina, E; Smoron, A; Strom, D; Varelas, N; Akgun, U; Albayrak, E A; Bilki, B; Cankocak, K; Clarida, W; Duru, F; Lae, C K; McCliment, E; Merlo, J-P; Mestvirishvili, A; Moeller, A; Nachtman, J; Newsom, C R; Norbeck, E; Olson, J; Onel, Y; Ozok, F; Sen, S; Wetzel, J; Yetkin, T; Yi, K; Barnett, B A; Blumenfeld, B; Bonato, A; Eskew, C; Fehling, D; Giurgiu, G; Gritsan, A V; Guo, Z J; Hu, G; Maksimovic, P; Rappoccio, S; Swartz, M; Tran, N V; Whitbeck, A; Baringer, P; Bean, A; Benelli, G; Grachov, O; Murray, M; Radicci, V; Sanders, S; Wood, J S; Zhukova, V; Bandurin, D; Bolton, T; Chakaberia, I; Ivanov, A; Kaadze, K; Maravin, Y; Shrestha, S; Svintradze, I; Wan, Z; Gronberg, J; Lange, D; Wright, D; Baden, D; Boutemeur, M; Eno, S C; Ferencek, D; Hadley, N J; Kellogg, R G; Kirn, M; Mignerey, A; Rossato, K; Rumerio, P; Santanastasio, F; Skuja, A; Temple, J; Tonjes, M B; Tonwar, S C; Twedt, E; Alver, B; Bauer, G; Bendavid, J; Busza, W; Butz, E; Cali, I A; Chan, M; D'Enterria, D; Everaerts, P; Gomez Ceballos, G; Goncharov, M; Hahn, K A; Harris, P; Kim, Y; Klute, M; Lee, Y-J; Li, W; Loizides, C; Luckey, P D; Ma, T; Nahn, S; Paus, C; Roland, C; Roland, G; Rudolph, M; Stephans, G S F; Sumorok, K; Sung, K; Wenger, E A; Wyslouch, B; Xie, S; Yilmaz, Y; Yoon, A S; Zanetti, M; Cole, P; Cooper, S I; Cushman, P; Dahmes, B; De Benedetti, A; Dudero, P R; Franzoni, G; Haupt, J; Klapoetke, K; Kubota, Y; Mans, J; Petyt, D; Rekovic, V; Rusack, R; Sasseville, M; Singovsky, A; Cremaldi, L M; Godang, R; Kroeger, R; Perera, L; Rahmat, R; Sanders, D A; Sonnek, P; Summers, D; Bloom, K; Bose, S; Butt, J; Claes, D R; Dominguez, A; Eads, M; Keller, J; Kelly, T; Kravchenko, I; Lazo-Flores, J; Lundstedt, C; Malbouisson, H; Malik, S; Snow, G R; Baur, U; Iashvili, I; Kharchilava, A; Kumar, A; Smith, K; Strang, M; Zennamo, J; Alverson, G; Barberis, E; Baumgartel, D; Boeriu, O; Reucroft, S; Swain, J; Wood, D; Zhang, J; Anastassov, A; Kubik, A; Ofierzynski, R A; Pozdnyakov, A; Schmitt, M; Stoynev, S; Velasco, M; Won, S; Antonelli, L; Berry, D; Hildreth, M; Jessop, C; Karmgard, D J; Kolb, J; Kolberg, T; Lannon, K; Lynch, S; Marinelli, N; Morse, D M; Ruchti, R; Slaunwhite, J; Valls, N; Warchol, J; Wayne, M; Ziegler, J; Bylsma, B; Durkin, L S; Gu, J; Killewald, P; Ling, T Y; Williams, G; Adam, N; Berry, E; Elmer, P; Gerbaudo, D; Halyo, V; Hunt, A; Jones, J; Laird, E; Lopes Pegna, D; Marlow, D; Medvedeva, T; Mooney, M; Olsen, J; Piroué, P; Stickland, D; Tully, C; Werner, J S; Zuranski, A; Acosta, J G; Huang, X T; Lopez, A; Mendez, H; Oliveros, S; Ramirez Vargas, J E; Zatzerklyaniy, A; Alagoz, E; Barnes, V E; Bolla, G; Borrello, L; Bortoletto, D; Everett, A; Garfinkel, A F; Gecse, Z; Gutay, L; Jones, M; Koybasi, O; Laasanen, A T; Leonardo, N; Liu, C; Maroussov, V; Merkel, P; Miller, D H; Neumeister, N; Potamianos, K; Shipsey, I; Silvers, D; Yoo, H D; Zablocki, J; Zheng, Y; Jindal, P; Parashar, N; Cuplov, V; Ecklund, K M; Geurts, F J M; Liu, J H; Morales, J; Padley, B P; Redjimi, R; Roberts, J; Betchart, B; Bodek, A; Chung, Y S; de Barbaro, P; Demina, R; Flacher, H; Garcia-Bellido, A; Gotra, Y; Han, J; Harel, A; Miner, D C; Orbaker, D; Petrillo, G; Vishnevskiy, D; Zielinski, M; Bhatti, A; Demortier, L; Goulianos, K; Hatakeyama, K; Lungu, G; Mesropian, C; Yan, M; Atramentov, O; Gershtein, Y; Gray, R; Halkiadakis, E; Hidas, D; Hits, D; Lath, A; Rose, K; Schnetzer, S; Somalwar, S; Stone, R; Thomas, S; Cerizza, G; Hollingsworth, M; Spanier, S; Yang, Z C; York, A; Asaadi, J; Eusebi, R; Gilmore, J; Gurrola, A; Kamon, T; Khotilovich, V; Montalvo, R; Nguyen, C N; Pivarski, J; Safonov, A; Sengupta, S; Toback, D; Weinberger, M; Akchurin, N; Bardak, C; Damgov, J; Jeong, C; Kovitanggoon, K; Lee, S W; Mane, P; Roh, Y; Sill, A; Volobouev, I; Wigmans, R; Yazgan, E; Appelt, E; Brownson, E; Engh, D; Florez, C; Gabella, W; Johns, W; Kurt, P; Maguire, C; Melo, A; Sheldon, P; Velkovska, J; Arenton, M W; Balazs, M; Buehler, M; Conetti, S; Cox, B; Hirosky, R; Ledovskoy, A; Neu, C; Yohay, R; Gollapinni, S; Gunthoti, K; Harr, R; Karchin, P E; Mattson, M; Milstène, C; Sakharov, A; Anderson, M; Bachtis, M; Bellinger, J N; Carlsmith, D; Dasu, S; Dutta, S; Efron, J; Gray, L; Grogg, K S; Grothe, M; Hall-Wilton, R; Herndon, M; Klabbers, P; Klukas, J; Lanaro, A; Lazaridis, C; Leonard, J; Lomidze, D; Loveless, R; Mohapatra, A; Polese, G; Reeder, D; Savin, A; Smith, W H; Swanson, J; Weinberg, M
2010-07-01
Charged-hadron transverse-momentum and pseudorapidity distributions in proton-proton collisions at square root of s = 7 TeV are measured with the inner tracking system of the CMS detector at the LHC. The charged-hadron yield is obtained by counting the number of reconstructed hits, hit pairs, and fully reconstructed charged-particle tracks. The combination of the three methods gives a charged-particle multiplicity per unit of pseudorapidity dN(ch)/dη|(|η|<0.5) = 5.78 ± 0.01(stat) ± 0.23(syst) for non-single-diffractive events, higher than predicted by commonly used models. The relative increase in charged-particle multiplicity from square root of s = 0.9 to 7 TeV is [66.1 ± 1.0(stat) ± 4.2(syst)]%. The mean transverse momentum is measured to be 0.545 ± 0.005(stat) ± 0.015(syst) GeV/c. The results are compared with similar measurements at lower energies.
Khachatryan, V; Sirunyan, A M; Tumasyan, A; Adam, W; Bergauer, T; Dragicevic, M; Erö, J; Fabjan, C; Friedl, M; Frühwirth, R; Ghete, V M; Hammer, J; Hänsel, S; Hoch, M; Hörmann, N; Hrubec, J; Jeitler, M; Kasieczka, G; Kiesenhofer, W; Krammer, M; Liko, D; Mikulec, I; Pernicka, M; Rohringer, H; Schöfbeck, R; Strauss, J; Taurok, A; Teischinger, F; Waltenberger, W; Walzel, G; Widl, E; Wulz, C-E; Mossolov, V; Shumeiko, N; Suarez Gonzalez, J; Benucci, L; Ceard, L; De Wolf, E A; Hashemi, M; Janssen, X; Maes, T; Mucibello, L; Ochesanu, S; Roland, B; Rougny, R; Selvaggi, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Adler, V; Beauceron, S; Blyweert, S; D'Hondt, J; Devroede, O; Kalogeropoulos, A; Maes, J; Maes, M; Tavernier, S; Van Doninck, W; Van Mulders, P; Villella, I; Chabert, E C; Charaf, O; Clerbaux, B; De Lentdecker, G; Dero, V; Gay, A P R; Hammad, G H; Marage, P E; Vander Velde, C; Vanlaer, P; Wickens, J; Costantini, S; Grunewald, M; Klein, B; Marinov, A; Ryckbosch, D; Thyssen, F; Tytgat, M; Vanelderen, L; Verwilligen, P; Walsh, S; Zaganidis, N; Basegmez, S; Bruno, G; Caudron, J; De Favereau De Jeneret, J; Delaere, C; Demin, P; Favart, D; Giammanco, A; Grégoire, G; Hollar, J; Lemaitre, V; Militaru, O; Ovyn, S; Pagano, D; Pin, A; Piotrzkowski, K; Quertenmont, L; Schul, N; Beliy, N; Caebergs, T; Daubie, E; Alves, G A; Pol, M E; Souza, M H G; Carvalho, W; Da Costa, E M; De Jesus Damiao, D; De Oliveira Martins, C; Fonseca De Souza, S; Mundim, L; Oguri, V; Santoro, A; Silva Do Amaral, S M; Sznajder, A; Torres Da Silva De Araujo, F; Dias, F A; Dias, M A F; Fernandez Perez Tomei, T R; Gregores, E M; Marinho, F; Novaes, S F; Padula, Sandra S; Darmenov, N; Dimitrov, L; Genchev, V; Iaydjiev, P; Piperov, S; Stoykova, S; Sultanov, G; Trayanov, R; Vankov, I; Dyulendarova, M; Hadjiiska, R; Kozhuharov, V; Litov, L; Marinova, E; Mateev, M; Pavlov, B; Petkov, P; Bian, J G; Chen, G M; Chen, H S; Jiang, C H; Liang, D; Liang, S; Wang, J; Wang, J; Wang, X; Wang, Z; Yang, M; Zang, J; Zhang, Z; Ban, Y; Guo, S; Hu, Z; Mao, Y; Qian, S J; Teng, H; Zhu, B; Cabrera, A; Carrillo Montoya, C A; Gomez Moreno, B; Ocampo Rios, A A; Osorio Oliveros, A F; Sanabria, J C; Godinovic, N; Lelas, D; Lelas, K; Plestina, R; Polic, D; Puljak, I; Antunovic, Z; Dzelalija, M; Brigljevic, V; Duric, S; Kadija, K; Morovic, S; Attikis, A; Fereos, R; Galanti, M; Mousa, J; Nicolaou, C; Papadakis, A; Ptochos, F; Razis, P A; Rykaczewski, H; Tsiakkouri, D; Zinonos, Z; Mahmoud, M; Hektor, A; Kadastik, M; Kannike, K; Müntel, M; Raidal, M; Rebane, L; Azzolini, V; Eerola, P; Czellar, S; Härkönen, J; Heikkinen, A; Karimäki, V; Kinnunen, R; Klem, J; Kortelainen, M J; Lampén, T; Lassila-Perini, K; Lehti, S; Lindén, T; Luukka, P; Mäenpää, T; Tuominen, E; Tuominiemi, J; Tuovinen, E; Ungaro, D; Wendland, L; Banzuzi, K; Korpela, A; Tuuva, T; Sillou, D; Besancon, M; Dejardin, M; Denegri, D; Descamps, J; Fabbro, B; Faure, J L; Ferri, F; Ganjour, S; Gentit, F X; Givernaud, A; Gras, P; Hamel de Monchenault, G; Jarry, P; Locci, E; Malcles, J; Marionneau, M; Millischer, L; Rander, J; Rosowsky, A; Rousseau, D; Titov, M; Verrecchia, P; Baffioni, S; Bianchini, L; Bluj, M; Broutin, C; Busson, P; Charlot, C; Dobrzynski, L; Elgammal, S; Granier de Cassagnac, R; Haguenauer, M; Kalinowski, A; Miné, P; Paganini, P; Sabes, D; Sirois, Y; Thiebaux, C; Zabi, A; Agram, J-L; Besson, A; Bloch, D; Bodin, D; Brom, J-M; Cardaci, M; Conte, E; Drouhin, F; Ferro, C; Fontaine, J-C; Gelé, D; Goerlach, U; Greder, S; Juillot, P; Karim, M; Le Bihan, A-C; Mikami, Y; Speck, J; Van Hove, P; Fassi, F; Mercier, D; Baty, C; Beaupere, N; Bedjidian, M; Bondu, O; Boudoul, G; Boumediene, D; Brun, H; Chanon, N; Chierici, R; Contardo, D; Depasse, P; El Mamouni, H; Fay, J; Gascon, S; Ille, B; Kurca, T; Le Grand, T; Lethuillier, M; Mirabito, L; Perries, S; Tosi, S; Tschudi, Y; Verdier, P; Xiao, H; Roinishvili, V; Anagnostou, G; Edelhoff, M; Feld, L; Heracleous, N; Hindrichs, O; Jussen, R; Klein, K; Merz, J; Mohr, N; Ostapchuk, A; Perieanu, A; Raupach, F; Sammet, J; Schael, S; Sprenger, D; Weber, H; Weber, M; Wittmer, B; Actis, O; Ata, M; Bender, W; Biallass, P; Erdmann, M; Frangenheim, J; Hebbeker, T; Hinzmann, A; Hoepfner, K; Hof, C; Kirsch, M; Klimkovich, T; Kreuzer, P; Lanske, D; Magass, C; Merschmeyer, M; Meyer, A; Papacz, P; Pieta, H; Reithler, H; Schmitz, S A; Sonnenschein, L; Sowa, M; Steggemann, J; Teyssier, D; Zeidler, C; Bontenackels, M; Davids, M; Duda, M; Flügge, G; Geenen, H; Giffels, M; Haj Ahmad, W; Heydhausen, D; Kress, T; Kuessel, Y; Linn, A; Nowack, A; Perchalla, L; Pooth, O; Sauerland, P; Stahl, A; Thomas, M; Tornier, D; Zoeller, M H; Aldaya Martin, M; Behrenhoff, W; Behrens, U; Bergholz, M; Borras, K; Campbell, A; Castro, E; Dammann, D; Eckerlin, G; Flossdorf, A; Flucke, G; Geiser, A; Hauk, J; Jung, H; Kasemann, M; Katkov, I; Kleinwort, C; Kluge, H
2010-07-01
Charged-hadron transverse-momentum and pseudorapidity distributions in proton-proton collisions at square root of s = 7 TeV are measured with the inner tracking system of the CMS detector at the LHC. The charged-hadron yield is obtained by counting the number of reconstructed hits, hit pairs, and fully reconstructed charged-particle tracks. The combination of the three methods gives a charged-particle multiplicity per unit of pseudorapidity dN(ch)/dη|(|η|<0.5) = 5.78 ± 0.01(stat) ± 0.23(syst) for non-single-diffractive events, higher than predicted by commonly used models. The relative increase in charged-particle multiplicity from square root of s = 0.9 to 7 TeV is [66.1 ± 1.0(stat) ± 4.2(syst)]%. The mean transverse momentum is measured to be 0.545 ± 0.005(stat) ± 0.015(syst) GeV/c. The results are compared with similar measurements at lower energies. PMID:20867699
NASA Astrophysics Data System (ADS)
Ruden, E. L.; Amdahl, D. J.; Cooksey, R. H.; Robinson, P. R.; Analla, F. T.; Brown, D. J.; Kostora, M. R.; Camacho, J. F.
2014-10-01
Measurements are presented of the current per unit length as a function of the transverse distance from the center of a water-tamped 80 μm Al foil that narrows to a central width of 15.2 cm as it explodes into warm dense matter by Ohmic heating. Current is delivered by the discharge of a 36 μF capacitor bank charged to 30 kV and discharged to a peak current of 342 kA in 2.0 μs. The distribution is calculated by the linear regularized inversion of signals from an array of B-dot probes distributed along the foil's central half-width. The probes are far enough away from the foil (1 cm) be noninvasive and mechanically undisturbed during the time of interest. These results are compared to 3-D MHD ALEGRA simulations of the geometry driven by an external coupled two-loop lumped circuit model which accurately represents the driver. The goal of the effort is to test, in conjunction with other diagnostics, ab initio models of the equation of state and electrical conductivity of matter under conditions encountered in single-shot pulsed power devices (1 - 10 eV and 0.1 - 1 × solid density). This work was supported by AFOSR LRIR 11RD02COR.
A Simple Parameterization of 3 x 3 Magic Squares
ERIC Educational Resources Information Center
Trenkler, Gotz; Schmidt, Karsten; Trenkler, Dietrich
2012-01-01
In this article a new parameterization of magic squares of order three is presented. This parameterization permits an easy computation of their inverses, eigenvalues, eigenvectors and adjoints. Some attention is paid to the Luoshu, one of the oldest magic squares.
NASA Astrophysics Data System (ADS)
Nishida, Kazuhiro; Namita, Takeshi; Kato, Yuji; Shimizu, Koichi
2015-03-01
We have proposed a new nonlinear inversion technique to estimate the spatial distribution of the absorption coefficient (μa) in the depth direction of a turbid medium by spatially resolved backscattering measurement. With this technique, we can obtain cross-sectional image of μa as deep as the backscattered light traveled even when the transmitted light through the medium cannot be detected. In this technique, the depth distribution of absorption coefficient is determined by iterative calculation using the spatial path-length distribution (SPD) of traveled photons as a function of source-detector distance. In this calculation, the variance of path-length of many photons in each layer is also required. The SPD and the variance of path-length are obtained by Monte Carlo simulation using a known reduced scattering coefficient (μs'). Therefore, we need to know the μs' of the turbid medium beforehand. We have shown in computer simulation that this technique works well when the μs' is the typical values of mammalian body tissue, or 1.0 /mm. In this study, the accuracy of the μa estimation was analyzed and its dependence on the μs' was clarified quantitatively in various situations expected in practice. 10% deviations in μs' resulted in about 30% error in μa estimation, in average. This suggested that the measurement or the appropriate estimation of μs' is required to utilize the proposed technique effectively. Through this analysis, the effectiveness and the limitation of the newly proposed technique were clarified, and the problems to be solved were identified.
NASA Astrophysics Data System (ADS)
Pagnoni, G.; Tinti, S.; Armigliato, A.; Tonini, R.; Gallazzi, S.; Manucci, A.; Zaniboni, F.
2006-12-01
study the run-up heights. In both cases, we divide the earthquake fault in a given number of sub-faults, and then compute the tsunami generated by each sub-fault by means of two different codes: a finite-difference code implementing the linear shallow-water equations for the ocean-wide domain, and a finite-element code solving the non-linear version of the same equations in the local domain. In the case of the altimeter data, the adopted inversion technique is an implementation of the classical generalized linear least-squares theory. A more sophisticated technique, allowing one to determine also different amplification factors along different coastal segments, is employed to invert run-up data. We discuss the slip distributions obtained separately in the two approaches, and compare the results with those retrieved by modeling seismic and geodetic data.
Joint inversion for mapping subsurface hydrologicalparameters
Tseng, Hung-Wen; Lee, Ki Ha
2001-03-07
Using electromagnetic (EM) and seismic travel time data and a least-square criteria, a two-dimensional joint inversion algorithm is under development to assess the feasibility of directly mapping subsurface hydrological properties in a crosswell setup. A simplified Archie's law combined with the time average equation relates the magnetic fields and seismic travel time to two hydrological parameters; rock porosity and pore fluid electrical conductivity. For simplicity, the hydrological parameter distributions are assumed to be two-dimensional. Preliminary results show that joint inversion does have better resolving power for the interpretation than using the EM method alone. Various inversion scenarios have been tested, and it has been found that alternately perturbing just one of the two parameters at each iteration gives the best data fit.
Han, Sung Gu; Lim, Jongchul; Shin, Jinsub; Lee, Sung-Min; Park, Taiho; Yoon, Jongseung; Woo, Kyoungja; Lee, Hyunjung; Lee, Wonmok
2014-08-15
We demonstrate an optical amplification of organic dye within a TiO2 inverse-opal (IO) distributed feedback (DFB) reflector prepared by a slide-coating method. Highly reflective TiO2 IO film was fabricated by slide coating the binary aqueous dispersions of polystyrene microspheres and charge-stabilized TiO2 nanoparticles on a glass slide and subsequently removing the polymer-opal template. TiO2 IO film was infiltrated, in turn, with the solutions of DCM, a fluorescent dye in various solvents with different indices of refraction. Optical pumping by frequency-doubled Nd:YAG laser resulted in amplified spontaneous emission in each dye solution. In accordance with the semi-empirical simulation by the FDTD method, DCM in ethanol showed the best emission/stopband matching for the TiO2 IO film used in this study. Therefore, photo excitation of a DCM/ethanol cavity showed a single-mode DFB lasing at 640 nm wavelength at moderate pump energy. PMID:25121863
Han, Sung Gu; Lim, Jongchul; Shin, Jinsub; Lee, Sung-Min; Park, Taiho; Yoon, Jongseung; Woo, Kyoungja; Lee, Hyunjung; Lee, Wonmok
2014-08-15
We demonstrate an optical amplification of organic dye within a TiO2 inverse-opal (IO) distributed feedback (DFB) reflector prepared by a slide-coating method. Highly reflective TiO2 IO film was fabricated by slide coating the binary aqueous dispersions of polystyrene microspheres and charge-stabilized TiO2 nanoparticles on a glass slide and subsequently removing the polymer-opal template. TiO2 IO film was infiltrated, in turn, with the solutions of DCM, a fluorescent dye in various solvents with different indices of refraction. Optical pumping by frequency-doubled Nd:YAG laser resulted in amplified spontaneous emission in each dye solution. In accordance with the semi-empirical simulation by the FDTD method, DCM in ethanol showed the best emission/stopband matching for the TiO2 IO film used in this study. Therefore, photo excitation of a DCM/ethanol cavity showed a single-mode DFB lasing at 640 nm wavelength at moderate pump energy.
NASA Astrophysics Data System (ADS)
Shubitidze, Fridon; Karkashadze, David; Fernández, Juan Pablo; Barrowes, Benjamin E.; O'Neill, Kevin; Grzegorczyk, Tomasz M.; Shamatava, Irma
2010-04-01
Discrimination between UXO and harmless objects is particularly difficult in highly contaminated sites where two or more objects are simultaneously present in the field of view of the sensor and produce overlapping signals. The first step in overcoming this problem is estimating the number of targets. In this work an orthonormalized volume magnetic source (ONVMS) approach is introduced for estimating the number of targets, along with their locations and orientations. The technique is based on the discrete dipole approximation, which distributes dipoles inside the computational volume. First, a set of orthogonal functions are constructed using fundamental solutions of the Helmholtz equations (i.e., Green's functions). Then, the scattered magnetic field is approximated as a series of these orthogonal functions. The magnitudes of the expansion coefficients are determined directly from the measurement data without solving an ill-posed inverse-scattering problem. The expansion coefficients are then used to determine the amplitudes of the responding volume magnetic dipoles. The algorithm's superior performance and applicability to live UXO sites are illustrated by applying it to the bi-static TEMTADS multi-target data sets collected by NRL personnel at the Aberdeen Proving Ground UXO teststand site.
Inverse problem for Bremsstrahlung radiation
Voss, K.E.; Fisch, N.J.
1991-10-01
For certain predominantly one-dimensional distribution functions, an analytic inversion has been found which yields the velocity distribution of superthermal electrons given their Bremsstrahlung radiation. 5 refs.
NASA Astrophysics Data System (ADS)
Chen, T.
2009-12-01
102 uplift and subsidence measurements over the southeastern end of the rupture zone from two field surveys shortly after 1 Apr 2007 Solomon Islands Earthquake provide a unique geodetic constraint in the following inversion of distributed slip. In the conventional inversion of geodetic data for spatial distribution of fault slip the solution is maintained by minimizing the second-order spatial derivative of slip and the smoothing parameter is often selected subjectively at the bend of the trade-off curve of misfit as a function of slip roughness. A fully Bayesian slip inversion method[Fukuda et al.,2008] is used to overcome the deficiency of selecting the smoothing parameter subjectively. The smoothing parameter is estimated with the distributed slip at the same time under a unified theoretical Bayesian framework. The joint posterior probability density function of distributed slip and smoothing parameter is formulated using Bayes’ theorem and sampled with Markov chain Monte Carlo method. I will apply this method to coseismic slip distribution associated with the 2007 Mw8.1 Solomon Islands earthquake and compare the results of this method with conventional method and the coseismic finite fault model of Furlong et al.[2009].
AVO inversion based on inverse operator estimation in trust region
NASA Astrophysics Data System (ADS)
Yin, Xing-Yao; Deng, Wei; Zong, Zhao-Yun
2016-04-01
Amplitude variation with offset (AVO) inversion is widely utilized in exploration geophysics, especially for reservoir prediction and fluid identification. Inverse operator estimation in the trust region algorithm is applied for solving AVO inversion problems in which optimization and inversion directly are integrated. The L1 norm constraint is considered on the basis of reasonable initial model in order to improve effciency and stability during the AVO inversion process. In this study, high-order Zoeppritz approximation is utilized to establish the inversion objective function in which variation of {{v}\\text{p}}/{{v}\\text{s}} with time is taken into consideration. A model test indicates that the algorithm has a relatively higher stability and accuracy than the damp least-squares algorithm. Seismic data inversion is feasible and inversion values of three parameters ({{v}\\text{p}},{{v}\\text{s}},ρ ) maintain good consistency with logging curves.
Conover, W.J.; Cox, D.D.; Martz, H.F.
1997-12-01
When using parametric empirical Bayes estimation methods for estimating the binomial or Poisson parameter, the validity of the assumed beta or gamma conjugate prior distribution is an important diagnostic consideration. Chi-square goodness-of-fit tests of the beta or gamma prior hypothesis are developed for use when the binomial sample sizes or Poisson exposure times vary. Nine examples illustrate the application of the methods, using real data from such diverse applications as the loss of feedwater flow rates in nuclear power plants, the probability of failure to run on demand and the failure rates of the high pressure coolant injection systems at US commercial boiling water reactors, the probability of failure to run on demand of emergency diesel generators in US commercial nuclear power plants, the rate of failure of aircraft air conditioners, baseball batting averages, the probability of testing positive for toxoplasmosis, and the probability of tumors in rats. The tests are easily applied in practice by means of corresponding Mathematica{reg_sign} computer programs which are provided.
NASA Astrophysics Data System (ADS)
Hanuš, J.; Ďurech, J.; Brož, M.; Warner, B. D.; Pilcher, F.; Stephens, R.; Oey, J.; Bernasconi, L.; Casulli, S.; Behrend, R.; Polishook, D.; Henych, T.; Lehký, M.; Yoshida, F.; Ito, T.
2011-06-01
Context. In the past decade, more than one hundred asteroid models were derived using the lightcurve inversion method. Measured by the number of derived models, lightcurve inversion has become the leading method for asteroid shape determination. Aims: Tens of thousands of sparse-in-time lightcurves from astrometric projects are publicly available. We investigate these data and use them in the lightcurve inversion method to derive new asteroid models. By having a greater number of models with known physical properties, we can gain a better insight into the nature of individual objects and into the whole asteroid population. Methods: We use sparse photometry from selected observatories from the AstDyS database (Asteroids - Dynamic Site), either alone or in combination with dense lightcurves, to determine new asteroid models by the lightcurve inversion method. We investigate various correlations between several asteroid parameters and characteristics such as the rotational state and diameter or family membership. We focus on the distribution of ecliptic latitudes of pole directions. We create a synthetic uniform distribution of latitudes, compute the method bias, and compare the results with the distribution of known models. We also construct a model for the long-term evolution of spins. Results: We present 80 new asteroid models derived from combined data sets where sparse photometry is taken from the AstDyS database and dense lightcurves are from the Uppsala Asteroid Photometric Catalogue (UAPC) and from several individual observers. For 18 asteroids, we present updated shape solutions based on new photometric data. For another 30 asteroids we present their partial models, i.e., an accurate period value and an estimate of the ecliptic latitude of the pole. The addition of new models increases the total number of models derived by the lightcurve inversion method to ~200. We also present a simple statistical analysis of physical properties of asteroids where we look
All Square Chiliagonal Numbers
ERIC Educational Resources Information Center
A?iru, Muniru A.
2016-01-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…
Cortese, Filomeno; Nilsson, Josefin; Westall, Carol
2013-01-01
Spatial–temporal partial least squares (ST-PLS) is a multivariate statistical analysis that has improved the analysis of modern imaging techniques. Multifocal electroretinograms (mfERGs) contain a large amount of data, and averaging and grouping have been used to reduce the amount of data to levels that can be handled using traditional statistical methods. In contrast, using all acquired data points, ST-PLS enables statistically rigorous testing of changes in waveform shape and in the distributed signal related to retinal function. We hypothesise that ST-PLS will improve analysis of the mfERG. Two mfERG protocols, a 103 hexagon clinical protocol and a slow-flash mfERG (sf-mfERG) protocol, were recorded from an adolescent population with type 1 diabetes and an age similar control population. The standard mfERGs were analysed using a template-fitting algorithm and the sf-mfERG using a signal-to-noise measure. The results of these traditional analysis techniques are compared with those of the ST-PLS analysis. Traditional analysis of the mfERG recordings revealed changes between groups for implicit time but not amplitude; however, the spatial location of these changes could not be identified. In contrast, ST-PLS detected significant changes between groups and displayed the spatial location of these changes on the retinal map and the temporal location within the mfERG waveforms. ST-PLS confirmed that changes to diabetic retinal function occur before the onset of clinical pathology. In addition, it revealed two distinct patterns of change depending on whether the multifocal paradigm was optimised to target outer retinal function (photoreceptors) or middle/inner retinal function (collector cells). PMID:22610144
Weighted conditional least-squares estimation
Booth, J.G.
1987-01-01
A two-stage estimation procedure is proposed that generalizes the concept of conditional least squares. The method is instead based upon the minimization of a weighted sum of squares, where the weights are inverses of estimated conditional variance terms. Some general conditions are given under which the estimators are consistent and jointly asymptotically normal. More specific details are given for ergodic Markov processes with stationary transition probabilities. A comparison is made with the ordinary conditional least-squares estimators for two simple branching processes with immigration. The relationship between weighted conditional least squares and other, more well-known, estimators is also investigated. In particular, it is shown that in many cases estimated generalized least-squares estimators can be obtained using the weighted conditional least-squares approach. Applications to stochastic compartmental models, and linear models with nested error structures are considered.
A Bibliometric Distribution Which Really Works.
ERIC Educational Resources Information Center
Sichel, H. S.
1985-01-01
The Generalized Inverse Gaussian-Poisson Distribution is suggested as an all-embracing mathematical model for bibliometric frequency distributions. Twelve examples are given which show that the new model cannot be rejected by virtue of an objective chi-squared test. A mathematical appendix and 20 references are included. (Author/EJS)
Discrete square root smoothing.
NASA Technical Reports Server (NTRS)
Kaminski, P. G.; Bryson, A. E., Jr.
1972-01-01
The basic techniques applied in the square root least squares and square root filtering solutions are applied to the smoothing problem. Both conventional and square root solutions are obtained by computing the filtered solutions, then modifying the results to include the effect of all measurements. A comparison of computation requirements indicates that the square root information smoother (SRIS) is more efficient than conventional solutions in a large class of fixed interval smoothing problems.
Chang, M.E.; Hartley, D.; Cardelino, C.; Chang, W.L.
1996-12-31
The Urban Airshed Model (UAM) has been used by the State of Georgia in an attempt to demonstrate attainment of the ozone standard for Atlanta. A recent comparison of UAM data to ambient data collected during the 1992 Southern Oxidants Study Atlanta intensive revealed that the model accurately predicts ozone concentrations, but is poorly simulates the concurrent ozone precursors. There were discrepancies in both the anthropogenic and biogenic precursors. For anthropogenic emissions, the ambient ratios of anthropogenic hydrocarbons (AHC) to oxides of nitrogen (NO{sub x}), AHC/NO{sub x}, and carbon monoxide (CO) to NO{sub x}, CO/NO{sub x}, were higher than the emission ratios by 20% and 73% respectively. In this study, the authors use an inverse method to reconcile the differences between the observed and predicted concentrations of ozone precursors. Inverse methods have been successfully applied to many fields including medical imaging, missile guidance, and underground tomography. This study is the first to apply the inverse method to estimate the emissions of the relatively short-lived species important to urban oxidants formation.
NASA Technical Reports Server (NTRS)
Fymat, A. L.; Smith, C. B.
1979-01-01
It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.
Direct and indirect inversions
NASA Astrophysics Data System (ADS)
Virieux, Jean; Brossier, Romain; Métivier, Ludovic; Operto, Stéphane; Ribodetti, Alessandra
2016-06-01
A bridge is highlighted between the direct inversion and the indirect inversion. They are based on fundamental different approaches: one is looking after a projection from the data space to the model space while the other one is reducing a misfit between observed data and synthetic data obtained from a given model. However, it is possible to obtain similar structures for model perturbation, and we shall focus on P-wave velocity reconstruction. This bridge is built up through the Born approximation linearizing the forward problem with respect to model perturbation and through asymptotic approximations of the Green functions of the wave propagation equation. We first describe the direct inversion and its ingredients and then we focus on a specific misfit function design leading to a indirect inversion. Finally, we shall compare this indirect inversion with more standard least-squares inversion as the FWI, enabling the focus on small weak velocity perturbations on one side and the speed-up of the velocity perturbation reconstruction on the other side. This bridge has been proposed by the group led by Raul Madariaga in the early nineties, emphasizing his leading role in efficient imaging workflows for seismic velocity reconstruction, a drastic requirement at that time.
ERIC Educational Resources Information Center
Watson, Gale A.
2003-01-01
Demonstrates the transformations that are possible to construct a variety of magic squares, including modifications to challenge students from elementary grades through algebra. Presents an example of using magic squares with students who have special needs. (YDS)
NASA Technical Reports Server (NTRS)
Gross, Bernard
1996-01-01
Material characterization parameters obtained from naturally flawed specimens are necessary for reliability evaluation of non-deterministic advanced ceramic structural components. The least squares best fit method is applied to the three parameter uniaxial Weibull model to obtain the material parameters from experimental tests on volume or surface flawed specimens subjected to pure tension, pure bending, four point or three point loading. Several illustrative example problems are provided.
NASA Astrophysics Data System (ADS)
Wood, W.; Knapp, C. C.; Knapp, J. H.
2010-12-01
The seafloor mound at the Gulf of Mexico lease block MC (Mississippi Canyon) 118 is a known active seep lying directly above a salt dome. The site lies at 850-900 m water depth - within the methane hydrate stability zone, but there is no obvious BSR or other indicator of large quantities of gas or gas hydrate. Air-gun seismic data acquired with a 4180 cu in source and 7200 m, 288-channel hydrophone array, exhibit several bright, but laterally-limited reflections in the ~500 m sediment column above the salt. The bright spots are largely conformable with the strata, and there is no apparent pull-up or push-down associated with the bright spots, suggesting they are thin. There are also no significant frequency changes below the bright spots. We interpret the bright spots to be caused by gas, gas hydrate, or carbonate, or combinations of the three. The long offsets used to acquire these data allow for the analysis of refracted arrivals that not only provide accurate P-wave velocities, but also provide a background velocity profile for full waveform inversion. Preliminary results from the waveform inversion confirm at least some of the bright spots are free gas, constraining the position of the gas hydrate stability zone, but very thin (sub-wavelength) layers of carbonate and hydrate may also be present. Knowing the exact composition of the material responsible for the bright spots will better constrain the linkage between the salt tectonics (with implied fault activity) and seep activity, as well as the longevity of the hydrate system at MC 118.
All square chiliagonal numbers
NASA Astrophysics Data System (ADS)
Aṣiru, Muniru A.
2016-10-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square numbers. The study revealed that the determination of square chiliagonal numbers naturally leads to a generalized Pell equation x2 - Dy2 = N with D = 1996 and N = 9962, and has six fundamental solutions out of which only three yielded integer values for use as indices of chiliagonal numbers. The crossing/independent recurrence relations satisfied by each class of indices of the corresponding chiliagonal numbers and square numbers are obtained. Finally, the generating functions serve as a clothesline to hang up the indices of the corresponding chiliagonal numbers and square numbers for easy display and this was used to obtain the first few sequence of square chiliagonal numbers.
Joint inversion of fundamental and higher mode Rayleigh waves
Luo, Y.-H.; Xia, J.-H.; Liu, J.-P.; Liu, Q.-S.
2008-01-01
In this paper, we analyze the characteristics of the phase velocity of fundamental and higher mode Rayleigh waves in a six-layer earth model. The results show that fundamental mode is more sensitive to the shear velocities of shallow layers (< 7 m) and concentrated in a very narrow band (around 18 Hz) while higher modes are more sensitive to the parameters of relatively deeper layers and distributed over a wider frequency band. These properties provide a foundation of using a multi-mode joint inversion to define S-wave velocity. Inversion results of both synthetic data and a real-world example demonstrate that joint inversion with the damped least squares method and the SVD (Singular Value Decomposition) technique to invert Rayleigh waves of fundamental and higher modes can effectively reduce the ambiguity and improve the accuracy of inverted S-wave velocities.
High-Resolution Cortical Dipole Imaging Using Spatial Inverse Filter Based on Filtering Property
2016-01-01
Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter that optimizes filtering property using a sigmoid function. The ability of the proposed method was compared with the traditional inverse techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD), and truncated total least squares (TTLS), in a computer simulation. The proposed method was applied to human experimental data of visual evoked potentials. As a result, the estimation accuracy was improved and the localized dipole distribution was obtained with less noise. PMID:27688747
High-Resolution Cortical Dipole Imaging Using Spatial Inverse Filter Based on Filtering Property
2016-01-01
Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter that optimizes filtering property using a sigmoid function. The ability of the proposed method was compared with the traditional inverse techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD), and truncated total least squares (TTLS), in a computer simulation. The proposed method was applied to human experimental data of visual evoked potentials. As a result, the estimation accuracy was improved and the localized dipole distribution was obtained with less noise.
NASA Astrophysics Data System (ADS)
Salewski, M.; Geiger, B.; Jacobsen, A. S.; García-Muñoz, M.; Heidbrink, W. W.; Korsholm, S. B.; Leipold, F.; Madsen, J.; Moseev, D.; Nielsen, S. K.; Rasmussen, J.; Stejner, M.; Tardini, G.; Weiland, M.; the ASDEX Upgrade Team
2014-02-01
We present the first measurement of a local fast-ion 2D velocity distribution function f(v‖, v⊥). To this end, we heated a plasma in ASDEX Upgrade by neutral beam injection and measured spectra of fast-ion Dα (FIDA) light from the plasma centre in three views simultaneously. The measured spectra agree very well with synthetic spectra calculated from a TRANSP/NUBEAM simulation. Based on the measured FIDA spectra alone, we infer f(v‖, v⊥) by tomographic inversion. Salient features of our measurement of f(v‖, v⊥) agree reasonably well with the simulation: the measured as well as the simulated f(v‖, v⊥) are lopsided towards negative velocities parallel to the magnetic field, and they have similar shapes. Further, the peaks in the simulation of f(v‖, v⊥) at full and half injection energies of the neutral beam also appear in the measurement at similar velocity-space locations. We expect that we can measure spectra in up to seven views simultaneously in the next ASDEX Upgrade campaign which would further improve measurements of f(v‖, v⊥) by tomographic inversion.
Inversion of magnetotelluric data in a sparse model domain
NASA Astrophysics Data System (ADS)
Nittinger, Christian G.; Becken, Michael
2016-06-01
The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least squares ℓ2 sense and of a model coefficient norm in a ℓ1 sense (ℓ2-ℓ1 minimization). The ℓ1 coefficient norm renders the solution sparse in a suitable representation such as the multi-resolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for ℓ2 regularization. The presented numerical algorithm solves the mixed ℓ2-ℓ1 norm minimization problem for the non-linear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.
Inversion of magnetotelluric data in a sparse model domain
NASA Astrophysics Data System (ADS)
Nittinger, Christian G.; Becken, Michael
2016-08-01
The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least-squares ℓ2 sense and of a model coefficient norm in an ℓ1 sense (ℓ2-ℓ1 minimization). The ℓ1 coefficient norm renders the solution sparse in a suitable representation such as the multiresolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for ℓ2 regularization. The presented numerical algorithm solves the mixed ℓ2-ℓ1 norm minimization problem for the nonlinear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.
Adcox, K; Adler, S S; Ajitanand, N N; Akiba, Y; Alexander, J; Aphecetche, L; Arai, Y; Aronson, S H; Averbeck, R; Awes, T C; Barish, K N; Barnes, P D; Barrette, J; Bassalleck, B; Bathe, S; Baublis, V; Bazilevsky, A; Belikov, S; Bellaiche, F G; Belyaev, S T; Bennett, M J; Berdnikov, Y; Botelho, S; Brooks, M L; Brown, D S; Bruner, N; Bucher, D; Buesching, H; Bumazhnov, V; Bunce, G; Burward-Hoy, J; Butsyk, S; Carey, T A; Chand, P; Chang, J; Chang, W C; Chavez, L L; Chernichenko, S; Chi, C Y; Chiba, J; Chiu, M; Choudhury, R K; Christ, T; Chujo, T; Chung, M S; Chung, P; Cianciolo, V; Cole, B A; D'Enterria, D G; David, G; Delagrange, H; Denisov, A; Deshpande, A; Desmond, E J; Dietzsch, O; Dinesh, B V; Drees, A; Durum, A; Dutta, D; Ebisu, K; Efremenko, Y V; El Chenawi, K; En'yo, H; Esumi, S; Ewell, L; Ferdousi, T; Fields, D E; Fokin, S L; Fraenkel, Z; Franz, A; Frawley, A D; Fung, S Y; Garpman, S; Ghosh, T K; Glenn, A; Godoi, A L; Goto, Y; Greene, S V; Grosse Perdekamp, M; Gupta, S K; Guryn, W; Gustafsson, H A; Haggerty, J S; Hamagaki, H; Hansen, A G; Hara, H; Hartouni, E P; Hayano, R; Hayashi, N; He, X; Hemmick, T K; Heuser, J M; Hibino, M; Hill, J C; Ho, D S; Homma, K; Hong, B; Hoover, A; Ichihara, T; Imai, K; Ippolitov, M S; Ishihara, M; Jacak, B V; Jang, W Y; Jia, J; Johnson, B M; Johnson, S C; Joo, K S; Kametani, S; Kang, J H; Kann, M; Kapoor, S S; Kelly, S; Khachaturov, B; Khanzadeev, A; Kikuchi, J; Kim, D J; Kim, H J; Kim, S Y; Kim, Y G; Kinnison, W W; Kistenev, E; Kiyomichi, A; Klein-Boesing, C; Klinksiek, S; Kochenda, L; Kochetkov, D; Kochetkov, V; Koehler, D; Kohama, T; Kozlov, A; Kroon, P J; Kurita, K; Kweon, M J; Kwon, Y; Kyle, G S; Lacey, R; Lajoie, J G; Lauret, J; Lebedev, A; Lee, D M; Leitch, M J; Li, X H; Li, Z; Lim, D J; Liu, M X; Liu, X; Liu, Z; Maguire, C F; Mahon, J; Makdisi, Y I; Manko, V I; Mao, Y; Mark, S K; Markacs, S; Martinez, G; Marx, M D; Masaike, A; Matathias, F; Matsumoto, T; McGaughey, P L; Melnikov, E; Merschmeyer, M; Messer, F; Messer, M; Miake, Y; Miller, T E; Milov, A; Mioduszewski, S; Mischke, R E; Mishra, G C; Mitchell, J T; Mohanty, A K; Morrison, D P; Moss, J M; Mühlbacher, F; Muniruzzaman, M; Murata, J; Nagamiya, S; Nagasaka, Y; Nagle, J L; Nakada, Y; Nandi, B K; Newby, J; Nikkinen, L; Nilsson, P; Nishimura, S; Nyanin, A S; Nystrand, J; O'Brien, E; Ogilvie, C A; Ohnishi, H; Ojha, I D; Ono, M; Onuchin, V; Oskarsson, A; Osterman, L; Otterlund, I; Oyama, K; Paffrath, L; Palounek, A P; Pantuev, V S; Papavassiliou, V; Pate, S F; Peitzmann, T; Petridis, A N; Pinkenburg, C; Pisani, R P; Pitukhin, P; Plasil, F; Pollack, M; Pope, K; Purschke, M L; Ravinovich, I; Read, K F; Reygers, K; Riabov, V; Riabov, Y; Rosati, M; Rose, A A; Ryu, S S; Saito, N; Sakaguchi, A; Sakaguchi, T; Sako, H; Sakuma, T; Samsonov, V; Sangster, T C; Santo, R; Sato, H D; Sato, S; Sawada, S; Schlei, B R; Schutz, Y; Semenov, V; Seto, R; Shea, T K; Shein, I; Shibata, T A; Shigaki, K; Shiina, T; Shin, Y H; Sibiriak, I G; Silvermyr, D; Sim, K S; Simon-Gillo, J; Singh, C P; Singh, V; Sivertz, M; Soldatov, A; Soltz, R A; Sorensen, S; Stankus, P W; Starinsky, N; Steinberg, P; Stenlund, E; Ster, A; Stoll, S P; Sugioka, M; Sugitate, T; Sullivan, J P; Sumi, Y; Sun, Z; Suzuki, M; Takagui, E M; Taketani, A; Tamai, M; Tanaka, K H; Tanaka, Y; Taniguchi, E; Tannenbaum, M J; Thomas, J; Thomas, J H; Thomas, T L; Tian, W; Tojo, J; Torii, H; Towell, R S; Tserruya, I; Tsuruoka, H; Tsvetkov, A A; Tuli, S K; Tydesjö, H; Tyurin, N; Ushiroda, T; van Hecke, H W; Velissaris, C; Velkovska, J; Velkovsky, M; Vinogradov, A A; Volkov, M A; Vorobyov, A; Vznuzdaev, E; Wang, H; Watanabe, Y; White, S N; Witzig, C; Wohn, F K; Woody, C L; Xie, W; Yagi, K; Yokkaichi, S; Young, G R; Yushmanov, I E; Zajc, W A; Zhang, Z; Zhou, S
2001-07-30
The first measurement of energy produced transverse to the beam direction at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory is presented. The midrapidity transverse energy density per participating nucleon rises steadily with the number of participants, closely paralleling the rise in charged-particle density, such that
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices.
Piñeros, William D; Baldea, Michael; Truskett, Thomas M
2016-08-01
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices
NASA Astrophysics Data System (ADS)
Piñeros, William D.; Baldea, Michael; Truskett, Thomas M.
2016-08-01
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.
Rubin, R.M.; Leggett, D.; Wells, M.B.
1980-12-01
This report describes a set of radiation transport calculations that were run with the AHISN S/sub n/ discrete ordinates code and a point kernel code to determine the energy, polar angle and height in air distributions of the total and direct gamma-ray flux densities from: (1) uranium sources of 3.2, 200 and 800 ppM in a sandstone orebody covered with biomass densities of 0, 10.2, 20.4, 51.0 and 102.0 kg/m/sup 2/; (2) thorium sources of 12, 25 and 80 ppM in a sandstone ore body covered with biomass densities of 0, 10.2, 20.4, 51.0 and 102.0 kg/m/sup 2/; (3) potassium source (2.5 wt %) in a sandstone ore body covered with biomass densities of 0, 10.2, 20.4, 51.0 and 102.0 kg/m/sup 2/; (4) constant airborne source with height for no inversion and for inversion layer heights of 65.22, 260.32 and 458.43 m; (5) exponentially decreasing airborne source for no inversion and inversion layer heights of 65.22, 260.32 and 458.43 m; (6) 3.2 ppM uranium source in overburden layers of 10.266, 17.110, 26.399 and 32.509 cm thick; (7) 12 ppM thorium source in overburden layers of 10.266, 17.110, 26.399 and 32.509 cm; (8) 2.5 wt % of potassium in overburden layers of 10.266, 17.110, 26.399 and 32.509 cm thick; and (9) 3.2 ppM, 200 ppM, and 800 ppM uranium source in sandstone orebody covered with overburden thicknesses of 10.266, 17.110, 26.399 and 32.509 cm. Gamma-ray emission from the decay of natural uranium, thorium, radon, and potassium are given in a 45-energy group structure applicable to the energy windows used to map the potential uranium ore reserves.
ERIC Educational Resources Information Center
Misiurewicz, Michal
2013-01-01
If students are presented the standard proof of irrationality of [square root]2, can they generalize it to a proof of the irrationality of "[square root]p", "p" a prime if, instead of considering divisibility by "p", they cling to the notions of even and odd used in the standard proof?
ERIC Educational Resources Information Center
Wagon, Stan; Cox, Barry
2009-01-01
A technique discovered in 1939 can be used to build a device that is driven by standard circular motion (as in a drill press) and drills exact square holes. This device is quite different from the classic design by Watts, which uses a Reuleaux triangle and drills a hole that is almost, but not exactly, square. We describe the device in detail,…
ERIC Educational Resources Information Center
Hester, Yvette
Least squares methods are sophisticated mathematical curve fitting procedures used in all classical parametric methods. The linear least squares approximation is most often associated with finding the "line of best fit" or the regression line. Since all statistical analyses are correlational and all classical parametric methods are least square…
ERIC Educational Resources Information Center
Adams, Deborah
2006-01-01
This article describes an approach to teaching square dance that is advantageous for both the teacher and students. Lessons in dance become more meaningful to students when the music and vocabulary is consistent with experiences in their own lives. When students create their own squaring to the rap, lessons become more student-centered,…
NASA Astrophysics Data System (ADS)
McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.
2014-10-01
A series of reduced models are used to study the fast ion tail in the vicinity of a transition layer between plasmas at disparate temperatures and densities, which is typical of the gas-pusher interface in inertial confinement fusion targets. Emphasis is placed on utilizing progressively more comprehensive models in order to identify the essential physics for computing the fast ion tail at energies comparable to the Gamow peak. The resulting fast ion tail distribution is subsequently used to compute the fusion reactivity as a function of collisionality and temperature. It is found that while the fast ion distribution can be significantly depleted in the hot spot, leading to a reduction of the fusion reactivity in this region, a surplus of fast ions is present in the neighboring cold region. The presence of this fast ion surplus in the neighboring cold region is shown to lead to a partial recovery of the fusion yield lost in the hot spot.
Leavitt, M.A.; Lutz, I.C.
1958-08-01
An amplifier circuit is described for amplifying sigmals having an alternating current component superimposed upon a direct current component, without loss of any segnnent of the alternating current component. The general circuit arrangement includes a vibrator, two square wave amplifiers, and recombination means. The amplifier input is connected to the vibrating element of the vibrator and is thereby alternately applied to the input of each square wave amplifier. The detailed circuitry of the recombination means constitutes the novelty of the annplifier and consists of a separate, dual triode amplifier coupled to the output of each square wave amplifier with a recombination connection from the plate of one amplifier section to a grid of one section of the other amplifier. The recombination circuit has provisions for correcting distortion caused by overlapping of the two square wave voltages from the square wave amplifiers.
NASA Astrophysics Data System (ADS)
van Hout, Rene; Rabencov, Boris; Arca, Javier
2014-11-01
Near neutrally buoyant, polystyrene beads (583 micrometers) were tracked in a square (50 × 50 mm2), closed-loop, turbulent water duct at a bulk flow Reynolds number of 10,602 (friction velocity 0.0208 m/s) using single view, inline digital holographic cinematography (at 1 kHz). The volume of interest (50 × 17.4 × 17.4 mm3) was positioned at the bottom part of the channel. The mean bead diameter normalized by inner wall coordinates was d+ = 14.2, with Stokes numbers of 8.5. In-house developed algorithms, fine-tuned to tracking single and overlapping beads were developed. Bead in-focus positions were determined by maximum intensity gradient method. Results showed that in agreement with literature publications, ascending beads lagged the mean streamwise water velocity while descending ones had similar velocities. Average streamwise bead velocities and number densities collapsed onto wall-normal-streamwise and spanwise-streamwise planes, indicated preferential segregation of ascending and descending beads up to a height of 100 wall units. Spanwise ``lane'' separation distances ranged between 150-200 wall units, larger but of the same order as the spanwise extent of coherent near-wall turbulence structures. Duct corners were nearly devoid of beads likely caused by secondary flows. Israel Science Foundation Grant 915/10 and COST Actions MP0806 and FP1005.
Abelev, B I; Aggarwal, M M; Ahammed, Z; Anderson, B D; Anderson, M; Arkhipkin, D; Averichev, G S; Bai, Y; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Bekele, S; Belaga, V V; Bellingeri-Laurikainen, A; Bellwied, R; Benedosso, F; Bhardwaj, S; Bhasin, A; Bhati, A K; Bichsel, H; Bielcik, J; Bielcikova, J; Bland, L C; Blyth, S-L; Bonner, B E; Botje, M; Bouchet, J; Brandin, A V; Bravar, A; Burton, T P; Bystersky, M; Cadman, R V; Cai, X Z; Caines, H; Calderón de la Barca Sánchez, M; Castillo, J; Catu, O; Cebra, D; Chajecki, Z; Chaloupka, P; Chattopadhyay, S; Chen, H F; Chen, J H; Cheng, J; Cherney, M; Chikanian, A; Christie, W; Coffin, J P; Cormier, T M; Cosentino, M R; Cramer, J G; Crawford, H J; Das, D; Das, S; Dash, S; Daugherity, M; de Moura, M M; Dedovich, T G; Dephillips, M; Derevschikov, A A; Didenko, L; Dietel, T; Djawotho, P; Dogra, S M; Dong, W J; Dong, X; Draper, J E; Du, F; Dunin, V B; Dunlop, J C; Dutta Mazumdar, M R; Eckardt, V; Edwards, W R; Efimov, L G; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Estienne, M; Fachini, P; Fatemi, R; Fedorisin, J; Filip, P; Finch, E; Fine, V; Fisyak, Y; Fu, J; Gagliardi, C A; Gaillard, L; Ganti, M S; Ghazikhanian, V; Ghosh, P; Gonzalez, J E; Gorbunov, Y G; Gos, H; Grebenyuk, O; Grosnick, D; Guertin, S M; Guimaraes, K S F F; Gupta, N; Gutierrez, T D; Haag, B; Hallman, T J; Hamed, A; Harris, J W; He, W; Heinz, M; Henry, T W; Hepplemann, S; Hippolyte, B; Hirsch, A; Hjort, E; Hoffman, A M; Hoffmann, G W; Horner, M J; Huang, H Z; Huang, S L; Hughes, E W; Humanic, T J; Igo, G; Jacobs, P; Jacobs, W W; Jakl, P; Jia, F; Jiang, H; Jones, P G; Judd, E G; Kabana, S; Kang, K; Kapitan, J; Kaplan, M; Keane, D; Kechechyan, A; Khodyrev, V Yu; Kim, B C; Kiryluk, J; Kisiel, A; Kislov, E M; Klein, S R; Kocoloski, A; Koetke, D D; Kollegger, T; Kopytine, M; Kotchenda, L; Kouchpil, V; Kowalik, K L; Kramer, M; Kravtsov, P; Kravtsov, V I; Krueger, K; Kuhn, C; Kulikov, A I; Kumar, A; Kuznetsov, A A; Lamont, M A C; Landgraf, J M; Lange, S; Lapointe, S; Laue, F; Lauret, J; Lebedev, A; Lednicky, R; Lee, C-H; Lehocka, S; Levine, M J; Li, C; Li, Q; Li, Y; Lin, G; Lin, X; Lindenbaum, S J; Lisa, M A; Liu, F; Liu, H; Liu, J; Liu, L; Liu, Z; Ljubicic, T; Llope, W J; Long, H; Longacre, R S; Love, W A; Lu, Y; Ludlam, T; Lynn, D; Ma, G L; Ma, J G; Ma, Y G; Magestro, D; Mahapatra, D P; Majka, R; Mangotra, L K; Manweiler, R; Margetis, S; Markert, C; Martin, L; Matis, H S; Matulenko, Yu A; McClain, C J; McShane, T S; Melnick, Yu; Meschanin, A; Millane, J; Miller, M L; Minaev, N G; Mioduszewski, S; Mironov, C; Mischke, A; Mishra, D K; Mitchell, J; Mohanty, B; Molnar, L; Moore, C F; Morozov, D A; Munhoz, M G; Nandi, B K; Nattrass, C; Nayak, T K; Nelson, J M; Nepali, N S; Netrakanti, P K; Nogach, L V; Nurushev, S B; Odyniec, G; Ogawa, A; Okorokov, V; Oldenburg, M; Olson, D; Pachr, M; Pal, S K; Panebratsev, Y; Panitkin, S Y; Pavlinov, A I; Pawlak, T; Peitzmann, T; Perevoztchikov, V; Perkins, C; Peryt, W; Phatak, S C; Picha, R; Planinic, M; Pluta, J; Poljak, N; Porile, N; Porter, J; Poskanzer, A M; Potekhin, M; Potrebenikova, E; Potukuchi, B V K S; Prindle, D; Pruneau, C; Putschke, J; Rakness, G; Raniwala, R; Raniwala, S; Ray, R L; Razin, S V; Reinnarth, J; Relyea, D; Ridiger, A; Ritter, H G; Roberts, J B; Rogachevskiy, O V; Romero, J L; Rose, A; Roy, C; Ruan, L; Russcher, M J; Sahoo, R; Sakuma, T; Salur, S; Sandweiss, J; Sarsour, M; Sazhin, P S; Schambach, J; Scharenberg, R P; Schmitz, N; Seger, J; Selyuzhenkov, I; Seyboth, P; Shabetai, A; Shahaliev, E; Shao, M; Sharma, M; Shen, W Q; Shimanskiy, S S; Sichtermann, E P; Simon, F; Singaraju, R N; Smirnov, N; Snellings, R; Sood, G; Sorensen, P; Sowinski, J; Speltz, J; Spinka, H M; Srivastava, B; Stadnik, A; Stanislaus, T D S; Stock, R; Stolpovsky, A; Strikhanov, M; Stringfellow, B; Suaide, A A P; Subba, N L; Sugarbaker, E; Sumbera, M; Sun, Z; Surrow, B; Swanger, M; Symons, T J M; Szanto de Toledo, A; Tai, A; Takahashi, J; Tang, A H; Tarnowsky, T; Thein, D; Thomas, J H; Timmins, A R; Timoshenko, S; Tokarev, M; Trainor, T A; Trentalange, S; Tribble, R E; Tsai, O D; Ulery, J; Ullrich, T; Underwood, D G; Van Buren, G; van der Kolk, N; van Leeuwen, M; Vander Molen, A M; Varma, R; Vasilevski, I M; Vasiliev, A N; Vernet, R; Vigdor, S E; Viyogi, Y P; Vokal, S; Voloshin, S A; Waggoner, W T; Wang, F; Wang, G; Wang, J S; Wang, X L; Wang, Y; Watson, J W; Webb, J C; Westfall, G D; Wetzler, A; Whitten, C; Wieman, H; Wissink, S W; Witt, R; Wood, J; Wu, J; Xu, N; Xu, Q H; Xu, Z; Yepes, P; Yoo, I-K; Yurevich, V I; Zhan, W; Zhang, H; Zhang, W M; Zhang, Y; Zhang, Z P; Zhao, Y; Zhong, C; Zoulkarneev, R; Zoulkarneeva, Y; Zubarev, A N; Zuo, J X
2006-10-13
Transverse momentum spectra of pi+/-, p, and p up to 12 GeV/c at midrapidity in centrality selected Au + Au collisions at square root sNN=200 GeV are presented. In central Au + Au collisions, both pi +/- and p(p) show significant suppression with respect to binary scaling at pT approximately >4 GeV/c. Protons and antiprotons are less suppressed than pi+/-, in the range 1.5 approximately < pT approximately < 6 GeV/c. The pi-/pi+ and p/p ratios show at most a weak pT dependence and no significant centrality dependence. The p/pi ratios in central Au + Au collisions approach the values in p + p and d + Au collisions at pT approximately >5 GeV/c. The results at high pT indicate that the partonic sources of pi+/-, p, and p have similar energy loss when traversing the nuclear medium. PMID:17155321
NASA Astrophysics Data System (ADS)
Atmadja, J.; Bagtzoglou, A. C.
2001-05-01
In this paper, a comparison between the Marching-Jury Backward Beam Equation (MJBBE) and the Quasi-Reversibility (QR) methods to reconstruct conservative contaminant plume spatial distributions is presented. The MJBBE, developed by Atmadja and Bagtzoglou [2001], was used to recover contaminant spatial distributions in heterogeneous porous media, while the QR method, first applied to groundwater contamination problems by Skaggs and Kabala [1995], was modified to incorporate heterogeneity and explicitly handle the advective term of the transport equation. Spatially uncorrelated and correlated, stationary and non-stationary, heterogeneous dispersion coefficient fields were generated using the Bayesian Nearest Neighbor Method (B-NNM). Homogeneous and deterministically heterogeneous cases are also presented for comparison. In addition, contaminant plume initial data with uncertainty were also analyzed using the MJBBE and QR methods. The MJBBE is found to be robust enough to handle highly heterogeneous parameters and is able to preserve the salient features of the initial input data. On the other hand, the QR method is superior in handling cases with homogeneous parameters and with initial data that are plagued by uncertainty but it performs very poorly in cases with heterogeneous media.
ERIC Educational Resources Information Center
Wilson, William Wynne
1976-01-01
This article describes techniques which enable the user of a comparatively simple calculator to perform calculations of cube roots, nth roots, trigonometric, and inverse trigonometric functions, logarithms, and exponentials. (DT)
The inverse electroencephalography pipeline
NASA Astrophysics Data System (ADS)
Weinstein, David Michael
The inverse electroencephalography (EEG) problem is defined as determining which regions of the brain are active based on remote measurements recorded with scalp EEG electrodes. An accurate solution to this problem would benefit both fundamental neuroscience research and clinical neuroscience applications. However, constructing accurate patient-specific inverse EEG solutions requires complex modeling, simulation, and visualization algorithms, and to date only a few systems have been developed that provide such capabilities. In this dissertation, a computational system for generating and investigating patient-specific inverse EEG solutions is introduced, and the requirements for each stage of this Inverse EEG Pipeline are defined and discussed. While the requirements of many of the stages are satisfied with existing algorithms, others have motivated research into novel modeling and simulation methods. The principal technical results of this work include novel surface-based volume modeling techniques, an efficient construction for the EEG lead field, and the Open Source release of the Inverse EEG Pipeline software for use by the bioelectric field research community. In this work, the Inverse EEG Pipeline is applied to three research problems in neurology: comparing focal and distributed source imaging algorithms; separating measurements into independent activation components for multifocal epilepsy; and localizing the cortical activity that produces the P300 effect in schizophrenia.
Wang, Zhengxin; Marcus, R Kenneth
2014-07-18
Capillary-channeled polymer (C-CP) fibers have been utilized as liquid chromatography stationary phases, primarily for biomacromolecule separations on the analytical and preparative scales. The collinear packing of the eight-channeled C-CP fibers provides for very efficient flow, allowing operation at high linear velocity (u>100mm s(-1)) and low backpressure (<2000psi) in analytical-scale separations. To take advantage of these fluid transport properties, there must not be mass transfer limitations as would be imposed by having an appreciably porous phase, wherein solute diffusion limits the overall mass transport rates. To better understand the physical nano-/micro- structure of C-CP fibers, inverse size exclusion chromatography (iSEC) has been employed to determine the pore size distribution (PSD) within C-CP fibers. A diversity of test species (from metal ions to large proteins) was used as probes under non-retaining conditions to obtain a response curve reflecting the apparent partition coefficient (Kd) versus hydrodynamic radii (rm). A mean pore radius (rp) of 4.2nm with standard deviation (sp) of ±1.1nm was calculated by fitting the Kd versus rm data to model equations with a Gaussian pore size distribution, and a pore radius of 4.0±0.1nm was calculated based on a log-normal distribution. The derived mean pore radius is much smaller than traditional support materials, with the standard deviation showing a relatively uniform pore distribution. van Deemter plots were analyzed to provide practical confirmation of the structural implications. Large molecules (e.g., proteins) that are fully excluded from pores have no significant C-terms in the van Deemter plots whereas small molecules that can access the pore volumes display appreciable C-terms, as expected. Fitting of retention data to the Knox equation suggests that the columns operate with a characteristic particle diameter (dp) of ∼53μm. PMID:24877979
NASA Astrophysics Data System (ADS)
Bagtzoglou, Amvrossios C.; Atmadja, Juliana
2003-02-01
In this paper, a comparison between the marching-jury backward beam equation (MJBBE) and the quasi-reversibility (QR) methods to perform hydrologic inversion and, more specifically, to reconstruct conservative contaminant plume spatial distributions is presented. The MJBBE, developed by Atmadja and Bagtzoglou [2000, 2001a], was used to recover contaminant spatial distributions in heterogeneous porous media, while the QR method, first applied to groundwater contamination problems by Skaggs and Kabala [1995], was modified to incorporate heterogeneity and explicitly handle the advective term of the transport equation. Spatially uncorrelated and correlated, stationary and nonstationary, heterogeneous dispersion coefficient fields were generated using the Bayesian nearest neighbor method (BNNM). Homogeneous and deterministically heterogeneous cases are also presented for comparison. In addition, contaminant plume initial data with uncertainty were also analyzed using the MJBBE and QR methods. The MJBBE is found to be robust enough to handle highly heterogeneous parameters and is able to preserve the salient features of the initial input data. On the other hand, the QR method is superior in handling cases with homogeneous parameters and with initial data that are plagued by uncertainty but it performs very poorly in cases with heterogeneous media.
The inverse-square law and quantum gravity
NASA Technical Reports Server (NTRS)
Nieto, Michael Martin; Goldman, T.; Hughes, Richard J.
1989-01-01
A program is described which measures the gravitational acceleration of antiprotons. This idea was approached from a particle physics point of view. That point of view is examined starting with some history of physics over the last 200 years.
NASA Astrophysics Data System (ADS)
Piatanesi, Alessio; Romano, Fabrizio; Lorito, Stefano; Tolomei, Cristiano; Atzori, Simone
2016-04-01
On September 16, 2015 an Mw 8.3 interplate earthquake occurred offshore the Illapel region, Chile, approximately in the area of the 1943 Mw 8.1 earthquake. The epicenter is located at 71.7 °W, 31.6 °S at a depth of ~25 km. In this region the Nazca Plate is subducting under the South America Plate with a convergence rate of ˜74mm/yr. This earthquake generated a tsunami that struck the Chilean coast from ~24 °S to ~38 °S, with particularly severe damages around the area of Coquimbo city where a tide gauge recorded a maximum tsunami wave amplitude of ~4.7 m. The tsunami has been distinctly recorded by several tide gauges distributed along the Chilean coast and also by some DART buoys located in the South Pacific ocean. The inland coseismic deformation has been detected through InSAR processing of Sentinel-1 images, acquired from ascending and descending orbits. In this work we present the slip distribution of the earthquake obtained by jointly inverting the tsunami waveforms recorded by 3 DART buoys and 15 tide gauges, and the ground displacement retrieved by InSAR data. In order to honour the geometry of the subducting plate, we use a fault model that accounts for the variability of the strike and dip angles along the slipping surface composed by 20x20 km subfaults. We use the Green's function approach and a simulated annealing technique to solve the inverse problem. Synthetic checkerboard tests indicate that tsunami and InSAR data well constrain the offshore and onshore part of the slip distribution respectively, whereas the overall target slip distribution is well recovered by jointly using the two datasets. The slip distribution of the Illapel event features a main patch of slip updip of the hypocenter, extending for ~200 km along strike, ~120 km along dip and reaching the trench with a maximum slip of ~9 m; the slip direction is ~110°, pretty consistent with the relative convergence axis between the Nazca and the South America Plates. We also observe a
Jones, F. Andrew; Erickson, David L.; Bernal, Moises A.; Bermingham, Eldredge; Kress, W. John; Herre, Edward Allen; Muller-Landau, Helene C.; Turner, Benjamin L.
2011-01-01
Background Plants interact with each other, nutrients, and microbial communities in soils through extensive root networks. Understanding these below ground interactions has been difficult in natural systems, particularly those with high plant species diversity where morphological identification of fine roots is difficult. We combine DNA-based root identification with a DNA barcode database and above ground stem locations in a floristically diverse lowland tropical wet forest on Barro Colorado Island, Panama, where all trees and lianas >1 cm diameter have been mapped to investigate richness patterns below ground and model rooting distributions. Methodology/Principal Findings DNA barcode loci, particularly the cpDNA locus trnH-psba, can be used to identify fine and small coarse roots to species. We recovered 33 species of roots from 117 fragments sequenced from 12 soil cores. Despite limited sampling, we recovered a high proportion of the known species in the focal hectare, representing approximately 14% of the measured woody plant richness. This high value is emphasized by the fact that we would need to sample on average 13 m2 at the seedling layer and 45 m2 for woody plants >1 cm diameter to obtain the same number of species above ground. Results from inverse models parameterized with the locations and sizes of adults and the species identifications of roots and sampling locations indicates a high potential for distal underground interactions among plants. Conclusions DNA barcoding techniques coupled with modeling approaches should be broadly applicable to studying root distributions in any mapped vegetation plot. We discuss the implications of our results and outline how second-generation sequencing technology and environmental sampling can be combined to increase our understanding of how root distributions influence the potential for plant interactions in natural ecosystems. PMID:21949723
Eckert-Gallup, Aubrey C.; Sallaberry, Cédric J.; Dallman, Ann R.; Neary, Vincent S.
2016-01-06
Environmental contours describing extreme sea states are generated as the input for numerical or physical model simulations as a part of the standard current practice for designing marine structures to survive extreme sea states. These environmental contours are characterized by combinations of significant wave height (Hs) and either energy period (Te) or peak period (Tp) values calculated for a given recurrence interval using a set of data based on hindcast simulations or buoy observations over a sufficient period of record. The use of the inverse first-order reliability method (I-FORM) is a standard design practice for generating environmental contours. This papermore » develops enhanced methodologies for data analysis prior to the application of the I-FORM, including the use of principal component analysis (PCA) to create an uncorrelated representation of the variables under consideration as well as new distribution and parameter fitting techniques. As a result, these modifications better represent the measured data and, therefore, should contribute to the development of more realistic representations of environmental contours of extreme sea states for determining design loads for marine structures.« less
NASA Astrophysics Data System (ADS)
Laminack, William; Gole, James
2015-12-01
A unique MEMS/NEMS approach is presented for the modeling of a detection platform for mixed gas interactions. Mixed gas analytes interact with nanostructured decorating metal oxide island sites supported on a microporous silicon substrate. The Inverse Hard/Soft acid/base (IHSAB) concept is used to assess a diversity of conductometric responses for mixed gas interactions as a function of these nanostructured metal oxides. The analyte conductometric responses are well represented using a combination diffusion/absorption-based model for multi-gas interactions where a newly developed response absorption isotherm, based on the Fermi distribution function is applied. A further coupling of this model with the IHSAB concept describes the considerations in modeling of multi-gas mixed analyte-interface, and analyte-analyte interactions. Taking into account the molecular electronic interaction of both the analytes with each other and an extrinsic semiconductor interface we demonstrate how the presence of one gas can enhance or diminish the reversible interaction of a second gas with the extrinsic semiconductor interface. These concepts demonstrate important considerations in the array-based formats for multi-gas sensing and its applications.
NASA Astrophysics Data System (ADS)
Sergienko, Olga
2013-04-01
Since Doug MacAyeal's pioneering studies of the ice-stream basal traction optimizations by control methods, inversions for unknown parameters (e.g., basal traction, accumulation patterns, etc) have become a hallmark of the present-day ice-sheet modeling. The common feature of such inversion exercises is a direct relationship between optimized parameters and observations used in the optimization procedure. For instance, in the standard optimization for basal traction by the control method, ice-stream surface velocities constitute the control data. The optimized basal traction parameters explicitly appear in the momentum equations for the ice-stream velocities (compared to the control data). The inversion for basal traction is carried out by minimization of the cost (or objective, misfit) function that includes the momentum equations facilitated by the Lagrange multipliers. Here, we build upon this idea, and demonstrate how to optimize for parameters indirectly related to observed data using a suite of nested constraints (like Russian dolls) with additional sets of Lagrange multipliers in the cost function. This method opens the opportunity to use data from a variety of sources and types (e.g., velocities, radar layers, surface elevation changes, etc.) in the same optimization process.
ERIC Educational Resources Information Center
Smith, Scott G.
1993-01-01
A Reuleaux triangle is constructed by drawing an arc connecting each pair of vertices of an equilateral triangle with radius equal to the side of the triangle. Investigates the application of drilling a square hole using a drill bit in the shape of a Reuleaux triangle. (MDH)
ERIC Educational Resources Information Center
Schulman, Steven M.
2014-01-01
In this article the author describes a problem posed to his class, "How many squares are there on a checkerboard?" The problem is deliberately vague so that the teacher can get the students to begin asking questions. The first goal is to come to an agreement about what the problem means (Identify the problem). The second goal is to get…
Least-squares RTM with L1 norm regularisation
NASA Astrophysics Data System (ADS)
Wu, Di; Yao, Gang; Cao, Jingjie; Wang, Yanghua
2016-10-01
Reverse time migration (RTM), for imaging complex Earth models, is a reversal procedure of the forward modelling of seismic wavefields, and hence can be formulated as an inverse problem. The least-squares RTM method attempts to minimise the difference between the observed field data and the synthetic data generated by the migration image. It can reduce the artefacts in the images of a conventional RTM which uses an adjoint operator, instead of an inverse operator, for the migration. However, as the least-squares inversion provides an average solution with minimal variation, the resolution of the reflectivity image is compromised. This paper presents the least-squares RTM method with a model constraint defined by an L1-norm of the reflectivity image. For solving the least-squares RTM with L1 norm regularisation, the inversion is reformulated as a ‘basis pursuit de-noise (BPDN)’ problem, and is solved directly using an algorithm called ‘spectral projected gradient for L1 minimisation (SPGL1)’. Three numerical examples demonstrate the effectiveness of the method which can mitigate artefacts and produce clean images with significantly higher resolution than the least-squares RTM without such a constraint.
Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks
NASA Astrophysics Data System (ADS)
Jiang, Fei-Bo; Dai, Qian-Wei; Dong, Li
2016-06-01
Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.
Hybrid least squares multivariate spectral analysis methods
Haaland, David M.
2002-01-01
A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following estimation or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The "hybrid" method herein means a combination of an initial classical least squares analysis calibration step with subsequent analysis by an inverse multivariate analysis method. A "spectral shape" herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The "shape" can be continuous, discontinuous, or even discrete points illustrative of the particular effect.
A New Approach for Inversion of Large Random Matrices in Massive MIMO Systems
Anjum, Muhammad Ali Raza; Ahmed, Muhammad Mansoor
2014-01-01
We report a novel approach for inversion of large random matrices in massive Multiple-Input Multiple Output (MIMO) systems. It is based on the concept of inverse vectors in which an inverse vector is defined for each column of the principal matrix. Such an inverse vector has to satisfy two constraints. Firstly, it has to be in the null-space of all the remaining columns. We call it the null-space problem. Secondly, it has to form a projection of value equal to one in the direction of selected column. We term it as the normalization problem. The process essentially decomposes the inversion problem and distributes it over columns. Each column can be thought of as a node in the network or a particle in a swarm seeking its own solution, the inverse vector, which lightens the computational load on it. Another benefit of this approach is its applicability to all three cases pertaining to a linear system: the fully-determined, the over-determined, and the under-determined case. It eliminates the need of forming the generalized inverse for the last two cases by providing a new way to solve the least squares problem and the Moore and Penrose's pseudoinverse problem. The approach makes no assumption regarding the size, structure or sparsity of the matrix. This makes it fully applicable to much in vogue large random matrices arising in massive MIMO systems. Also, the null-space problem opens the door for a plethora of methods available in literature for null-space computation to enter the realm of matrix inversion. There is even a flexibility of finding an exact or approximate inverse depending on the null-space method employed. We employ the Householder's null-space method for exact solution and present a complete exposition of the new approach. A detailed comparison with well-established matrix inversion methods in literature is also given. PMID:24733148
A new approach for inversion of large random matrices in massive MIMO systems.
Anjum, Muhammad Ali Raza; Ahmed, Muhammad Mansoor
2014-01-01
We report a novel approach for inversion of large random matrices in massive Multiple-Input Multiple Output (MIMO) systems. It is based on the concept of inverse vectors in which an inverse vector is defined for each column of the principal matrix. Such an inverse vector has to satisfy two constraints. Firstly, it has to be in the null-space of all the remaining columns. We call it the null-space problem. Secondly, it has to form a projection of value equal to one in the direction of selected column. We term it as the normalization problem. The process essentially decomposes the inversion problem and distributes it over columns. Each column can be thought of as a node in the network or a particle in a swarm seeking its own solution, the inverse vector, which lightens the computational load on it. Another benefit of this approach is its applicability to all three cases pertaining to a linear system: the fully-determined, the over-determined, and the under-determined case. It eliminates the need of forming the generalized inverse for the last two cases by providing a new way to solve the least squares problem and the Moore and Penrose's pseudoinverse problem. The approach makes no assumption regarding the size, structure or sparsity of the matrix. This makes it fully applicable to much in vogue large random matrices arising in massive MIMO systems. Also, the null-space problem opens the door for a plethora of methods available in literature for null-space computation to enter the realm of matrix inversion. There is even a flexibility of finding an exact or approximate inverse depending on the null-space method employed. We employ the Householder's null-space method for exact solution and present a complete exposition of the new approach. A detailed comparison with well-established matrix inversion methods in literature is also given.
Dory, R.A.; Uckan, N.A.; Ard, W.B.; Batchelor, D.B.; Berry, L.A.; Bryan, W.E.; Dandl, R.A.; Guest, G.E.; Haste, G.R.; Hastings, D.E.
1986-10-01
The ELMO Bumpy Square (EBS) concept consists of four straight magnetic mirror arrays linked by four high-field corner coils. Extensive calculations show that this configuration offers major improvements over the ELMO Bumpy Torus (EBT) in particle confinement, heating, transport, ring production, and stability. The components of the EBT device at Oak Ridge National Laboratory can be reconfigured into a square arrangement having straight sides composed of EBT coils, with new microwave cavities and high-field corners designed and built for this application. The elimination of neoclassical convection, identified as the dominant mechanism for the limited confinement in EBT, will give the EBS device substantially improved confinement and the flexibility to explore the concepts that produce this improvement. The primary goals of the EBS program are twofold: first, to improve the physics of confinement in toroidal systems by developing the concepts of plasma stabilization using the effects of energetic electrons and confinement optimization using magnetic field shaping and electrostatic potential control to limit particle drift, and second, to develop bumpy toroid devices as attractive candidates for fusion reactors. This report presents a brief review of the physics analyses that support the EBS concept, discussions of the design and expected performance of the EBS device, a description of the EBS experimental program, and a review of the reactor potential of bumpy toroid configurations. Detailed information is presented in the appendices.
The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions
NASA Astrophysics Data System (ADS)
Loaiciga, Hugo A.; MariñO, Miguel A.
1987-01-01
The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.
Fouka, M.; Ouichaoui, S. E-mail: souichaoui@usthb.dz
2011-08-20
We have calculated the inverse Compton (IC) integrated spectral power within the Thomson limit for a monoenergetic isotropic photon field upscattered off highly relativistic electrons assuming an isotropic power-law distribution of the latter, N({gamma}) = C{gamma}{sup -p}, with Lorentz parameter values {gamma}{sub 1} < {gamma} < {gamma}{sub 2}. Our interest was essentially focused on the case of a finite energy range (finite {gamma}{sub 2}) possibly having realistic applications in high-energy astrophysical sites, mainly relativistic shock regions. To this end, we have defined and derived a dimensionless parametric function, F{sub p} (z{sub 1}, {eta}), with variables z{sub 1} = {epsilon}{sub 1}/4{gamma}{sup 2}{sub 1}{epsilon} and {eta} = {gamma}{sub 2}/{gamma}{sub 1}. This result was used to derive the IC-integrated spectral power for an upscattered blackbody (BB) photon field using a dimensionless parametric function, W{sub p} ({xi}, {eta}), with variable {xi} = {epsilon}{sub 1}/4{gamma}{sup 2}{sub 1} kT. Asymptotic forms of this function have been derived for three energy ranges, i.e., {xi} << 1, 1 << {xi} << {eta}{sup 2}, and {xi} >> {eta}{sup 2}. Then, a characteristic value, {eta}{sub c}(p, {epsilon}) with {epsilon} << 1, of parameter {eta} was defined such that the middle range asymptotic form of W{sub p} ({xi}, {eta}) could be valid and good when {eta} {approx}> {eta}{sub c}(p, {epsilon}), by deriving an approximate expression of this particular value for {epsilon} = 10{sup -3}. The resulting spectra featured by a high-energy cutoff in the case of low values of the ratio {eta} can be discussed at least for a population of short gamma-ray bursts (GRBs), those best described by the cutoff power-law model with a low-energy spectral index, {alpha} {approx} 0. Furthermore, it is suggested that for GRB spectra with {alpha} < -1/2 pertaining to the prompt emission phase, the IC is a likely emission mechanism for both monoenergetic and BB photon fields if one
View of Corto Square Road from Corto Square. Buildings No. ...
View of Corto Square Road from Corto Square. Buildings No. 27 at left, Building No. 25 at rear, and Building No. 26 at right. Parking areas on left and right, looking north - Easter Hill Village, Bordered by South Twenty-sixth Street, South Twenty-eighth Street, Hinkley Avenue, Foothill Avenue & Corto Square, Richmond, Contra Costa County, CA
NASA Astrophysics Data System (ADS)
Nath, Saurabh; Mukherjee, Anish; Chatterjee, Souvick; Ganguly, Ranjan; Sen, Swarnendu; Mukhopadhyay, Achintya; Boreyko, Jonathan
2014-11-01
We have observed that capillarity forces may cause floatation in a few non-intuitive configurations. These may be divided into 2 categories: i) floatation of heavier liquid droplets on lighter immiscible ones and ii) fully submerged floatation of lighter liquid droplets in a heavier immiscible medium. We call these counter-intuitive because of the inverse floatation configuration. For case (i) we have identified and studied in detail the several factors affecting the shape and maximum volume of the floating drop. We used water and vegetable oil combinations as test fluids and established the relation between Bond Number and maximum volume contained in a floating drop (in the order of μL). For case (ii), we injected vegetable oil drop-wise into a pool of water. The fully submerged configuration of the drop is not stable and a slight perturbation to the system causes the droplet to burst and float in partially submerged condition. Temporal variation of a characteristic length of the droplet is analyzed using MATLAB image processing. The constraint of small Bond Number establishes the assumption of lubrication regime in the thin gap. A brief theoretical formulation also shows the temporal variation of the gap thickness. Jadavpur University, Jagadis Bose Centre of Excellence, Virginia Tech.
NASA Astrophysics Data System (ADS)
Kelbert, A.; Schultz, A.; Egbert, G.
2006-12-01
We address the non-linear ill-posed inverse problem of reconstructing the global three-dimensional distribution of electrical conductivity in Earth's mantle. The authors have developed a numerical regularized least-squares inverse solution based on the non-linear conjugate gradients approach. We apply this methodology to the most current low-frequency global observatory data set by Fujii &Schultz (2002), that includes c- and d-responses. We obtain 4-8 layer models satisfying the data. We then describe the features common to all these models and discuss the resolution of our method.
Bayesian least squares deconvolution
NASA Astrophysics Data System (ADS)
Asensio Ramos, A.; Petit, P.
2015-11-01
Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Generalized conjugate gradient squared
Fokkema, D.R.; Sleijpen, G.L.G.
1994-12-31
In order to solve non-symmetric linear systems of equations, the Conjugate Gradient Squared (CGS) is a well-known and widely used iterative method. In practice the method converges fast, often twice as fast as the Bi-Conjugate Gradient method. This is what you may expect, since CGS uses the square of the BiCG polynomial. However, CGS may suffer from its erratic convergence behavior. The method may diverge or the approximate solution may be inaccurate. BiCGSTAB uses the BiCG polynomial and a product of linear factors in an attempt to smoothen the convergence. In many cases, this has proven to be very effective. Unfortunately, the convergence of BiCGSTAB may stall when a linear factor (nearly) degenerates. BiCGstab({ell}) is designed to overcome this degeneration of linear factors. It generalizes BiCGSTAB and uses both the BiCG polynomial and a product of higher order factors. Still, CGS may converge faster than BiCGSTAB or BiCGstab({ell}). So instead of using a product of linear or higher order factors, it may be worthwhile to look for other polynomials. Since the BiCG polynomial is based on a three term recursion, a natural choice would be a polynomial based on another three term recursion. Possibly, a suitable choice of recursion coefficients would result in method that converges faster or as fast as CGS, but less erratic. It turns out that an algorithm for such a method can easily be formulated. One particular choice for the recursion coefficients leads to CGS. Therefore one could call this algorithm generalized CGS. Another choice for the recursion coefficients leads to BiCGSTAB. It is therefore possible to mix linear factors and some polynomial based on a three term recursion. This way one may get the best of both worlds. The authors will report on their findings.
Latin square three dimensional gage master
Jones, Lynn L.
1982-01-01
A gage master for coordinate measuring machines has an nxn array of objects distributed in the Z coordinate utilizing the concept of a Latin square experimental design. Using analysis of variance techniques, the invention may be used to identify sources of error in machine geometry and quantify machine accuracy.
Square-Spiral Microstrip Antennas
NASA Technical Reports Server (NTRS)
Shively, David G.
1994-01-01
Square-spiral microstrip antennas for wideband reception at frequencies of several gigahertz proposed. These could be made to conform to surfaces of aircraft and other vehicles. Offers advantage of thinness. Square shapes of spirals in these spiral microstrip antennas offers advantage over curved shapes of spirals of other spiral microstrip antennas in that square shapes simplifies fabrication.
Magnetization patterns of permalloy square frames
NASA Astrophysics Data System (ADS)
Lai, Mei-Feng; Wei, Zung-Hang; Chang, Ching-Ray; Wu, J. C.; Hsieh, W. Z.; Usov, Nickolai A.; Lai, Jun-Yang; Yao, Y. D.
2003-05-01
Four different magnetization configurations of micron- and submicron-sized permalloy square frames are investigated by numerical simulations and experiments. Beside the pure conventional 90° Neel type wall with zero net magnetic pole, we also obtain numerically another high energy domain wall with positive or negative net magnetic poles in the corner. These three kinds of domain walls constitute four different patterns in square frames. We compare the magnetic pole density distributions derived from the spin configurations of simulation results with the images taken by magnetic force microscopy, and find reasonable agreement between them.
Dielectric square resonator investigated with microwave experiments.
Bittner, S; Bogomolny, E; Dietz, B; Miski-Oglu, M; Richter, A
2014-11-01
We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination of the refractive index. Measurements with different arrangements of the emitting and the receiving antennas were performed and their influence on the symmetry properties of the field distributions was investigated in detail, showing that resonances with specific symmetries can be selected purposefully. In addition, the length spectrum deduced from the measured resonance spectra and the trace formula for the dielectric square resonator are discussed in the framework of the semiclassical model.
NASA Astrophysics Data System (ADS)
Terzian, Yervant; Lazio, Joseph
2006-06-01
The Square Kilometre Array (SKA) is the future centimeter- and meter-wavelength telescope with a sensitivity about 50 times higher than present instruments. Its Key Science Projects are (a) Astrobiology including planetary formation within protoplanetary disks; (b) Testing theories of gravitation using an array of pulsars to search for gravitational waves and relativistic binaries to probe the strong-field regime; (c) The origin and evolution of cosmic magnetism, both within the Galaxy and in intergalactic space, via an all-sky grid of magnetic field measurements; (d) The end of the Dark Ages, involving searches for a neutral hydrogen signature, the first supermassive black holes, and the first metal-rich systems; and (e) A hydrogen census to a redshift z greater than or equal to 1 from which to study the evolution of galaxies, dark matter, and dark energy. The SKA will operate at wavelengths from 1.2 cm to 3 m (0.1-25 GHz), providing milliarcsecond resolution at the shortest wavelengths. Its instantaneous field of view will be about 1° (20 cm wavelength), with many simultaneous beams on the sky. The Reference Design is composed of a large number of small dish antennas, building upon an original US proposal. In order to obtain these capabilities at a reasonable cost, significant engineering investments are being made in antennas, wideband feeds and receivers, and signal processing; aperture arrays (phased feeds) are also being investigated in Europe for the lower frequencies. Candidate sites are in Argentina, Australia, China, and South Africa, with a short list of acceptable sites anticipated late in 2006.
Dynamics of paramagnetic squares in uniform magnetic fields
NASA Astrophysics Data System (ADS)
Du, Di; He, Peng; Zeng, Yongchao; Biswal, Sibani Lisa
2016-11-01
The magnetic forces between paramagnetic squares cannot be calculated using a classic dipolar model because the magnetic field distribution is not uniform within square particles. Here, we present the calculation of magnetic forces and torques on paramagnetic squares in a uniform 2-D magnetic field using a Laplace's equation solver. With these calculations, we simulate the variations in equilibrium configurations as a function of number of interacting squares. For example, a single square orients with its diagonal directed to the external field while a system of multiple squares will assemble into chain-like structures with their edges directed to the external field. Unlike chains of spherical magnetic particles, that easily stagger themselves to aggregate, chains consisting of magnetic squares are unable to aggregate due to interchain repulsion.
Experimental observation of localized modes in a dielectric square resonator.
Bittner, S; Bogomolny, E; Dietz, B; Miski-Oglu, M; Richter, A
2013-12-01
We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the experimental studies of their properties are indispensable. The momentum representation of the measured field distributions shows that all resonant modes are localized on specific classical tori of the square billiard. Based on these observations a semiclassical model was developed. It shows excellent agreement with all but a single class of measured field distributions that will be treated separately.
Orthogonalizing EM: A design-based least squares algorithm
Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z. G.
2016-01-01
We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online. PMID:27499558
Teaching Tip: When a Matrix and Its Inverse Are Stochastic
ERIC Educational Resources Information Center
Ding, J.; Rhee, N. H.
2013-01-01
A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.
NASA Astrophysics Data System (ADS)
Aso, N.; Ohta, K.; Ide, S.
2014-12-01
Deformation in a small volume of earth interior is expressed by a symmetric moment tensor located on a point source. The tensor contains information of characteristic directions, source amplitude, and source types such as isotropic, double-couple, or compensated-linear-vector-dipole (CLVD). Although we often assume a double couple as the source type of an earthquake, significant non-double-couple component including isotropic component is often reported for induced earthquakes and volcanic earthquakes. For discussions on source types including double-couple and non-double-couple components, it is helpful to display them using some visual diagrams. Since the information of source type has two degrees of freedom, it can be displayed onto a two-dimensional flat plane. Although the diagram developed by Hudson et al. [1989] is popular, the trace corresponding to the mechanism combined by two mechanisms is not always a smooth line. To overcome this problem, Chapman and Leaney [2012] developed a new diagram. This diagram has an advantage that a straight line passing through the center corresponds to the mechanism obtained by a combination of an arbitrary mechanism and a double-couple [Tape and Tape, 2012], but this diagram has some difficulties in use. First, it is slightly difficult to produce the diagram because of its curved shape. Second, it is also difficult to read out the ratios among isotropic, double-couple, and CLVD components, which we want to obtain from the estimated moment tensors, because they do not appear directly on the horizontal or vertical axes. In the present study, we developed another new square diagram that overcomes the difficulties of previous diagrams. This diagram is an orthogonal system of isotropic and deviatoric axes, so it is easy to get the ratios among isotropic, double-couple, and CLVD components. Our diagram has another advantage that the probability density is obtained simply from the area within the diagram if the probability density
Non-linear Conjugate Gradient Time-Domain Controlled Inversion Source
2006-11-16
Software that simulates and inverts time-domain electromagnetic field data for subsurface electrical properties (electrical conductivity) of geological media. The software treats data produced by a step-wise source signal from either galvanic (grounded wires) or inductive (magnetic loops) sources. The inversion process is carried inductive (magnetic loops) sources. The inversion process is carried out using a non-linear conjugate gradient optimization scheme, which minimizes the misfit between field data and model data using a least squares criteria.more » The software is an upgrade from the code TEM3D ver. 2.0. The upgrade includes the following components: (1) Improved (faster)memory access during gradient computation. (2) Data parellelization scheme: Multiple transmitters (sources) can be distributed accross several banks of processors (daa-planes). Similarly, the receivers of each source are also distributed accross the corresponding data-plane. (3) Improved data-IO.« less
Non-linear Conjugate Gradient Time-Domain Controlled Inversion Source
Newman, Gregory A.; Commer, Michael
2006-11-16
Software that simulates and inverts time-domain electromagnetic field data for subsurface electrical properties (electrical conductivity) of geological media. The software treats data produced by a step-wise source signal from either galvanic (grounded wires) or inductive (magnetic loops) sources. The inversion process is carried inductive (magnetic loops) sources. The inversion process is carried out using a non-linear conjugate gradient optimization scheme, which minimizes the misfit between field data and model data using a least squares criteria. The software is an upgrade from the code TEM3D ver. 2.0. The upgrade includes the following components: (1) Improved (faster)memory access during gradient computation. (2) Data parellelization scheme: Multiple transmitters (sources) can be distributed accross several banks of processors (daa-planes). Similarly, the receivers of each source are also distributed accross the corresponding data-plane. (3) Improved data-IO.
NASA Astrophysics Data System (ADS)
Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L. R.
2013-04-01
This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.
NASA Astrophysics Data System (ADS)
Chaikovsky, A.; Dubovik, O.; Holben, B.; Bril, A.; Goloub, P.; Tanré, D.; Pappalardo, G.; Wandinger, U.; Chaikovskaya, L.; Denisov, S.; Grudo, Y.; Lopatin, A.; Karol, Y.; Lapyonok, T.; Amiridis, V.; Ansmann, A.; Apituley, A.; Allados-Arboledas, L.; Binietoglou, I.; Boselli, A.; D'Amico, G.; Freudenthaler, V.; Giles, D.; Granados-Muñoz, M. J.; Kokkalis, P.; Nicolae, D.; Oshchepkov, S.; Papayannis, A.; Perrone, M. R.; Pietruczuk, A.; Rocadenbosch, F.; Sicard, M.; Slutsker, I.; Talianu, C.; De Tomasi, F.; Tsekeri, A.; Wagner, J.; Wang, X.
2015-12-01
This paper presents a detailed description of LIRIC (LIdar-Radiometer Inversion Code) algorithm for simultaneous processing of coincident lidar and radiometric (sun photometric) observations for the retrieval of the aerosol concentration vertical profiles. As the lidar/radiometric input data we use measurements from European Aerosol Research Lidar Network (EARLINET) lidars and collocated sun-photometers of Aerosol Robotic Network (AERONET). The LIRIC data processing provides sequential inversion of the combined lidar and radiometric data by the estimations of column-integrated aerosol parameters from radiometric measurements followed by the retrieval of height-dependent concentrations of fine and coarse aerosols from lidar signals using integrated column characteristics of aerosol layer as a priori constraints. The use of polarized lidar observations allows us to discriminate between spherical and non-spherical particles of the coarse aerosol mode. The LIRIC software package was implemented and tested at a number of EARLINET stations. Intercomparison of the LIRIC-based aerosol retrievals was performed for the observations by seven EARLNET lidars in Leipzig, Germany on 25 May 2009. We found close agreement between the aerosol parameters derived from different lidars that supports high robustness of the LIRIC algorithm. The sensitivity of the retrieval results to the possible reduction of the available observation data is also discussed.
NASA Astrophysics Data System (ADS)
Chaikovsky, Anatoli; Dubovik, Oleg; Holben, Brent; Bril, Andrey; Goloub, Philippe; Tanré, Didier; Pappalardo, Gelsomina; Wandinger, Ulla; Chaikovskaya, Ludmila; Denisov, Sergey; Grudo, Jan; Lopatin, Anton; Karol, Yana; Lapyonok, Tatsiana; Amiridis, Vassilis; Ansmann, Albert; Apituley, Arnoud; Allados-Arboledas, Lucas; Binietoglou, Ioannis; Boselli, Antonella; D'Amico, Giuseppe; Freudenthaler, Volker; Giles, David; José Granados-Muñoz, María; Kokkalis, Panayotis; Nicolae, Doina; Oshchepkov, Sergey; Papayannis, Alex; Perrone, Maria Rita; Pietruczuk, Alexander; Rocadenbosch, Francesc; Sicard, Michaël; Slutsker, Ilya; Talianu, Camelia; De Tomasi, Ferdinando; Tsekeri, Alexandra; Wagner, Janet; Wang, Xuan
2016-03-01
This paper presents a detailed description of LIRIC (LIdar-Radiometer Inversion Code) algorithm for simultaneous processing of coincident lidar and radiometric (sun photometric) observations for the retrieval of the aerosol concentration vertical profiles. As the lidar/radiometric input data we use measurements from European Aerosol Research Lidar Network (EARLINET) lidars and collocated sun-photometers of Aerosol Robotic Network (AERONET). The LIRIC data processing provides sequential inversion of the combined lidar and radiometric data. The algorithm starts with the estimations of column-integrated aerosol parameters from radiometric measurements followed by the retrieval of height dependent concentrations of fine and coarse aerosols from lidar signals using integrated column characteristics of aerosol layer as a priori constraints. The use of polarized lidar observations allows us to discriminate between spherical and non-spherical particles of the coarse aerosol mode.The LIRIC software package was implemented and tested at a number of EARLINET stations. Intercomparison of the LIRIC-based aerosol retrievals was performed for the observations by seven EARLINET lidars in Leipzig, Germany on 25 May 2009. We found close agreement between the aerosol parameters derived from different lidars that supports high robustness of the LIRIC algorithm. The sensitivity of the retrieval results to the possible reduction of the available observation data is also discussed.
ERIC Educational Resources Information Center
Emanouilidis, Emanuel
2008-01-01
Latin squares were first introduced and studied by the famous mathematician Leonhard Euler in the 1700s. Through the years, Latin squares have been used in areas such as statistics, graph theory, coding theory, the generation of random numbers as well as in the design and analysis of experiments. Recently, with the international popularity of…
From Square Dance to Mathematics
ERIC Educational Resources Information Center
Bremer, Zoe
2010-01-01
In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…
Fixed memory least squares filtering
NASA Technical Reports Server (NTRS)
Bierman, G. J.
1975-01-01
Buxbaum has reported on three algorithms for computing least squares estimates that are based on fixed amounts of data. In this correspondence, the filter is arranged as a point-deleting Kalman filter concatenated with the standard point-inclusion Kalman filter. The resulting algorithm is couched in a square root framework for greater numerical stability, and special attention is given to computer implementation.
Annibaldi, A; Truzzi, C; Illuminati, S; Bassotti, E; Scarponi, G
2007-02-01
Eight PM10 aerosol samples were collected in the vicinity of the "Mario Zucchelli" Italian Antarctic Station (formerly Terra Nova Bay Station) during the 2000-2001 austral summer using a high-volume sampler and precleaned cellulose filters. The aerosol mass was determined by differential weighing of filters carried out in a clean chemistry laboratory under controlled temperature and humidity. A two-step sequential extraction procedure was used to separate the water-soluble and the insoluble (dilute-HCl-extractable) fractions. Cd, Pb and Cu were determined in the two fractions using an ultrasensitive square wave anodic stripping voltammetric (SWASV) procedure set up for and applied to aerosol samples for the first time. Total extractable metals showed maxima at midsummer for Cd and Pb and a less clear trend for Cu. In particular, particulate metal concentrations ranged as follows: Cd 0.84-9.2 microg g(-1) (average 4.7 microg g(-1)), Pb 13.2-81 microg g(-1) (average 33 microg g(-1)), Cu 126-628 microg g(-1) (average 378 microg g(-1)). In terms of atmospheric concentration, the values were: Cd 0.55-6.3 pg m(-3) (average 3.4 pg m(-3)), Pb 8.7-48 pg m(-3) (average 24 pg m(-3)), Cu 75-365 pg m(-3) (average 266 pg m(-3)). At the beginning of the season the three metals appear widely distributed in the insoluble (HCl-extractable) fraction (higher proportions for Cd and Pb, 90-100%, and lower for Cu, 70-90%) with maxima in the second half of December. The soluble fraction then increases, and at the end of the season Cd and Pb are approximately equidistributed between the two fractions, while for Cu the soluble fraction reaches its maximum level of 36%. Practically negligible contributions are estimated for crustal and sea-spray sources. Low but significant volcanic contributions are estimated for Cd and Pb (approximately 10% and approximately 5%, respectively), while there is an evident although not quantified marine biogenic source, at least for Cd. The estimated natural
An exact inverse method for subsonic flows
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1988-01-01
A new inverse method for the aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arclength of the still unknown body. It is shown that this inverse problem is mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary.
Hybrid least squares multivariate spectral analysis methods
Haaland, David M.
2004-03-23
A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following prediction or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The hybrid method herein means a combination of an initial calibration step with subsequent analysis by an inverse multivariate analysis method. A spectral shape herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The shape can be continuous, discontinuous, or even discrete points illustrative of the particular effect.
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices.
Piñeros, William D; Baldea, Michael; Truskett, Thomas M
2016-08-01
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability. PMID:27497576
NASA Astrophysics Data System (ADS)
Luo, Wei-Ping; Li, Hong-Qi; Shi, Ning
2016-06-01
At the early stages of deep-water oil exploration and development, fewer and further apart wells are drilled than in onshore oilfields. Supervised least squares support vector machine algorithms are used to predict the reservoir parameters but the prediction accuracy is low. We combined the least squares support vector machine (LSSVM) algorithm with semi-supervised learning and established a semi-supervised regression model, which we call the semi-supervised least squares support vector machine (SLSSVM) model. The iterative matrix inversion is also introduced to improve the training ability and training time of the model. We use the UCI data to test the generalization of a semi-supervised and a supervised LSSVM models. The test results suggest that the generalization performance of the LSSVM model greatly improves and with decreasing training samples the generalization performance is better. Moreover, for small-sample models, the SLSSVM method has higher precision than the semi-supervised K-nearest neighbor (SKNN) method. The new semisupervised LSSVM algorithm was used to predict the distribution of porosity and sandstone in the Jingzhou study area.
Analytic solutions of inverse heat conduction problems
NASA Astrophysics Data System (ADS)
Al-Najem, N. M.
A direct analytic approach is systematically developed for solving inverse heat conduction problems in multi-dimensional finite regions. The inverse problems involve the determination of the surface conditions from the knowledge of the time variation of the temperature at an interior point in the region. In the present approach, the unknown surface temperature is represented by a polynominal in time and a splitting-up procedure is employed to develop a rapidly converging inverse solution. The least square technique is then utilized to estimate the unknown parameters associated with the solution. The method is developed first for the analysis of one-dimensional cases, and then it is generalized to handle two- and three-dimensional situations. It provides an efficient, stable and systematic approach for inverse heat condition problems. The stability and accuracy of the current method of analysis are demonstrated by several numerical examples chosen to provide a very strict test.
Inverse sequential procedures for the monitoring of time series
NASA Technical Reports Server (NTRS)
Radok, Uwe; Brown, Timothy
1993-01-01
Climate changes traditionally have been detected from long series of observations and long after they happened. The 'inverse sequential' monitoring procedure is designed to detect changes as soon as they occur. Frequency distribution parameters are estimated both from the most recent existing set of observations and from the same set augmented by 1,2,...j new observations. Individual-value probability products ('likelihoods') are then calculated which yield probabilities for erroneously accepting the existing parameter(s) as valid for the augmented data set and vice versa. A parameter change is signaled when these probabilities (or a more convenient and robust compound 'no change' probability) show a progressive decrease. New parameters are then estimated from the new observations alone to restart the procedure. The detailed algebra is developed and tested for Gaussian means and variances, Poisson and chi-square means, and linear or exponential trends; a comprehensive and interactive Fortran program is provided in the appendix.
Normal versus Noncentral Chi-Square Asymptotics of Misspecified Models
ERIC Educational Resources Information Center
Chun, So Yeon; Shapiro, Alexander
2009-01-01
The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…
An inversion method for cometary atmospheres
NASA Astrophysics Data System (ADS)
Hubert, B.; Opitom, C.; Hutsemékers, D.; Jehin, E.; Munhoven, G.; Manfroid, J.; Bisikalo, D. V.; Shematovich, V. I.
2016-10-01
Remote observation of cometary atmospheres produces a measurement of the cometary emissions integrated along the line of sight. This integration is the so-called Abel transform of the local emission rate. The observation is generally interpreted under the hypothesis of spherical symmetry of the coma. Under that hypothesis, the Abel transform can be inverted. We derive a numerical inversion method adapted to cometary atmospheres using both analytical results and least squares fitting techniques. This method, derived under the usual hypothesis of spherical symmetry, allows us to retrieve the radial distribution of the emission rate of any unabsorbed emission, which is the fundamental, physically meaningful quantity governing the observation. A Tikhonov regularization technique is also applied to reduce the possibly deleterious effects of the noise present in the observation and to warrant that the problem remains well posed. Standard error propagation techniques are included in order to estimate the uncertainties affecting the retrieved emission rate. Several theoretical tests of the inversion techniques are carried out to show its validity and robustness. In particular, we show that the Abel inversion of real data is only weakly sensitive to an offset applied to the input flux, which implies that the method, applied to the study of a cometary atmosphere, is only weakly dependent on uncertainties on the sky background which has to be subtracted from the raw observations of the coma. We apply the method to observations of three different comets observed using the TRAPPIST telescope: 103P/ Hartley 2, F6/ Lemmon and A1/ Siding Spring. We show that the method retrieves realistic emission rates, and that characteristic lengths and production rates can be derived from the emission rate for both CN and C2 molecules. We show that the retrieved characteristic lengths can differ from those obtained from a direct least squares fitting over the observed flux of radiation, and
Counting Triangles to Sum Squares
ERIC Educational Resources Information Center
DeMaio, Joe
2012-01-01
Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.
3D Electromagnetic inversion using conjugate gradients
Newman, G.A.; Alumbaugh, D.L.
1997-06-01
In large scale 3D EM inverse problems it may not be possible to directly invert a full least-squares system matrix involving model sensitivity elements. Thus iterative methods must be employed. For the inverse problem, we favor either a linear or non-linear (NL) CG scheme, depending on the application. In a NL CG scheme, the gradient of the objective function is required at each relaxation step along with a univariate line search needed to determine the optimum model update. Solution examples based on both approaches will be presented.
AKLSQF - LEAST SQUARES CURVE FITTING
NASA Technical Reports Server (NTRS)
Kantak, A. V.
1994-01-01
The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.
Inverse anticipating chaos synchronization.
Shahverdiev, E M; Sivaprakasam, S; Shore, K A
2002-07-01
We derive conditions for achieving inverse anticipating synchronization where a driven time-delay chaotic system synchronizes to the inverse future state of the driver. The significance of inverse anticipating chaos in delineating synchronization regimes in time-delay systems is elucidated. The concept is extended to cascaded time-delay systems.
Hartzell, S.; Liu, P.; Mendoza, C.; Ji, C.; Larson, K.M.
2007-01-01
The 2004 Parkfield, California, earthquake is used to investigate stability and uncertainty aspects of the finite-fault slip inversion problem with different a priori model assumptions. We utilize records from 54 strong ground motion stations and 13 continuous, 1-Hz sampled, geodetic instruments. Two inversion procedures are compared: a linear least-squares subfault-based methodology and a nonlinear global search algorithm. These two methods encompass a wide range of the different approaches that have been used to solve the finite-fault slip inversion problem. For the Parkfield earthquake and the inversion of velocity or displacement waveforms, near-surface related site response (top 100 m, frequencies above 1 Hz) is shown to not significantly affect the solution. Results are also insensitive to selection of slip rate functions with similar duration and to subfault size if proper stabilizing constraints are used. The linear and nonlinear formulations yield consistent results when the same limitations in model parameters are in place and the same inversion norm is used. However, the solution is sensitive to the choice of inversion norm, the bounds on model parameters, such as rake and rupture velocity, and the size of the model fault plane. The geodetic data set for Parkfield gives a slip distribution different from that of the strong-motion data, which may be due to the spatial limitation of the geodetic stations and the bandlimited nature of the strong-motion data. Cross validation and the bootstrap method are used to set limits on the upper bound for rupture velocity and to derive mean slip models and standard deviations in model parameters. This analysis shows that slip on the northwestern half of the Parkfield rupture plane from the inversion of strong-motion data is model dependent and has a greater uncertainty than slip near the hypocenter.
NASA Astrophysics Data System (ADS)
Chugunov, Svyatoslav; Li, Changying
2015-09-01
Parallel implementation of two numerical tools popular in optical studies of biological materials-Inverse Adding-Doubling (IAD) program and Monte Carlo Multi-Layered (MCML) program-was developed and tested in this study. The implementation was based on Message Passing Interface (MPI) and standard C-language. Parallel versions of IAD and MCML programs were compared to their sequential counterparts in validation and performance tests. Additionally, the portability of the programs was tested using a local high performance computing (HPC) cluster, Penguin-On-Demand HPC cluster, and Amazon EC2 cluster. Parallel IAD was tested with up to 150 parallel cores using 1223 input datasets. It demonstrated linear scalability and the speedup was proportional to the number of parallel cores (up to 150x). Parallel MCML was tested with up to 1001 parallel cores using problem sizes of 104-109 photon packets. It demonstrated classical performance curves featuring communication overhead and performance saturation point. Optimal performance curve was derived for parallel MCML as a function of problem size. Typical speedup achieved for parallel MCML (up to 326x) demonstrated linear increase with problem size. Precision of MCML results was estimated in a series of tests - problem size of 106 photon packets was found optimal for calculations of total optical response and 108 photon packets for spatially-resolved results. The presented parallel versions of MCML and IAD programs are portable on multiple computing platforms. The parallel programs could significantly speed up the simulation for scientists and be utilized to their full potential in computing systems that are readily available without additional costs.
Constrained resistivity inversion using seismic data
NASA Astrophysics Data System (ADS)
Saunders, J. H.; Herwanger, J. V.; Pain, C. C.; Worthington, M. H.; de Oliveira, C. R. E.
2005-03-01
In this paper we describe and apply a method for constraining structure in anisotropic electrical resistivity inversion. Structural constraints are routinely used to achieve improved model inversion. Here, a second-order (curvature-based) regularization tensor (model covariance) is used to build structure in the model. This structure could be obtained from other imaging methods such as seismic tomography, core samples or otherwise known structure in the model. Our method allows the incorporation of existing geophysical data into the inversion, in a general form that does not rely on any one-to-one correlation between data sets or material properties. Ambiguities in the resistivity distribution from electrical inversion, and in particular anisotropic inversion, may be reduced with this approach. To demonstrate the approach we invert a synthetic data set, showing the regularization tensor explicitly in different locations. We then apply the method to field data where we have some knowledge of the subsurface from seismic imaging. Our results show that it is possible to achieve a high level of convergence while using spatially varying structural constraints. Common problems associated with resistivity inversion such as source/receiver effects and false imaging of strongly resistive or conductive zones may also be reduced. As part of the inversion method we show how the magnitude of the constraints in the form of penalty parameters appropriate to an inversion may be estimated, reducing the computational expense of resistivity inversion.
Dibrov, Sergey M.; McLean, Jaime; Parsons, Jerod; Hermann, Thomas
2011-12-22
The three-dimensional structures of noncoding RNA molecules reveal recurring architectural motifs that have been exploited for the design of artificial RNA nanomaterials. Programmed assembly of RNA nanoobjects from autonomously folding tetraloop-receptor complexes as well as junction motifs has been achieved previously through sequence-directed hybridization of complex sets of long oligonucleotides. Due to size and complexity, structural characterization of artificial RNA nanoobjects has been limited to low-resolution microscopy studies. Here we present the design, construction, and crystal structure determination at 2.2 {angstrom} of the smallest yet square-shaped nanoobject made entirely of double-stranded RNA. The RNA square is comprised of 100 residues and self-assembles from four copies each of two oligonucleotides of 10 and 15 bases length. Despite the high symmetry on the level of secondary structure, the three-dimensional architecture of the square is asymmetric, with all four corners adopting distinct folding patterns. We demonstrate the programmed self-assembly of RNA squares from complex mixtures of corner units and establish a concept to exploit the RNA square as a combinatorial nanoscale platform.
Inversions for axisymmetric galactic disks
NASA Astrophysics Data System (ADS)
Hiotelis, N.; Patsis, P. A.
1993-08-01
We use two models for the distribution function to solve an inverse problem for axisymmetric disks. These systems may be considered - under certain assumptions - as galactic disks. In some cases the solutions of the resulting integral equations are simple, which allows the determination of the kinematic properties of self-consistent models for these systems. These properties for then = 1 Toomre disk are presented in this study.
On the edge of an inverse cascade.
Seshasayanan, Kannabiran; Benavides, Santiago Jose; Alexakis, Alexandros
2014-11-01
We demonstrate that systems with a parameter-controlled inverse cascade can exhibit critical behavior for which at the critical value of the control parameter the inverse cascade stops. In the vicinity of such a critical point, standard phenomenological estimates for the energy balance will fail since the energy flux towards large length scales becomes zero. We demonstrate this using the computationally tractable model of two-dimensional (2D) magnetohydrodynamics in a periodic box. In the absence of any external magnetic forcing, the system reduces to hydrodynamic fluid turbulence with an inverse energy cascade. In the presence of strong magnetic forcing, the system behaves as 2D magnetohydrodynamic turbulence with forward energy cascade. As the amplitude of the magnetic forcing is varied, a critical value is met for which the energy flux towards the large scales becomes zero. Close to this point, the energy flux scales as a power law with the departure from the critical point and the normalized amplitude of the fluctuations diverges. Similar behavior is observed for the flux of the square vector potential for which no inverse flux is observed for weak magnetic forcing, while a finite inverse flux is observed for magnetic forcing above the critical point. We conjecture that this behavior is generic for systems of variable inverse cascade. PMID:25493730
A Solution to Weighted Sums of Squares as a Square
ERIC Educational Resources Information Center
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
For n = 1, 2, ... , we give a solution (x[subscript 1], ... , x[subscript n], N) to the Diophantine integer equation [image omitted]. Our solution has N of the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given n and given integer weights m[subscript…
Error handling strategies in multiphase inverse modeling
Finsterle, S.; Zhang, Y.
2010-12-01
Parameter estimation by inverse modeling involves the repeated evaluation of a function of residuals. These residuals represent both errors in the model and errors in the data. In practical applications of inverse modeling of multiphase flow and transport, the error structure of the final residuals often significantly deviates from the statistical assumptions that underlie standard maximum likelihood estimation using the least-squares method. Large random or systematic errors are likely to lead to convergence problems, biased parameter estimates, misleading uncertainty measures, or poor predictive capabilities of the calibrated model. The multiphase inverse modeling code iTOUGH2 supports strategies that identify and mitigate the impact of systematic or non-normal error structures. We discuss these approaches and provide an overview of the error handling features implemented in iTOUGH2.
A new strategy for helioseismic inversions
NASA Astrophysics Data System (ADS)
Eff-Darwich, A.; Perez Hernandez, F.
1997-10-01
Helioseismic inversion techniques have been revealed as powerful tools for inferring the internal structure and dynamics of the Sun. One of the most popular techniques is Regularized Least Squares. When it is used, it is necessary to define an inversion mesh and a penalty function, without an a priori knowledge of the behaviour of the solution. In addition, this penalty function is weighted by a trade-off parameter that must be fixed in order to obtain the solution. We present here a new technique, developed in order to find the optimal mesh and smoothing function by means of a deep analysis of the basis functions of the inversion problem. We have found that the method is suitable in particular for obtaining the sound speed and density profiles simultaneously, without any reference to the equation of state.
A cosmological redshift-distance square law
NASA Technical Reports Server (NTRS)
Soneira, R. M.
1979-01-01
This paper directly examines the claims of Segal (1976) that the (m,z) Hubble diagram is fitted best by a square law z = Kr-squared rather than by the traditional Hubble law z = Hr in the low-redshift range, z no more than about 0.01, corresponding to galaxies brighter than 14th mag. Segal attempts to fit a distance relation to the (m,z) scatter diagram in which each individual galaxy is plotted. The exact relation between the mean redshift for all galaxies in a small magnitude interval and the apparent magnitude is calculated. This relation is independent of luminosity function and peculiar velocity distribution about the general expansion, and is not affected by sample incompleteness as a function of apparent magnitude or the clustering of galaxies in the sample. Segal's method is affected by all of these and requires a highly sophisticated statistical analysis to deal with the non-Gaussian pointwise scatter. The present analysis favors the Hubble law and conclusively rules out the square law for the small redshift region.
Nonlinear mode conversion in monodomain magnetic squares
NASA Astrophysics Data System (ADS)
Kostylev, Mikhail; Demidov, Vladislav E.; Hansen, Ulf-Hendrik; Demokritov, Sergej O.
2007-12-01
Modifications of the spatial distributions of dynamic magnetization corresponding to spin-wave eigenmodes of magnetic squares subjected to a strong microwave excitation field have been studied experimentally and theoretically. We show that an increase of the excitation power leads to nonlinear generation of long-wavelength spatial harmonics caused by the nonlinear cross coupling between the eigenmodes. The analysis of the experimental data shows that this process is mainly governed by the action of the nonlinear spin-wave damping. This conclusion is further supported by numerical calculations based on the complex Ginzburg-Landau equation, phenomenologically taking into account the nonlinear damping.
Inversion strategies for visco-acoustic waveform inversion
NASA Astrophysics Data System (ADS)
Kamei, R.; Pratt, R. G.
2013-08-01
Visco-acoustic waveform inversion can potentially yield quantitative images of the distribution of both velocity and the attenuation parameters from seismic data. Intrinsic P-wave attenuation has been of particular interest, but has also proven challenging. Frequency-domain inversion allows attenuation and velocity relations to be easily incorporated, and allows a natural multiscale approach. The Laplace-Fourier approach extends this to allow the natural damping of waveforms to enhance early arrivals. Nevertheless, simultaneous inversion of velocity and attenuation leads to significant `cross-talk' between the resulting images, reflecting a lack of parameter resolution and indicating the need for pre-conditioning and regularization of the inverse problem. We analyse the cross-talk issue by partitioning the inversion parameters into two classes; the velocity parameter class, and the attenuation parameter class. Both parameters are defined at a reference frequency, and a dispersion relation is assumed that describes these parameters at any other frequency. We formulate the model gradients at a forward modelling frequency, and convert them to the reference frequency by employing the Jacobian of the coordinate change represented by the dispersion relation. We show that at a given modelling frequency, the Fréchet derivatives corresponding to these two parameter classes differ only by a 90° phase shift, meaning that the magnitudes of resulting model updates will be unscaled, and will not reflect the expected magnitudes in realistic (Q-1 ≪ 1) media. Due to the lack of scaling, cross-talk will be enhanced by poor subsurface illumination, by errors in kinematics, and by data noise. To solve these issues, we introduce an attenuation scaling term (the inverse of a penalty term) that is used to pre-condition the gradient by controlling the magnitudes of the updates to the attenuation parameters. Initial results from a suite of synthetic cross-hole tests using a three
Source Localization using Stochastic Approximation and Least Squares Methods
Sahyoun, Samir S.; Djouadi, Seddik M.; Qi, Hairong; Drira, Anis
2009-03-05
This paper presents two approaches to locate the source of a chemical plume; Nonlinear Least Squares and Stochastic Approximation (SA) algorithms. Concentration levels of the chemical measured by special sensors are used to locate this source. Non-linear Least Squares technique is applied at different noise levels and compared with the localization using SA. For a noise corrupted data collected from a distributed set of chemical sensors, we show that SA methods are more efficient than Least Squares method. SA methods are often better at coping with noisy input information than other search methods.
Inverse modeling of tracer experiments in FEBEX compacted Ca-bentonite
NASA Astrophysics Data System (ADS)
Samper, Javier; Dai, Zhenxue; Molinero, Jorge; García-Gutiérrez, M.; Missana, T.; Mingarro, M.
Solute transport parameters of compacted Ca-bentonite used in the FEBEX Project were derived by García-Gutiérrez et al. (2001) from through- and in-diffusion experiments using analytical solutions for their interpretation. Here we expand their work and present the numerical interpretation of diffusion and permeation experiments by solving the inverse transport problem which is formulated as the minimization of a weighted least squares criterion measuring the differences between computed and measured concentration values. The inverse problem is solved with INVERSE-CORE 2 D© , a finite element code which accounts for both dissolved and sorbed concentration data, uses either the Golden section search or Gauss-Newton-Marquardt methods for minimizing the objective function and allows the estimation of transport and retardation parameters such as diffusion coefficient, total and kinematic porosity and distribution coefficients. Diffusion and permeation experiments performed on FEBEX compacted bentonite using tritium, cesium, selenium, and strontium have been effectively interpreted by inverse modeling. Estimated parameters are within the range of reported values for these tracers in bentonites. It has been found that failing to account for the role of sinters may lead to erroneous diffusion coefficients by a factor of 1.4. Possible ways to improve the design of in-diffusion and permeation experiments have been identified. The interpretation of the tritium permeation experiment requires the use of a double-porosity model with mobile porosity of 0.14 for a dry density of 1.18 g/cm 3.
Joint inversion of high-frequency surface waves with fundamental and higher modes
Luo, Y.; Xia, J.; Liu, J.; Liu, Q.; Xu, S.
2007-01-01
Joint inversion of multimode surface waves for estimating the shear (S)-wave velocity has received much attention in recent years. In this paper, we first analyze sensitivity of phase velocities of multimodes of surface waves for a six-layer earth model, and then we invert surface-wave dispersion curves of the theoretical model and a real-world example. Sensitivity analysis shows that fundamental mode data are more sensitive to the S-wave velocities of shallow layers and are concentrated on a very narrow frequency band, while higher mode data are more sensitive to the parameters of relatively deeper layers and are distributed over a wider frequency band. These properties provide a foundation of using a multimode joint inversion to define S-wave velocities. Inversion results of both synthetic data and a real-world example demonstrate that joint inversion with the damped least-square method and the singular-value decomposition technique to invert high-frequency surface waves with fundamental and higher mode data simultaneously can effectively reduce the ambiguity and improve the accuracy of S-wave velocities. ?? 2007.
Hirata, K.; Geist, E.; Satake, K.; Tanioka, Y.; Yamaki, S.
2003-01-01
We inverted 13 tsunami waveforms recorded in Japan to estimate the slip distribution of the 1952 Tokachi-Oki earthquake (M 8.1), which occurred southeast off Hokkaido along the southern Kuril subduction zone. The previously estimated source area determined from tsunami travel times [Hatori, 1973] did not coincide with the observed aftershock distribution. Our results show that a large amount of slip occurred in the aftershock area east of Hatori's tsunami source area, suggesting that a portion of the interplate thrust near the trench was ruptured by the main shock. We also found more than 5 m of slip along the deeper part of the seismogenic interface, just below the central part of Hatori's tsunami source area. This region, which also has the largest stress drop during the main shock, had few aftershocks. Large tsunami heights on the eastern Hokkaido coast are better explained by the heterogeneous slip model than previous uniform-slip fault models. The total seismic moment is estimated to be 1.87 ?? 1021 N m, giving a moment magnitude of Mw = 8.1. The revised tsunami source area is estimated to be 25.2 ?? 103 km2, ???3 times larger than the previous tsunami source area. Out of four large earthquakes with M ??? 7 that subsequently occurred in and around the rupture area of the 1952 event, three were at the edges of regions with relatively small amount of slip. We also found that a subducted seamount near the edge of the rupture area possibly impeded slip along the plate interface.
NASA Astrophysics Data System (ADS)
Hirata, Kenji; Geist, Eric; Satake, Kenji; Tanioka, Yuichiro; Yamaki, Shigeru
2003-04-01
We inverted 13 tsunami waveforms recorded in Japan to estimate the slip distribution of the 1952 Tokachi-Oki earthquake (M 8.1), which occurred southeast off Hokkaido along the southern Kuril subduction zone. The previously estimated source area determined from tsunami travel times [, 1973] did not coincide with the observed aftershock distribution. Our results show that a large amount of slip occurred in the aftershock area east of Hatori's tsunami source area, suggesting that a portion of the interplate thrust near the trench was ruptured by the main shock. We also found more than 5 m of slip along the deeper part of the seismogenic interface, just below the central part of Hatori's tsunami source area. This region, which also has the largest stress drop during the main shock, had few aftershocks. Large tsunami heights on the eastern Hokkaido coast are better explained by the heterogeneous slip model than previous uniform-slip fault models. The total seismic moment is estimated to be 1.87 × 1021 N m, giving a moment magnitude of Mw = 8.1. The revised tsunami source area is estimated to be 25.2 × 103 km2, ˜3 times larger than the previous tsunami source area. Out of four large earthquakes with M ˜ 7 that subsequently occurred in and around the rupture area of the 1952 event, three were at the edges of regions with relatively small amount of slip. We also found that a subducted seamount near the edge of the rupture area possibly impeded slip along the plate interface.
A Higher Order Iterative Method for Computing the Drazin Inverse
Soleymani, F.; Stanimirović, Predrag S.
2013-01-01
A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747
NASA Astrophysics Data System (ADS)
Jackiewicz, Jason
2009-09-01
With the rapid advances in sophisticated solar modeling and the abundance of high-quality solar pulsation data, efficient and robust inversion techniques are crucial for seismic studies. We present some aspects of an efficient Fourier Optimally Localized Averaging (OLA) inversion method with an example applied to time-distance helioseismology.
Jackiewicz, Jason
2009-09-16
With the rapid advances in sophisticated solar modeling and the abundance of high-quality solar pulsation data, efficient and robust inversion techniques are crucial for seismic studies. We present some aspects of an efficient Fourier Optimally Localized Averaging (OLA) inversion method with an example applied to time-distance helioseismology.
ERIC Educational Resources Information Center
Bedard, Catherine; Belin, Pascal
2004-01-01
Voice is the carrier of speech but is also an ''auditory face'' rich in information on the speaker's identity and affective state. Three experiments explored the possibility of a ''voice inversion effect,'' by analogy to the classical ''face inversion effect,'' which could support the hypothesis of a voice-specific module. Experiment 1 consisted…
Multikernel least mean square algorithm.
Tobar, Felipe A; Kung, Sun-Yuan; Mandic, Danilo P
2014-02-01
The multikernel least-mean-square algorithm is introduced for adaptive estimation of vector-valued nonlinear and nonstationary signals. This is achieved by mapping the multivariate input data to a Hilbert space of time-varying vector-valued functions, whose inner products (kernels) are combined in an online fashion. The proposed algorithm is equipped with novel adaptive sparsification criteria ensuring a finite dictionary, and is computationally efficient and suitable for nonstationary environments. We also show the ability of the proposed vector-valued reproducing kernel Hilbert space to serve as a feature space for the class of multikernel least-squares algorithms. The benefits of adaptive multikernel (MK) estimation algorithms are illuminated in the nonlinear multivariate adaptive prediction setting. Simulations on nonlinear inertial body sensor signals and nonstationary real-world wind signals of low, medium, and high dynamic regimes support the approach. PMID:24807027
Square ice in graphene nanocapillaries
NASA Astrophysics Data System (ADS)
Algara-Siller, G.; Lehtinen, O.; Wang, F. C.; Nair, R. R.; Kaiser, U.; Wu, H. A.; Geim, A. K.; Grigorieva, I. V.
2015-03-01
Bulk water exists in many forms, including liquid, vapour and numerous crystalline and amorphous phases of ice, with hexagonal ice being responsible for the fascinating variety of snowflakes. Much less noticeable but equally ubiquitous is water adsorbed at interfaces and confined in microscopic pores. Such low-dimensional water determines aspects of various phenomena in materials science, geology, biology, tribology and nanotechnology. Theory suggests many possible phases for adsorbed and confined water, but it has proved challenging to assess its crystal structure experimentally. Here we report high-resolution electron microscopy imaging of water locked between two graphene sheets, an archetypal example of hydrophobic confinement. The observations show that the nanoconfined water at room temperature forms `square ice'--a phase having symmetry qualitatively different from the conventional tetrahedral geometry of hydrogen bonding between water molecules. Square ice has a high packing density with a lattice constant of 2.83 Å and can assemble in bilayer and trilayer crystallites. Molecular dynamics simulations indicate that square ice should be present inside hydrophobic nanochannels independently of their exact atomic nature.
Square ice in graphene nanocapillaries.
Algara-Siller, G; Lehtinen, O; Wang, F C; Nair, R R; Kaiser, U; Wu, H A; Geim, A K; Grigorieva, I V
2015-03-26
Bulk water exists in many forms, including liquid, vapour and numerous crystalline and amorphous phases of ice, with hexagonal ice being responsible for the fascinating variety of snowflakes. Much less noticeable but equally ubiquitous is water adsorbed at interfaces and confined in microscopic pores. Such low-dimensional water determines aspects of various phenomena in materials science, geology, biology, tribology and nanotechnology. Theory suggests many possible phases for adsorbed and confined water, but it has proved challenging to assess its crystal structure experimentally. Here we report high-resolution electron microscopy imaging of water locked between two graphene sheets, an archetypal example of hydrophobic confinement. The observations show that the nanoconfined water at room temperature forms 'square ice'--a phase having symmetry qualitatively different from the conventional tetrahedral geometry of hydrogen bonding between water molecules. Square ice has a high packing density with a lattice constant of 2.83 Å and can assemble in bilayer and trilayer crystallites. Molecular dynamics simulations indicate that square ice should be present inside hydrophobic nanochannels independently of their exact atomic nature. PMID:25810206
High-resolution moisture profiles from full-waveform probabilistic inversion of TDR signals
NASA Astrophysics Data System (ADS)
Laloy, Eric; Huisman, Johan Alexander; Jacques, Diederik
2014-11-01
This study presents an novel Bayesian inversion scheme for high-dimensional undetermined TDR waveform inversion. The methodology quantifies uncertainty in the moisture content distribution, using a Gaussian Markov random field (GMRF) prior as regularization operator. A spatial resolution of 1 cm along a 70-cm long TDR probe is considered for the inferred moisture content. Numerical testing shows that the proposed inversion approach works very well in case of a perfect model and Gaussian measurement errors. Real-world application results are generally satisfying. For a series of TDR measurements made during imbibition and evaporation from a laboratory soil column, the average root-mean-square error (RMSE) between maximum a posteriori (MAP) moisture distribution and reference TDR measurements is 0.04 cm3 cm-3. This RMSE value reduces to less than 0.02 cm3 cm-3 for a field application in a podzol soil. The observed model-data discrepancies are primarily due to model inadequacy, such as our simplified modeling of the bulk soil electrical conductivity profile. Among the important issues that should be addressed in future work are the explicit inference of the soil electrical conductivity profile along with the other sampled variables, the modeling of the temperature-dependence of the coaxial cable properties and the definition of an appropriate statistical model of the residual errors.
A New Class of Pandiagonal Squares
ERIC Educational Resources Information Center
Loly, P. D.; Steeds, M. J.
2005-01-01
An interesting class of purely pandiagonal, i.e. non-magic, whole number (integer) squares of orders (row/column dimension) of the powers of two which are related to Gray codes and square Karnaugh maps has been identified. Treated as matrices these squares possess just two non-zero eigenvalues. The construction of these squares has been automated…
Beam shaping to provide round and square-shaped beams in optical systems of high-power lasers
NASA Astrophysics Data System (ADS)
Laskin, Alexander; Laskin, Vadim
2016-05-01
Optical systems of modern high-power lasers require control of irradiance distribution: round or square-shaped flat-top or super-Gaussian irradiance profiles are optimum for amplification in MOPA lasers and for thermal load management while pumping of crystals of solid-state ultra-short pulse lasers to control heat and minimize its impact on the laser power and beam quality while maximizing overall laser efficiency, variable profiles are also important in irradiating of photocathode of Free Electron lasers (FEL). It is suggested to solve the task of irradiance re-distribution using field mapping refractive beam shapers like piShaper. The operational principle of these devices presumes transformation of laser beam intensity from Gaussian to flat-top one with high flatness of output wavefront, saving of beam consistency, providing collimated output beam of low divergence, high transmittance, extended depth of field, negligible residual wave aberration, and achromatic design provides capability to work with ultra-short pulse lasers having broad spectrum. Using the same piShaper device it is possible to realize beams with flat-top, inverse Gauss or super Gauss irradiance distribution by simple variation of input beam diameter, and the beam shape can be round or square with soft edges. This paper will describe some design basics of refractive beam shapers of the field mapping type and optical layouts of their applying in optical systems of high-power lasers. Examples of real implementations and experimental results will be presented as well.
NASA Astrophysics Data System (ADS)
Mohapatra, S. K.; Maity, K. P.
2016-02-01
The effect of various process parameters for determining extrusion load has been studied for square to square extrusion of Al-6061 alloy, a most used aluminium alloy series in forming industries. Parameters like operating temperature, friction condition, ram velocity, extrusion ratio and die length have been chosen as an input variable for the above study. Twenty five combinations of parameters were set for the investigation by considering aforementioned five parameters in five levels. The simulations have been carried out by Deform-3D software for predicting maximum load requirement for the complete extrusion process. Effective stress and strain distribution across the billet has been checked. Operating temperature, extrusion ratio, friction factor, ram velocity and die length have the significant effect in decreasing order on the maximum load requirement.
Connectivity percolation in suspensions of attractive square-well spherocylinders
NASA Astrophysics Data System (ADS)
Dixit, Mohit; Meyer, Hugues; Schilling, Tanja
2016-01-01
We have studied the connectivity percolation transition in suspensions of attractive square-well spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. In the 1980s the percolation threshold of slender fibers has been predicted to scale as the fibers' inverse aspect ratio [Phys. Rev. B 30, 3933 (1984), 10.1103/PhysRevB.30.3933]. The main finding of our study is that the attractive spherocylinder system reaches this inverse scaling regime at much lower aspect ratios than found in suspensions of hard spherocylinders. We explain this difference by showing that third virial corrections of the pair connectedness functions, which are responsible for the deviation from the scaling regime, are less important for attractive potentials than for hard particles.
Uncertainty quantification for ice sheet inverse problems
NASA Astrophysics Data System (ADS)
Petra, N.; Ghattas, O.; Stadler, G.; Zhu, H.
2011-12-01
Modeling the dynamics of polar ice sheets is critical for projections of future sea level rise. Yet, there remain large uncertainties in the basal boundary conditions and in the non-Newtonian constitutive relations employed within ice sheet models. In this presentation, we consider the problem of estimating uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem-i.e., the posterior probability density-is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal slipperiness field and the Glen's law exponent field). However, under the assumption of Gaussian noise and prior probability densities, and after linearizing the parameter-to-observable map, the posterior density becomes Gaussian, and can therefore be characterized by its mean and covariance. The mean is given by the solution of a nonlinear least squares optimization problem, which is equivalent to a deterministic inverse problem with appropriate interpretation and weighting of the data misfit and regularization terms. To obtain this mean, we solve a deterministic ice sheet inverse problem; here, we infer parameters arising from discretizations of basal slipperiness and rheological exponent fields. For this purpose, we minimize a regularized misfit functional between observed and modeled surface flow velocities. The resulting least squares minimization problem is solved using an adjoint-based inexact Newton method, which uses first and second derivative information. The posterior covariance matrix is given (in the linear-Gaussian case) by the inverse of the Hessian of the least squares cost functional of the deterministic inverse problem. Direct computation of the Hessian matrix is prohibitive, since it would
[Mixed-Spectral Spatial Information Decomposition Model of Water Hyperspectral Inversion].
Pan, Bang-long; Wang, Xian-hua; Zhu, Jin; Yi, Wei-ning; Fang, Ting-yong
2015-03-01
The effect of Mixed-hyperspectral in the water is difficult in quantitative remote sensing of water. Studies have shown that the only scalar spectrum information is difficult to solve the problem of complex mixed spectra of water. Besides the spectral information, spatial distribution of information is one of the obvious characteristics of the broad waters pollution, and can be used as a useful complement to the remote sensing information and facilitate water complex spectral unmixing. Taking Chaohu as an example, the paper applies the HJ-1A HSI hyperspectral data and the supplemental surface spectral measurement data to discuss the mixed spectra of lake water by spatial statistics and genetic algorithm theory. By using the spatial variogram of geostatistics to simulate the distribution difference of two adjacent pixels, the space-informational decomposition model of mixed spectral in lake water is established by co-kriging genetic algorithm, which is a improved algorithm applying the spatial variogram function of neighborhood pixel as the constraint of the objective function of the genetic algorithm. Finally, the model inversion results of suspended matter concentration are verified. Compared with the conventional spectral unmixing model, the results show the correlation coefficient of the predicted and measured value of suspended sediment concentration is 0.82, the root mean square error 9.25 mg x L(-1) by mixed spectral space information decomposition model, so the correlation coefficient is increased by 8.9%, the root mean square error reduced by 2.78 mg x L(-1), indicating that the model of suspended matter concentration has a strong predictive ability. Therefore, the effective combination of spatial and spectral information of water, can avoid inversion result distortion due to weak spectral signal of water color parameters, and large amount of calculation of information extraction because of the high spectral band numbers, and also provides an effective way
NASA Astrophysics Data System (ADS)
Gough, D.
1984-12-01
Helioseismological inversion, as with the inversion of any other data, is divided into three phases. The first is the solution of the so-called forward problem: namely, the calculation of the eigenfrequencies of a theoretical equilibrium state. The second is an attempt to understand the results, either empirically by determining how those frequencies vary as chosen parameters defining the equilibrium model are varied, or analytically from asymptotic expansions in limiting cases of high order or degree. The third phase is to pose and solve an inverse problem, which seeks to find a plausible equilibrium model of the Sun whose eigenfrequencies are consistent with observation. The three phases are briefly discussed in this review, and the third, which is not yet widely used in helioseismology, is illustrated with some selected inversions of artificial solar data.
Stochastic inversion by ray continuation
Haas, A.; Viallix
1989-05-01
The conventional tomographic inversion consists in minimizing residuals between measured and modelled traveltimes. The process tends to be unstable and some additional constraints are required to stabilize it. The stochastic formulation generalizes the technique and sets it on firmer theoretical bases. The Stochastic Inversion by Ray Continuation (SIRC) is a probabilistic approach, which takes a priori geological information into account and uses probability distributions to characterize data correlations and errors. It makes it possible to tie uncertainties to the results. The estimated parameters are interval velocities and B-spline coefficients used to represent smoothed interfaces. Ray tracing is done by a continuation technique between source and receives. The ray coordinates are computed from one path to the next by solving a linear system derived from Fermat's principle. The main advantages are fast computations, accurate traveltimes and derivatives. The seismic traces are gathered in CMPs. For a particular CMP, several reflecting elements are characterized by their time gradient measured on the stacked section, and related to a mean emergence direction. The program capabilities are tested on a synthetic example as well as on a field example. The strategy consists in inverting the parameters for one layer, then for the next one down. An inversion step is divided in two parts. First the parameters for the layer concerned are inverted, while the parameters for the upper layers remain fixed. Then all the parameters are reinverted. The velocity-depth section computed by the program together with the corresponding errors can be used directly for the interpretation, as an initial model for depth migration or for the complete inversion program under development.
Generalized emissivity inverse problem.
Ming, DengMing; Wen, Tao; Dai, XianXi; Dai, JiXin; Evenson, William E
2002-04-01
Inverse problems have recently drawn considerable attention from the physics community due to of potential widespread applications [K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer Verlag, Berlin, 1989)]. An inverse emissivity problem that determines the emissivity g(nu) from measurements of only the total radiated power J(T) has recently been studied [Tao Wen, DengMing Ming, Xianxi Dai, Jixin Dai, and William E. Evenson, Phys. Rev. E 63, 045601(R) (2001)]. In this paper, a new type of generalized emissivity and transmissivity inverse (GETI) problem is proposed. The present problem differs from our previous work on inverse problems by allowing the unknown (emissivity) function g(nu) to be temperature dependent as well as frequency dependent. Based on published experimental information, we have developed an exact solution formula for this GETI problem. A universal function set suggested for numerical calculation is shown to be robust, making this inversion method practical and convenient for realistic calculations.
ERIC Educational Resources Information Center
Dalton, Starrett
The amount of variance accounted for by treatment can be estimated with omega squared or with the squared multiple correlation coefficient. Monte Carlo methods were employed to compare omega squared, the squared multiple correlation coefficient, and the squared multiple correlation coefficient to which a shrinkage formula had been applied, in…
Varying prior information in Bayesian inversion
NASA Astrophysics Data System (ADS)
Walker, Matthew; Curtis, Andrew
2014-06-01
Bayes' rule is used to combine likelihood and prior probability distributions. The former represents knowledge derived from new data, the latter represents pre-existing knowledge; the Bayesian combination is the so-called posterior distribution, representing the resultant new state of knowledge. While varying the likelihood due to differing data observations is common, there are also situations where the prior distribution must be changed or replaced repeatedly. For example, in mixture density neural network (MDN) inversion, using current methods the neural network employed for inversion needs to be retrained every time prior information changes. We develop a method of prior replacement to vary the prior without re-training the network. Thus the efficiency of MDN inversions can be increased, typically by orders of magnitude when applied to geophysical problems. We demonstrate this for the inversion of seismic attributes in a synthetic subsurface geological reservoir model. We also present results which suggest that prior replacement can be used to control the statistical properties (such as variance) of the final estimate of the posterior in more general (e.g., Monte Carlo based) inverse problem solutions.
Structural state testing using eddy current inversion
NASA Astrophysics Data System (ADS)
Dolgov, N. Y.; Chernov, L. A.
2000-05-01
The inverse eddy current problem can be described as the task of reconstructing an unknown distribution of electrical conductivity from eddy-current probe voltage measurements recorded as function of excitation frequency. Conductivity variation may be a result of surface processing with substances like hydrogen and carbon or surface heating. We developed mathematical reasons and supporting software for inverse conductivity profiling. Inverse problem was solved for layered plane and cylindrical conductors. Because the inverse problem is nonlinear, we propose using an iterative algorithm which can be formalized as the minimization of an error functional related to the difference between the probe voltages theoretically predicted by the direct problem solving and the measured probe voltages. Numerical results were obtained for some models of conductivity distribution. It was shown that inverse problem can be solved exactly in case of correct measurements. Good estimation of the true conductivity distribution takes place also for measurement noise about 2 percent but in the case of 5 percent error, results are worse.
Multifrequency inversion in magnetic resonance elastography.
Papazoglou, Sebastian; Hirsch, Sebastian; Braun, Jürgen; Sack, Ingolf
2012-04-21
Time-harmonic shear wave elastography is capable of measuring viscoelastic parameters in living tissue. However, finite tissue boundaries and waveguide effects give rise to wave interferences which are not accounted for by standard elasticity reconstruction methods. Furthermore, the viscoelasticity of tissue causes dispersion of the complex shear modulus, rendering the recovered moduli frequency dependent. Therefore, we here propose the use of multifrequency wave data from magnetic resonance elastography (MRE) for solving the inverse problem of viscoelasticity reconstruction by an algebraic least-squares solution based on the springpot model. Advantages of the method are twofold: (i) amplitude nulls appearing in single-frequency standing wave patterns are mitigated and (ii) the dispersion of storage and loss modulus with drive frequency is taken into account by the inversion procedure, thereby avoiding subsequent model fitting. As a result, multifrequency inversion produces fewer artifacts in the viscoelastic parameter map than standard single-frequency parameter recovery and may thus support image-based viscoelasticity measurement. The feasibility of the method is demonstrated by simulated wave data and MRE experiments on a phantom and in vivo human brain. Implemented as a clinical method, multifrequency inversion may improve the diagnostic value of time-harmonic MRE in a large variety of applications.
Multifrequency inversion in magnetic resonance elastography
NASA Astrophysics Data System (ADS)
Papazoglou, Sebastian; Hirsch, Sebastian; Braun, Jürgen; Sack, Ingolf
2012-04-01
Time-harmonic shear wave elastography is capable of measuring viscoelastic parameters in living tissue. However, finite tissue boundaries and waveguide effects give rise to wave interferences which are not accounted for by standard elasticity reconstruction methods. Furthermore, the viscoelasticity of tissue causes dispersion of the complex shear modulus, rendering the recovered moduli frequency dependent. Therefore, we here propose the use of multifrequency wave data from magnetic resonance elastography (MRE) for solving the inverse problem of viscoelasticity reconstruction by an algebraic least-squares solution based on the springpot model. Advantages of the method are twofold: (i) amplitude nulls appearing in single-frequency standing wave patterns are mitigated and (ii) the dispersion of storage and loss modulus with drive frequency is taken into account by the inversion procedure, thereby avoiding subsequent model fitting. As a result, multifrequency inversion produces fewer artifacts in the viscoelastic parameter map than standard single-frequency parameter recovery and may thus support image-based viscoelasticity measurement. The feasibility of the method is demonstrated by simulated wave data and MRE experiments on a phantom and in vivo human brain. Implemented as a clinical method, multifrequency inversion may improve the diagnostic value of time-harmonic MRE in a large variety of applications.
Latin-square three-dimensional gage master
Jones, L.
1981-05-12
A gage master for coordinate measuring machines has an nxn array of objects distributed in the Z coordinate utilizing the concept of a Latin square experimental design. Using analysis of variance techniques, the invention may be used to identify sources of error in machine geometry and quantify machine accuracy.
Understanding Least Squares through Monte Carlo Calculations
ERIC Educational Resources Information Center
Tellinghuisen, Joel
2005-01-01
The method of least squares (LS) is considered as an important data analysis tool available to physical scientists. The mathematics of linear least squares(LLS) is summarized in a very compact matrix rotation that renders it practically "formulaic".
Recurrent Neural Network Approach Based on the Integral Representation of the Drazin Inverse.
Stanimirović, Predrag S; Živković, Ivan S; Wei, Yimin
2015-10-01
In this letter, we present the dynamical equation and corresponding artificial recurrent neural network for computing the Drazin inverse for arbitrary square real matrix, without any restriction on its eigenvalues. Conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the Drazin inverse are considered. Several illustrative examples present the results of computer simulations.
Abazov, V M; Abbott, B; Abolins, M; Acharya, B S; Adams, M; Adams, T; Aguilo, E; Ahn, S H; Ahsan, M; Alexeev, G D; Alkhazov, G; Alton, A; Alverson, G; Alves, G A; Anastasoaie, M; Ancu, L S; Andeen, T; Anderson, S; Andrieu, B; Anzelc, M S; Arnoud, Y; Arov, M; Arthaud, M; Askew, A; Asman, B; Jesus, A C S Assis; Atramentov, O; Autermann, C; Avila, C; Ay, C; Badaud, F; Baden, A; Bagby, L; Baldin, B; Bandurin, D V; Banerjee, S; Banerjee, P; Barberis, E; Barfuss, A-F; Bargassa, P; Baringer, P; Barreto, J; Bartlett, J F; Bassler, U; Bauer, D; Beale, S; Bean, A; Begalli, M; Begel, M; Belanger-Champagne, C; Bellantoni, L; Bellavance, A; Benitez, J A; Beri, S B; Bernardi, G; Bernhard, R; Bertram, I; Besançon, M; Beuselinck, R; Bezzubov, V A; Bhat, P C; Bhatnagar, V; Biscarat, C; Blazey, G; Blekman, F; Blessing, S; Bloch, D; Bloom, K; Boehnlein, A; Boline, D; Bolton, T A; Borissov, G; Bose, T; Brandt, A; Brock, R; Brooijmans, G; Bross, A; Brown, D; Buchanan, N J; Buchholz, D; Buehler, M; Buescher, V; Bunichev, V; Burdin, S; Burke, S; Burnett, T H; Buszello, C P; Butler, J M; Calfayan, P; Calvet, S; Cammin, J; Carvalho, W; Casey, B C K; Cason, N M; Castilla-Valdez, H; Chakrabarti, S; Chakraborty, D; Chan, K M; Chan, K; Chandra, A; Charles, F; Cheu, E; Chevallier, F; Cho, D K; Choi, S; Choudhary, B; Christofek, L; Christoudias, T; Cihangir, S; Claes, D; Coadou, Y; Cooke, M; Cooper, W E; Corcoran, M; Couderc, F; Cousinou, M-C; Crépé-Renaudin, S; Cutts, D; Cwiok, M; da Motta, H; Das, A; Davies, G; De, K; de Jong, S J; De La Cruz-Burelo, E; De Oliveira Martins, C; Degenhardt, J D; Déliot, F; Demarteau, M; Demina, R; Denisov, D; Denisov, S P; Desai, S; Diehl, H T; Diesburg, M; Dominguez, A; Dong, H; Dudko, L V; Duflot, L; Dugad, S R; Duggan, D; Duperrin, A; Dyer, J; Dyshkant, A; Eads, M; Edmunds, D; Ellison, J; Elvira, V D; Enari, Y; Eno, S; Ermolov, P; Evans, H; Evdokimov, A; Evdokimov, V N; Ferapontov, A V; Ferbel, T; Fiedler, F; Filthaut, F; Fisher, W; Fisk, H E; Ford, M; Fortner, M; Fox, H; Fu, S; Fuess, S; Gadfort, T; Galea, C F; Gallas, E; Galyaev, E; Garcia, C; Garcia-Bellido, A; Gavrilov, V; Gay, P; Geist, W; Gelé, D; Gerber, C E; Gershtein, Y; Gillberg, D; Ginther, G; Gollub, N; Gómez, B; Goussiou, A; Grannis, P D; Greenlee, H; Greenwood, Z D; Gregores, E M; Grenier, G; Gris, Ph; Grivaz, J-F; Grohsjean, A; Grünendahl, S; Grünewald, M W; Guo, J; Guo, F; Gutierrez, P; Gutierrez, G; Haas, A; Hadley, N J; Haefner, P; Hagopian, S; Haley, J; Hall, I; Hall, R E; Han, L; Hanagaki, K; Hansson, P; Harder, K; Harel, A; Harrington, R; Hauptman, J M; Hauser, R; Hays, J; Hebbeker, T; Hedin, D; Hegeman, J G; Heinmiller, J M; Heinson, A P; Heintz, U; Hensel, C; Herner, K; Hesketh, G; Hildreth, M D; Hirosky, R; Hobbs, J D; Hoeneisen, B; Hoeth, H; Hohlfeld, M; Hong, S J; Hossain, S; Houben, P; Hu, Y; Hubacek, Z; Hynek, V; Iashvili, I; Illingworth, R; Ito, A S; Jabeen, S; Jaffré, M; Jain, S; Jakobs, K; Jarvis, C; Jesik, R; Johns, K; Johnson, C; Johnson, M; Jonckheere, A; Jonsson, P; Juste, A; Käfer, D; Kajfasz, E; Kalinin, A M; Kalk, J R; Kalk, J M; Kappler, S; Karmanov, D; Kasper, P; Katsanos, I; Kau, D; Kaur, R; Kaushik, V; Kehoe, R; Kermiche, S; Khalatyan, N; Khanov, A; Kharchilava, A; Kharzheev, Y M; Khatidze, D; Kim, H; Kim, T J; Kirby, M H; Kirsch, M; Klima, B; Kohli, J M; Konrath, J-P; Kopal, M; Korablev, V M; Kozelov, A V; Krop, D; Kuhl, T; Kumar, A; Kunori, S; Kupco, A; Kurca, T; Kvita, J; Lacroix, F; Lam, D; Lammers, S; Landsberg, G; Lebrun, P; Lee, W M; Leflat, A; Lehner, F; Lellouch, J; Leveque, J; Lewis, P; Li, J; Li, Q Z; Li, L; Lietti, S M; Lima, J G R; Lincoln, D; Linnemann, J; Lipaev, V V; Lipton, R; Liu, Y; Liu, Z; Lobo, L; Lobodenko, A; Lokajicek, M; Love, P; Lubatti, H J; Lyon, A L; Maciel, A K A; Mackin, D; Madaras, R J; Mättig, P; Magass, C; Magerkurth, A; Mal, P K; Malbouisson, H B; Malik, S; Malyshev, V L; Mao, H S; Maravin, Y; Martin, B; McCarthy, R; Melnitchouk, A; Mendes, A; Mendoza, L; Mercadante, P G; Merkin, M; Merritt, K W; Meyer, J; Meyer, A; Millet, T; Mitrevski, J; Molina, J; Mommsen, R K; Mondal, N K; Moore, R W; Moulik, T; Muanza, G S; Mulders, M; Mulhearn, M; Mundal, O; Mundim, L; Nagy, E; Naimuddin, M; Narain, M; Naumann, N A; Neal, H A; Negret, J P; Neustroev, P; Nilsen, H; Nogima, H; Nomerotski, A; Novaes, S F; Nunnemann, T; O'Dell, V; O'Neil, D C; Obrant, G; Ochando, C; Onoprienko, D; Oshima, N; Osta, J; Otec, R; Y Garzón, G J Otero; Owen, M; Padley, P; Pangilinan, M; Parashar, N; Park, S-J; Park, S K; Parsons, J; Partridge, R; Parua, N; Patwa, A; Pawloski, G; Penning, B; Perfilov, M; Peters, K; Peters, Y; Pétroff, P; Petteni, M; Piegaia, R; Piper, J; Pleier, M-A; Podesta-Lerma, P L M; Podstavkov, V M; Pogorelov, Y; Pol, M-E; Polozov, P; Pope, B G; Popov, A V; Potter, C; da Silva, W L Prado; Prosper, H B; Protopopescu, S; Qian, J; Quadt, A; Quinn, B; Rakitine, A; Rangel, M S; Ranjan, K; Ratoff, P N; Renkel, P; Reucroft, S; Rich, P; Rijssenbeek, M; Ripp-Baudot, I; Rizatdinova, F; Robinson, S; Rodrigues, R F; Rominsky, M; Royon, C; Rubinov, P; Ruchti, R; Safronov, G; Sajot, G; Sánchez-Hernández, A; Sanders, M P; Santoro, A; Savage, G; Sawyer, L; Scanlon, T; Schaile, D; Schamberger, R D; Scheglov, Y; Schellman, H; Schieferdecker, P; Schliephake, T; Schwanenberger, C; Schwartzman, A; Schwienhorst, R; Sekaric, J; Severini, H; Shabalina, E; Shamim, M; Shary, V; Shchukin, A A; Shivpuri, R K; Siccardi, V; Simak, V; Sirotenko, V; Skubic, P; Slattery, P; Smirnov, D; Snow, J; Snow, G R; Snyder, S; Söldner-Rembold, S; Sonnenschein, L; Sopczak, A; Sosebee, M; Soustruznik, K; Souza, M; Spurlock, B; Stark, J; Steele, J; Stolin, V; Stoyanova, D A; Strandberg, J; Strandberg, S; Strang, M A; Strauss, M; Strauss, E; Ströhmer, R; Strom, D; Stutte, L; Sumowidagdo, S; Svoisky, P; Sznajder, A; Talby, M; Tamburello, P; Tanasijczuk, A; Taylor, W; Temple, J; Tiller, B; Tissandier, F; Titov, M; Tokmenin, V V; Toole, T; Torchiani, I; Trefzger, T; Tsybychev, D; Tuchming, B; Tully, C; Tuts, P M; Unalan, R; Uvarov, S; Uvarov, L; Uzunyan, S; Vachon, B; van den Berg, P J; Van Kooten, R; van Leeuwen, W M; Varelas, N; Varnes, E W; Vasilyev, I A; Vaupel, M; Verdier, P; Vertogradov, L S; Verzocchi, M; Villeneuve-Seguier, F; Vint, P; Vokac, P; Von Toerne, E; Voutilainen, M; Wagner, R; Wahl, H D; Wang, L; Wang, M H L S; Warchol, J; Watts, G; Wayne, M; Weber, M; Weber, G; Wenger, A; Wermes, N; Wetstein, M; White, A; Wicke, D; Wilson, G W; Wimpenny, S J; Wobisch, M; Wood, D R; Wyatt, T R; Xie, Y; Yacoob, S; Yamada, R; Yan, M; Yasuda, T; Yatsunenko, Y A; Yip, K; Yoo, H D; Youn, S W; Yu, J; Zatserklyaniy, A; Zeitnitz, C; Zhao, T; Zhou, B; Zhu, J; Zielinski, M; Zieminska, D; Zieminski, A; Zivkovic, L; Zutshi, V; Zverev, E G
2008-03-14
We present a measurement of the shape of the Z/gamma* boson transverse momentum (q(T)) distribution in pp --> Z/gamma* --> e(+)e(-) + X events at a center-of-mass energy of 1.96 TeV using 0.98 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low q(T), but above the perturbative QCD calculation in the region of q(T)>30 GeV/c. Using events with q(T)<30 GeV/c, we extract the value of g(2), one of the nonperturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function. PMID:18352175
Least-Squares Curve-Fitting Program
NASA Technical Reports Server (NTRS)
Kantak, Anil V.
1990-01-01
Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.
Can the square law be validated
Hartley, D.S. III.
1989-03-01
This paper addresses the question of validating the homogeneous Lanchestrian square law of attrition by the use of historical data. The available data and some analysis techniques are examined. The result is that the homogeneous Lanchester square law cannot be regarded as a proven attrition algorithm for warfare; however, the square law cannot be regarded as disproved either. To validate the square law or any other proposed attrition law, data on more battles are required. 21 refs., 31 figs., 11 tabs.
Story Squares. CATESOL Occasional Papers, No. 4.
ERIC Educational Resources Information Center
Sasaki, Ruth A.
A set of specific and practical ideas for teaching language skills are presented, centered around the use of charts or "squares" of pictures that represent ideas that can be expressed in basic English. The focus is a story square, a system of pictures tied together by a plot and presented to the class as a puzzle. Squares for pronunciation can be…
Using Least Squares for Error Propagation
ERIC Educational Resources Information Center
Tellinghuisen, Joel
2015-01-01
The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…
Full waveform inversion with an auxiliary bump functional
NASA Astrophysics Data System (ADS)
Bharadwaj, Pawan; Mulder, Wim; Drijkoningen, Guy
2016-08-01
Least-squares inversion of seismic arrivals can provide remarkably detailed models of the Earth's subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the least-squares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an accurate initial large-scale velocity estimate. The low frequencies in the arrivals, needed to update the large-scale components in the velocity model, are usually unreliable or absent. To overcome this difficulty, we propose a multi-objective inversion scheme that uses the conventional least-squares functional along with an auxiliary data-domain objective. As the auxiliary objective effectively replaces the seismic arrivals by bumps, we call it the bump functional. The bump functional minimization can be made far less sensitive to cycle skipping and can deal with multiple arrivals in the data. However, it can only be used as an auxiliary objective since it usually does not provide a unique model after minimization even when the regularized-least-squares functional has a unique global minimum and hence a unique solution. The role of the bump functional during the multi-objective inversion is to guide the optimization towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. The computational complexity of the bump functional is equivalent to that of the least-squares functional. In this paper, we describe various characteristics of the bump functional using simple and illustrative numerical examples. We also demonstrate the effectiveness of the proposed multi-objective inversion scheme by considering more realistic examples. These include synthetic and field data from a cross-well experiment, surface-seismic synthetic data with reflections and synthetic data with refracted arrivals at long offsets.
Restoration of A Tsunami Source By Inversion of The Coastal Tide-gauge Records
NASA Astrophysics Data System (ADS)
Gusiakov, V. K.; Tcheverda, V. A.; Voronina, T. A.
The inversion of the tsunami wave records obtained on the coastal tide-gauges is widely used to determine the initial water displacement in a tsunami source area. Mathematically, this problem is formulated as inverse problem of mathematical physics for restoration of the initial water displacement in the source area by surface oscillations observed at a number of points distributed along the coastline. As it was shown by Kaistrenko (1972), in a general case of an arbitrary source, this inverse prob- lem does not have a unique solution. Its solvability depends on a number of a priori assumptions, one of which is that the source function can be presented as product of space- and time-dependent functions, where the time-dependent function is supposed to be known. Even under this assumption, the problem remains to be an ill-posed problem whose solvability depends on the number and length of waveforms used in the inversion, their spatial distribution and the signal-to-noise ratio. As a mathematical model of the problem, we use the linear shallow water equations numerically solved (by finite difference method) on the model bottom relief having some basic morpho- logical features typical for the island arc regions. The inverse problem is solved by least square inversion using a truncated SVD approach. The quality of the solution obtained is evaluated as relative errors (in L2-norm) in restoration of the source func- tion. As a model of the initial water displacement we used a dipolar displacement rep- resenting the surface deformation due to the typical tsunamigenic earthquakes with the reverse dip-slip or the low-angle thrust mechanisms. On the basis of a series of numerical experiments made we conclude that (1) the quality of the source restoration strongly depends on the number of waveforms used and their azimuthal coverage; (2) to obtain a reasonable quality of source restoration we need to use at least 5 records smoothly distributed over the space domain that is
Inverse Bremsstrahlung in Shocked Astrophysical Plasmas
NASA Technical Reports Server (NTRS)
Baring, Matthew G.; Jones, Frank C.; Ellison, Donald C.
2000-01-01
There has recently been interest in the role of inverse bremsstrahlung, the emission of photons by fast suprathermal ions in collisions with ambient electrons possessing relatively low velocities, in tenuous plasmas in various astrophysical contexts. This follows a long hiatus in the application of suprathermal ion bremsstrahlung to astrophysical models since the early 1970s. The potential importance of inverse bremsstrahlung relative to normal bremsstrahlung, i.e. where ions are at rest, hinges upon the underlying velocity distributions of the interacting species. In this paper, we identify the conditions under which the inverse bremsstrahlung emissivity is significant relative to that for normal bremsstrahlung in shocked astrophysical plasmas. We determine that, since both observational and theoretical evidence favors electron temperatures almost comparable to, and certainly not very deficient relative to proton temperatures in shocked plasmas, these environments generally render inverse bremsstrahlung at best a minor contributor to the overall emission. Hence inverse bremsstrahlung can be safely neglected in most models invoking shock acceleration in discrete sources such as supernova remnants. However, on scales approximately > 100 pc distant from these sources, Coulomb collisional losses can deplete the cosmic ray electrons, rendering inverse bremsstrahlung, and perhaps bremsstrahlung from knock-on electrons, possibly detectable.
Deming's General Least Square Fitting
1992-02-18
DEM4-26 is a generalized least square fitting program based on Deming''s method. Functions built into the program for fitting include linear, quadratic, cubic, power, Howard''s, exponential, and Gaussian; others can easily be added. The program has the following capabilities: (1) entry, editing, and saving of data; (2) fitting of any of the built-in functions or of a user-supplied function; (3) plotting the data and fitted function on the display screen, with error limits if requested,more » and with the option of copying the plot to the printer; (4) interpolation of x or y values from the fitted curve with error estimates based on error limits selected by the user; and (5) plotting the residuals between the y data values and the fitted curve, with the option of copying the plot to the printer. If the plot is to be copied to a printer, GRAPHICS should be called from the operating system disk before the BASIC interpreter is loaded.« less
Deming's General Least Square Fitting
Rinard, Phillip
1992-02-18
DEM4-26 is a generalized least square fitting program based on Deming''s method. Functions built into the program for fitting include linear, quadratic, cubic, power, Howard''s, exponential, and Gaussian; others can easily be added. The program has the following capabilities: (1) entry, editing, and saving of data; (2) fitting of any of the built-in functions or of a user-supplied function; (3) plotting the data and fitted function on the display screen, with error limits if requested, and with the option of copying the plot to the printer; (4) interpolation of x or y values from the fitted curve with error estimates based on error limits selected by the user; and (5) plotting the residuals between the y data values and the fitted curve, with the option of copying the plot to the printer. If the plot is to be copied to a printer, GRAPHICS should be called from the operating system disk before the BASIC interpreter is loaded.
Semiautomatic and Automatic Cooperative Inversion of Seismic and Magnetotelluric Data
NASA Astrophysics Data System (ADS)
Le, Cuong V. A.; Harris, Brett D.; Pethick, Andrew M.; Takam Takougang, Eric M.; Howe, Brendan
2016-09-01
Natural source electromagnetic methods have the potential to recover rock property distributions from the surface to great depths. Unfortunately, results in complex 3D geo-electrical settings can be disappointing, especially where significant near-surface conductivity variations exist. In such settings, unconstrained inversion of magnetotelluric data is inexorably non-unique. We believe that: (1) correctly introduced information from seismic reflection can substantially improve MT inversion, (2) a cooperative inversion approach can be automated, and (3) massively parallel computing can make such a process viable. Nine inversion strategies including baseline unconstrained inversion and new automated/semiautomated cooperative inversion approaches are applied to industry-scale co-located 3D seismic and magnetotelluric data sets. These data sets were acquired in one of the Carlin gold deposit districts in north-central Nevada, USA. In our approach, seismic information feeds directly into the creation of sets of prior conductivity model and covariance coefficient distributions. We demonstrate how statistical analysis of the distribution of selected seismic attributes can be used to automatically extract subvolumes that form the framework for prior model 3D conductivity distribution. Our cooperative inversion strategies result in detailed subsurface conductivity distributions that are consistent with seismic, electrical logs and geochemical analysis of cores. Such 3D conductivity distributions would be expected to provide clues to 3D velocity structures that could feed back into full seismic inversion for an iterative practical and truly cooperative inversion process. We anticipate that, with the aid of parallel computing, cooperative inversion of seismic and magnetotelluric data can be fully automated, and we hold confidence that significant and practical advances in this direction have been accomplished.
Colloquial and Literary Uses of Inversions. Technical Report No. 217.
ERIC Educational Resources Information Center
Green, Georgia M.
Inversion constructions (declarative sentence constructions in which the subject follows part or all of its verb phrase) are distributed over the whole range of spoken and written language, not along the spoken-written dimension but along a colloquial-literary dimension. Some of these inversions are colloquial or literary for functional reasons,…
Orthogonal basis functions in discrete least-squares rational approximation
NASA Astrophysics Data System (ADS)
Bultheel, A.; van Barel, M.; van Gucht, P.
2004-03-01
We consider a problem that arises in the field of frequency domain system identification. If a discrete-time system has an input-output relation Y(z)=G(z)U(z), with transfer function G, then the problem is to find a rational approximation for G. The data given are measurements of input and output spectra in the frequency points zk: {U(zk),Y(zk)}k=1N together with some weight. The approximation criterion is to minimize the weighted discrete least squares norm of the vector obtained by evaluating in the measurement points. If the poles of the system are fixed, then the problem reduces to a linear least-squares problem in two possible ways: by multiplying out the denominators and hide these in the weight, which leads to the construction of orthogonal vector polynomials, or the problem can be solved directly using an orthogonal basis of rational functions. The orthogonality of the basis is important because if the transfer function is represented with respect to a nonorthogonal basis, then this least-squares problem can be very ill conditioned. Even if an orthogonal basis is used, but with respect to the wrong inner product (e.g., the Lebesgue measure on the unit circle) numerical instability can be fatal in practice. We show that both approaches lead to an inverse eigenvalue problem, which forms the common framework in which fast and numerically stable algorithms can be designed for the computation of the orthonormal basis.
Recursive least-squares learning algorithms for neural networks
Lewis, P.S. ); Hwang, Jenq-Neng . Dept. of Electrical Engineering)
1990-01-01
This paper presents the development of a pair of recursive least squares (RLS) algorithms for online training of multilayer perceptrons, which are a class of feedforward artificial neural networks. These algorithms incorporate second order information about the training error surface in order to achieve faster learning rates than are possible using first order gradient descent algorithms such as the generalized delta rule. A least squares formulation is derived from a linearization of the training error function. Individual training pattern errors are linearized about the network parameters that were in effect when the pattern was presented. This permits the recursive solution of the least squares approximation, either via conventional RLS recursions or by recursive QR decomposition-based techniques. The computational complexity of the update is in the order of (N{sup 2}), where N is the number of network parameters. This is due to the estimation of the N {times} N inverse Hessian matrix. Less computationally intensive approximations of the RLS algorithms can be easily derived by using only block diagonal elements of this matrix, thereby partitioning the learning into independent sets. A simulation example is presented in which a neural network is trained to approximate a two dimensional Gaussian bump. In this example, RLS training required an order of magnitude fewer iterations on average (527) than did training with the generalized delta rule (6331). 14 refs., 3 figs.
NASA Astrophysics Data System (ADS)
Clare, R. B.; Levinger, J. S.
1981-02-01
We use the formalism of hyperspherical harmonics to calculate several moments for the triton photoeffect, for a Volkov spin-independent potential. First, we improve the accuracy of Maleki's calculations of the moments σ2 and σ3 by including more terms in the hyperspherical expansion. We also calculate moments σ0 and σ1 for a Serber mixture. We find reasonable agreement between our moments found by sum rules and those found from the cross sections calculated by Fang et al. and Levinger-Fitzgibbon. We then develop a technique of inversion of a finite number of moments by making the assumption that the cross section can be written as a sum of several Laguerre polynomials multiplied by a decreasing exponential. We test our inversion technique successfully on several model potentials. We then modify it and apply it to the five moments (σ-1 to σ3) for a force without exchange, and find fair agreement with Fang's values of the cross section. Finally, we apply the inversion technique to our three moments (σ-1,σ0,and σ1) for a Serber mixture, and find reasonable agreement with Gorbunov's measurements of the 3He photoeffect. NUCLEAR REACTIONS Triton photoeffects, hyperspherical harmonics, moments of photoeffect, inversion of moments.
Aerosol physical properties from satellite horizon inversion
NASA Technical Reports Server (NTRS)
Gray, C. R.; Malchow, H. L.; Merritt, D. C.; Var, R. E.; Whitney, C. K.
1973-01-01
The feasibility is investigated of determining the physical properties of aerosols globally in the altitude region of 10 to 100 km from a satellite horizon scanning experiment. The investigation utilizes a horizon inversion technique previously developed and extended. Aerosol physical properties such as number density, size distribution, and the real and imaginary components of the index of refraction are demonstrated to be invertible in the aerosol size ranges (0.01-0.1 microns), (0.1-1.0 microns), (1.0-10 microns). Extensions of previously developed radiative transfer models and recursive inversion algorithms are displayed.
Square pulse linear transformer driver
NASA Astrophysics Data System (ADS)
Kim, A. A.; Mazarakis, M. G.; Sinebryukhov, V. A.; Volkov, S. N.; Kondratiev, S. S.; Alexeenko, V. M.; Bayol, F.; Demol, G.; Stygar, W. A.
2012-04-01
The linear transformer driver (LTD) technological approach can result in relatively compact devices that can deliver fast, high current, and high-voltage pulses straight out of the LTD cavity without any complicated pulse forming and pulse compression network. Through multistage inductively insulated voltage adders, the output pulse, increased in voltage amplitude, can be applied directly to the load. The usual LTD architecture [A. A. Kim, M. G. Mazarakis, V. A. Sinebryukhov, B. M. Kovalchuk, V. A. Vizir, S. N Volkov, F. Bayol, A. N. Bastrikov, V. G. Durakov, S. V. Frolov, V. M. Alexeenko, D. H. McDaniel, W. E. Fowler, K. LeCheen, C. Olson, W. A. Stygar, K. W. Struve, J. Porter, and R. M. Gilgenbach, Phys. Rev. ST Accel. Beams 12, 050402 (2009)PRABFM1098-440210.1103/PhysRevSTAB.12.050402; M. G. Mazarakis, W. E. Fowler, A. A. Kim, V. A. Sinebryukhov, S. T. Rogowski, R. A. Sharpe, D. H. McDaniel, C. L. Olson, J. L. Porter, K. W. Struve, W. A. Stygar, and J. R. Woodworth, Phys. Rev. ST Accel. Beams 12, 050401 (2009)PRABFM1098-440210.1103/PhysRevSTAB.12.050401] provides sine shaped output pulses that may not be well suited for some applications like z-pinch drivers, flash radiography, high power microwaves, etc. A more suitable power pulse would have a flat or trapezoidal (rising or falling) top. In this paper, we present the design and first test results of an LTD cavity that generates such a type of output pulse by including within its circular array a number of third harmonic bricks in addition to the main bricks. A voltage adder made out of a square pulse cavity linear array will produce the same shape output pulses provided that the timing of each cavity is synchronized with the propagation of the electromagnetic pulse.
Commer, Michael; Helwig, Stefan, L.; Hordt, Andreas; Scholl,Carsten; Tezkan, Bulent
2006-06-14
Three long-offset transient electromagnetic (LOTEM) surveyswerecarried out at the active volcano Merapi in Central Java (Indonesia)during the years 1998, 2000, and 2001. The measurements focused on thegeneral resistivity structure of the volcanic edifice at depths of 0.5-2km and the further investigation of a southside anomaly. The measurementswere insufficient for a full 3D inversion scheme, which could enable theimaging of finely discretized resistivity distributions. Therefore, astable, damped least-squares joint-inversion approach is used to optimize3D models with a limited number of parameters. The mode ls feature therealistic simulation of topography, a layered background structure, andadditional coarse 3D blocks representing conductivity anomalies.Twenty-eight LOTEM transients, comprising both horizontal and verticalcomponents of the magnetic induction time derivative, were analyzed. Inview of the few unknowns, we were able to achieve reasonable data fits.The inversion results indicate an upwelling conductor below the summit,suggesting hydrothermal activity in the central volcanic complex. Ashallow conductor due to a magma-filled chamber, at depths down to 1 kmbelow the summit, suggested by earlier seismic studies, is not indicatedby the inversion results. In conjunction with an anomalous-density model,derived from arecent gravity study, our inversion results provideinformation about the southern geological structure resulting from amajor sector collapse during the Middle Merapi period. The density modelallows to assess a porosity range andthus an estimated vertical salinityprofile to explain the high conductivities on a larger scale, extendingbeyond the foothills of Merapi.
A Parallel Processing Algorithm for Gravity Inversion
NASA Astrophysics Data System (ADS)
Frasheri, Neki; Bushati, Salvatore; Frasheri, Alfred
2013-04-01
The paper presents results of using MPI parallel processing for the 3D inversion of gravity anomalies. The work is done under the FP7 project HP-SEE (http://www.hp-see.eu/). The inversion of geophysical anomalies remains a challenge, and the use of parallel processing can be a tool to achieve better results, "compensating" the complexity of the ill-posed problem of inversion with the increase of volume of calculations. We considered the gravity as the simplest case of physical fields and experimented an algorithm based in the methodology known as CLEAN and developed by Högbom in 1974. The 3D geosection was discretized in finite cuboid elements and represented by a 3D array of nodes, while the ground surface where the anomaly is observed as a 2D array of points. Starting from a geosection with mass density zero in all nodes, iteratively the algorithm defines the 3D node that offers the best anomaly shape that approximates the observed anomaly minimizing the least squares error; the mass density in the best 3D node is modified with a prefixed density step and the related effect subtracted from the observed anomaly; the process continues until some criteria is fulfilled. Theoretical complexity of he algorithm was evaluated on the basis of iterations and run-time for a geosection discretized in different scales. We considered the average number N of nodes in one edge of the 3D array. The order of number of iterations was evaluated O(N^3); and the order of run-time was evaluated O(N^8). We used several different methods for the identification of the 3D node which effect offers the best least squares error in approximating the observed anomaly: unweighted least squares error for the whole 2D array of anomalous points; weighting least squares error by the inverted value of observed anomaly over each 3D node; and limiting the area of 2D anomalous points where least squares are calculated over shallow 3D nodes. By comparing results from the inversion of single body and two
Reservoir parameter inversion based on weighted statistics
NASA Astrophysics Data System (ADS)
Gui, Jin-Yong; Gao, Jian-Hu; Yong, Xue-Shan; Li, Sheng-Jun; Liu, Bin-Yang; Zhao, Wan-Jin
2015-12-01
Variation of reservoir physical properties can cause changes in its elastic parameters. However, this is not a simple linear relation. Furthermore, the lack of observations, data overlap, noise interference, and idealized models increases the uncertainties of the inversion result. Thus, we propose an inversion method that is different from traditional statistical rock physics modeling. First, we use deterministic and stochastic rock physics models considering the uncertainties of elastic parameters obtained by prestack seismic inversion and introduce weighting coefficients to establish a weighted statistical relation between reservoir and elastic parameters. Second, based on the weighted statistical relation, we use Markov chain Monte Carlo simulations to generate the random joint distribution space of reservoir and elastic parameters that serves as a sample solution space of an objective function. Finally, we propose a fast solution criterion to maximize the posterior probability density and obtain reservoir parameters. The method has high efficiency and application potential.
A Bayesian method for microseismic source inversion
NASA Astrophysics Data System (ADS)
Pugh, D. J.; White, R. S.; Christie, P. A. F.
2016-08-01
Earthquake source inversion is highly dependent on location determination and velocity models. Uncertainties in both the model parameters and the observations need to be rigorously incorporated into an inversion approach. Here, we show a probabilistic Bayesian method that allows formal inclusion of the uncertainties in the moment tensor inversion. This method allows the combination of different sets of far-field observations, such as P-wave and S-wave polarities and amplitude ratios, into one inversion. Additional observations can be included by deriving a suitable likelihood function from the uncertainties. This inversion produces samples from the source posterior probability distribution, including a best-fitting solution for the source mechanism and associated probability. The inversion can be constrained to the double-couple space or allowed to explore the gamut of moment tensor solutions, allowing volumetric and other non-double-couple components. The posterior probability of the double-couple and full moment tensor source models can be evaluated from the Bayesian evidence, using samples from the likelihood distributions for the two source models, producing an estimate of whether or not a source is double-couple. Such an approach is ideally suited to microseismic studies where there are many sources of uncertainty and it is often difficult to produce reliability estimates of the source mechanism, although this can be true of many other cases. Using full-waveform synthetic seismograms, we also show the effects of noise, location, network distribution and velocity model uncertainty on the source probability density function. The noise has the largest effect on the results, especially as it can affect other parts of the event processing. This uncertainty can lead to erroneous non-double-couple source probability distributions, even when no other uncertainties exist. Although including amplitude ratios can improve the constraint on the source probability
Inverse heat conduction problems
NASA Astrophysics Data System (ADS)
Orlande, Helcio Rangel Barreto
We present the solution of the following inverse problems: (1) Inverse Problem of Estimating Interface Conductance Between Periodically Contacting Surfaces; (2) Inverse Problem of Estimating Interface Conductance During Solidification via Conjugate Gradient Method; (3) Determination of the Reaction Function in a Reaction-Diffusion Parabolic Problem; and (4) Simultaneous Estimation of Thermal Diffusivity and Relaxation Time with Hyperbolic Heat Conduction Model. Also, we present the solution of a direct problem entitled: Transient Thermal Constriction Resistance in a Finite Heat Flux Tube. The Conjugate Gradient Method with Adjoint Equation was used in chapters 1-3. The more general function estimation approach was treated in these chapters. In chapter 1, we solve the inverse problem of estimating the timewise variation of the interface conductance between periodically contacting solids, under quasi-steady-state conditions. The present method is found to be more accurate than the B-Spline approach for situations involving small periods, which are the most difficult on which to perform the inverse analysis. In chapter 2, we estimate the timewise variation of the interface conductance between casting and mold during the solidification of aluminum. The experimental apparatus used in this study is described. In chapter 3, we present the estimation of the reaction function in a one dimensional parabolic problem. A comparison of the present function estimation approach with the parameter estimation technique, wing B-Splines to approximate the reaction function, revealed that the use of function estimation reduces the computer time requirements. In chapter 4 we present a finite difference solution for the transient constriction resistance in a cylinder of finite length with a circular contact surface. A numerical grid generation scheme was used to concentrate grid points in the regions of high temperature gradients in order to reduce discretization errors. In chapter 6, we
Sets of Mutually Orthogonal Sudoku Latin Squares
ERIC Educational Resources Information Center
Vis, Timothy; Petersen, Ryan M.
2009-01-01
A Latin square of order "n" is an "n" x "n" array using n symbols, such that each symbol appears exactly once in each row and column. A set of Latin squares is c ordered pairs of symbols appearing in the cells of the array are distinct. The popular puzzle Sudoku involves Latin squares with n = 9, along with the added condition that each of the 9…
The Square Light Clock and Special Relativity
ERIC Educational Resources Information Center
Galli, J. Ronald; Amiri, Farhang
2012-01-01
A thought experiment that includes a square light clock is similar to the traditional vertical light beam and mirror clock, except it is made up of four mirrors placed at a 45[degree] angle at each corner of a square of length L[subscript 0], shown in Fig. 1. Here we have shown the events as measured in the rest frame of the square light clock. By…
Generalized adjustment by least squares ( GALS).
Elassal, A.A.
1983-01-01
The least-squares principle is universally accepted as the basis for adjustment procedures in the allied fields of geodesy, photogrammetry and surveying. A prototype software package for Generalized Adjustment by Least Squares (GALS) is described. The package is designed to perform all least-squares-related functions in a typical adjustment program. GALS is capable of supporting development of adjustment programs of any size or degree of complexity. -Author
Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion
NASA Technical Reports Server (NTRS)
Von Frese, R. R. B.; Hinze, W. J.; Braile, L. W.
1981-01-01
To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1 deg-averaged surface free-air gravity anomalies of POGO satellite magnetometer data for the United States, Mexico, and Central America illustrate the capabilities of the method.
Neutron spectrum unfolding using artificial neural network and modified least square method
NASA Astrophysics Data System (ADS)
Hosseini, Seyed Abolfazl
2016-09-01
In the present paper, neutron spectrum is reconstructed using the Artificial Neural Network (ANN) and Modified Least Square (MLSQR) methods. The detector's response (pulse height distribution) as a required data for unfolding of energy spectrum is calculated using the developed MCNPX-ESUT computational code (MCNPX-Energy engineering of Sharif University of Technology). Unlike the usual methods that apply inversion procedures to unfold the energy spectrum from the Fredholm integral equation, the MLSQR method uses the direct procedure. Since liquid organic scintillators like NE-213 are well suited and routinely used for spectrometry of neutron sources, the neutron pulse height distribution is simulated/measured in the NE-213 detector. The response matrix is calculated using the MCNPX-ESUT computational code through the simulation of NE-213 detector's response to monoenergetic neutron sources. For known neutron pulse height distribution, the energy spectrum of the neutron source is unfolded using the MLSQR method. In the developed multilayer perception neural network for reconstruction of the energy spectrum of the neutron source, there is no need for formation of the response matrix. The multilayer perception neural network is developed based on logsig, tansig and purelin transfer functions. The developed artificial neural network consists of two hidden layers of type hyperbolic tangent sigmoid transfer function and a linear transfer function in the output layer. The motivation of applying the ANN method may be explained by the fact that no matrix inversion is needed for energy spectrum unfolding. The simulated neutron pulse height distributions in each light bin due to randomly generated neutron spectrum are considered as the input data of ANN. Also, the randomly generated energy spectra are considered as the output data of the ANN. Energy spectrum of the neutron source is identified with high accuracy using both MLSQR and ANN methods. The results obtained from
Inversion of SOHO/EPHIN data using regularization techniques
NASA Astrophysics Data System (ADS)
Wimmer-Schweingruber, R. F.; Böhm, E.; Kharytonov, A.; Müller-Mellin, R.; Gomez-Herrero, R.; Heber, B.
2006-12-01
We analyze data from the Solar and Heliospheric Observatory (SOHO) instrument EPHIN (electron, proton, helium instrument) by full deconvolution of the measured data with the instrument response function. We show how regularization methods can be applied to energetic particle measurements to derive unambiguously the original particle spectrum - devoid of any assumptions made about its functional behaviour. This inversion thechnique still requires knowledge of the instrument response function, however, it is an improvement upon normal least-squares or maximum-likelihood fitting procedures because it does not require any a-priori knowlwdge of the underlying particle spectra. Given the instrument response function in matrix form (here derived using Monte Carlo techniques), the original Fredholm integral equations reduce to a discrete system of linear algebraic equations that can be solved by ordinary regularization methods such as singular value decomposition or the Tikhonov method. This procedure alone may laed to unphysical negative results, requiring the further constraint of non-negative count rates. We apply the SVD and Thikonov methods with and without constraints to measured data from SOHO/EPHIN. The derived results agree well with those of other methods that rely on a-priori knowledge of the spectral shape of the particle distribution function, demonstrating the power of the method for more general cases.
Inverse problems for linear hyperbolic equations using mixed formulations
NASA Astrophysics Data System (ADS)
Cîndea, Nicolae; Münch, Arnaud
2015-07-01
We introduce a direct method which allows the solving of numerically inverse problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the equation posed in Ω × (0,T)—Ω being a bounded subset of {{{R}}N}—from a partial distributed observation. We employ a least-squares technique and minimize the L2-norm of the distance from the observation to any solution. Taking the hyperbolic equation as the main constraint of the problem, the optimality conditions are reduced to a mixed formulation involving both the state to reconstruct and a Lagrange multiplier. Under usual geometric optic conditions, we show the well-posedness of this mixed formulation (in particular the inf-sup condition) and then introduce a numerical approximation based on space-time finite element discretization. We prove the strong convergence of the approximation and then discuss several examples for N = 1 and N = 2. The problem of the reconstruction of both the state and the source terms is also addressed.
Inverse Functions and their Derivatives.
ERIC Educational Resources Information Center
Snapper, Ernst
1990-01-01
Presented is a method of interchanging the x-axis and y-axis for viewing the graph of the inverse function. Discussed are the inverse function and the usual proofs that are used for the function. (KR)
Intersections, ideals, and inversion
Vasco, D.W.
1998-10-01
Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly onedimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons.
Schiller, Helmut
2007-05-01
The usage of inverse models to derive parameters of interest from measurements is widespread in science and technology. The operational usage of many inverse models became feasible just by emulation of the inverse model via a neural net (NN). This paper shows how NNs can be used to improve inversion accuracy by minimizing the sum of error squares. The procedure is very fast as it takes advantage of the Jacobian which is a byproduct of the NN calculation. An example from remote sensing is shown. It is also possible to take into account a non-diagonal covariance matrix of the measurement to derive the covariance matrix of the retrieved parameters.
Methods for solving of inverse heat conduction problems
NASA Astrophysics Data System (ADS)
Kobilskaya, E.; Lyashenko, V.
2016-10-01
A general mathematical model of the high-temperature thermodiffusion that occurs in a limited environment is considered. Based on this model a formulation of inverse problems for homogeneous and inhomogeneous parabolic equations is proposed. The inverse problem aims at identifying one or several unknown parameters of the mathematical model. These parameters allow maintaining the required temperature distribution and concentration of distribution of substance in the whole area or in part. For each case (internal, external heat source or a combination) the appropriate method for solving the inverse problem is proposed.
Computational methods for inverse problems in geophysics: inversion of travel time observations
Pereyra, V.; Keller, H.B.; Lee, W.H.K.
1980-01-01
General ways of solving various inverse problems are studied for given travel time observations between sources and receivers. These problems are separated into three components: (a) the representation of the unknown quantities appearing in the model; (b) the nonlinear least-squares problem; (c) the direct, two-point ray-tracing problem used to compute travel time once the model parameters are given. Novel software is described for (b) and (c), and some ideas given on (a). Numerical results obtained with artificial data and an implementation of the algorithm are also presented. ?? 1980.
Towards a Full Waveform Ambient Noise Inversion
NASA Astrophysics Data System (ADS)
Sager, K.; Ermert, L. A.; Boehm, C.; Fichtner, A.
2015-12-01
Noise tomography usually works under the assumption that the inter-station ambient noise correlation is equal to a scaled version of the Green's function between the two receivers. This assumption, however, is only met under specific conditions, for instance, wavefield diffusivity and equipartitioning, zero attenuation, etc., that are typically not satisfied in the Earth. This inconsistency inhibits the exploitation of the full waveform information contained in noise correlations regarding Earth structure and noise generation. To overcome this limitation we attempt to develop a method that consistently accounts for noise distribution, 3D heterogeneous Earth structure and the full seismic wave propagation physics in order to improve the current resolution of tomographic images of the Earth. As an initial step towards a full waveform ambient noise inversion we develop a preliminary inversion scheme based on a 2D finite-difference code simulating correlation functions and on adjoint techniques. With respect to our final goal, a simultaneous inversion for noise distribution and Earth structure, we address the following two aspects: (1) the capabilities of different misfit functionals to image wave speed anomalies and source distribution and (2) possible source-structure trade-offs, especially to what extent unresolvable structure could be mapped into the inverted noise source distribution and vice versa.
Kriging and its relation to least squares
Oden, N.
1984-11-01
Kriging is a technique for producing contour maps that, under certain conditions, are optimal in a mean squared error sense. The relation of Kriging to Least Squares is reviewed here. New methods for analyzing residuals are suggsted, ML estimators inspected, and an expression derived for calculating cross-validation error. An example using ground water data is provided.
Enhancing Students' Understanding of Square Roots
ERIC Educational Resources Information Center
Wiesman, Jeff L.
2015-01-01
Students enrolled in a middle school prealgebra or algebra course often struggle to conceptualize and understand the meaning of radical notation when it is introduced. For example, although it is important for students to approximate the decimal value of a number such as [square root of] 30 and estimate the value of a square root in the form of…
Collinearity in Least-Squares Analysis
ERIC Educational Resources Information Center
de Levie, Robert
2012-01-01
How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually independent, as is often assumed, they are reliable estimators of imprecision and so are the functions…
Three Perspectives on Teaching Least Squares
ERIC Educational Resources Information Center
Scariano, Stephen M.; Calzada, Maria
2004-01-01
The method of Least Squares is the most widely used technique for fitting a straight line to data, and it is typically discussed in several undergraduate courses. This article focuses on three developmentally different approaches for solving the Least Squares problem that are suitable for classroom exposition.
Discovering the Magic of Magic Squares
ERIC Educational Resources Information Center
Semanisinova, Ingrid; Trenkler, Marian
2007-01-01
The purpose of this article is to present a collection of problems that allow students to investigate magic squares and Latin squares, formulate their own conjectures about these mathematical objects, look for arguments supporting or disproving their conjectures, and finally establish and prove mathematical assertions. Each problem is completed…
Sums of Integer Squares: A New Look.
ERIC Educational Resources Information Center
Sastry, K. R. S.; Pranesachar, C. R.; Venkatachala, B. J.
1998-01-01
Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)
BIOMECHANICS. Why the seahorse tail is square.
Porter, Michael M; Adriaens, Dominique; Hatton, Ross L; Meyers, Marc A; McKittrick, Joanna
2015-07-01
Whereas the predominant shapes of most animal tails are cylindrical, seahorse tails are square prisms. Seahorses use their tails as flexible grasping appendages, in spite of a rigid bony armor that fully encases their bodies. We explore the mechanics of two three-dimensional-printed models that mimic either the natural (square prism) or hypothetical (cylindrical) architecture of a seahorse tail to uncover whether or not the square geometry provides any functional advantages. Our results show that the square prism is more resilient when crushed and provides a mechanism for preserving articulatory organization upon extensive bending and twisting, as compared with its cylindrical counterpart. Thus, the square architecture is better than the circular one in the context of two integrated functions: grasping ability and crushing resistance.
Flow Applications of the Least Squares Finite Element Method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
NASA Astrophysics Data System (ADS)
Anderson, J.; Johnson, J. B.; Arechiga, R. O.; Edens, H. E.; Thomas, R. J.
2011-12-01
We use radio frequency (VHF) pulse locations mapped with the New Mexico Tech Lightning Mapping Array (LMA) to study the distribution of thunder sources in lightning channels. A least squares inversion is used to fit channel acoustic energy radiation with broadband (0.01 to 500 Hz) acoustic recordings using microphones deployed local (< 10 km) to the lightning. We model the thunder (acoustic) source as a superposition of line segments connecting the LMA VHF pulses. An optimum branching algorithm is used to reconstruct conductive channels delineated by VHF sources, which we discretize as a superposition of finely-spaced (0.25 m) acoustic point sources. We consider total radiated thunder as a weighted superposition of acoustic waves from individual channels, each with a constant current along its length that is presumed to be proportional to acoustic energy density radiated per unit length. Merged channels are considered as a linear sum of current-carrying branches and radiate proportionally greater acoustic energy. Synthetic energy time series for a given microphone location are calculated for each independent channel. We then use a non-negative least squares inversion to solve for channel energy densities to match the energy time series determined from broadband acoustic recordings across a 4-station microphone network. Events analyzed by this method have so far included 300-1000 VHF sources, and correlations as high as 0.5 between synthetic and recorded thunder energy were obtained, despite the presence of wind noise and 10-30 m uncertainty in VHF source locations.
Bayesian inversion for optical diffraction tomography
NASA Astrophysics Data System (ADS)
Ayasso, H.; Duchêne, B.; Mohammad-Djafari, A.
2010-05-01
In this paper, optical diffraction tomography is considered as a non-linear inverse scattering problem and tackled within the Bayesian estimation framework. The object under test is a man-made object known to be composed of compact regions made of a finite number of different homogeneous materials. This a priori knowledge is appropriately translated by a Gauss-Markov-Potts prior. Hence, a Gauss-Markov random field is used to model the contrast distribution whereas a hidden Potts-Markov field accounts for the compactness of the regions. First, we express the a posteriori distributions of all the unknowns and then a Gibbs sampling algorithm is used to generate samples and estimate the posterior mean of the unknowns. Some preliminary results, obtained by applying the inversion algorithm to laboratory controlled data, are presented.
An efficient method for inverse problems
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1987-01-01
A new inverse method for aerodynamic design of subcritical airfoils is presented. The pressure distribution in this method can be prescribed in a natural way, i.e. as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving a single nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the free stream Mach number M(sub x) and the upstream flow direction theta(sub x). The existence of a solution for any given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils.
NASA Astrophysics Data System (ADS)
Mohammad khaninezhad, M.; Jafarpour, B.
2012-12-01
Data limitation and heterogeneity of the geologic formations introduce significant uncertainty in predicting the related flow and transport processes in these environments. Fluid flow and displacement behavior in subsurface systems is mainly controlled by the structural connectivity models that create preferential flow pathways (or barriers). The connectivity of extreme geologic features strongly constrains the evolution of the related flow and transport processes in subsurface formations. Therefore, characterization of the geologic continuity and facies connectivity is critical for reliable prediction of the flow and transport behavior. The goal of this study is to develop a robust and geologically consistent framework for solving large-scale nonlinear subsurface characterization inverse problems under uncertainty about geologic continuity and structural connectivity. We formulate a novel inverse modeling approach by adopting a sparse reconstruction perspective, which involves two major components: 1) sparse description of hydraulic property distribution under significant uncertainty in structural connectivity and 2) formulation of an effective sparsity-promoting inversion method that is robust against prior model uncertainty. To account for the significant variability in the structural connectivity, we use, as prior, multiple distinct connectivity models. For sparse/compact representation of high-dimensional hydraulic property maps, we investigate two methods. In one approach, we apply the principle component analysis (PCA) to each prior connectivity model individually and combine the resulting leading components from each model to form a diverse geologic dictionary. Alternatively, we combine many realizations of the hydraulic properties from different prior connectivity models and use them to generate a diverse training dataset. We use the training dataset with a sparsifying transform, such as K-SVD, to construct a sparse geologic dictionary that is robust to
The Moore-Penrose Inverse of Block Magic Rectangles
ERIC Educational Resources Information Center
Hakopian, Y. R.; Eloyan, A. N.
2007-01-01
As is known, a semi-magic square is an "n x n" matrix having the sum of entries in each row and each column equal to a constant. This note generalizes this notion and introduce a special class of block matrices called "block magic rectangles." It is proved that the Moore-Penrose inverse of a block magic rectangle is also a block magic rectangle.
Trimming and procrastination as inversion techniques
NASA Astrophysics Data System (ADS)
Backus, George E.
1996-12-01
By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.
NASA Astrophysics Data System (ADS)
Martin, Roland; Monteiller, Vadim; Komatitsch, Dimitri; Perrouty, Stéphane; Jessell, Mark; Bonvalot, Sylvain; Lindsay, Mark
2013-12-01
We solve the 3-D gravity inverse problem using a massively parallel voxel (or finite element) implementation on a hybrid multi-CPU/multi-GPU (graphics processing units/GPUs) cluster. This allows us to obtain information on density distributions in heterogeneous media with an efficient computational time. In a new software package called TOMOFAST3D, the inversion is solved with an iterative least-square or a gradient technique, which minimizes a hybrid L1-/L2-norm-based misfit function. It is drastically accelerated using either Haar or fourth-order Daubechies wavelet compression operators, which are applied to the sensitivity matrix kernels involved in the misfit minimization. The compression process behaves like a pre-conditioning of the huge linear system to be solved and a reduction of two or three orders of magnitude of the computational time can be obtained for a given number of CPU processor cores. The memory storage required is also significantly reduced by a similar factor. Finally, we show how this CPU parallel inversion code can be accelerated further by a factor between 3.5 and 10 using GPU computing. Performance levels are given for an application to Ghana, and physical information obtained after 3-D inversion using a sensitivity matrix with around 5.37 trillion elements is discussed. Using compression the whole inversion process can last from a few minutes to less than an hour for a given number of processor cores instead of tens of hours for a similar number of processor cores when compression is not used.
Pole EXpansion and Selected Inversion (PEXSI)
2014-03-01
The Pole EXpansion and Selected Inversion method (PEXSI) is a fast method for evaluating certain selected elements of a matrix function. PEXSI is highly scalable on distributed memory parallel machines. For sparse matrices, the PEXSI method can be more efficient than the widely used diagonalization method for evaluating matrix functions, especially when a relatively large number of eigenpairs are needed to be computed in the diagonalization methond
Population genomics of inversion polymorphisms in Drosophila melanogaster.
Corbett-Detig, Russell B; Hartl, Daniel L
2012-01-01
Chromosomal inversions have been an enduring interest of population geneticists since their discovery in Drosophila melanogaster. Numerous lines of evidence suggest powerful selective pressures govern the distributions of polymorphic inversions, and these observations have spurred the development of many explanatory models. However, due to a paucity of nucleotide data, little progress has been made towards investigating selective hypotheses or towards inferring the genealogical histories of inversions, which can inform models of inversion evolution and suggest selective mechanisms. Here, we utilize population genomic data to address persisting gaps in our knowledge of D. melanogaster's inversions. We develop a method, termed Reference-Assisted Reassembly, to assemble unbiased, highly accurate sequences near inversion breakpoints, which we use to estimate the age and the geographic origins of polymorphic inversions. We find that inversions are young, and most are African in origin, which is consistent with the demography of the species. The data suggest that inversions interact with polymorphism not only in breakpoint regions but also chromosome-wide. Inversions remain differentiated at low levels from standard haplotypes even in regions that are distant from breakpoints. Although genetic exchange appears fairly extensive, we identify numerous regions that are qualitatively consistent with selective hypotheses. Finally, we show that In(1)Be, which we estimate to be ∼60 years old (95% CI 5.9 to 372.8 years), has likely achieved high frequency via sex-ratio segregation distortion in males. With deeper sampling, it will be possible to build on our inferences of inversion histories to rigorously test selective models-particularly those that postulate that inversions achieve a selective advantage through the maintenance of co-adapted allele complexes.
Spacecraft inertia estimation via constrained least squares
NASA Technical Reports Server (NTRS)
Keim, Jason A.; Acikmese, Behcet A.; Shields, Joel F.
2006-01-01
This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.
Free coherent spinons in quantum square ice
NASA Astrophysics Data System (ADS)
Kourtis, Stefanos; Castelnovo, Claudio
2016-09-01
We investigate the quantum dynamics of monopolelike excitations in quantum square ice, as captured by the strongly anisotropic spin-1/2 XXZ model on the checkerboard lattice. We obtain exact results for excitation dynamics in both analytically solvable effective models and a fully interacting model of quantum square ice on finite clusters. We find that the dispersive lower bound of the dynamic response of freely propagating spinons is recovered in the dynamic structure factor of the interacting system, yielding a marked fingerprint of coherent spinon dispersion. Our results provide unbiased evidence for the formation of coherent quasiparticles propagating freely in the correlated "vacuum" of quantum square ice.
Efficient Geostatistical Inversion under Transient Flow Conditions in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Klein, Ole; Cirpka, Olaf A.; Bastian, Peter; Ippisch, Olaf
2014-05-01
The assessment of hydraulic aquifer parameters is important for the evaluation of anthropogenic impacts on groundwater resources. The distribution of these parameters determines flow paths and solute travel times and is therefore critical for the successful design and deployment of remediation schemes at contaminated sites. Direct measurement of these properties is not possible, making indirect observations through dependent quantities and parameter estimation a necessity. The geostatistical approach characterizes these hydraulic parameters without predetermined zonation. The parameter fields are treated as stochastic processes, optionally incorporating a priori information in the probability distribution. Maximizing the likelihood of the parameters with regard to the given observations yields a parameter estimate with high spatial resolution. This approach naturally leads to nonlinear least squares optimization problems, namely objective functions of the form L(Y ) = 1(Y ')TQ -Y1YY ' + 1[F(Y) - z]T Q-z1z [F(Y )- z], 2 2 where Y are the parameters, Y ' their deviations from the a priori estimate, QY Y their covariance matrix, z the measurements, Qzz their covariance matrix and F the forward model mapping parameters to observations. In theory, this objective function may be minimized using standard gradient-based techniques like Gauss-Newton. Due to the typically high number of parameters, however, this is not practical. Let nY be the number of parameters and nz the number of observations. Then QY Y and its inverse are both dense nY ×nY matrices, and the sensitivity matrix Hz := δz/δY is a nz ×nY matrix that has to be assembled using forward or adjoint model runs. Specialized schemes have been developed to reduce the dimensionality of the problem and avoid the high cost of handling products with QY Y -1. This enables efficient inversion in the case of a moderate number of observations as encountered in stationary inversion, where the cost of assembling Hz is in
Alkhazov, G. D.; Vorobyov, A. A.; Dobrovolsky, A. V. Inglessi, A. G.; Korolev, G. A.; Khanzadeev, A. V.
2015-05-15
In order to study the spatial structure of exotic nuclei, it was proposed at the Petersburg Nuclear Physics Institute (PNPI) to measure the differential cross section for small-angle proton elastic scattering in inverse kinematics. Several experiments in beams of 0.7-GeV/nucleon exotic nuclei were performed at the heavy-ion accelerator facility of GSI (Gesellschaft für Schwerionenforschung, Darmstadt, Germany) by using the IKAR ionization spectrometer developed at PNPI. The IKAR ionization chamber filled with hydrogen at a pressure of 10 bar served simultaneously as a target and as a recoil-proton detector, which measured the recoil-proton energy. The beam-particle scattering angle was also measured. The results obtained for the cross sections in question were analyzed on the basis of the Glauber-Sitenko theory using phenomenological nuclear-density distributions with two free parameters. Nuclear-matter distributions and root-mean-square radii were found for the nuclei under investigation. The size of the halo in the {sup 6}He, {sup 8}He, {sup 11}Li, and {sup 14}Be nuclei was determined among other things. Information about neutron distributions in nuclei was deduced by combining the data obtained here with the known values of the radii of proton distributions. A sizable neutron skin was revealed in the {sup 8}Li, {sup 9}Li, and {sup 12}Be nuclei.
NASA Astrophysics Data System (ADS)
Alkhazov, G. D.; Vorobyov, A. A.; Dobrovolsky, A. V.; Inglessi, A. G.; Korolev, G. A.; Khanzadeev, A. V.
2015-05-01
In order to study the spatial structure of exotic nuclei, it was proposed at the Petersburg Nuclear Physics Institute (PNPI) to measure the differential cross section for small-angle proton elastic scattering in inverse kinematics. Several experiments in beams of 0.7-GeV/nucleon exotic nuclei were performed at the heavy-ion accelerator facility of GSI (Gesellschaft für Schwerionenforschung, Darmstadt, Germany) by using the IKAR ionization spectrometer developed at PNPI. The IKAR ionization chamber filled with hydrogen at a pressure of 10 bar served simultaneously as a target and as a recoil-proton detector, which measured the recoil-proton energy. The beam-particle scattering angle was also measured. The results obtained for the cross sections in question were analyzed on the basis of the Glauber-Sitenko theory using phenomenological nuclear-density distributions with two free parameters. Nuclear-matter distributions and root-mean-square radii were found for the nuclei under investigation. The size of the halo in the 6He, 8He, 11Li, and 14Be nuclei was determined among other things. Information about neutron distributions in nuclei was deduced by combining the data obtained here with the known values of the radii of proton distributions. A sizable neutron skin was revealed in the 8Li, 9Li, and 12Be nuclei.
A spectral mimetic least-squares method
Bochev, Pavel; Gerritsma, Marc
2014-09-01
We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.
Filling Squares: Variations on a Theme.
ERIC Educational Resources Information Center
Senteni, Alain
1986-01-01
Four methods of filling a square using programing with Logo are presented, with comments on children's solutions. Analysis of the mathematical or programing concepts underlying a few simple algorithms is the focus. (MNS)
A spectral mimetic least-squares method
Bochev, Pavel; Gerritsma, Marc
2014-09-01
We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less
NASA Astrophysics Data System (ADS)
Zhou, Shiqi; Solana, J. R.
2013-10-01
Monte Carlo simulations in the canonical ensemble are performed for fluid with potential consisting of a square-well plus a square-barrier to obtain thermodynamic properties such as pressure, excess energy, constant volume excess heat capacity, and excess chemical potential, and structural property such as radial distribution function. The simulations cover a wide density range for the fluid phase, several temperatures, and different combinations of the parameters defining the potential. These simulation data have been used to test performances of a coupling parameter series expansion (CPSE) recently proposed by one of the authors [S. Zhou, Phys. Rev. E 74, 031119 (2006)], and a traditional 2nd-order high temperature series expansion (HTSE) based on a macroscopic compressibility approximation (MAC) used with confidence since its introduction in 1967. It is found that (i) the MCA-based 2nd-order HTSE unexpectedly and depressingly fails for most situations investigated, and the present simulation results can serve well as strict criteria for testing liquid state theories. (ii) The CPSE perturbation scheme is shown to be capable of predicting very accurately most of the thermodynamic properties simulated, but the most appropriate level of truncating the CPSE differs and depends on the range of the potential to be calculated; in particular, the shorter the potential range is, the higher the most appropriate truncating level can be, and along with rising of the potential range the performance of the CPSE perturbation scheme will decrease at higher truncating level. (iii) The CPSE perturbation scheme can calculate satisfactorily bulk fluid rdf, and such calculations can be done for all fluid states of the whole phase diagram. (iv) The CPSE is a convergent series at higher temperatures, but show attribute of asymptotic series at lower temperatures, and as a result, the surest asymptotic value occurs at lower-order truncation.
An inverse problem by boundary element method
Tran-Cong, T.; Nguyen-Thien, T.; Graham, A.L.
1996-02-01
Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.
Applications of square-related theorems
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
Identification of Selective ERRγ Inverse Agonists.
Kim, Jina; Im, Chun Young; Yoo, Eun Kyung; Ma, Min Jung; Kim, Sang-Bum; Hong, Eunmi; Chin, Jungwook; Hwang, Hayoung; Lee, Sungwoo; Kim, Nam Doo; Jeon, Jae-Han; Lee, In-Kyu; Jeon, Yong Hyun; Choi, Hueng-Sik; Kim, Seong Heon; Cho, Sung Jin
2016-01-12
GSK5182 (4) is currently one of the lead compounds for the development of estrogen-related receptor gamma (ERRγ) inverse agonists. Here, we report the design, synthesis, pharmacological and in vitro absorption, distribution, metabolism, excretion, toxicity (ADMET) properties of a series of compounds related to 4. Starting from 4, a series of analogs were structurally modified and their ERRγ inverse agonist activity was measured. A key pharmacophore feature of this novel class of ligands is the introduction of a heterocyclic group for A-ring substitution in the core scaffold. Among the tested compounds, several of them are potent ERRγ inverse agonists as determined by binding and functional assays. The most promising compound, 15g, had excellent binding selectivity over related subtypes (IC50 = 0.44, >10, >10, and 10 μM at the ERRγ, ERRα, ERRβ, and ERα subtypes, respectively). Compound 15g also resulted in 95% transcriptional repression at a concentration of 10 μM, while still maintaining an acceptable in vitro ADMET profile. This novel class of ERRγ inverse agonists shows promise in the development of drugs targeting ERRγ-related diseases.
The NYU inverse swept wing code
NASA Technical Reports Server (NTRS)
Bauer, F.; Garabedian, P.; Mcfadden, G.
1983-01-01
An inverse swept wing code is described that is based on the widely used transonic flow program FLO22. The new code incorporates a free boundary algorithm permitting the pressure distribution to be prescribed over a portion of the wing surface. A special routine is included to calculate the wave drag, which can be minimized in its dependence on the pressure distribution. An alternate formulation of the boundary condition at infinity was introduced to enhance the speed and accuracy of the code. A FORTRAN listing of the code and a listing of a sample run are presented. There is also a user's manual as well as glossaries of input and output parameters.
Stress inversion assumptions review
NASA Astrophysics Data System (ADS)
Lejri, Mostfa; Maerten, Frantz; Maerten, Laurent; Joonnenkindt, Jean Pierre; Soliva, Roger
2014-05-01
Wallace (1951) and Bott (1959) were the first to introduce the idea that the slip on each fault surface has the same direction and sense as the maximum shear stress resolved on that surface. This hypothesis are based on the assumptions that (i) faults are planar, (ii) blocks are rigid, (iii) neither stress perturbations nor block rotations along fault surfaces occur and (iv), the applied stress state is uniform. However, this simplified hypothesis is questionable since complex fault geometries, heterogeneous fault slip directions, evidences of stress perturbations in microstructures and block rotations along fault surfaces were reported in the literature. Earlier numerical geomechanical models confirmed that the striation lines (slip vectors) are not necessarily parallel to the maximum shear stress vector but is consistent with local stress perturbations. This leads us to ask as to what extent the Wallace and Bott simplifications are reliable as a basis hypothesis for stress inversion. In this presentation, a geomechanical multi-parametric study using 3D boundary element method (BEM), covering (i) fault geometries such as intersected faults or corrugated fault surfaces, (ii) the full range of Andersonian state of stress, (iii) fault friction, (iv) half space effect and (v), rock properties, is performed in order to understand the effect of each parameter on the angular misfit between geomechanical slip vectors and the resolved shear stresses. It is shown that significant angular misfits can be found under specific configurations and therefore we conclude that stress inversions based on the Wallace-Bott hypothesis might sometime give results that should be interpreted with care. Major observations are that (i) applying optimum tectonic stress conditions on complex fault geometries can increase the angular misfit, (ii) elastic material properties, combined to half-space effect, can enhance this effect, and (iii) an increase of the sliding friction leads to a
Inverse magnetorheological fluids.
Rodríguez-Arco, L; López-López, M T; Zubarev, A Y; Gdula, K; Durán, J D G
2014-09-01
We report a new kind of field-responsive fluid consisting of suspensions of diamagnetic (DM) and ferromagnetic (FM) microparticles in ferrofluids. We designate them as inverse magnetorheological (IMR) fluids for analogy with inverse ferrofluids (IFFs). Observations on the particle self-assembly in IMR fluids upon magnetic field application showed that DM and FM microparticles were assembled into alternating chains oriented along the field direction. We explain such assembly on the basis of the dipolar interaction energy between particles. We also present results on the rheological properties of IMR fluids and, for comparison, those of IFFs and bidispersed magnetorheological (MR) fluids. Interestingly, we found that upon magnetic field application, the rheological properties of IMR fluids were enhanced with respect to bidispersed MR fluids with the same FM particle concentration, by an amount greater than the sum of the isolated contribution of DM particles. Furthermore, the field-induced yield stress was moderately increased when up to 30% of the total FM particle content was replaced with DM particles. Beyond this point, the dependence of the yield stress on the DM content was non-monotonic, as expected for FM concentrations decreasing to zero. We explain these synergistic results by two separate phenomena: the formation of exclusion areas for FM particles due to the perturbation of the magnetic field by DM particles and the dipole-dipole interaction between DM and FM particles, which enhances the field-induced structures. Based on the second phenomenon, we present a theoretical model for the yield stress that semi-quantitatively predicts the experimental results. PMID:25022363
Wavelet Sparse Approximate Inverse Preconditioners
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Tang, W.-P.; Wan, W. L.
1996-01-01
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Inverse statistical mechanics, lattice packings, and glasses
NASA Astrophysics Data System (ADS)
Marcotte, Etienne
Computer simulation methods enable the investigation of systems and properties that are intractable by purely analytical or experimental approaches. Each chapter of this dissertation contains an application of simulation methods to solve complex physical problems consisting of interacting many-particle or many-spin systems. The problems studied in this dissertation can be divided up into the following two broad categories: inverse and forward problems. The inverse problems considered are those in which we construct an interaction potential such that the corresponding ground state is a targeted configuration. In Chapters 2 and 3, we devise convex pair-potential functions that result in low-coordinated ground states. Chapter 2 describes targeted ground states that are the square and honeycomb crystals, while in Chapter 3 the targeted ground state is the diamond crystal. Chapter 4 applies similar techniques to explicitly enumerate all unique ground states up to a given system size, for spin configurations that interact according to generalized isotropic Ising potentials with finite range. We also consider forward statistical-mechanical problems. In Chapter 5, we adapt a linear programming algorithm to find the densest lattice packings across Euclidean space dimensions. In Chapter 6, we demonstrate that for two different glass models a signature of the glass transition is apparent well before the transition temperature is reached. In both models, this signature appears as nonequilibrium length scales that grow upon supercooling.
Inverse problems biomechanical imaging (Conference Presentation)
NASA Astrophysics Data System (ADS)
Oberai, Assad A.
2016-03-01
It is now well recognized that a host of imaging modalities (a list that includes Ultrasound, MRI, Optical Coherence Tomography, and optical microscopy) can be used to "watch" tissue as it deforms in response to an internal or external excitation. The result is a detailed map of the deformation field in the interior of the tissue. This deformation field can be used in conjunction with a material mechanical response to determine the spatial distribution of material properties of the tissue by solving an inverse problem. Images of material properties thus obtained can be used to quantify the health of the tissue. Recently, they have been used to detect, diagnose and monitor cancerous lesions, detect vulnerable plaque in arteries, diagnose liver cirrhosis, and possibly detect the onset of Alzheimer's disease. In this talk I will describe the mathematical and computational aspects of solving this class of inverse problems, and their applications in biology and medicine. In particular, I will discuss the well-posedness of these problems and quantify the amount of displacement data necessary to obtain a unique property distribution. I will describe an efficient algorithm for solving the resulting inverse problem. I will also describe some recent developments based on Bayesian inference in estimating the variance in the estimates of material properties. I will conclude with the applications of these techniques in diagnosing breast cancer and in characterizing the mechanical properties of cells with sub-cellular resolution.
Inverse models: A necessary next step in ground-water modeling
Poeter, E.P.; Hill, M.C.
1997-01-01
Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.
Probability distributions for magnetotellurics
Stodt, John A.
1982-11-01
Estimates of the magnetotelluric transfer functions can be viewed as ratios of two complex random variables. It is assumed that the numerator and denominator are governed approximately by a joint complex normal distribution. Under this assumption, probability distributions are obtained for the magnitude, squared magnitude, logarithm of the squared magnitude, and the phase of the estimates. Normal approximations to the distributions are obtained by calculating mean values and variances from error propagation, and the distributions are plotted with their normal approximations for different percentage errors in the numerator and denominator of the estimates, ranging from 10% to 75%. The distribution of the phase is approximated well by a normal distribution for the range of errors considered, while the distribution of the logarithm of the squared magnitude is approximated by a normal distribution for a much larger range of errors than is the distribution of the squared magnitude. The distribution of the squared magnitude is most sensitive to the presence of noise in the denominator of the estimate, in which case the true distribution deviates significantly from normal behavior as the percentage errors exceed 10%. In contrast, the normal approximation to the distribution of the logarithm of the magnitude is useful for errors as large as 75%.
Aquifer Structure Identification Using Stochastic Inversion
Harp, Dylan R; Dai, Zhenxue; Wolfsberg, Andrew V; Vrugt, Jasper A
2008-01-01
This study presents a stochastic inverse method for aquifer structure identification using sparse geophysical and hydraulic response data. The method is based on updating structure parameters from a transition probability model to iteratively modify the aquifer structure and parameter zonation. The method is extended to the adaptive parameterization of facies hydraulic parameters by including these parameters as optimization variables. The stochastic nature of the statistical structure parameters leads to nonconvex objective functions. A multi-method genetically adaptive evolutionary approach (AMALGAM-SO) was selected to perform the inversion given its search capabilities. Results are obtained as a probabilistic assessment of facies distribution based on indicator cokriging simulation of the optimized structural parameters. The method is illustrated by estimating the structure and facies hydraulic parameters of a synthetic example with a transient hydraulic response.
Linear functional minimization for inverse modeling
Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; Tartakovsky, Daniel M.
2015-06-01
In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulic head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.
Compression scheme for geophysical electromagnetic inversions
NASA Astrophysics Data System (ADS)
Abubakar, A.
2014-12-01
We have developed a model-compression scheme for improving the efficiency of the regularized Gauss-Newton inversion algorithm for geophysical electromagnetic applications. In this scheme, the unknown model parameters (the conductivity/resistivity distribution) are represented in terms of a basis such as Fourier and wavelet (Haar and Daubechies). By applying a truncation criterion, the model may then be approximated by a reduced number of basis functions, which is usually much less than the number of the model parameters. Further, because the geophysical electromagnetic measurements have low resolution, it is sufficient for inversion to only keep the low-spatial frequency part of the image. This model-compression scheme accelerates the computational time and also reduces the memory usage of the Gauss-Newton method. We are able to significantly reduce the algorithm computational complexity without compromising the quality of the inverted models.
[Inversion of leaf area index during different growth stages in winter wheat].
Zhao, Juan; Huang, Wen-jiang; Zhang, Yao-hong; Jing, Yuan-shu
2013-09-01
Being orientated to the low prescion of crop leaf area index (LAI) inversion using the same spectral vegetation index during different crop growth stages, the present paper analyzed the precision of LAI inversion by employing NDVI(normalized difference vegetation index). Ten vegetation indices were chosen including six broad-band vegetation indices and four narrow-band vegetation indices responding to vegetation cover to inverse LAI in different growth stages. Several conclusions were drawn according to the analysis. The determinant coefficient (R2) and root mean square error (RMSE) between LAI inversion value and true value were 0.5585 and 0.3209 respectively during the whole growth duraton. The mSR (modified simple ratio index) index was appropriate to inverse of LAI during earlier growth stages (before jointing stage) in winter wheat. The R2 and RMSE between LAI inversion value and true value were 0.7287 and 0.2971 respectively. The SR (simple ratio index) index was suitable enough to inverse of LAI during medium growth stages (from joingting stagess to heading stages). The R2 and RMSE between LAI inversion value and true value were 0.6546 and 0.3061 respectively. The NDVI (normalized difference vegetation index) index was proven to be fine to inverse LAI during later growth stages(from heading stage to ripening stage). The R2 and RMSE between LAI inversion value and true value were 0.6794 and 0.3164 respectively. Therefore it was indicated that the results of LAI inversion was much better inverse of winter wheat LAI choosing different vegetation indices during differen growth stages for winter wheat according to the change of vegetation cover and canopy reflectance than merely with NDVI to inverse LAI in the whole growth stages. It was concluded that the precision of LAI inversion was significantly improved with segmented models based on different vegetation indices.
Modular theory of inverse systems
NASA Technical Reports Server (NTRS)
1979-01-01
The relationship between multivariable zeros and inverse systems was explored. A definition of zero module is given in such a way that it is basis independent. The existence of essential right and left inverses were established. The way in which the abstract zero module captured previous definitions of multivariable zeros is explained and examples are presented.
Inversion exercises inspired by mechanics
NASA Astrophysics Data System (ADS)
Groetsch, C. W.
2016-02-01
An elementary calculus transform, inspired by the centroid and gyration radius, is introduced as a prelude to the study of more advanced transforms. Analysis of the transform, including its inversion, makes use of several key concepts from basic calculus and exercises in the application and inversion of the transform provide practice in the use of technology in calculus.
Inverse Problems of Thermoelectricity
NASA Astrophysics Data System (ADS)
Anatychuk, L. I.; Luste, O. J.; Kuz, R. V.; Strutinsky, M. N.
2011-05-01
Classical thermoelectricity is based on the use of the Seebeck and Thomson effects that occur in the near-contact areas between n- and p-type materials. A conceptually different approach to thermoelectric power converter design that is based on the law of thermoelectric induction of currents is also known. The efficiency of this approach has already been demonstrated by its first applications. More than 10 basically new types of thermoelements were discovered with properties that cannot be achieved by thermocouple power converters. Therefore, further development of this concept is of practical interest. This paper provides a classification and theory for solving the inverse problems of thermoelectricity that form the basis for devising new thermoelement types. Computer methods for their solution for anisotropic and inhomogeneous media are elaborated. Regularities related to thermoelectric current excitation in anisotropic and inhomogeneous media are established. The possibility of obtaining eddy currents of a particular configuration through control of the temperature field and material parameters for the creation of new thermo- element types is demonstrated for three-dimensional (3D) models of anisotropic and inhomogeneous media.
Inverse problem in hydrogeology
NASA Astrophysics Data System (ADS)
Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.
2005-03-01
The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice. L'état du problème inverse des eaux souterraines est synthétisé. L'accent est placé sur la caractérisation de l'aquifère, où les modélisateurs doivent jouer avec l'incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d'échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d'état (charges hydrauliques, concentrations) des propriétés de l'aquifère. A cause de ces difficultés, le calibrage ne peut êtreséparé du processus de modélisation, comme c'est le
Polarization of inverse plasmon scattering
NASA Technical Reports Server (NTRS)
Windsor, R. A.; Kellogg, P. J.
1974-01-01
The scattering of electrostatic plasma waves by a flux of ultrarelativistic electrons passing through a plasma gives rise to a radiation spectrum which is similar to a synchrotron radiation spectrum. This mechanism, first considered by Gailitis and Tsytovich, is analagous to inverse Compton scattering, and we have named it inverse plasmon scattering. For a power-law electron flux, both inverse plasmon scattering and synchrotron radiation have the same spectral index. In an attempt to distinguish between these mechanisms, we have calculated the polarization level expected from inverse plasmon scattering. The polarization level found is similar to that obtained from a synchrotron radiation source. This means that the radiation produced by two mechanisms, synchrotron radiation and inverse plasmon scattering, is indistinguishable; and this attempt to differentiate between them by polarization effects has been unsuccessful.
Finding A Minimally Informative Dirichlet Prior Using Least Squares
Dana Kelly
2011-03-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson \\lambda, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in the form of a standard distribution (e.g., beta, gamma), and so a beta distribution is used as an approximation in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial model for common-cause failure, must be estimated from data that are often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Square wave analysis of dielectric rectangular waveguide
NASA Astrophysics Data System (ADS)
Dabas, Deepender; Sharma, Jigyasa; Raghava, N. S.; De, Asok
2013-01-01
In this paper, rectangular wave guides have been analyzed using a square wave incidence which can be used for digital communicat ion techniques . The E 1/mnmode of propagation is solved using Eigen functions taking transverse propagation constant in different regions of dielectric waveguide and then the characteristic equations have been derived. The characteristic equations are solved graphically by mode matching inside and outside fields of waveguide. The normalized propagation constant so obtained, for square wave incidence is compared with the sinusoidal wave obtained by Marcatili method and other methods. The results match fairly well at frequencies near the cut-off of dielectric waveguide.
On the Classification of Fractal Squares
NASA Astrophysics Data System (ADS)
Luo, Jun Jason; Liu, Jing-Cheng
2016-01-01
In the previous paper [K. S. Lau, J. J. Luo and H. Rao, Topological structure of fractal squares, Math. Proc. Camb. Phil. Soc. 155 (2013) 73-86], Lau, Luo and Rao completely classified the topological structure of so called fractal square F defined by F = (F + 𝒟)/n, where 𝒟 ⊊ {0, 1,…,n - 1}2,n ≥ 2. In this paper, we further provide simple criteria for the F to be totally disconnected, then we discuss the Lipschitz classification of F in the case n = 3, which is an attempt to consider non-totally disconnected sets.
NASA Technical Reports Server (NTRS)
Nelson, Michael R.; Mccaffrey, Robert; Molnar, Peter
1987-01-01
The style and the distribution of faulting occurring today in the Tien Shan region were studied, by digitizing long-period World-Wide Standard Seismograph Network P and SH waveforms of 11 of the largest Tien Shan earthquakes between 1965 and 1982 and then using a least squares inversion routine to constrain their fault plane solutions and depths. The results of the examination indicate that north-south shortening is presently occurring in the Tien Shan, with the formation of basement uplifts flanked by moderately dipping thrust faults. The present-day tectonics of the Tien Shan seem to be analogous to those of the Rocky Mountains in Colorado, Wyoming, and Utah during the Laramide orogeny in Late Cretaceous and Early Tertiary time.
Scaling of Greenwood Peierls conductance on a diluted square lattice
NASA Astrophysics Data System (ADS)
Schwalm, William; Schmitz, Albert
The modified rectangle lattice of Dhar is a bond-diluted square lattice. The structure is self-similar and finitely ramified, like a fractal. Nevertheless certain discrete Schrödinger equation Green functions for the modified rectangle are known in closed form in the infinite lattice limit and the spectrum is continuous. By standard transfer matrix renormalization methods we present a study scaling properties of the Greenwood Peierls conductance distribution across the lattice with one dimensional lead wires attached as a function of lattice size and of additional disorder of several types.
Creation of identical multiple focal spots with prescribed axial distribution.
Yu, Yanzhong; Zhan, Qiwen
2015-01-01
We present a scheme for the construction of coaxially equidistant multiple focal spots with identical intensity profiles for each individual focus and a predetermined number and spacing. To achieve this, the radiation field from an antenna is reversed and then gathered by high numerical aperture objective lenses. Radiation patterns from three types of line sources, i.e., the electric current, magnetic current and electromagnetic current distributions, with cosine-squared taper are respectively employed to generate predominately longitudinally polarized bright spots, azimuthally polarized doughnuts, and focal spots with a perfect spherically symmetric intensity distribution. The required illuminations at the pupil plane of a 4Pi focusing configuration for the creation of these identical multiple focal spots can be easily derived by solving the inverse problem of the antenna radiation field. These unique focal field distributions may find potential applications in laser direct writing and optical microscopy, as well as multiple-particle trapping, alignment, and acceleration along the optical axis. PMID:26424051
Creation of identical multiple focal spots with prescribed axial distribution
NASA Astrophysics Data System (ADS)
Yu, Yanzhong; Zhan, Qiwen
2015-10-01
We present a scheme for the construction of coaxially equidistant multiple focal spots with identical intensity profiles for each individual focus and a predetermined number and spacing. To achieve this, the radiation field from an antenna is reversed and then gathered by high numerical aperture objective lenses. Radiation patterns from three types of line sources, i.e., the electric current, magnetic current and electromagnetic current distributions, with cosine-squared taper are respectively employed to generate predominately longitudinally polarized bright spots, azimuthally polarized doughnuts, and focal spots with a perfect spherically symmetric intensity distribution. The required illuminations at the pupil plane of a 4Pi focusing configuration for the creation of these identical multiple focal spots can be easily derived by solving the inverse problem of the antenna radiation field. These unique focal field distributions may find potential applications in laser direct writing and optical microscopy, as well as multiple-particle trapping, alignment, and acceleration along the optical axis.
NASA Astrophysics Data System (ADS)
Koehn, Daniel; Toussaint, Renaud; Ebner, Marcus; Gomez-Rivas, Enrique; Bons, Paul; Rood, Daisy
2014-05-01
Stylolites are localized dissolution seams that can be found in a variety of rocks, and can form due to sediment compaction or tectonic forces. Dissolution of the host-rock next to the stylolite is a function of the applied stress on the stylolite plane. Stylolite teeth indicate the direction of the main compressive stress. Recent advances have shown that the stylolite roughness also shows a stress scaling relation that can be used to calculate magnitudes of stress. Elastic and surface energies produce a different roughness, and the transition between the two is stress dependent and can be quantified. In order to measure the roughness a two or three-dimensional section of a stylolite plane is taken and transferred to a one-dimensional function. The cross-over in the roughness is then picked with the help of an FFT plot. Using this method the burial depth of sedimentary stylolites can be determined. Moreover, tectonic stylolites can be used to determine the full three-dimensional stress tensor if the paleodepth of the tectonic stylolite is known. Stylolites can also be used to find fault offsets and to understand when these faults were active and how the paleotopography looked like at the time the stylolites grew. However, uncertainties remain since Youngs Modulus, Poisson Ratio and surface energy may vary in rocks. In addition, the stylolites record only a snapshot in time, probably the moment when they closed and stopped dissolving. We show examples of the use of stress inversion for stylolite formation conditions in different tectonic settings, and discuss the potential of the method.
Microwave inverse Cerenkov accelerator
NASA Astrophysics Data System (ADS)
Zhang, T. B.; Marshall, T. C.; LaPointe, M. A.; Hirshfield, J. L.
1997-03-01
A Microwave Inverse Cerenkov Accelerator (MICA) is currently under construction at the Yale Beam Physics Laboratory. The accelerating structure in MICA consists of an axisymmetric dielectrically lined waveguide. For the injection of 6 MeV microbunches from a 2.856 GHz RF gun, and subsequent acceleration by the TM01 fields, particle simulation studies predict that an acceleration gradient of 6.3 MV/m can be achieved with a traveling-wave power of 15 MW applied to the structure. Synchronous injection into a narrow phase window is shown to allow trapping of all injected particles. The RF fields of the accelerating structure are shown to provide radial focusing, so that longitudinal and transverse emittance growth during acceleration is small, and that no external magnetic fields are required for focusing. For 0.16 nC, 5 psec microbunches, the normalized emittance of the accelerated beam is predicted to be less than 5πmm-mrad. Experiments on sample alumina tubes have been conducted that verify the theoretical dispersion relation for the TM01 mode over a two-to-one range in frequency. No excitation of axisymmetric or non-axisymmetric competing waveguide modes was observed. High power tests showed that tangential electric fields at the inner surface of an uncoated sample of alumina pipe could be sustained up to at least 8.4 MV/m without breakdown. These considerations suggest that a MICA test accelerator can be built to examine these predictions using an available RF power source, 6 MeV RF gun and associated beam line.
Eta Squared and Partial Eta Squared as Measures of Effect Size in Educational Research
ERIC Educational Resources Information Center
Richardson, John T. E.
2011-01-01
Eta squared measures the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable. Partial eta squared is a similar measure in which the effects of other independent variables and interactions are partialled out. The development of these measures is…
Least Squares Estimation of Item Response Theory Linking Coefficients.
ERIC Educational Resources Information Center
Ogasawara, Haruhiko
2001-01-01
Discusses three types of least squares estimation (generalized, unweighted, and weighted). Results from a Monte Carlo simulation show that, in comparison with other least squares methods, the weighted least squared method generally reduced bias without increasing asymptotic standard errors. (SLD)
Temperature inversion in China seas
NASA Astrophysics Data System (ADS)
Hao, Jiajia; Chen, Yongli; Wang, Fan
2010-12-01
Temperature inversion was reported as a common phenomenon in the areas near the southeastern Chinese coast (region A), west and south of the Korean Peninsula (region B), and north and east of the Shandong Peninsula (region C) during October-May in the present study, based on hydrographic data archived from 1930 through 2001 (319,029 profiles). The inversion was found to be remarkable with obvious temporal and spatial variabilities in both magnitude and coverage, with higher probabilities in region A (up to about 60%) and region C (40%-50%) than in region B (15%-20%). The analysis shows that seasonal variation of the net air-sea heat flux is closely related to the occurrence time of the inversion in the three areas, while the Yangtze and Yellow river freshwater plumes in the surface layer and ocean origin saline water in the subsurface layer maintain stable stratification. It seems that the evaporation/excessive precipitation flux makes little contribution to maintaining the stable inversion. Advection of surface fresh water by the wind-driven coastal currents results in the expansion of inversion in regions A and C. The inversion lasts for the longest period in region A (October-May) sustained by the Taiwan Warm Current carrying the subsurface saline water, while evolution of the inversion in region B is mainly controlled by the Yellow Sea Warm Current.
On Least Squares Fitting Nonlinear Submodels.
ERIC Educational Resources Information Center
Bechtel, Gordon G.
Three simplifying conditions are given for obtaining least squares (LS) estimates for a nonlinear submodel of a linear model. If these are satisfied, and if the subset of nonlinear parameters may be LS fit to the corresponding LS estimates of the linear model, then one attains the desired LS estimates for the entire submodel. Two illustrative…
Interpreting Least Squares without Sampling Assumptions.
ERIC Educational Resources Information Center
Beaton, Albert E.
Least squares fitting process as a method of data reduction is presented. The general strategy is to consider fitting (linear) models as partitioning data into a fit and residuals. The fit can be parsimoniously represented by a summary of the data. A fit is considered adequate if the residuals are small enough so that manipulating their signs and…
Combinatorics of least-squares trees.
Mihaescu, Radu; Pachter, Lior
2008-09-01
A recurring theme in the least-squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least-squares estimates of edge lengths. These formulas have proved useful for the development of efficient algorithms, and have also been important for understanding connections among popular phylogeny algorithms. For example, the selection criterion of the neighbor-joining algorithm is now understood in terms of the combinatorial formulas of Pauplin for estimating tree length. We highlight a phylogenetically desirable property that weighted least-squares methods should satisfy, and provide a complete characterization of methods that satisfy the property. The necessary and sufficient condition is a multiplicative four-point condition that the variance matrix needs to satisfy. The proof is based on the observation that the Lagrange multipliers in the proof of the Gauss-Markov theorem are tree-additive. Our results generalize and complete previous work on ordinary least squares, balanced minimum evolution, and the taxon-weighted variance model. They also provide a time-optimal algorithm for computation.
Least squares estimation of avian molt rates
Johnson, D.H.
1989-01-01
A straightforward least squares method of estimating the rate at which birds molt feathers is presented, suitable for birds captured more than once during the period of molt. The date of molt onset can also be estimated. The method is applied to male and female mourning doves.
Least-squares fitting Gompertz curve
NASA Astrophysics Data System (ADS)
Jukic, Dragan; Kralik, Gordana; Scitovski, Rudolf
2004-08-01
In this paper we consider the least-squares (LS) fitting of the Gompertz curve to the given nonconstant data (pi,ti,yi), i=1,...,m, m≥3. We give necessary and sufficient conditions which guarantee the existence of the LS estimate, suggest a choice of a good initial approximation and give some numerical examples.
BLS: Box-fitting Least Squares
NASA Astrophysics Data System (ADS)
Kovács, G.; Zucker, S.; Mazeh, T.
2016-07-01
BLS (Box-fitting Least Squares) is a box-fitting algorithm that analyzes stellar photometric time series to search for periodic transits of extrasolar planets. It searches for signals characterized by a periodic alternation between two discrete levels, with much less time spent at the lower level.
Non-Circular Wheels: Reuleaux and Squares
ERIC Educational Resources Information Center
Mills, Allan
2011-01-01
Circular wheels are so familiar on vehicles of all types that it is seldom realized that alternatives do exist. This short non-mathematical article describes Reuleaux and square wheels that, rolling along appropriate tracks, can maintain a moving platform at a constant height. Easily made working models lend themselves to demonstrations at science…
A Limitation with Least Squares Predictions
ERIC Educational Resources Information Center
Bittner, Teresa L.
2013-01-01
Although researchers have documented that some data make larger contributions than others to predictions made with least squares models, it is relatively unknown that some data actually make no contribution to the predictions produced by these models. This article explores such noncontributory data. (Contains 1 table and 2 figures.)
Iterative methods for weighted least-squares
Bobrovnikova, E.Y.; Vavasis, S.A.
1996-12-31
A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.
36 CFR 910.67 - Square guidelines.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 36 Parks, Forests, and Public Property 3 2010-07-01 2010-07-01 false Square guidelines. 910.67 Section 910.67 Parks, Forests, and Public Property PENNSYLVANIA AVENUE DEVELOPMENT CORPORATION GENERAL GUIDELINES AND UNIFORM STANDARDS FOR URBAN PLANNING AND DESIGN OF DEVELOPMENT WITHIN THE PENNSYLVANIA...
Square One TV, Curriculum Connections Teacher's Guide.
ERIC Educational Resources Information Center
Children's Television Workshop, New York, NY.
This cross curriculum guide links mathematics, language arts, and social studies. The guide is divided into two sections. The first section provides a series of language arts activities and the second social studies activities. Within these two curriculum areas, the activities provided are based on three Square One TV formats: (1) Mathnet, the…
New broadband square-law detector
NASA Technical Reports Server (NTRS)
Reid, M. S.; Gardner, R. A.; Stelzried, C. T.
1975-01-01
Compact device has wide dynamic range, accurate square-law response, good thermal stability, high-level dc output with immunity to ground-loop problems, ability to insert known time constants for radiometric applications, and fast response times compatible with computer systems.
Squaring Matrices: Connecting Mathematics and Science
ERIC Educational Resources Information Center
Horton, Robert M.; Wiegert, Elaine M.; Marshall, Jeff C.
2008-01-01
This article shows how a matrix can be used to represent a food chain and how the square of this matrix represents the indirect food sources for each animal in the chain. By exploring, through mathematics, the implications when the bottom of the food chain is destroyed, students will see an important connection between mathematics and science.…
NASA Astrophysics Data System (ADS)
Benavente, Roberto; Cummins, Phil; Dettmer, Jan
2016-04-01
Rapid estimation of the spatial and temporal rupture characteristics of large megathrust earthquakes by finite fault inversion is important for disaster mitigation. For example, estimates of the spatio-temporal evolution of rupture can be used to evaluate population exposure to tsunami waves and ground shaking soon after the event by providing more accurate predictions than possible with point source approximations. In addition, rapid inversion results can reveal seismic source complexity to guide additional, more detailed subsequent studies. This work develops a method to rapidly estimate the slip distribution of megathrust events while reducing subjective parameter choices by automation. The method is simple yet robust and we show that it provides excellent preliminary rupture models as soon as 30 minutes for three great earthquakes in the South-American subduction zone. This may slightly change for other regions depending on seismic station coverage but method can be applied to any subduction region. The inversion is based on W-phase data since it is rapidly and widely available and of low amplitude which avoids clipping at close stations for large events. In addition, prior knowledge of the slab geometry (e.g. SLAB 1.0) is applied and rapid W-phase point source information (time delay and centroid location) is used to constrain the fault geometry and extent. Since the linearization by multiple time window (MTW) parametrization requires regularization, objective smoothing is achieved by the discrepancy principle in two fully automated steps. First, the residuals are estimated assuming unknown noise levels, and second, seeking a subsequent solution which fits the data to noise level. The MTW scheme is applied with positivity constraints and a solution is obtained by an efficient non-negative least squares solver. Systematic application of the algorithm to the Maule (2010), Iquique (2014) and Illapel (2015) events illustrates that rapid finite fault inversion with
Mathematical Construction of Magic Squares Utilizing Base-N Arithmetic
ERIC Educational Resources Information Center
O'Brien, Thomas D.
2006-01-01
Magic squares have been of interest as a source of recreation for over 4,500 years. A magic square consists of a square array of n[squared] positive and distinct integers arranged so that the sum of any column, row, or main diagonal is the same. In particular, an array of consecutive integers from 1 to n[squared] forming an nxn magic square is…
Givental Graphs and Inversion Symmetry
NASA Astrophysics Data System (ADS)
Dunin-Barkowski, Petr; Shadrin, Sergey; Spitz, Loek
2013-05-01
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.
Deformation of square objects and boudins
NASA Astrophysics Data System (ADS)
Treagus, Susan H.; Lan, Labao
2004-08-01
Some geological objects, such as clasts and boudins, may have had original shapes close to square, that have been modified by ductile deformation. We demonstrate through finite element models presented here and in earlier papers that square objects in a matrix with contrasting viscosity can deform to a variety of curved shapes. The maximum shape change is where the square edges are parallel to the principal bulk strains. Competent objects with viscosity ratio to matrix ( m) of 2-20 become barrel shaped, showing concave 'fish mouth' shortened edges. Incompetent objects ( m<1) show a narrower variety of shapes with m, all becoming smoothed to bone, dumb-bell or lobate shapes, and losing the original corners. We compare the results for square objects with linear and non-linear rheology (power law, stress exponent n=1, 3 or 10), and with previous modelling with different object-matrix proportions. Competent objects with higher n values deform slightly less, and more irregularly, than linearly viscous ( n=1) objects, but the distinctions between n=3 and 10 are only slight. The differences are even slighter (in the opposite sense) for incompetent objects. The proportion of object to matrix is as important, if not more, in controlling the deformation and shape of these objects. The results are compared via graphs of object strain and concavity versus bulk strain. The concavity graph for competent square objects with linear viscosity up to very high strain can be compared with examples of ductile boudins with barrel or fish mouth shapes. Subject to a number of assumptions, this provides a method of estimating boudin-matrix viscosity ratios and post-boudinage ductile strain, of potential use in highly deformed rocks lacking other strain markers. The approach may also be suitable for deformed porphyroblasts, but is more difficult to apply to single clasts in breccias and conglomerates.
An analysis of the least-squares problem for the DSN systematic pointing error model
NASA Technical Reports Server (NTRS)
Alvarez, L. S.
1991-01-01
A systematic pointing error model is used to calibrate antennas in the Deep Space Network. The least squares problem is described and analyzed along with the solution methods used to determine the model's parameters. Specifically studied are the rank degeneracy problems resulting from beam pointing error measurement sets that incorporate inadequate sky coverage. A least squares parameter subset selection method is described and its applicability to the systematic error modeling process is demonstrated on Voyager 2 measurement distribution.
Appraisal of geodynamic inversion results: a data mining approach
NASA Astrophysics Data System (ADS)
Baumann, T. S.
2016-11-01
Bayesian sampling based inversions require many thousands or even millions of forward models, depending on how nonlinear or non-unique the inverse problem is, and how many unknowns are involved. The result of such a probabilistic inversion is not a single `best-fit' model, but rather a probability distribution that is represented by the entire model ensemble. Often, a geophysical inverse problem is non-unique, and the corresponding posterior distribution is multimodal, meaning that the distribution consists of clusters with similar models that represent the observations equally well. In these cases, we would like to visualize the characteristic model properties within each of these clusters of models. However, even for a moderate number of inversion parameters, a manual appraisal for a large number of models is not feasible. This poses the question whether it is possible to extract end-member models that represent each of the best-fit regions including their uncertainties. Here, I show how a machine learning tool can be used to characterize end-member models, including their uncertainties, from a complete model ensemble that represents a posterior probability distribution. The model ensemble used here results from a nonlinear geodynamic inverse problem, where rheological properties of the lithosphere are constrained from multiple geophysical observations. It is demonstrated that by taking vertical cross-sections through the effective viscosity structure of each of the models, the entire model ensemble can be classified into four end-member model categories that have a similar effective viscosity structure. These classification results are helpful to explore the non-uniqueness of the inverse problem and can be used to compute representative data fits for each of the end-member models. Conversely, these insights also reveal how new observational constraints could reduce the non-uniqueness. The method is not limited to geodynamic applications and a generalized MATLAB
Appraisal of geodynamic inversion results: A data mining approach
NASA Astrophysics Data System (ADS)
Baumann, T. S.
2016-07-01
Bayesian sampling based inversions require many thousands or even millions of forward models, depending on how non-linear or non-unique the inverse problem is, and how many unknowns are involved. The result of such a probabilistic inversion is not a single `best-fit' model, but rather a probability distribution that is represented by the entire model ensemble. Often, a geophysical inverse problem is non-unique, and the corresponding posterior distribution is multimodal, meaning that the distribution consists of clusters with similar models that represent the observations equally well. In these cases, we would like to visualise the characteristic model properties within each of these clusters of models. However, even for a moderate number of inversion parameters, a manual appraisal for a large number of models is not feasible. This poses the question whether it is possible to extract end-member models that represent each of the best fit regions including their uncertainties. Here, I show how a machine learning tool can be used to characterise end-member models, including their uncertainties, from a complete model ensemble that represents a posterior probability distribution. The model ensemble used here, results from a non-linear geodynamic inverse problem, where rheological properties of the lithosphere are constrained from multiple geophysical observations. It is demonstrated that by taking vertical cross-sections through the effective viscosity structure of each of the models, the entire model ensemble can be classified into 4 end-member model categories that have a similar effective viscosity structure. These classification results are helpful to explore the non-uniqueness of the inverse problem and can be used to compute representative data fits for each of the end member models. Conversely, these insights also reveal how new observational constraints could reduce the non-uniqueness. The method is not limited to geodynamic applications and a generalised MATLAB
Seismic stochastic inversion identify river channel sand body
NASA Astrophysics Data System (ADS)
He, Z.
2015-12-01
The technology of seismic inversion is regarded as one of the most important part of geophysics. By using the technology of seismic inversion and the theory of stochastic simulation, the concept of seismic stochastic inversion is proposed.Seismic stochastic inversion can play an significant role in the identifying river channel sand body. Accurate sand body description is a crucial parameter to measure oilfield development and oilfield stimulation during the middle and later periods. Besides, rational well spacing density is an essential condition for efficient production. Based on the geological knowledge of a certain oilfield, in line with the use of seismic stochastic inversion, the river channel sand body in the work area is identified. In this paper, firstly, the single river channel body from the composite river channel body is subdivided. Secondly, the distribution of river channel body is ascertained in order to ascertain the direction of rivers. Morever, the superimposed relationship among the sand body is analyzed, especially among the inter-well sand body. The last but not at the least, via the analysis of inversion results of first vacuating the wells and continuous infilling later, it is meeted the most needs well spacing density that can obtain the optimal inversion result. It would serve effective guidance for oilfield stimulation.
MAP estimators for piecewise continuous inversion
NASA Astrophysics Data System (ADS)
Dunlop, M. M.; Stuart, A. M.
2016-10-01
We study the inverse problem of estimating a field u a from data comprising a finite set of nonlinear functionals of u a , subject to additive noise; we denote this observed data by y. Our interest is in the reconstruction of piecewise continuous fields u a in which the discontinuity set is described by a finite number of geometric parameters a. Natural applications include groundwater flow and electrical impedance tomography. We take a Bayesian approach, placing a prior distribution on u a and determining the conditional distribution on u a given the data y. It is then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP estimators can be characterised as minimisers of a generalised Onsager-Machlup functional, in the case where the prior measure is a Gaussian random field. We extend this theory to a more general class of prior distributions which allows for piecewise continuous fields. Specifically, the prior field is assumed to be piecewise Gaussian with random interfaces between the different Gaussians defined by a finite number of parameters. We also make connections with recent work on MAP estimators for linear problems and possibly non-Gaussian priors (Helin and Burger 2015 Inverse Problems 31 085009) which employs the notion of Fomin derivative. In showing applicability of our theory we focus on the groundwater flow and EIT models, though the theory holds more generally. Numerical experiments are implemented for the groundwater flow model, demonstrating the feasibility of determining MAP estimators for these piecewise continuous models, but also that the geometric formulation can lead to multiple nearby (local) MAP estimators. We relate these MAP estimators to the behaviour of output from MCMC samples of the posterior, obtained using a state-of-the-art function space Metropolis-Hastings method.
Source Inversion Validation: Quantifying Uncertainties in Earthquake Source Inversions
NASA Astrophysics Data System (ADS)
Mai, P. M.; Page, M. T.; Schorlemmer, D.
2010-12-01
Earthquake source inversions image the spatio-temporal rupture evolution on one or more fault planes using seismic and/or geodetic data. Source inversion methods thus represent an important research tool in seismology to unravel the complexity of earthquake ruptures. Subsequently, source-inversion results are used to study earthquake mechanics, to develop spontaneous dynamic rupture models, to build models for generating rupture realizations for ground-motion simulations, and to perform Coulomb-stress modeling. In all these applications, the underlying finite-source rupture models are treated as “data” (input information), but the uncertainties in these data (i.e. source models obtained from solving an inherently ill-posed inverse problem) are hardly known, and almost always neglected. The Source Inversion Validation (SIV) project attempts to better understand the intra-event variability of earthquake rupture models. We plan to build a long-standing and rigorous testing platform to examine the current state-of-the-art in earthquake source inversion that also facilitates to develop robust approaches to quantify rupture-model uncertainties. Our contribution reviews the current status of the SIV project, recent forward-modeling tests for point and extended sources in layered media, and discusses the strategy of the SIV-project for the coming years.
Inverse Statistics and Asset Allocation Efficiency
NASA Astrophysics Data System (ADS)
Bolgorian, Meysam
In this paper using inverse statistics analysis, the effect of investment horizon on the efficiency of portfolio selection is examined. Inverse statistics analysis is a general tool also known as probability distribution of exit time that is used for detecting the distribution of the time in which a stochastic process exits from a zone. This analysis was used in Refs. 1 and 2 for studying the financial returns time series. This distribution provides an optimal investment horizon which determines the most likely horizon for gaining a specific return. Using samples of stocks from Tehran Stock Exchange (TSE) as an emerging market and S&P 500 as a developed market, effect of optimal investment horizon in asset allocation is assessed. It is found that taking into account the optimal investment horizon in TSE leads to more efficiency for large size portfolios while for stocks selected from S&P 500, regardless of portfolio size, this strategy does not only not produce more efficient portfolios, but also longer investment horizons provides more efficiency.
Fast Gibbs sampling for high-dimensional Bayesian inversion
NASA Astrophysics Data System (ADS)
Lucka, Felix
2016-11-01
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and quantify its uncertainties. In applications where the inverse solution is subject to further analysis procedures can be a significant advantage. Alongside theoretical progress, various new computational techniques allow us to sample very high dimensional posterior distributions: in (Lucka 2012 Inverse Problems 28 125012), and a Markov chain Monte Carlo posterior sampler was developed for linear inverse problems with {{\\ell }}1-type priors. In this article, we extend this single component (SC) Gibbs-type sampler to a wide range of priors used in Bayesian inversion, such as general {{\\ell }}pq priors with additional hard constraints. In addition, a fast computation of the conditional, SC densities in an explicit, parameterized form, a fast, robust and exact sampling from these one-dimensional densities is key to obtain an efficient algorithm. We demonstrate that a generalization of slice sampling can utilize their specific structure for this task and illustrate the performance of the resulting slice-within-Gibbs samplers by different computed examples. These new samplers allow us to perform sample-based Bayesian inference in high-dimensional scenarios with certain priors for the first time, including the inversion of computed tomography data with the popular isotropic total variation prior.
The inverse energy cascade of two-dimensional turbulence
NASA Astrophysics Data System (ADS)
Rivera, Michael Kelly
2000-10-01
This thesis presents an experimental study of the inverse energy cascade as it occurs in an electromagnetically forced soap film. It focuses on characterizing important features of the inverse cascade such as it's range, how energy is distributed over the range and how energy flows through the range. The thesis also probes the assumption of scale invariance that is associated with the existence of an inverse cascade. These investigations demonstrate that the extent of the inverse cascade range and the behavior of the energy distribution are in agreement with dimensional predictions. The energy flow in the inverse cascade range is shown to be well described by exact mathematical predictions obtained from the Navier-Stokes equation. At no time does the energy flow in the inverse cascade range produced by the e-m cell behave inertially or in a scale invariant manner. Evidence that the cascade could become scale invariant should an inertial range develop is presented, as are the requirements that a system must satisfy to create such an inertial range.
TOPICAL REVIEW: Inverse problems in elasticity
NASA Astrophysics Data System (ADS)
Bonnet, Marc; Constantinescu, Andrei
2005-04-01
This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.
Joint inversion of surface and borehole magnetic amplitude data
NASA Astrophysics Data System (ADS)
Li, Zelin; Yao, Changli; Zheng, Yuanman; Yuan, Xiaoyu
2016-04-01
3D magnetic inversion for susceptibility distribution is a powerful tool in quantitative interpretation of magnetic data in mineral exploration. However, the inversion and interpretation of such data are faced with two problems. One problem is the poor imaging results of deep sources when only surface data are inverted. The other is the unknown total magnetization directions of sources when strong remanence exists. To deal with these problems simultaneously, we propose a method through the joint inversion of surface and borehole magnetic amplitude data. In this method, we first transform both surface and borehole magnetic data to magnetic amplitude data that are less sensitive to the directions of total magnetization, and then preform a joint inversion of the whole amplitude data to generate a 3D susceptibility distribution. The amplitude inversion algorithm uses Tikhonov regularization and imposes a positivity constraint on the effective susceptibility defined as the ratio of magnetization magnitude over the geomagnetic field strength. In addition, a distance-based weighting function is used to make the algorithm applicable to joint data sets. To solve this positivity-constraint inversion problem efficiently, an appropriate optimization method must be chosen. We first use an interior-point method to incorporate the positivity constraint into the total objective function, and then minimize the objective function via a Gauss-Newton method due to the nonlinearity introduced by the positivity constraint and the amplitude data. To further improve the efficiency of the inversion algorithm, we use a conjugate gradient method to carry out the fast matrix-vector multiplication during the minimization. To verify the utility of the proposed method, we invert the synthetic and field data using three inversion methods, including the joint inversion of surface and borehole three-component magnetic data, the inversion of surface magnetic amplitude data, and the proposed joint
SISYPHUS: A high performance seismic inversion factory
NASA Astrophysics Data System (ADS)
Gokhberg, Alexey; Simutė, Saulė; Boehm, Christian; Fichtner, Andreas
2016-04-01
branches for the static process setup, inversion iterations, and solver runs, each branch specifying information at the event, station and channel levels. The workflow management framework is based on an embedded scripting engine that allows definition of various workflow scenarios using a high-level scripting language and provides access to all available inversion components represented as standard library functions. At present the SES3D wave propagation solver is integrated in the solution; the work is in progress for interfacing with SPECFEM3D. A separate framework is designed for interoperability with an optimization module; the workflow manager and optimization process run in parallel and cooperate by exchanging messages according to a specially designed protocol. A library of high-performance modules implementing signal pre-processing, misfit and adjoint computations according to established good practices is included. Monitoring is based on information stored in the inversion state database and at present implements a command line interface; design of a graphical user interface is in progress. The software design fits well into the common massively parallel system architecture featuring a large number of computational nodes running distributed applications under control of batch-oriented resource managers. The solution prototype has been implemented on the "Piz Daint" supercomputer provided by the Swiss Supercomputing Centre (CSCS).
Uterine Inversion; A case report.
Bouchikhi, C; Saadi, H; Fakhir, B; Chaara, H; Bouguern, H; Banani, A; Melhouf, Ma
2008-01-01
The puerperal uterine inversion is a rare and severe complication occurring in the third stage of labour. The mechanisms are not completely known. However, extrinsic factors such as oxytocic arrests after a prolonged labour, umbilical cord traction or abdominal expression are pointed. Other intrinsic factors such as primiparity, uterine hypotonia, various placental localizations, fundic myoma or short umbilical cord were also reported. The diagnosis of the uterine inversion is mainly supported by clinical symptoms. It is based on three elements: haemorrhage, shock and a strong pelvic pain. The immediate treatment of the uterine inversion is required. It is based on a medical reanimation associated with firstly a manual reduction then surgical treatment using various techniques. We report an observation of a 25 years old grand multiparous patient with a subacute uterine inversion after delivery at home. PMID:21516244
Uterine Inversion; A case report
Bouchikhi, C; Saadi, H; Fakhir, B; Chaara, H; Bouguern, H; Banani, A; Melhouf, MA
2008-01-01
The puerperal uterine inversion is a rare and severe complication occurring in the third stage of labour. The mechanisms are not completely known. However, extrinsic factors such as oxytocic arrests after a prolonged labour, umbilical cord traction or abdominal expression are pointed. Other intrinsic factors such as primiparity, uterine hypotonia, various placental localizations, fundic myoma or short umbilical cord were also reported. The diagnosis of the uterine inversion is mainly supported by clinical symptoms. It is based on three elements: haemorrhage, shock and a strong pelvic pain. The immediate treatment of the uterine inversion is required. It is based on a medical reanimation associated with firstly a manual reduction then surgical treatment using various techniques. We report an observation of a 25 years old grand multiparous patient with a subacute uterine inversion after delivery at home. PMID:21516244
Testing earthquake source inversion methodologies
Page, M.; Mai, P.M.; Schorlemmer, D.
2011-01-01
Source Inversion Validation Workshop; Palm Springs, California, 11-12 September 2010; Nowadays earthquake source inversions are routinely performed after large earthquakes and represent a key connection between recorded seismic and geodetic data and the complex rupture process at depth. The resulting earthquake source models quantify the spatiotemporal evolution of ruptures. They are also used to provide a rapid assessment of the severity of an earthquake and to estimate losses. However, because of uncertainties in the data, assumed fault geometry and velocity structure, and chosen rupture parameterization, it is not clear which features of these source models are robust. Improved understanding of the uncertainty and reliability of earthquake source inversions will allow the scientific community to use the robust features of kinematic inversions to more thoroughly investigate the complexity of the rupture process and to better constrain other earthquakerelated computations, such as ground motion simulations and static stress change calculations.
Mahan, G. D.
2014-09-21
We calculate the binding energy of an electron bound to a donor in a semiconductor inverse opal. Inverse opals have two kinds of cavities, which we call octahedral and tetrahedral, according to their group symmetry. We put the donor in the center of each of these two cavities and obtain the binding energy. The binding energies become very large when the inverse opal is made from templates with small spheres. For spheres less than 50 nm in diameter, the donor binding can increase to several times its unconfined value. Then electrons become tightly bound to the donor and are unlikely to be thermally activated to the semiconductor conduction band. This conclusion suggests that inverse opals will be poor conductors.
Inversion layer MOS solar cells
NASA Technical Reports Server (NTRS)
Ho, Fat Duen
1986-01-01
Inversion layer (IL) Metal Oxide Semiconductor (MOS) solar cells were fabricated. The fabrication technique and problems are discussed. A plan for modeling IL cells is presented. Future work in this area is addressed.
Temperature Inversions Have Cold Bottoms.
ERIC Educational Resources Information Center
Bohren, Craig F.; Brown, Gail M.
1982-01-01
Uses discussion and illustrations of several demonstrations on air temperature differences and atmospheric stability to explain the phenomena of temperature inversions. Relates this to the smog in Los Angeles and discusses the implications. (DC)
NASA Astrophysics Data System (ADS)
Mahan, G. D.
2014-09-01
We calculate the binding energy of an electron bound to a donor in a semiconductor inverse opal. Inverse opals have two kinds of cavities, which we call octahedral and tetrahedral, according to their group symmetry. We put the donor in the center of each of these two cavities and obtain the binding energy. The binding energies become very large when the inverse opal is made from templates with small spheres. For spheres less than 50 nm in diameter, the donor binding can increase to several times its unconfined value. Then electrons become tightly bound to the donor and are unlikely to be thermally activated to the semiconductor conduction band. This conclusion suggests that inverse opals will be poor conductors.
Moebius inversion formula and inverting lattice sums
NASA Astrophysics Data System (ADS)
Millane, Rick P.
2000-11-01
The Mobius inversion formula is an interesting theorem from number theory that has application to a number inverse problems, particularly lattice problems. Specific inverse problems, however, often require related Mobius inversion formulae that can be derived from the fundamental formula. Derivation of such formulae is not easy for the non- specialist, however. Examples of the kinds of inversion formulae that can be derived and their application to inverse lattice problems are described.
Multiresolution MR elastography using nonlinear inversion
McGarry, M. D. J.; Van Houten, E. E. W.; Johnson, C. L.; Georgiadis, J. G.; Sutton, B. P.; Weaver, J. B.; Paulsen, K. D.
2012-01-01
Purpose: Nonlinear inversion (NLI) in MR elastography requires discretization of the displacement field for a finite element (FE) solution of the “forward problem”, and discretization of the unknown mechanical property field for the iterative solution of the “inverse problem”. The resolution requirements for these two discretizations are different: the forward problem requires sufficient resolution of the displacement FE mesh to ensure convergence, whereas lowering the mechanical property resolution in the inverse problem stabilizes the mechanical property estimates in the presence of measurement noise. Previous NLI implementations use the same FE mesh to support the displacement and property fields, requiring a trade-off between the competing resolution requirements. Methods: This work implements and evaluates multiresolution FE meshes for NLI elastography, allowing independent discretizations of the displacements and each mechanical property parameter to be estimated. The displacement resolution can then be selected to ensure mesh convergence, and the resolution of the property meshes can be independently manipulated to control the stability of the inversion. Results: Phantom experiments indicate that eight nodes per wavelength (NPW) are sufficient for accurate mechanical property recovery, whereas mechanical property estimation from 50 Hz in vivo brain data stabilizes once the displacement resolution reaches 1.7 mm (approximately 19 NPW). Viscoelastic mechanical property estimates of in vivo brain tissue show that subsampling the loss modulus while holding the storage modulus resolution constant does not substantially alter the storage modulus images. Controlling the ratio of the number of measurements to unknown mechanical properties by subsampling the mechanical property distributions (relative to the data resolution) improves the repeatability of the property estimates, at a cost of modestly decreased spatial resolution. Conclusions: Multiresolution
The Estimation and Inversion of Magnetotelluric Data with Static Shift
NASA Astrophysics Data System (ADS)
Wang, X.; Zhou, J.; Zhang, J.; Min, G.; Xia, S.
2015-12-01
IntroductionIn magnetotelluric sounding data processing, the static shift correction is one of the most important steps. Due to the complexity of near-surface inhomogeneous bodies distribution, it is difficult to estimate the static shift of measured data. For this problem, we put forward on the basis of the inversion model for static shift estimation, and reconstructed the initial model with using the original data for 2D or 3D inversion. Estimation and Inversion methodThe magnetotelluric impedance phase has the characteristics of not influenced by the static shift in Two-dimensional electrical structure. The objective function for static shift estimation can be constructed based on impedance phase data. On the basis of normal inversion, utilizing one-dimensional linear search algorithm, combined with the forward modeling, the MT static shift can be estimated.Using estimation results for translation of anomaly measured curve. According to the inversion(1-D) of these translated curve, the initial model for two-dimensional or two-dimensional inversion can be reconstructed. On this basis, we do inversion for the original data, which not only can effectively eliminate the influence of static shift on the deep structure of inversion model, but also can get the right shallow electrical structure in the inversionConclusionThe estimation value of static shift based on impedance phase can be close to the true value. This estimation results can be used to modify the initial model, which makes the deep electric structure of the model more reasonable. On this basis, the inversion of the original data can ensure the correctness of the final inversion results (including shallow and deep).Acknowledgement This paper is supported by National Natural Science Foundation (41274078) and National 863 High Technology Research and Development Program (2014AA06A612).Reference[1] deGroot-Hedlin C. Removal of static shift in two dimensions by regularized inversion[J]. Geophysics, 1991, 56
The onset of turbulence in a square duct flow
NASA Astrophysics Data System (ADS)
Lemoult, Gregoire; Hof, Bjorn
2014-11-01
Wall bounded shear flows experience a sudden transition from a laminar state to turbulence as Reynolds number, Re , increases. K. Avila et al. (Science 333, 2011) recently characterized the onset of turbulence in pipe flow. They measured the probability for a localized disturbance to decay or spread and defined the critical Reynolds number, Rec , where the characteristic time for both process is equal. Using the same methodology, we measure these probabilities, decay and splitting, as a function of Re in a 1200 D long square duct, where D is the width of the duct. We found the expected exponential probability distribution for both processes which underlines their memoryless character. From the characteristic time of these distributions, we estimate the point where turbulence first becomes sustained in a square duct flow. The main difference with pipe flow is that the characteristic time at Rec is shorter making it more suitable for measurements of critical exponents in the framework of phase transition. These results also emphasize the universal behavior of the transition to turbulence in wall bounded shear flows.
Sutton, G W; Weiner, M M; Mani, S A
1976-09-01
Theoretical Fraunhofer diffraction patterns are presented for uniformly illuminated square apertures with noncentered square obscurations. The energy within a given subtended solid angle in the far field is calculated. It is shown that the cornered-off-axis obscuration provides much more far-field energy in a given spot size than the centered obscuration for the same clear aperture area and total energy, for example, 82% more far-field energy in the first Airy square for 50% obscuration, thus providing superior performance for practical systems.
Building Generalized Inverses of Matrices Using Only Row and Column Operations
ERIC Educational Resources Information Center
Stuart, Jeffrey
2010-01-01
Most students complete their first and only course in linear algebra with the understanding that a real, square matrix "A" has an inverse if and only if "rref"("A"), the reduced row echelon form of "A", is the identity matrix I[subscript n]. That is, if they apply elementary row operations via the Gauss-Jordan algorithm to the partitioned matrix…
Corbett-Detig, Russell B
2016-09-01
Chromosomal inversions are widespread among taxa, and have been implicated in a number of biological processes including adaptation, sex chromosome evolution, and segregation distortion. Consistent with selection favoring linkage between loci, it is well established that length is a selected trait of inversions. However, the factors that affect the distribution of inversion breakpoints remain poorly understood. "Sensitive sites" have been mapped on all euchromatic chromosome arms in Drosophila melanogaster, and may be a source of natural selection on inversion breakpoint positions. Briefly, sensitive sites are genomic regions wherein proximal structural rearrangements result in large reductions in local recombination rates in heterozygotes. Here, I show that breakpoints of common inversions are significantly more likely to lie within a cytological band containing a sensitive site than are breakpoints of rare inversions. Furthermore, common inversions for which neither breakpoint intersects a sensitive site are significantly longer than rare inversions, but common inversions whose breakpoints intersect a sensitive site show no evidence for increased length. I interpret these results to mean that selection favors inversions whose breakpoints disrupt synteny near to sensitive sites, possibly because these inversions suppress recombination in large genomic regions. To my knowledge this is the first evidence consistent with positive selection acting on inversion breakpoint positions. PMID:27343234
The face inversion effect in opponent-stimulus rivalry
Persike, Malte; Meinhardt-Injac, Bozana; Meinhardt, Günter
2014-01-01
The face inversion effect is regarded as a hallmark of face-specific processing, and can be observed in a large variety of visual tasks. Face inversion effects are also reported in binocular rivalry. However, it is unclear whether these effects are face-specific, and distinct from the general tendency of visual awareness to privilege upright objects. We studied continuous rivalry across more than 600 dominance epochs for each observer, having faces and houses rival against their inverted counterparts, and letting faces rival against houses in both upright and inverted orientation. We found strong inversion effects for faces and houses in both the frequency of dominance epochs and their duration. Inversion effects for faces, however, were substantially larger, reaching a 70:30 distribution of dominance times for upright versus inverted faces, while a 60:40 distribution was obtained for upright versus inverted houses. Inversion effects for faces reached a Cohen's d of 0.85, compared to a value of 0.33 for houses. Dominance times for rivalry of faces against houses had a 60:40 distribution in favor of faces, independent of the orientation of the objects. These results confirm the general tendency of visual awareness to prefer upright objects, and demonstrate the outstanding role of faces. Since effect size measures clearly distinguish face stimuli in opponent-stimulus rivalry, the method is highly recommended for testing the effects of face manipulations against non-face reference objects. PMID:24860477
Least squares restoration of multichannel images
NASA Technical Reports Server (NTRS)
Galatsanos, Nikolas P.; Katsaggelos, Aggelos K.; Chin, Roland T.; Hillery, Allen D.
1991-01-01
Multichannel restoration using both within- and between-channel deterministic information is considered. A multichannel image is a set of image planes that exhibit cross-plane similarity. Existing optimal restoration filters for single-plane images yield suboptimal results when applied to multichannel images, since between-channel information is not utilized. Multichannel least squares restoration filters are developed using the set theoretic and the constrained optimization approaches. A geometric interpretation of the estimates of both filters is given. Color images (three-channel imagery with red, green, and blue components) are considered. Constraints that capture the within- and between-channel properties of color images are developed. Issues associated with the computation of the two estimates are addressed. A spatially adaptive, multichannel least squares filter that utilizes local within- and between-channel image properties is proposed. Experiments using color images are described.
Simple shear of deformable square objects
NASA Astrophysics Data System (ADS)
Treagus, Susan H.; Lan, Labao
2003-12-01
Finite element models of square objects in a contrasting matrix in simple shear show that the objects deform to a variety of shapes. For a range of viscosity contrasts, we catalogue the changing shapes and orientations of objects in progressive simple shear. At moderate simple shear ( γ=1.5), the shapes are virtually indistinguishable from those in equivalent pure shear models with the same bulk strain ( RS=4), examined in a previous study. In theory, differences would be expected, especially for very stiff objects or at very large strain. In all our simple shear models, relatively competent square objects become asymmetric barrel shapes with concave shortened edges, similar to some types of boudin. Incompetent objects develop shapes surprisingly similar to mica fish described in mylonites.
Skyrmions in square-lattice antiferromagnets
NASA Astrophysics Data System (ADS)
Keesman, Rick; Raaijmakers, Mark; Baerends, A. E.; Barkema, G. T.; Duine, R. A.
2016-08-01
The ground states of square-lattice two-dimensional antiferromagnets with anisotropy in an external magnetic field are determined using Monte Carlo simulations and compared to theoretical analysis. We find a phase in between the spin-flop and spiral phase that shows strong similarity to skyrmions in ferromagnetic thin films. We show that this phase arises as a result of the competition between Zeeman and Dzyaloshinskii-Moriya interaction energies of the magnetic system. Moreover, we find that isolated (anti-)skyrmions are stabilized in finite-sized systems, even at higher temperatures. The existence of thermodynamically stable skyrmions in square-lattice antiferromagnets provides an appealing alternative over skyrmions in ferromagnets as data carriers.
Total least squares for anomalous change detection
NASA Astrophysics Data System (ADS)
Theiler, James; Matsekh, Anna M.
2010-04-01
A family of subtraction-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQbased anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and special cases of it are equivalent to canonical correlation analysis and optimized covariance equalization. What whitened TLSQ offers is a generalization of these algorithms with the potential for better performance.
Square-loop cobalt/gold multilayers
NASA Astrophysics Data System (ADS)
Gambino, R. J.; Ruf, R. R.
1990-05-01
Multilayers of Co and Au with perpendicular hysteresis loop squareness ratios of ˜1 have been prepared by e-beam evaporation. These films have perpendicular anisotropy in the as-deposited condition in contrast to other work in which Co/Au multilayers, prepared by ion beam sputtering, showed perpendicular anisotropy only after annealing at 300 °C. The Faraday rotation of these square-loop multilayers is about 9×105 deg/cm of Co or 1×105 deg/cm of total thickness at a wavelength of 633 nm. These values indicate an enhancement of the Faraday rotation of Co at this wavelength by about a factor of 2. This may be a plasma-edge enhancement effect similar to that reported by Katayama et al. [Phys. Rev. Lett. 60, 1426 (1988)] in the Kerr effect of Fe/Au multilayers.
Bayesian inversions of a dynamic vegetation model in four European grassland sites
NASA Astrophysics Data System (ADS)
Minet, J.; Laloy, E.; Tychon, B.; François, L.
2015-01-01
Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB dynamic vegetation model (DVM) with ten unknown parameters, using the DREAM(ZS) Markov chain Monte Carlo (MCMC) sampler. We compare model inversions considering both homoscedastic and heteroscedastic eddy covariance residual errors, with variances either fixed a~priori or jointly inferred with the model parameters. Agreements between measured and simulated data during calibration are comparable with previous studies, with root-mean-square error (RMSE) of simulated daily gross primary productivity (GPP), ecosystem respiration (RECO) and evapotranspiration (ET) ranging from 1.73 to 2.19 g C m-2 day-1, 1.04 to 1.56 g C m-2 day-1, and 0.50 to 1.28 mm day-1, respectively. In validation, mismatches between measured and simulated data are larger, but still with Nash-Sutcliffe efficiency scores above 0.5 for three out of the four sites. Although measurement errors associated with eddy covariance data are known to be heteroscedastic, we showed that assuming a classical linear heteroscedastic model of the residual errors in the inversion do not fully remove heteroscedasticity. Since the employed heteroscedastic error model allows for larger deviations between simulated and measured data as the magnitude of the measured data increases, this error model expectedly lead to poorer data fitting compared to inversions considering a constant variance of the residual errors. Furthermore, sampling the residual error variances along with model parameters results in overall similar model parameter posterior distributions as those obtained by fixing these variances beforehand, while slightly improving model performance. Despite the fact that the calibrated model is generally capable of fitting the data within measurement errors, systematic bias in the model simulations are observed. These are likely due to model inadequacies such as shortcomings in the photosynthesis modelling
Highlighting High Performance: Four Times Square
Not Available
2001-11-01
4 Times Square is a 48-story environmentally responsible building in New York City. Developed by the Durst Organization, the building is the first project of its size to adopt standards for energy efficiency, indoor ecology, sustainable materials, and responsible construction, operations, and maintenance procedures. Designers used a whole-building approach--considering how the building's systems can work together most efficiently--and educated tenants on the benefits of the design.
Dynamic square superlattice of Faraday waves
NASA Astrophysics Data System (ADS)
Kahouadji, Lyes; Chergui, Jalel; Juric, Damir; Shin, Seungwon; Tuckerman, Laurette
2014-11-01
Faraday waves are computed in a 3D container using BLUE, a code based on a hybrid Front-Tracking/Level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. A new dynamic superlattice pattern is described which consists of a set of square waves arranged in a two-by-two array. The corners of this array are connected by a bridge whose position oscillates in time between the two diagonals.
Natural convective heat transfer from square cylinder
NASA Astrophysics Data System (ADS)
Novomestský, Marcel; Smatanová, Helena; Kapjor, Andrej
2016-06-01
This article is concerned with natural convective heat transfer from square cylinder mounted on a plane adiabatic base, the cylinders having an exposed cylinder surface according to different horizontal angle. The cylinder receives heat from a radiating heater which results in a buoyant flow. There are many industrial applications, including refrigeration, ventilation and the cooling of electrical components, for which the present study may be applicable
A Cautionary Note on Using G[squared](dif) to Assess Relative Model Fit in Categorical Data Analysis
ERIC Educational Resources Information Center
Maydeu-Olivares, Albert; Cai, Li
2006-01-01
The likelihood ratio test statistic G[squared](dif) is widely used for comparing the fit of nested models in categorical data analysis. In large samples, this statistic is distributed as a chi-square with degrees of freedom equal to the difference in degrees of freedom between the tested models, but only if the least restrictive model is correctly…
Sub-scale Inverse Wind Turbine Blade Design Using Bound Circulation
NASA Astrophysics Data System (ADS)
Kelley, Christopher; Berg, Jonathan
2014-11-01
A goal of the National Rotor Testbed project at Sandia is to design a sub-scale wind turbine blade that has similitude to a modern, commercial size blade. However, a smaller diameter wind turbine operating at the same tip-speed-ratio exhibits a different range of operating Reynolds numbers across the blade span, thus changing the local lift and drag coefficients. Differences to load distribution also affect the wake dynamics and stability. An inverse wind turbine blade design tool has been implemented which uses a target, dimensionless circulation distribution from a full-scale blade to find the chord and twist along a sub-scale blade. In addition, airfoil polar data are interpolated from a few specified span stations leading to a smooth, manufacturable blade. The iterative process perturbs chord and twist, after running a blade element momentum theory code, to reduce the residual sum of the squares between the modeled sub-scale circulation and the target full-scale circulation. It is shown that the converged sub-scale design also leads to performance similarity in thrust and power coefficients. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy under Contract DE-AC04-94AL85000.
Multidimensional NMR inversion without Kronecker products: Multilinear inversion.
Medellín, David; Ravi, Vivek R; Torres-Verdín, Carlos
2016-08-01
Multidimensional NMR inversion using Kronecker products poses several challenges. First, kernel compression is only possible when the kernel matrices are separable, and in recent years, there has been an increasing interest in NMR sequences with non-separable kernels. Second, in three or more dimensions, the singular value decomposition is not unique; therefore kernel compression is not well-defined for higher dimensions. Without kernel compression, the Kronecker product yields matrices that require large amounts of memory, making the inversion intractable for personal computers. Finally, incorporating arbitrary regularization terms is not possible using the Lawson-Hanson (LH) or the Butler-Reeds-Dawson (BRD) algorithms. We develop a minimization-based inversion method that circumvents the above problems by using multilinear forms to perform multidimensional NMR inversion without using kernel compression or Kronecker products. The new method is memory efficient, requiring less than 0.1% of the memory required by the LH or BRD methods. It can also be extended to arbitrary dimensions and adapted to include non-separable kernels, linear constraints, and arbitrary regularization terms. Additionally, it is easy to implement because only a cost function and its first derivative are required to perform the inversion. PMID:27209370
Multidimensional NMR inversion without Kronecker products: Multilinear inversion
NASA Astrophysics Data System (ADS)
Medellín, David; Ravi, Vivek R.; Torres-Verdín, Carlos
2016-08-01
Multidimensional NMR inversion using Kronecker products poses several challenges. First, kernel compression is only possible when the kernel matrices are separable, and in recent years, there has been an increasing interest in NMR sequences with non-separable kernels. Second, in three or more dimensions, the singular value decomposition is not unique; therefore kernel compression is not well-defined for higher dimensions. Without kernel compression, the Kronecker product yields matrices that require large amounts of memory, making the inversion intractable for personal computers. Finally, incorporating arbitrary regularization terms is not possible using the Lawson-Hanson (LH) or the Butler-Reeds-Dawson (BRD) algorithms. We develop a minimization-based inversion method that circumvents the above problems by using multilinear forms to perform multidimensional NMR inversion without using kernel compression or Kronecker products. The new method is memory efficient, requiring less than 0.1% of the memory required by the LH or BRD methods. It can also be extended to arbitrary dimensions and adapted to include non-separable kernels, linear constraints, and arbitrary regularization terms. Additionally, it is easy to implement because only a cost function and its first derivative are required to perform the inversion.
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
NASA Astrophysics Data System (ADS)
Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-08-01
X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.
Inversion of Airborne Contaminants in a Regional Model
Akcelik, V.; Biros, G.; Draganescu, A.; Ghattas, O.; Hill, J.; van Bloemen Waanders, B.; /SLAC /Pennsylvania U. /Texas U. /Sandia
2007-01-10
We are interested in a DDDAS problem of localization of airborne contaminant releases in regional atmospheric transport models from sparse observations. Given measurements of the contaminant over an observation window at a small number of points in space, and a velocity field as predicted for example by a mesoscopic weather model, we seek an estimate of the state of the contaminant at the beginning of the observation interval that minimizes the least squares misfit between measured and predicted contaminant field, subject to the convection-diffusion equation for the contaminant. Once the ''initial'' conditions are estimated by solution of the inverse problem, we issue predictions of the evolution of the contaminant, the observation window is advanced in time, and the process repeated to issue a new prediction, in the style of 4D-Var. We design an appropriate numerical strategy that exploits the spectral structure of the inverse operator, and leads to efficient and accurate resolution of the inverse problem. Numerical experiments verify that high resolution inversion can be carried out rapidly for a well-resolved terrain model of the greater Los Angeles area.
Hybrid Adaptive Flight Control with Model Inversion Adaptation
NASA Technical Reports Server (NTRS)
Nguyen, Nhan
2011-01-01
This study investigates a hybrid adaptive flight control method as a design possibility for a flight control system that can enable an effective adaptation strategy to deal with off-nominal flight conditions. The hybrid adaptive control blends both direct and indirect adaptive control in a model inversion flight control architecture. The blending of both direct and indirect adaptive control provides a much more flexible and effective adaptive flight control architecture than that with either direct or indirect adaptive control alone. The indirect adaptive control is used to update the model inversion controller by an on-line parameter estimation of uncertain plant dynamics based on two methods. The first parameter estimation method is an indirect adaptive law based on the Lyapunov theory, and the second method is a recursive least-squares indirect adaptive law. The model inversion controller is therefore made to adapt to changes in the plant dynamics due to uncertainty. As a result, the modeling error is reduced that directly leads to a decrease in the tracking error. In conjunction with the indirect adaptive control that updates the model inversion controller, a direct adaptive control is implemented as an augmented command to further reduce any residual tracking error that is not entirely eliminated by the indirect adaptive control.
Nonlocal Separable Solutions of the Inverse Scattering Problem
NASA Astrophysics Data System (ADS)
Gherghetta, Tony; Nambu, Yoichiro
We extend the nonlocal separable potential solutions of Gourdin and Martin for the inverse scattering problem to the case where sin δ0 has more than N zeroes, δ0 being the s-wave scattering phase shift and δ0(0) - δ0(∞) = Nπ. As an example we construct the solution for the particular case of 4He and show how to incorporate a weakly bound state. Using a local square well potential chosen to mimic the real 4He potential, we compare the off-shell extension of the nonlocal potential solution with the exactly solvable square well. We then discuss how a nonlocal potential might be used to simplify the many-body problem of liquid 4He.
Global inversion for anisotropy during full-waveform inversion
NASA Astrophysics Data System (ADS)
Debens, H. A.; Warner, M.; Umpleby, A.
2015-12-01
Full-waveform inversion (FWI) is a powerful tool for quantitative estimation of high-resolution high-fidelity models of subsurface seismic parameters, typically P-wave velocity. The solution to FWI's posed nonlinear inverse problem is obtained via an iterative series of linearized local updates to a start model, assuming this model lies within the basin of attraction to the global minimum. Thanks to many successful published applications to three-dimensional (3D) field datasets, its advance has been rapid and driven in large-part by the oil and gas industry. The consideration of seismic anisotropy during FWI is of vital importance, as it holds influence over both the kinematics and dynamics of seismic waveforms. If not appropriately taken into account then inadequacies in the anisotropy model are likely to manifest as significant error in the recovered velocity model. Conventionally, anisotropic FWI employs either an a priori anisotropy model, held fixed during FWI, or it uses a multi-parameter local inversion scheme to recover the anisotropy as part of the FWI; both of these methods can be problematic. Constructing an anisotropy model prior to FWI often involves intensive (and hence expensive) iterative procedures, such as travel-time tomography or moveout velocity analysis. On the other hand, introducing multiple parameters to FWI itself increases the complexity of what is already an underdetermined inverse problem. We propose that global rather than local FWI can be used to recover the long-wavelength acoustic anisotropy model, and that this can then be followed by more-conventional local FWI to recover the detailed model. We validate this approach using a full 3D field dataset, demonstrating that it avoids problems associated to crosstalk that can bedevil local inversion schemes, and reconciles well with in situ borehole measurements. Although our approach includes a global inversion for anisotropy, it is nonetheless affordable and practical for 3D field data.
3D stochastic geophysical inversion for contact surface geometry
NASA Astrophysics Data System (ADS)
Lelièvre, Peter; Farquharson, Colin; Bijani, Rodrigo
2015-04-01
Geologists' interpretations about the Earth typically involve distinct rock units with contacts (interfaces) between them. As such, 3D geological Earth models typically comprise wireframe contact surfaces of tessellated triangles or other polygonal planar facets. In contrast, standard minimum-structure geophysical inversions are performed on meshes of space-filling cells (typically prisms or tetrahedra) and recover smoothly varying physical property distributions that are inconsistent with typical geological interpretations. There are several approaches through which mesh-based geophysical inversion can help recover models with some of the desired characteristics. However, a more effective strategy is to consider a fundamentally different type of inversion that works directly with models that comprise surfaces representing contacts between rock units. We are researching such an approach, our goal being to perform geophysical forward and inverse modelling directly with 3D geological models of any complexity. Geological and geophysical models should be specified using the same parameterization such that they are, in essence, the same Earth model. We parameterize the wireframe contact surfaces in a 3D model as the coordinates of the nodes (facet vertices). The physical properties of each rock unit in a model remain fixed while the geophysical inversion controls the position of the contact surfaces via the control nodes, perturbing the surfaces as required to fit the geophysical data responses. This is essentially a "geometry inversion", which can be used to recover the unknown geometry of a target body or to investigate the viability of a proposed Earth model. We apply global optimization strategies to solve the inverse problem, including stochastic sampling to obtain statistical information regarding the likelihood of particular features in the model, helping to assess the viability of a proposed model. Jointly inverting multiple types of geophysical data is simple
Inverse problems in statistical mechanics and photonics
NASA Astrophysics Data System (ADS)
Rechtsman, Mikael C.
In an inverse problem, one seeks the nature of the components of a system with known (or targeted) resultant behavior---perhaps opposite to the traditional trajectory of problem solving in physical research. In this thesis, a number of inverse problems in two categories are considered. In the first, in many-body classical systems with isotropic two-body interactions, we target uncharacteristic, technologically relevant thermodynamic behavior. In the second, we consider two problems in electromagnetic scattering and photonics. Increasingly, experimentalists have been able to tailor isotropic interactions between micron-scale colloidal spheres, allowing for the possibility of targeted self-assembly of a desired crystal structure upon freezing. Self-assembly of certain structures, the diamond lattice in particular, has a great deal of technological potential in the fields of optoelectronics and photonics. We present here new computational algorithms that find isotropic interaction potentials that yield targeted ground state crystal structures. These algorithms are applied to find interaction potentials for the honeycomb lattice (which is the two-dimensional analog of diamond), the square lattice, the simple cubic lattice, the wurtzite as well as the diamond lattice. We also present an isotropic interaction potential that gives rise to negative thermal expansion, a macroscopic behavior that has previously been associated with a highly anisotropic microscopic mechanism. Furthermore, we show that systems with only isotropic interactions may exhibit a negative Poisson's ratio, as long as they are under tension. We derive linear constraints involving the derivatives of the pair potential that gives rise to this behavior. In a study of electromagnetic scattering in random dielectric two-component composites, we use a strong-contrast perturbation expansion to obtain analytic expressions for the effective dielectric tensor to arbitrary order in the dielectric contrast between
Numerical solution of a nonlinear least squares problem in digital breast tomosynthesis
NASA Astrophysics Data System (ADS)
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2015-11-01
In digital tomosynthesis imaging, multiple projections of an object are obtained along a small range of different incident angles in order to reconstruct a pseudo-3D representation (i.e., a set of 2D slices) of the object. In this paper we describe some mathematical models for polyenergetic digital breast tomosynthesis image reconstruction that explicitly takes into account various materials composing the object and the polyenergetic nature of the x-ray beam. A polyenergetic model helps to reduce beam hardening artifacts, but the disadvantage is that it requires solving a large-scale nonlinear ill-posed inverse problem. We formulate the image reconstruction process (i.e., the method to solve the ill-posed inverse problem) in a nonlinear least squares framework, and use a Levenberg-Marquardt scheme to solve it. Some implementation details are discussed, and numerical experiments are provided to illustrate the performance of the methods.
3D magnetotelluric inversion with full distortion matrix
NASA Astrophysics Data System (ADS)
Gribenko, A. V.; Zhdanov, M. S.
2014-12-01
Distortion of regional electric fields by local structures represent one of the major problems facing three-dimensional magnetotelluric (MT) interpretation. Effect of 3D local inhomogenities on MT data can be described by a real 2x2 distortion matrix. In this project we develop a method of simultaneous inversion of the full MT impedance data for 3D conductivity distribution and for the distortion matrix. Tikhonov regularization is employed to solve the resulting inverse problem. Integral equations method is used to compute MT responses. Minimization of the cost functional is achieved via conjugate gradient method. The inversion algorithm is tested on the synthetic data from Dublin Secret Model II (DSM 2) for which multiple inversion solutions are available for comparison. Inclusion of the distortion matrix provides faster convergence and allows coarser discretization of the near-surface while achievingsimilar or better data fits as inversion for the conductivity only with finely discretized shallow regions. As a field data example we chose a subset of the EarthScope MT dataset covering Great Basin and adjacent areas of the Western United States. Great Basin data inversion identified several prominent conductive zones which correlate well with areas of tectonic and geothermal activity.
Ribeiro, F B; Carlos, D U; Hiodo, F Y; Strobino, E F
2005-01-01
In this study, a least squares procedure for calculating the calibration constants of a portable gamma-ray spectrometer using the general inverse matrix method is presented. The procedure weights the model equations fitting to the calibration data, taking into account the variances in the counting rates and in the radioactive standard concentrations. The application of the described procedure is illustrated by calibrating twice the same gamma-ray spectrometer, with two independent data sets collected approximately 18 months apart in the same calibration facility.
The Square-Shoulder-Asakura-Oosawa model
NASA Astrophysics Data System (ADS)
Fantoni, Riccardo
2016-09-01
A new model for a colloidal size-asymmetric binary mixture is proposed: The Square-Shoulder-Asakura-Oosawa. This belongs to the larger class of non-additive hard-spheres models and has the property that its effective pair formulation is exact whenever the solvent particle fits inside the interstitial region of three touching solute particles. Therefore one can study its properties from the equivalent one-component effective problem. Some remarks on the phase diagram of this new model are also addressed.
[Partial lease squares approach to functional analysis].
Preda, C
2006-01-01
We extend the partial least squares (PLS) approach to functional data represented in our models by sample paths of stochastic process with continuous time. Due to the infinite dimension, when functional data are used as a predictor for linear regression and classification models, the estimation problem is an ill-posed one. In this context, PLS offers a simple and efficient alternative to the methods based on the principal components of the stochastic process. We compare the results given by the PLS approach and other linear models using several datasets from economy, industry and medical fields. PMID:17124795
A square titanium nanomesh on W(100)
NASA Astrophysics Data System (ADS)
Trembulowicz, A.; Ciszewski, A.
2007-08-01
A regular square mesh structure with 4.5 nm periodicity was formed after annealing an adsorption layer of Ti on W(100) at 1370 K. The nanomesh consists of two self-assembled layers on top of the Ti adlayer, ~3.5 physical monolayers thick on average. The first layer of the nanomesh is composed of wires ~1.3 nm wide arranged along the \\langle 010 \\rangle directions of the W(100) substrate. The second one is formed by islands of ~1.6 nm in diameter arrayed upon crossing sites of the wires. The nanomesh is thermally stable up to 1470 K.
Uranyl peroxide closed clusters containing topological squares
Unruh, Daniel K.; Burtner, Alicia; Pressprich, Laura; Sigmon, Ginger E.; Burns, Peter C
2010-01-01
Four self-assembling clusters of uranyl peroxide polyhedra have been formed in alkaline aqueous solutions and structurally characterized. These clusters consist of 28, 30, 36 and 44 uranyl polyhedra and exhibit complex new topologies. Each has a structure that contains topological squares, pentagons and hexagons. Analysis of possible topologies within boundary constraints indicates a tendency for adoption of higher symmetry topologies in these cases. Small angle X-ray scattering data demonstrated that crystals of one of these clusters can be dissolved in ultrapure water and that the clusters remain intact for at least several days.
Information fusion in regularized inversion of tomographic pumping tests
Bohling, G.C.; ,
2008-01-01
In this chapter we investigate a simple approach to incorporating geophysical information into the analysis of tomographic pumping tests for characterization of the hydraulic conductivity (K) field in an aquifer. A number of authors have suggested a tomographic approach to the analysis of hydraulic tests in aquifers - essentially simultaneous analysis of multiple tests or stresses on the flow system - in order to improve the resolution of the estimated parameter fields. However, even with a large amount of hydraulic data in hand, the inverse problem is still plagued by non-uniqueness and ill-conditioning and the parameter space for the inversion needs to be constrained in some sensible fashion in order to obtain plausible estimates of aquifer properties. For seismic and radar tomography problems, the parameter space is often constrained through the application of regularization terms that impose penalties on deviations of the estimated parameters from a prior or background model, with the tradeoff between data fit and model norm explored through systematic analysis of results for different levels of weighting on the regularization terms. In this study we apply systematic regularized inversion to analysis of tomographic pumping tests in an alluvial aquifer, taking advantage of the steady-shape flow regime exhibited in these tests to expedite the inversion process. In addition, we explore the possibility of incorporating geophysical information into the inversion through a regularization term relating the estimated K distribution to ground penetrating radar velocity and attenuation distributions through a smoothing spline model. ?? 2008 Springer-Verlag Berlin Heidelberg.
Thermoelectric properties of inverse opals
NASA Astrophysics Data System (ADS)
Mahan, G. D.; Poilvert, N.; Crespi, V. H.
2016-02-01
Rayleigh's method [Philos. Mag. Ser. 5 34, 481 (1892)] is used to solve for the classical thermoelectric equations in inverse opals. His theory predicts that in an inverse opal, with periodic holes, the Seebeck coefficient and the figure of merit are identical to that of the bulk material. We also provide a major revision to Rayleigh's method, in using the electrochemical potential as an important variable, instead of the electrostatic potential. We also show that in some cases, the thermal boundary resistance is important in the effective thermal conductivity.
Darwin's "strange inversion of reasoning".
Dennett, Daniel
2009-06-16
Darwin's theory of evolution by natural selection unifies the world of physics with the world of meaning and purpose by proposing a deeply counterintuitive "inversion of reasoning" (according to a 19th century critic): "to make a perfect and beautiful machine, it is not requisite to know how to make it" [MacKenzie RB (1868) (Nisbet & Co., London)]. Turing proposed a similar inversion: to be a perfect and beautiful computing machine, it is not requisite to know what arithmetic is. Together, these ideas help to explain how we human intelligences came to be able to discern the reasons for all of the adaptations of life, including our own.
Population inversion by chirped pulses
Lu Tianshi
2011-09-15
In this paper, we analyze the condition for complete population inversion by a chirped pulse over a finite duration. The nonadiabatic transition probability is mapped in the two-dimensional parameter space of coupling strength and detuning amplitude. Asymptotic forms of the probability are derived by the interference of nonadiabatic transitions for sinusoidal and triangular pulses. The qualitative difference between the maps for the two types of pulses is accounted for. The map is used for the design of stable inversion pulses under specific accuracy thresholds.
Multiphase inverse modeling: An Overview
Finsterle, S.
1998-03-01
Inverse modeling is a technique to derive model-related parameters from a variety of observations made on hydrogeologic systems, from small-scale laboratory experiments to field tests to long-term geothermal reservoir responses. If properly chosen, these observations contain information about the system behavior that is relevant to the performance of a geothermal field. Estimating model-related parameters and reducing their uncertainty is an important step in model development, because errors in the parameters constitute a major source of prediction errors. This paper contains an overview of inverse modeling applications using the ITOUGH2 code, demonstrating the possibilities and limitations of a formalized approach to the parameter estimation problem.
Mean-square radii of two-component three-body systems in two spatial dimensions
NASA Astrophysics Data System (ADS)
Sandoval, J. H.; Bellotti, F. F.; Jensen, A. S.; Yamashita, M. T.
2016-08-01
We calculate root-mean-square radii for a three-body system confined to two spatial dimensions and consisting of two identical bosons (A ) and one distinguishable particle (B ). We use zero-range two-body interactions between each of the pairs, and focus thereby directly on universal properties. We solve the Faddeev equations in momentum space and express the mean-square radii in terms of first-order derivatives of the Fourier transforms of densities. The strengths of the interactions are adjusted for each set of masses to produce equal two-body bound-state energies between different pairs. The mass ratio, A =mB/mA , between particles B and A are varied from 0.01 to 100, providing a number of bound states decreasing from 8 to 2. Energies and mean-square radii of these states are analyzed for small A by use of the Born-Oppenheimer potential between the two heavy A particles. For large A the radii of the two bound states are consistent with a slightly asymmetric three-body structure. When A approaches thresholds for binding of the three-body excited states, the corresponding mean-square radii diverge inversely proportional to the deviation of the three-body energy from the two-body thresholds. The structures at these three-body thresholds correspond to bound A B dimers and one loosely bound A particle.
NASA Astrophysics Data System (ADS)
Guo, Shiguang; Zhang, Bo; Wang, Qing; Cabrales-Vargas, Alejandro; Marfurt, Kurt J.
2016-08-01
Conventional Kirchhoff migration often suffers from artifacts such as aliasing and acquisition footprint, which come from sub-optimal seismic acquisition. The footprint can mask faults and fractures, while aliased noise can focus into false coherent events which affect interpretation and contaminate amplitude variation with offset, amplitude variation with azimuth and elastic inversion. Preconditioned least-squares migration minimizes these artifacts. We implement least-squares migration by minimizing the difference between the original data and the modeled demigrated data using an iterative conjugate gradient scheme. Unpreconditioned least-squares migration better estimates the subsurface amplitude, but does not suppress aliasing. In this work, we precondition the results by applying a 3D prestack structure-oriented LUM (lower–upper–middle) filter to each common offset and common azimuth gather at each iteration. The preconditioning algorithm not only suppresses aliasing of both signal and noise, but also improves the convergence rate. We apply the new preconditioned least-squares migration to the Marmousi model and demonstrate how it can improve the seismic image compared with conventional migration, and then apply it to one survey acquired over a new resource play in the Mid-Continent, USA. The acquisition footprint from the targets is attenuated and the signal to noise ratio is enhanced. To demonstrate the impact on interpretation, we generate a suite of seismic attributes to image the Mississippian limestone, and show that the karst-enhanced fractures in the Mississippian limestone can be better illuminated.
NASA Astrophysics Data System (ADS)
Guo, Shiguang; Zhang, Bo; Wang, Qing; Cabrales-Vargas, Alejandro; Marfurt, Kurt J.
2016-08-01
Conventional Kirchhoff migration often suffers from artifacts such as aliasing and acquisition footprint, which come from sub-optimal seismic acquisition. The footprint can mask faults and fractures, while aliased noise can focus into false coherent events which affect interpretation and contaminate amplitude variation with offset, amplitude variation with azimuth and elastic inversion. Preconditioned least-squares migration minimizes these artifacts. We implement least-squares migration by minimizing the difference between the original data and the modeled demigrated data using an iterative conjugate gradient scheme. Unpreconditioned least-squares migration better estimates the subsurface amplitude, but does not suppress aliasing. In this work, we precondition the results by applying a 3D prestack structure-oriented LUM (lower-upper-middle) filter to each common offset and common azimuth gather at each iteration. The preconditioning algorithm not only suppresses aliasing of both signal and noise, but also improves the convergence rate. We apply the new preconditioned least-squares migration to the Marmousi model and demonstrate how it can improve the seismic image compared with conventional migration, and then apply it to one survey acquired over a new resource play in the Mid-Continent, USA. The acquisition footprint from the targets is attenuated and the signal to noise ratio is enhanced. To demonstrate the impact on interpretation, we generate a suite of seismic attributes to image the Mississippian limestone, and show that the karst-enhanced fractures in the Mississippian limestone can be better illuminated.
Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.; Thomas, James L. (Technical Monitor)
2003-01-01
The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.
Unlocking the spatial inversion of large scanning magnetic microscopy datasets
NASA Astrophysics Data System (ADS)
Myre, J. M.; Lascu, I.; Andrade Lima, E.; Feinberg, J. M.; Saar, M. O.; Weiss, B. P.
2013-12-01
Modern scanning magnetic microscopy provides the ability to perform high-resolution, ultra-high sensitivity moment magnetometry, with spatial resolutions better than 10^-4 m and magnetic moments as weak as 10^-16 Am^2. These microscopy capabilities have enhanced numerous magnetic studies, including investigations of the paleointensity of the Earth's magnetic field, shock magnetization and demagnetization of impacts, magnetostratigraphy, the magnetic record in speleothems, and the records of ancient core dynamos of planetary bodies. A common component among many studies utilizing scanning magnetic microscopy is solving an inverse problem to determine the non-negative magnitude of the magnetic moments that produce the measured component of the magnetic field. The two most frequently used methods to solve this inverse problem are classic fast Fourier techniques in the frequency domain and non-negative least squares (NNLS) methods in the spatial domain. Although Fourier techniques are extremely fast, they typically violate non-negativity and it is difficult to implement constraints associated with the space domain. NNLS methods do not violate non-negativity, but have typically been computation time prohibitive for samples of practical size or resolution. Existing NNLS methods use multiple techniques to attain tractable computation. To reduce computation time in the past, typically sample size or scan resolution would have to be reduced. Similarly, multiple inversions of smaller sample subdivisions can be performed, although this frequently results in undesirable artifacts at subdivision boundaries. Dipole interactions can also be filtered to only compute interactions above a threshold which enables the use of sparse methods through artificial sparsity. To improve upon existing spatial domain techniques, we present the application of the TNT algorithm, named TNT as it is a "dynamite" non-negative least squares algorithm which enhances the performance and accuracy of
Magnetic Dipole Interaction on a Square Lattice
NASA Astrophysics Data System (ADS)
Zabel, Hartmut; Ewerlin, Melanie; Demirbas, Derya; Bruessing, Frank; Kronast, Florian
2013-03-01
We have studied interactions and phase transitions of circular magnetic islands with dipole character on a square lattice. By lithographic means we have prepared square patterns of periodicity 300 nm decorated with circular islands of 150 nm diameter using Pd0.87Fe0.13 as magnetic alloy. Below the Curie temperature of 260 K each island is in a ferromagnetic, single domain state with dipolar character and zero in-plane anisotropy. Below a second transition temperature the dipoles start to interact. MOKE measurements show a characteristic change in the magnetic hysteresis for temperatures below 160 K with increasing coercivity for decreasing temperatures. Furthermore, below the second transition the in-plane hysteresis becomes anisotropic, having an easy axis along [10] direction and a hard axis along [11] direction. SPEEM experiments at BESSY II of the HZB with circularly polarized incident photons tuned to the Fe L3 - edge show clearly the development of dipolar chains below the second phase transition that increase in length with decreasing temperature. Neighbouring chains are found to be oriented parallel as well as antiparallel. This work was supported by DFG-SFB 491 and BMBF under contracts 05K10PC2 and 05ES3xBA/5
Augmented Classical Least Squares Multivariate Spectral Analysis
Haaland, David M.; Melgaard, David K.
2005-01-11
A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.
Augmented Classical Least Squares Multivariate Spectral Analysis
Haaland, David M.; Melgaard, David K.
2005-07-26
A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.
Augmented classical least squares multivariate spectral analysis
Haaland, David M.; Melgaard, David K.
2004-02-03
A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.
Total least squares for anomalous change detection
Theiler, James P; Matsekh, Anna M
2010-01-01
A family of difference-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQ-based anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and furthermore it is shown to be equivalent to the optimized covariance equalization algorithm. What whitened TLSQ offers, in addition to connecting with a common language the derivations of two of the most popular anomalous change detection algorithms - chronochrome and covariance equalization - is a generalization of these algorithms with the potential for better performance.
Gravity as the square of gauge theory
Bern, Zvi; Dennen, Tristan; Huang Yutin; Kiermaier, Michael
2010-09-15
We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen, and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By ''squaring'' the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.
Groups of Negations on the Unit Square
2014-01-01
The main results are about the groups of the negations on the unit square, which is considered as a bilattice. It is proven that all the automorphisms on it form a group; the set, containing the monotonic isomorphisms and the strict negations of the first (or the second or the third) kind, with the operator “composition,” is a group G2 (or G3 or G4, correspondingly). All these four kinds of mappings form a group G5. And all the groups Gi, i = 2,3, 4 are normal subgroups of G5. Moreover, for G5, a generator set is given, which consists of all the involutive negations of the second kind and the standard negation of the first kind. As a subset of the unit square, the interval-valued set is also studied. Two groups are found: one group consists of all the isomorphisms on LI, and the other group contains all the isomorphisms and all the strict negations on LI, which keep the diagonal. Moreover, the former is a normal subgroup of the latter. And all the involutive negations on the interval-valued set form a generator set of the latter group. PMID:25197719
Analyzing industrial energy use through ordinary least squares regression models
NASA Astrophysics Data System (ADS)
Golden, Allyson Katherine
Extensive research has been performed using regression analysis and calibrated simulations to create baseline energy consumption models for residential buildings and commercial institutions. However, few attempts have been made to discuss the applicability of these methodologies to establish baseline energy consumption models for industrial manufacturing facilities. In the few studies of industrial facilities, the presented linear change-point and degree-day regression analyses illustrate ideal cases. It follows that there is a need in the established literature to discuss the methodologies and to determine their applicability for establishing baseline energy consumption models of industrial manufacturing facilities. The thesis determines the effectiveness of simple inverse linear statistical regression models when establishing baseline energy consumption models for industrial manufacturing facilities. Ordinary least squares change-point and degree-day regression methods are used to create baseline energy consumption models for nine different case studies of industrial manufacturing facilities located in the southeastern United States. The influence of ambient dry-bulb temperature and production on total facility energy consumption is observed. The energy consumption behavior of industrial manufacturing facilities is only sometimes sufficiently explained by temperature, production, or a combination of the two variables. This thesis also provides methods for generating baseline energy models that are straightforward and accessible to anyone in the industrial manufacturing community. The methods outlined in this thesis may be easily replicated by anyone that possesses basic spreadsheet software and general knowledge of the relationship between energy consumption and weather, production, or other influential variables. With the help of simple inverse linear regression models, industrial manufacturing facilities may better understand their energy consumption and
Measured and predicted root-mean-square errors in square and triangular antenna mesh facets
NASA Technical Reports Server (NTRS)
Fichter, W. B.
1989-01-01
Deflection shapes of square and equilateral triangular facets of two tricot-knit, gold plated molybdenum wire mesh antenna materials were measured and compared, on the basis of root mean square (rms) differences, with deflection shapes predicted by linear membrane theory, for several cases of biaxial mesh tension. The two mesh materials contained approximately 10 and 16 holes per linear inch, measured diagonally with respect to the course and wale directions. The deflection measurement system employed a non-contact eddy current proximity probe and an electromagnetic distance sensing probe in conjunction with a precision optical level. Despite experimental uncertainties, rms differences between measured and predicted deflection shapes suggest the following conclusions: that replacing flat antenna facets with facets conforming to parabolically curved structural members yields smaller rms surface error; that potential accuracy gains are greater for equilateral triangular facets than for square facets; and that linear membrane theory can be a useful tool in the design of tricot knit wire mesh antennas.
Specular surface measurement by using least squares light tracking technique
NASA Astrophysics Data System (ADS)
Guo, Hongwei; Feng, Peng; Tao, Tao
2010-02-01
This paper presents a novel technique for measuring the three-dimensional (3-D) shapes of specular surfaces. In this technique, an LCD monitor plane is used as the diffusive light source. It can be vertically moved to two or more different positions. At each position, sinusoid fringe patterns are displayed on the LCD plane and reflected by the measured specular surface. The distorted fringe patterns are captured with a camera, so that the phase distributions at these positions are measured. From the phases, the locus of the incident ray for each pixel is determined in the least squares sense, and further the three-dimensional shape of the specular surface is reconstructed. In so doing, the restrictions and limitations of the existing techniques in computational complexities, phase ambiguities, and error accumulations are eliminated. The validity of this technique has been demonstrated by experimental results.
WITHDRAWN--Performance Evaluation of Square Pore Microchannel Plates
NASA Astrophysics Data System (ADS)
Visco, A.
2005-10-01
Microchannel Plates (MCP) are used in a variety of imaging systems as a means of amplifying the incident radiation. Using a microchannel plate mount, developed at the University of Michigan, we compare square and round pore MCPs. Using a characterized x-ray source, we investigate the differences in the pulse height distribution, modular transfer function, and Quantum efficiency of these two types. Using a metal grid, we create a potential difference above the MCP that forces ejected electrons back into the pores, which may prove to increase the quantum efficiency of the system. Measurements of the effect of the reflecting grid on the quantum efficiency are presented. Work supported by the Naval Research Laboratory, National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grant DE-FG52-03NA00064, and through DE FG53 2005 NA26014, and Livermore National Laboratory.
Scaling behavior of explosive percolation on the square lattice
NASA Astrophysics Data System (ADS)
Ziff, Robert M.
2010-11-01
Clusters generated by the product-rule growth model of Achlioptas, D’Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold with unrestricted bond placement (allowing loops) is found precisely using several different criteria based on both moments and wrapping probabilities, yielding pc=0.526565±0.000005 , consistent with the recent result of Radicchi and Fortunato. The correlation-length exponent ν is found to be close to 1. The qualitative difference from regular percolation is shown dramatically in the behavior of the percolation probability P∞ (size of largest cluster), of the susceptibility, and of the second moment of finite clusters, where discontinuities appear at the threshold. The critical cluster-size distribution does not follow a consistent power law for the range of system sizes we study (L≤8192) but may approach a power law with τ>2 for larger L .