Full-disk nonlinear force-free field extrapolation of SDO/HMI and SOLIS/VSM magnetograms
Tadesse, T.; Wiegelmann, T.; Inhester, B.; MacNeice, P.; Pevtsov, A.; Sun, X.
2013-02-01
Context. The magnetic field configuration is essential for understanding solar explosive phenomena, such as flares and coronal mass ejections. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Two complications of this approach are that the measured photospheric magnetic field is not force-free and that one has to apply a preprocessing routine to achieve boundary conditions suitable for the force-free modeling. Furthermore the nonlinear force-free extrapolation code should take uncertainties into account in the photospheric field data. They occur due to noise, incomplete inversions, or azimuth ambiguity-removing techniques. Aims: Extrapolation codes in Cartesian geometry for modeling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modeling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure to full disk vector magnetograms. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) onboard the solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS). Methods: We used HMI and VSM photospheric magnetic field measurements to model the force-free coronal field above multiple solar active regions, assuming magnetic forces to dominate. We solved the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a full disk and excluding the poles. After searching for the optimum modeling parameters for the particular data sets, we compared the resulting nonlinear force-free model fields. We compared
Wiegelmann, T; Inhester, B; Tadesse, T; Sun, X; Hoeksema, J T
2012-01-01
The SDO/HMI instruments provide photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semi-analytic and numeric equilibria and been applied before to vector magnetograms from Hinode and ground based observations. Recently we implemented a new version which takes measurement errors in photospheric vector magnetograms into account. Photospheric field measurements are often due to measurement errors and finite nonmagnetic forces inconsistent as a boundary for a force-free field in the corona. In order to deal with these uncertainties, we developed two improvements: 1.) Preprocessing of the surface measurements in order to make them compatible with a force-free field 2.) The new code keeps a balance between the force-free constraint and deviation from the photospheric field m...
Nonlinear Force-free Coronal Magnetic Stereoscopy
Chifu, Iulia; Wiegelmann, Thomas; Inhester, Bernd
2017-03-01
Insights into the 3D structure of the solar coronal magnetic field have been obtained in the past by two completely different approaches. The first approach are nonlinear force-free field (NLFFF) extrapolations, which use photospheric vector magnetograms as boundary condition. The second approach uses stereoscopy of coronal magnetic loops observed in EUV coronal images from different vantage points. Both approaches have their strengths and weaknesses. Extrapolation methods are sensitive to noise and inconsistencies in the boundary data, and the accuracy of stereoscopy is affected by the ability of identifying the same structure in different images and by the separation angle between the view directions. As a consequence, for the same observational data, the 3D coronal magnetic fields computed with the two methods do not necessarily coincide. In an earlier work (Paper I) we extended our NLFFF optimization code by including stereoscopic constrains. The method was successfully tested with synthetic data, and within this work, we apply the newly developed code to a combined data set from SDO/HMI, SDO/AIA, and the two STEREO spacecraft. The extended method (called S-NLFFF) contains an additional term that monitors and minimizes the angle between the local magnetic field direction and the orientation of the 3D coronal loops reconstructed by stereoscopy. We find that when we prescribe the shape of the 3D stereoscopically reconstructed loops, the S-NLFFF method leads to a much better agreement between the modeled field and the stereoscopically reconstructed loops. We also find an appreciable decrease by a factor of two in the angle between the current and the magnetic field. This indicates the improved quality of the force-free solution obtained by S-NLFFF.
Stability of Nonlinear Force-Free Magnetic Fields
Institute of Scientific and Technical Information of China (English)
胡友秋
2001-01-01
Based on the magnetohydrodynamic energy principle, it is proved that Gold-Hoyle's nonlinear force-free magnetic field is unstable. This disproves the sufficient criterion for stability of nonlinear force-free magnetic fields given by Kriiger that a nonlinear force-free field is stable if the maximum absolute value of the force-free factor is smaller than the lowest eigenvalue associated with the domain of interest.
Nonlinear force-free modelling: influence of inaccuracies in the measured magnetic vector
Wiegelmann, T; Solanki, S K; Lagg, A
2009-01-01
Context: Solar magnetic fields are regularly extrapolated into the corona starting from photospheric magnetic measurements that can suffer from significant uncertainties. Aims: Here we study how inaccuracies introduced into the maps of the photospheric magnetic vector from the inversion of ideal and noisy Stokes parameters influence the extrapolation of nonlinear force-free magnetic fields. Methods: We compute nonlinear force-free magnetic fields based on simulated vector magnetograms, which have been produced by the inversion of Stokes profiles, computed froma 3-D radiation MHD simulation snapshot. These extrapolations are compared with extrapolations starting directly from the field in the MHD simulations, which is our reference. We investigate how line formation and instrumental effects such as noise, limited spatial resolution and the effect of employing a filter instrument influence the resulting magnetic field structure. The comparison is done qualitatively by visual inspection of the magnetic field dis...
Limitations of force-free magnetic field extrapolations: revisiting basic assumptions
Peter, H; Chitta, L P; Cameron, R H
2015-01-01
Force-free extrapolations are widely used to study the magnetic field in the solar corona based on surface measurements. The extrapolations assume that the ratio of internal energy of the plasma to magnetic energy, the plasma-beta is negligible. Despite the widespread use of this assumption observations, models, and theoretical considerations show that beta is of the order of a few percent to more than 10%, and thus not small. We investigate what consequences this has for the reliability of extrapolation results. We use basic concepts starting with the force and the energy balance to infer relations between plasma-beta and free magnetic energy, to study the direction of currents in the corona with respect to the magnetic field, and to estimate the errors in the free magnetic energy by neglecting effects of the plasma (beta<<1). A comparison with a 3D MHD model supports our basic considerations. If plasma-beta is of the order of the relative free energy (the ratio of the free magnetic energy to the total...
A Fluid Dynamics Approach for the Computation of Non-linear Force-Free Magnetic Field
Institute of Scientific and Technical Information of China (English)
Jing-Qun Li; Jing-Xiu Wang; Feng-Si Wei
2003-01-01
Inspired by the analogy between the magnetic field and velocity fieldof incompressible fluid flow, we propose a fluid dynamics approach for comput-ing nonlinear force-free magnetic fields. This method has the advantage that thedivergence-free condition is automatically satisfied, which is a sticky issue for manyother algorithms, and we can take advantage of modern high resolution algorithmsto process the force-free magnetic field. Several tests have been made based on thewell-known analytic solution proposed by Low & Lou. The numerical results arein satisfactory agreement with the analytic ones. It is suggested that the newlyproposed method is promising in extrapolating the active region or the whole sunmagnetic fields in the solar atmosphere based on the observed vector magnetic fieldon the photosphere.
Tadesse, T.; Wiegelmann, T.; Gosain, S.; MacNeice, P.; Pevtsov, A. A.
2014-01-01
Context. The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently, there are several modelling techniques being used to calculate three-dimensional field lines into the solar atmosphere. Aims. For the first time, synoptic maps of a photospheric-vector magnetic field synthesized from the vector spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. Methods. We solve the nonlinear force-free field equations using an optimization principle in spherical geometry. The resulting threedimensional magnetic fields are used to estimate the magnetic free energy content E(sub free) = E(sub nlfff) - E(sub pot), which is the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the atmospheric imaging assembly (AIA) on board the Solar Dynamics Observatory (SDO). Results. For a single Carrington rotation 2121, we find that the global nonlinear force-free field (NLFFF) magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.
The Influence of Spatial Resolution on Nonlinear Force-Free Modeling
DeRosa, M L; Leka, K D; Barnes, G; Amari, T; Canou, A; Gilchrist, S A; Thalmann, J K; Valori, G; Wiegelmann, T; Schrijver, C J; Malanushenko, A; Sun, X; Régnier, S
2015-01-01
The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-c...
Nonlinear Force-Free Magnetic Field Modeling of AR 10953: A Critical Assessment
De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan, J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
2009-05-01
Nonlinear force-free field (NLFFF) modeling seeks to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have failed to arrive at consistent solutions when applied to (thus far, two) cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not available). One issue is that NLFFF models require consistent, force-free vector magnetic boundary data, and vector magnetogram data sampling the photosphere do not satisfy this requirement. Consequently, several problems have arisen that are believed to affect such modeling efforts. We use AR 10953 to illustrate these problems, namely: (1) some of the far-reaching, current-carrying connections are exterior to the observational field of view, (2) the solution algorithms do not (yet) incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is needed to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models.
Tadesse, Tilaye; Gosain, S; MacNeice, P; Pevtsov, Alexei A
2013-01-01
The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently there are several modelling techniques being used to calculate three-dimension of the field lines into the solar atmosphere. For the first time, synoptic maps of photospheric vector magnetic field synthesized from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. We solve the nonlinear force-free field equations using optimizatio...
Magneto-frictional Modeling of Coronal Nonlinear Force-free Fields. II. Application to Observations
Guo, Y.; Xia, C.; Keppens, R.
2016-09-01
A magneto-frictional module has been implemented and tested in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC) in the first paper of this series. Here, we apply the magneto-frictional method to observations to demonstrate its applicability in both Cartesian and spherical coordinates, and in uniform and block-adaptive octree grids. We first reconstruct a nonlinear force-free field (NLFFF) on a uniform grid of 1803 cells in Cartesian coordinates, with boundary conditions provided by the vector magnetic field observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) at 06:00 UT on 2010 November 11 in active region NOAA 11123. The reconstructed NLFFF successfully reproduces the sheared and twisted field lines and magnetic null points. Next, we adopt a three-level block-adaptive grid to model the same active region with a higher spatial resolution on the bottom boundary and a coarser treatment of regions higher up. The force-free and divergence-free metrics obtained are comparable to the run with a uniform grid, and the reconstructed field topology is also very similar. Finally, a group of active regions, including NOAA 11401, 11402, 11405, and 11407, observed at 03:00 UT on 2012 January 23 by SDO/HMI is modeled with a five-level block-adaptive grid in spherical coordinates, where we reach a local resolution of 0\\buildrel{\\circ}\\over{.} 06 pixel-1 in an area of 790 Mm × 604 Mm. Local high spatial resolution and a large field of view in NLFFF modeling can be achieved simultaneously in parallel and block-adaptive magneto-frictional relaxations.
Guo, Y.; Xia, C.; Keppens, R.; Valori, G.
2016-09-01
We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov-Démoulin model. We compare different combinations of spatial and temporal discretizations, and find that the fourth-order central difference with a local Lax-Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper.
Nonlinear Force-Free Magnetic Field Modeling of the Solar Corona: A Critical Assessment
De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; McTiernan, J. M.; Régnier, S.; Thalmann, J.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
2008-12-01
Nonlinear force-free field (NLFFF) modeling promises to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have so far failed to arrive at consistent solutions when applied to cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not been available). It is our view that the lack of robust results indicates an endemic problem with the NLFFF modeling process, and that this process will likely continue to fail until (1) more of the far-reaching, current-carrying connections are within the observational field of view, (2) the solution algorithms incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is found to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models.
NONLINEAR FORCE-FREE MODELING OF A THREE-DIMENSIONAL SIGMOID OBSERVED ON THE SUN
Energy Technology Data Exchange (ETDEWEB)
Inoue, S.; Watari, S. [National Institute of Information and Communications Technology (NICT), 4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795 (Japan); Magara, T.; Choe, G. S., E-mail: inosato@khu.ac.kr [School of Space Research, Kyung Hee University, Yongin, Gyeonggi-do 446-701 (Korea, Republic of)
2012-03-01
In this work, we analyze the characteristics of the three-dimensional magnetic structure of a sigmoid observed over an active region (AR 10930) and followed by X-class flares. This is accomplished by combining a nonlinear force-free field (NLFFF) model of a coronal magnetic field and the high-resolution vector-field measurement of a photospheric magnetic field by Hinode. The key findings of our analysis reveal that the value of the X-ray intensity associated with the sigmoid is more sensitive to the strength of the electric current rather than the twist of the field lines. The strong electric current flows along the magnetic field lines and composes the central part of the sigmoid, even though the twist of the field lines is weak in that region. On the other hand, the outer region (i.e., the elbow part) of the sigmoid is basically occupied by field lines of strong twist and weak current density. Consequently, weak X-ray emission is observed. As the initial Ca II illumination basically occurs from the central part of the sigmoid, this region plays an important role in determining the onset mechanism of the flare despite its weak twisted field-line configuration. We also compare our results with the magnetohydrodynamic simulation for the formation of a sigmoid. Although the estimated values of the twist from the simulation are found to be a little higher than the values obtained from the NLFFF, we find that the field-line configurations generated by the simulation and NLFFF are remarkably analogous as long as we deal with the lower coronal region.
Aschwanden, Markus J
2016-01-01
In this work we provide an updated description of the Vertical Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, nonpotential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann (2004), we find agreement in the potential, nonpotential, and free energy within a factor of about 1.3, but the Wiegelmann code yields in the average a factor of 2 lower flare en...
Aschwanden, Markus J.
2016-06-01
In this work we provide an updated description of the Vertical-Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, non-potential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann, we find agreement in the potential, non-potential, and free energy within a factor of ≲ 1.3, but the Wiegelmann code yields in the average a factor of 2 lower flare energies. The VCA-NLFFF code is found to detect decreases in flare energies in most X, M, and C-class flares. The successful detection of energy decreases during a variety of flares with the VCA-NLFFF code indicates that current-driven twisting and untwisting of the magnetic field is an adequate model to quantify the storage of magnetic energies in active regions and their dissipation during flares. The VCA-NLFFF code is also publicly available in the Solar SoftWare.
Inoue, S; Kusano, K
2016-01-01
We analyze a three-dimensional (3D) magnetic structure and its stability in large solar active region(AR) 12192, using the 3D coronal magnetic field constructed under a nonlinear force-free field (NLFFF) approximation. In particular, we focus on the magnetic structure that produced an X3.1-class flare which is one of the X-class flares observed in AR 12192. According to our analysis, the AR contains multiple-flux-tube system, {\\it e.g.}, a large flux tube, both of whose footpoints are anchored to the large bipole field, under which other tubes exist close to a polarity inversion line (PIL). These various flux tubes of different sizes and shapes coexist there. In particular, the later are embedded along the PIL, which produces a favorable shape for the tether-cutting reconnection and is related to the X-class solar flare. We further found that most of magnetic twists are not released even after the flare, which is consistent with the fact that no observational evidence for major eruptions was found. On the oth...
Formation and Eruption of an Active Region Sigmoid: I. Study by Nonlinear Force-Free Field Modeling
Jiang, Chaowei; Feng, Xueshang; Hu, Qiang
2013-01-01
We present a magnetic analysis of the formation and eruption of an active region (AR) sigmoid in AR 11283 from 2011 September 4 to 6. To follow the quasi-static evolution of the coronal magnetic field, we reconstruct a time sequence of static fields using a recently developed nonlinear force-free field model constrained by the SDO/HMI vector magnetograms. A detailed analysis of the fields compared with the SDO/AIA observations suggests the following scenario for the evolution of the region. Initially, a new bipole emerges into the negative polarity of a pre-existing bipolar AR, forming a null point topology between the two flux systems. A weakly twisted flux rope (FR) is then built up slowly in the embedded core region, largely through flux-cancellation photospheric reconnections, forming a bald patch separatrix surface (BPSS) separating the FR from its ambient field. The FR grows gradually until its axis runs into a torus instability (TI) domain near the end of the third day, and the BPSS also develops a ful...
Energy Technology Data Exchange (ETDEWEB)
Inoue, S. [Max-Planck-Institute for Solar System Research, Justus-von-Liebig-Weg 3 D-37077 Göttingen Germany (Germany); Hayashi, K.; Kusano, K., E-mail: inoue@mps.mpg.de [Institute for Space-Earth Environmental Research, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601 (Japan)
2016-02-20
We analyze a three-dimensional (3D) magnetic structure and its stability in large solar active region (AR) 12192, using the 3D coronal magnetic field constructed under a nonlinear force-free field (NLFFF) approximation. In particular, we focus on the magnetic structure that produced an X3.1-class flare, which is one of the X-class flares observed in AR 12192. According to our analysis, the AR contains a multiple-flux-tube system, e.g., a large flux tube, with footpoints that are anchored to the large bipole field, under which other tubes exist close to a polarity inversion line (PIL). These various flux tubes of different sizes and shapes coexist there. In particular, the latter are embedded along the PIL, which produces a favorable shape for the tether-cutting reconnection and is related to the X-class solar flare. We further found that most of magnetic twists are not released even after the flare, which is consistent with the fact that no observational evidence for major eruptions was found. On the other hand, the upper part of the flux tube is beyond a critical decay index, essential for the excitation of torus instability before the flare, even though no coronal mass ejections were observed. We discuss the stability of the complicated flux tube system and suggest the reason for the existence of the stable flux tube. In addition, we further point out a possibility for tracing the shape of flare ribbons, on the basis of a detailed structural analysis of the NLFFF before a flare.
Directory of Open Access Journals (Sweden)
Lee HyunYoung
2010-01-01
Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.
Schrijver, C J; Metcalf, T; Barnes, G; Lites, B; Tarbell, T; McTiernan, J; Valori, G; Wiegelmann, T; Wheatland, M S; Amari, T; Aulanier, G; Demoulin, P; Fuhrmann, M; Kusano, K; Régnier, S; Thalmann, J K
2007-01-01
Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of pre-existing atmospheric magnetic flux subject to surface plasma flows, or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA Active Region 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with 4 different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the ...
Energy Technology Data Exchange (ETDEWEB)
Chitta, L. P.; Kariyappa, R. [Indian Institute of Astrophysics, Bangalore 560 034 (India); Van Ballegooijen, A. A.; DeLuca, E. E. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street MS-58, Cambridge, MA 02138 (United States); Solanki, S. K. [Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany)
2014-10-01
In the quiet solar photosphere, the mixed polarity fields form a magnetic carpet that continuously evolves due to dynamical interaction between the convective motions and magnetic field. This interplay is a viable source to heat the solar atmosphere. In this work, we used the line-of-sight (LOS) magnetograms obtained from the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory, and the Imaging Magnetograph eXperiment instrument on the Sunrise balloon-borne observatory, as time-dependent lower boundary conditions, to study the evolution of the coronal magnetic field. We use a magneto-frictional relaxation method, including hyperdiffusion, to produce a time series of three-dimensional nonlinear force-free fields from a sequence of photospheric LOS magnetograms. Vertical flows are added up to a height of 0.7 Mm in the modeling to simulate the non-force-freeness at the photosphere-chromosphere layers. Among the derived quantities, we study the spatial and temporal variations of the energy dissipation rate and energy flux. Our results show that the energy deposited in the solar atmosphere is concentrated within 2 Mm of the photosphere and there is not sufficient energy flux at the base of the corona to cover radiative and conductive losses. Possible reasons and implications are discussed. Better observational constraints of the magnetic field in the chromosphere are crucial to understand the role of the magnetic carpet in coronal heating.
Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations
Guoqiang, Han; Jiong, Wang
2001-09-01
In this paper, we analyze the existence of asymptotic error expansion of the Nystrom solution for two-dimensional nonlinear Fredholm integral equations of the second kind. We show that the Nystrom solution admits an error expansion in powers of the step-size h and the step-size k. For a special choice of the numerical quadrature, the leading terms in the error expansion for the Nystrom solution contain only even powers of h and k, beginning with terms h2p and k2q. These expansions are useful for the application of Richardson extrapolation and for obtaining sharper error bounds. Numerical examples show that how Richardson extrapolation gives a remarkable increase of precision, in addition to faster convergence.
ON THE FORCE-FREE NATURE OF PHOTOSPHERIC SUNSPOT MAGNETIC FIELDS AS OBSERVED FROM HINODE (SOT/SP)
Energy Technology Data Exchange (ETDEWEB)
Tiwari, Sanjiv Kumar, E-mail: tiwari@mps.mpg.de [Udaipur Solar Observatory, Physical Research Laboratory, Dewali, Bari Road, Udaipur 313 001 (India)
2012-01-01
A magnetic field is force-free if there is no interaction between it and the plasma in the surrounding atmosphere, i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of various magnetic parameters, such as magnetic energy (using the virial theorem), gradient of twist of sunspot magnetic fields (computed from the force-free parameter {alpha}), and any kind of extrapolation, heavily hinges on the force-free approximation of the photospheric sunspot magnetic fields. Thus, it is of vital importance to inspect the force-free behavior of sunspot magnetic fields. The force-free nature of sunspot magnetic fields has been examined earlier by some researchers, ending with incoherent results. Accurate photospheric vector field measurements with high spatial resolution are required to inspect the force-free nature of sunspots. For this purpose, we use several vector magnetograms of high spatial resolution obtained from the Solar Optical Telescope/Spectro-Polarimeter on board Hinode. Both the necessary and sufficient conditions for force-free nature are examined by checking the global and local nature of equilibrium magnetic forces over sunspots. We find that sunspot magnetic fields are not very far from the force-free configuration, although they are not completely force-free on the photosphere. The umbral and inner penumbral fields are more force-free than the middle and outer penumbral fields. During their evolution, sunspot magnetic fields are found to maintain their proximity to force-free field behavior. Although a dependence of net Lorentz force components is seen on the evolutionary stages of the sunspots, we do not find a systematic relationship between the nature of sunspot magnetic fields and the associated flare activity. Further, we examine whether the fields at the photosphere follow linear or nonlinear force-free conditions. After examining this in various complex and simple sunspots, we conclude that
Compère, Geoffrey; Lupsasca, Alexandru
2016-01-01
Electromagnetic field configurations with vanishing Lorentz force density are known as force-free and appear in terrestrial, space, and astrophysical plasmas. We explore a general method for finding such configurations based on formulating equations for the field lines rather than the field itself. The basic object becomes a foliation of spacetime or, in the stationary axisymmetric case, of the half-plane. We use this approach to find some new stationary and axisymmetric solutions, one of which could represent a rotating plasma vortex near a magnetic null point.
Solar Force-free Magnetic Fields
Wiegelmann, Thomas
2012-01-01
The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundar...
Spacetime approach to force-free magnetospheres
Gralla, Samuel E
2014-01-01
Force-Free Electrodynamics (FFE) describes magnetically dominated relativistic plasma via non-linear equations for the electromagnetic field alone. Such plasma is thought to play a key role in the physics of pulsars and active black holes. Despite its simple covariant formulation, FFE has primarily been studied in 3+1 frameworks, where spacetime is split into space and time. In this article we systematically develop the theory of force-free magnetospheres taking a spacetime perspective. Using a suite of spacetime tools and techniques (notably exterior calculus) we cover 1) the basics of the theory, 2) exact solutions that demonstrate the extraction and transport of the rotational energy of a compact object (in the case of a black hole, the Blandford-Znajek mechanism), 3) the behavior of current sheets, 4) the general theory of stationary, axisymmetric magnetospheres and 5) general properties of pulsar and black hole magnetospheres. We thereby synthesize, clarify and generalize known aspects of the physics of ...
Directory of Open Access Journals (Sweden)
Hyun Young Lee
2010-01-01
Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ℓ∞(L2 error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.
Force-Free Electromagnetic Fields within Spinor Framework
Directory of Open Access Journals (Sweden)
V. N. Trishin
2016-01-01
Full Text Available The article deals with spinor representation of the force-free electrodynamics. The equations of the force-free electromagnetic field describe the physics of pulsars and black holes whose magnetospheres are filled with magnetically dominated relativistic plasma.The paper is a brief pedagogical introduction to the mathematics of the subject, based on 2-spinor calculi. The objective is to present the nonlinear theory of force-free fields in a compact and elegant form that the spinor framework provides. First, the algebraic classification of the Maxwell tensor is presented. Then, the reduced system of differential equations is obtained for two types of electromagnetic field and the basic features of the solutions are described. The null force-free field is connected with the shear-free geodesic null congruence in a space-time and is derived from a linear equation for a complex function. The magnetic force-free field is associated with the time-like 2-surface that represents the world-sheet of magnetic field line. The simplified system includes 4 linear differential equations for a real function. The article is educational in nature and there are no new solutions of force-free equations obtained.
Fernandes, Ryan I
2012-01-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({\\cal N})$ operations where ${\\cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
Covariant Hyperbolization of Force-free Electrodynamics
Carrasco, Federico
2016-01-01
Force-Free Flectrodynamics (FFE) is a non-linear system of equations modeling the evolution of the electromagnetic field, in the presence of a magnetically dominated relativistic plasma. This configuration arises on several astrophysical scenarios, which represent exciting laboratories to understand physics in extreme regimes. We show that this system, when restricted to the correct constraint submanifold, is symmetric hyperbolic. In numerical applications is not feasible to keep the system in that submanifold, and so, it is necessary to analyze its structure first in the tangent space of that submanifold and then in a whole neighborhood of it. As already shown by Pfeiffer, a direct (or naive) formulation of this system (in the whole tangent space) results in a weakly hyperbolic system of evolution equations for which well-possednes for the initial value formulation does not follows. Using the generalized symmetric hyperbolic formalism due to Geroch, we introduce here a covariant hyperbolization for the FFE s...
Institute of Scientific and Technical Information of China (English)
Shu-hua Zhang; Tao Lin; Yan-ping Lin; Ming Rao
2001-01-01
In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initialvalue problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of aposteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.
Chaouche, L Yelles; Pillet, V Martínez; Moreno-Insertis, F
2012-01-01
The 3D structure of an active region (AR) filament is studied using nonlinear force-free field (NLFFF) extrapolations based on simultaneous observations at a photospheric and a chromospheric height. To that end, we used the Si I 10827 \\AA\\ line and the He I 10830 \\AA\\ triplet obtained with the Tenerife Infrared Polarimeter (TIP) at the VTT (Tenerife). The two extrapolations have been carried out independently from each other and their respective spatial domains overlap in a considerable height range. This opens up new possibilities for diagnostics in addition to the usual ones obtained through a single extrapolation from, typically, a photospheric layer. Among those possibilities, this method allows the determination of an average formation height of the He I 10830 \\AA\\ signal of \\approx 2 Mm above the surface of the sun. It allows, as well, to cross-check the obtained 3D magnetic structures in view of verifying a possible deviation from the force- free condition especially at the photosphere. The extrapolati...
An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta
Energy Technology Data Exchange (ETDEWEB)
Allanson, O., E-mail: oliver.allanson@st-andrews.ac.uk; Neukirch, T., E-mail: tn3@st-andrews.ac.uk; Wilson, F., E-mail: fw237@st-andrews.ac.uk; Troscheit, S., E-mail: s.troscheit@st-andrews.ac.uk [School of Mathematics and Statistics, University of St Andrews, St. Andrews, KY16 9SS (United Kingdom)
2015-10-15
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.
An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta
Allanson, O; Wilson, F; Troscheit, S
2015-01-01
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely the Force-Free Harris Sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite Polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.
Testing magnetofrictional extrapolation with the Titov-D\\'emoulin model of solar active regions
Valori, G; Török, T; Titov, V S
2010-01-01
We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and D\\'emoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version, having a parabolic current density profile, is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade-"hyperbolic flux tube" and "bald patch separatrix surface"-are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy...
Imbalanced Relativistic Force-Free Magnetohydrodynamic Turbulence
Cho, Jungyeon
2013-01-01
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfv\\'enic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., \\$b_+^2/b_-^2 \\propto (\\epsilon_+/\\epsilon_-)^n \\$ with n>2). These result...
Separable solutions of force-free spheres and applications to solar active regions
Prasad, A; Ravindra, B
2014-01-01
In this paper, we present a systematic study of the force-free field equation for simple axisymmetric configurations in spherical geometry and apply it to the solar active regions. The condition of separability of solutions in the radial and angular variables leads to two classes of solutions: linear and non-linear force-free fields. We have studied these linear solutions Chandrasekhar (1956) and extended the non-linear solutions given in Low & Lou (1990) for the radial power law index to the irreducible rational form $n= p/q$, which is allowed for all cases of odd $p$ and cases of $q>p$ for even $p$ (the poloidal flux $\\psi\\propto1/r^n$ and field $\\mathbf{B}\\propto 1/r^{n+2}$). We apply these solutions to simulate photospheric vector magnetograms obtained using the spectro-polarimeter onboard Hinode. The effectiveness of our search strategy is first demonstrated on test inputs of dipolar, axisymmetric and non-axisymmetric linear force-free fields. Using the best fit to these magnetograms, we build 3D axi...
Ill posedness of force-free electrodynamics in Euler potentials
Reula, Oscar A.; Rubio, Marcelo E.
2017-03-01
We prove that the initial value problem for force-free electrodynamics in Euler variables is not well posed. We establish this result by showing that a well-posedness criterion provided by Kreiss fails to hold for this theory, and using a theorem provided by Strang. To show the nature of the problem we display a particular bounded (in Sobolev norms) sequence of initial data for the force-free equations such that at any given time as close to zero as one wishes, the corresponding evolution sequence is not bounded. Thus, the force-free evolution is noncontinuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense.
Force-Free Magnetosphere of an Accreting Kerr Black Hole
Uzdensky, D A
2005-01-01
I consider a stationary axisymmetric force-free degenerate magnetosphere of a rotating Kerr black hole surrounded by a thin Keplerian infinitely-conducting accretion disk. I focus on the closed-field geometry with a direct magnetic coupling between the disk and the event horizon. I first present a simple physical argument that shows how the black hole's rotation limits the radial extent of the force-free link. I then confirm this result by solving numerically the general-relativistic force-free Grad--Shafranov equation in the magnetosphere, using the regularity condition at the inner light cylinder to determine the poloidal current. I indeed find that force-free solutions exist only when the magnetic link between the hole and the disk has a limited extent on the disk surface. I chart out the maximum allowable size of this magnetically-connected part of the disk as a function of the black hole spin. I also compute the angular momentum and energy transfer between the hole and the disk that takes place via the d...
Freely decaying turbulence in force-free electrodynamics
Zrake, Jonathan
2015-01-01
Freely decaying relativistic force-free turbulence is studied for the first time. We initiate the magnetic field at a short wavelength and simulate its relaxation toward equilibrium on two and three dimensional periodic domains, in both helical and non-helical settings. Force-free turbulent relaxation is found to exhibit an inverse cascade in all settings, and in 3D to have a magnetic energy spectrum consistent with the Kolmogorov $5/3$ power law. 3D relaxations also obey the Taylor hypothesis; they settle promptly into the lowest energy configuration allowed by conservation of the total magnetic helicity. But in 2D, the relaxed state is a force-free equilibrium whose energy greatly exceeds the Taylor minimum, and which contains persistent force-free current layers and isolated flux tubes. We explain this behavior in terms of additional topological invariants that exist only in two dimensions, namely the helicity enclosed within each level surface of the magnetic potential function. The speed and completeness...
FREELY DECAYING TURBULENCE IN FORCE-FREE ELECTRODYNAMICS
Energy Technology Data Exchange (ETDEWEB)
Zrake, Jonathan; East, William E. [Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, SLAC National Accelerator Laboratory, Menlo Park, CA 94025 (United States)
2016-02-01
Freely decaying, relativistic force-free turbulence is studied for the first time. We initiate the magnetic field at a short wavelength and simulate its relaxation toward equilibrium on two- and three-dimensional periodic domains in both helical and nonhelical settings. Force-free turbulent relaxation is found to exhibit an inverse cascade in all settings and in three dimensions to have a magnetic energy spectrum consistent with the Kolmogorov 5/3 power law. Three-dimensional relaxations also obey the Taylor hypothesis; they settle promptly into the lowest-energy configuration allowed by conservation of the total magnetic helicity. However, in two dimensions, the relaxed state is a force-free equilibrium whose energy greatly exceeds the Taylor minimum and that contains persistent force-free current layers and isolated flux tubes. We explain this behavior in terms of additional topological invariants that exist only in two dimensions, namely the helicity enclosed within each level surface of the magnetic potential function. The speed and completeness of turbulent magnetic free-energy discharge could help account for rapidly variable gamma-ray emission from the Crab Nebula, gamma-ray bursts, blazars, and radio galaxies.
RECIPROCAL POLYNOMIAL EXTRAPOLATION
Institute of Scientific and Technical Information of China (English)
SergioAmat; SoniaBusquier; VicenteF.Candela
2004-01-01
An alternative to the classical extrapolations is proposed. The stability and the accuracy are studied. The new extrapolation behaves better than the classical ones when there are problems of stability. This technique will be useful in those problems where the region of stability is very small and it forces to work with too fine scales.
Institute of Scientific and Technical Information of China (English)
郭海兵; 李润东; 牛伟力
2013-01-01
Distant extrapolation is usually used during the start-up of the research reactor, by lifting the control rods step by step to reach the critical state. Due to the non-linearity of the integral worth of the control rods, this process was risky or conservative, especially when the rods were positioned in the non-linear region. A formula could be derived from the point reactor model, in which the reciprocal of the count rate was proportional to Δkeff. Together with the integral worth curve of the control rods, the effect of the non-linearity could be corrected. This method was valideted by critical extrapolation data.%研究堆在物理启动时一般通过棒位外推法得出临界棒位,从而逐步达到临界.但由于控制棒积分价值的非线性,使得这一外推过程不安全或过于偏保守,特别是当临界棒位处于非线性区时.根据点堆模型可导出计数率倒数与Δkeff成正比,若根据积分价值曲线将棒位对应为△keff,则可修正控制棒价值非线性的影响.通过研究堆的临界外推数据验证了这一方法的准确性.
The spectral simulations of axisymmetric force-free pulsar magnetosphere
Cao, Gang; Sun, Sineng
2015-01-01
A pseudo-spectral method with an absorbing outer boundary is used to solve a set of the time-dependent force-free equations. In the method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergencelessness of magnetic field is analytically enforced by a projection method. Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be well reproduced by our pseudo-spectral code. Further the method is used to present the time-dependent simulation of the force-free pulsar magnetosphere for an aligned rotator. The simulations show that the current sheet in the equatorial plane can be resolved well, and the obtained spin-down luminosity in the steady state is in good agreement with the value given by Spitkovsky (2006).
Nonergodic dynamics of force-free granular gases
Bodrova, Anna; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Metzler, Ralf
2015-01-01
We study analytically and by event-driven molecular dynamics simulations the nonergodic and aging properties of force-free cooling granular gases with both constant and velocity-dependent (viscoelastic) restitution coefficient $\\varepsilon$ for particle pair collisions. We compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behavior of the ensembl...
The Force-Free Magnetosphere of a Rotating Black Hole
Contopoulos, Ioannis; Kazanas, Demosthenes; Papadopoulos, Demetrios B.
2013-01-01
We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity and the poloidal electric current. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner "light surface" located inside the ergosphere and the outer "light surface" which is the generalization of the pulsar light cylinder.We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both "light surfaces."
Particle energization in a chaotic force-free magnetic field
Li, Xiaocan; Li, Gang; Dasgupta, Brahmananda
2015-04-01
A force-free field (FFF) is believed to be a reasonable description of the solar corona and in general a good approximation for low-beta plasma. The equations describing the magnetic field of FFF is similar to the ABC fluid equations which has been demonstrated to be chaotic. This implies that charged particles will experience chaotic magnetic field in the corona. Here, we study particle energization in a time-dependent FFF using a test particle approach. An inductive electric field is introduced by turbulent motions of plasma parcels. We find efficient particle acceleration with power-law like particle energy spectra. The power-law indices depend on the amplitude of plasma parcel velocity field and the spatial scales of the magnetic field fluctuation. The spectra are similar for different particle species. This model provide a possible mechanism for seed population generation for particle acceleration by, e.g., CME-driven shocks. Generalization of our results to certain non-force-free-field (NFFF) is straightforward as the sum of two or multiple FFFs naturally yield NFFF.
Energy buildup in sheared force-free magnetic fields
Wolfson, Richard; Low, Boon C.
1992-01-01
Photospheric displacement of the footpoints of solar magnetic field lines results in shearing and twisting of the field, and consequently in the buildup of electric currents and magnetic free energy in the corona. The sudden release of this free energy may be the origin of eruptive events like coronal mass ejections, prominence eruptions, and flares. An important question is whether such an energy release may be accompanied by the opening of magnetic field lines that were previously closed, for such open field lines can provide a route for matter frozen into the field to escape the sun altogether. This paper presents the results of numerical calculations showing that opening of the magnetic field is permitted energetically, in that it is possible to build up more free energy in a sheared, closed, force-free magnetic field than is in a related magnetic configuration having both closed and open field lines. Whether or not the closed force-free field attains enough energy to become partially open depends on the form of the shear profile; the results presented compare the energy buildup for different shear profiles. Implications for solar activity are discussed briefly.
Ecotoxicological effects extrapolation models
Energy Technology Data Exchange (ETDEWEB)
Suter, G.W. II
1996-09-01
One of the central problems of ecological risk assessment is modeling the relationship between test endpoints (numerical summaries of the results of toxicity tests) and assessment endpoints (formal expressions of the properties of the environment that are to be protected). For example, one may wish to estimate the reduction in species richness of fishes in a stream reach exposed to an effluent and have only a fathead minnow 96 hr LC50 as an effects metric. The problem is to extrapolate from what is known (the fathead minnow LC50) to what matters to the decision maker, the loss of fish species. Models used for this purpose may be termed Effects Extrapolation Models (EEMs) or Activity-Activity Relationships (AARs), by analogy to Structure-Activity Relationships (SARs). These models have been previously reviewed in Ch. 7 and 9 of and by an OECD workshop. This paper updates those reviews and attempts to further clarify the issues involved in the development and use of EEMs. Although there is some overlap, this paper does not repeat those reviews and the reader is referred to the previous reviews for a more complete historical perspective, and for treatment of additional extrapolation issues.
Georgoulis, M K
2007-01-01
We self-consistently derive the magnetic energy and relative magnetic helicity budgets of a three-dimensional linear force-free magnetic structure rooted in a lower boundary plane. For the potential magnetic energy we derive a general expression that gives results practically equivalent to those of the magnetic Virial theorem. All magnetic energy and helicity budgets are formulated in terms of surface integrals applied to the lower boundary, thus avoiding computationally intensive three-dimensional magnetic field extrapolations. We analytically and numerically connect our derivations with classical expressions for the magnetic energy and helicity, thus presenting a so-far lacking unified treatment of the energy/helicity budgets in the constant-alpha approximation. Applying our derivations to photospheric vector magnetograms of an eruptive and a noneruptive solar active regions, we find that the most profound quantitative difference between these regions lies in the estimated free magnetic energy and relative ...
Evidence for Solar Tether-cutting Magnetic Reconnection from Coronal Field Extrapolations
Liu, Chang; Lee, Jeongwoo; Wiegelmann, Thomas; Moore, Ronald L; Wang, Haimin
2013-01-01
Magnetic reconnection is one of the primary mechanisms for triggering solar eruptive events, but direct observation of its rapid process has been of challenge. In this Letter we present, using a nonlinear force-free field (NLFFF) extrapolation technique, a visualization of field line connectivity changes resulting from tether-cutting reconnection over about 30 minutes during the 2011 February 13 M6.6 flare in NOAA AR 11158. Evidence for the tether-cutting reconnection was first collected through multiwavelength observations and then by the analysis of the field lines traced from positions of four conspicuous flare 1700 A footpoints observed at the event onset. Right before the flare, the four footpoints are located very close to the regions of local maxima of magnetic twist index. Especially, the field lines from the inner two footpoints form two strongly twisted flux bundles (up to ~1.2 turns), which shear past each other and reach out close to the outer two footpoints, respectively. Immediately after the fl...
A novel look at the pulsar force-free magnetosphere
Petrova, S A
2016-01-01
The stationary axisymmetric force-free magnetosphere of a pulsar is considered. We present an exact dipolar solution of the pulsar equation, construct the magnetospheric model on its basis and examine its observational support. The new model has toroidal rather than common cylindrical geometry, in line with that of the plasma outflow observed directly as the pulsar wind nebula at much larger spatial scale. In its new configuration, the axisymmetric magnetosphere consumes the neutron star rotational energy much more efficiently, implying re-estimation of the stellar magnetic field, $B_{\\mathrm new}^0=3.3\\times 10^{-4}B/P$, where $P$ is the pulsar period. Then the 7-order scatter of the magnetic field derived from the rotational characteristics of the pulsars observed appears consistent with the $\\cot\\chi$-law, where $\\chi$ is a random quantity uniformly distributed in the interval $[0,\\pi/2]$. Our result is suggestive of a unique actual magnetic field strength of the neutron stars along with a random angle bet...
Non Linear Force Free Field Modeling for a Pseudostreamer
Karna, Nishu; Savcheva, Antonia; Gibson, Sarah; Tassev, Svetlin V.
2017-08-01
In this study we present a magnetic configuration of a pseudostreamer observed on April 18, 2015 on southern west limb embedding a filament cavity. We constructed Non Linear Force Free Field (NLFFF) model using the flux rope insertion method. The NLFFF model produces the three-dimensional coronal magnetic field constrained by observed coronal structures and photospheric magnetogram. SDO/HMI magnetogram was used as an input for the model. The high spatial and temporal resolution of the SDO/AIA allows us to select best-fit models that match the observations. The MLSO/CoMP observations provide full-Sun observations of the magnetic field in the corona. The primary observables of CoMP are the four Stokes parameters (I, Q, U, V). In addition, we perform a topology analysis of the models in order to determine the location of quasi-separatrix layers (QSLs). QSLs are used as a proxy to determine where the strong electric current sheets can develop in the corona and also provide important information about the connectivity in complicated magnetic field configuration. We present the major properties of the 3D QSL and FLEDGE maps and the evolution of 3D coronal structures during the magnetofrictional process. We produce FORWARD-modeled observables from our NLFFF models and compare to a toy MHD FORWARD model and the observations.
The force-free twisted magnetosphere of a neutron star
Akgün, Taner; Pons, José A; Cerdá-Durán, Pablo
2016-01-01
We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to 40% with respect to a vacuum model with the same surface magnetic field, due to the contribution of magnetospheric currents to the global magnetic field. Thus, estimates of the surface magnetic field based on the large scale dipolar braking torque are slightly overestimating the surface value by the same amount. Consistently, there is a moderate increase in the total energy of the model with respect to the vacuum solution of up to 25%, which would be the available...
Force-free black hole jet power from impedance matching
Penna, Robert F
2015-01-01
The standard model of spin-powered black hole jets is the Blandford-Znajek (BZ) model. Unfortunately, the BZ jet power depends on an arbitrary function, $\\Omega_F(\\theta)$, which controls the angular distribution of field line velocities at the horizon. In practice, this function is fixed by finding exact solutions of force-free electrodynamics (FFE) and reading off $\\Omega_F(\\theta)$. We prove that all stationary, axisymmetric solutions of FFE with roughly uniform distributions of field lines at the horizon and at infinity have $\\Omega_F/\\Omega_H\\approx 0.5$, where $\\Omega_H$ is the angular velocity of the horizon. We derive a formula for $\\Omega_F(\\theta)$ that depends only on the angular distribution of field lines at the horizon and at infinity (the full FFE solution is not needed). We give a physical interpretation of our results using the black hole membrane paradigm and a recent extension which treats future null infinity as a resistive membrane. We show that $\\Omega_F/\\Omega_H$ is controlled by impeda...
Cosmological extrapolation of MOND
Kiselev, V V
2011-01-01
Regime of MOND, which is used in astronomy to describe the gravitating systems of island type without the need to postulate the existence of a hypothetical dark matter, is generalized to the case of homogeneous distribution of usual matter by introducing a linear dependence of the critical acceleration on the size of region under consideration. We show that such the extrapolation of MOND in cosmology is consistent with both the observed dependence of brightness on the redshift for type Ia supernovae and the parameters of large-scale structure of Universe in the evolution, that is determined by the presence of a cosmological constant, the ordinary matter of baryons and electrons as well as the photon and neutrino radiation without any dark matter.
The force-free twisted magnetosphere of a neutron star
Akgün, T.; Miralles, J. A.; Pons, J. A.; Cerdá-Durán, P.
2016-10-01
We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to 40 per cent with respect to a vacuum model with the same surface magnetic field, due to the contribution of magnetospheric currents to the global magnetic field. Thus, estimates of the surface magnetic field based on the large-scale dipolar braking torque are slightly overestimating the surface value by the same amount. Consistently, there is a moderate increase in the total energy of the model with respect to the vacuum solution of up to 25 per cent, which would be the available energy budget in the event of a fast, global magnetospheric reorganization commonly associated with magnetar flares. We have also found the interesting result of the existence of a critical twist (ϕmax ≲ 1.5 rad), beyond which we cannot find any more numerical solutions. Combining the models considered in this paper with the evolution of the interior of neutron stars will allow us to study the influence of the magnetosphere on the long-term magnetic, thermal, and rotational evolution.
Kink instability of force-free jets: a parameter space study
Sobacchi, E.; Lyubarsky, Y. E.; Sormani, M. C.
2017-07-01
In the paradigm of magnetic acceleration of relativistic jets, one of the key points is identifying a viable mechanism to convert the Poynting flux into the kinetic energy of the plasma beyond equipartition. A promising candidate is the kink instability, which deforms the body of the jet through helical perturbations. Since the detailed structure of real jets is unknown, we explore a large family of cylindrical, force-free equilibria to get robust conclusions. We find that the growth rate of the instability depends primarily on two parameters: (i) the gradient of the poloidal magnetic field and (ii) the Lorentz factor of the perturbation, which is closely related to the velocity of the plasma. We provide a simple fitting formula for the growth rate of the instability. As a tentative application, we use our results to interpret the dynamics of the jet in the nearby active galaxy M87. We show that the kink instability becomes non-linear at a distance from the central black hole comparable to where the jet stops accelerating. Hence (at least for this object), the kink instability of the jet is a good candidate to drive the transition from a Poynting-dominated to a kinetic-energy-dominated flow.
Temporal and spatial relationship of flare signatures and the force-free coronal magnetic field
Thalmann, Julia K; Su, Yang
2016-01-01
We investigate the plasma and magnetic environment of active region NOAA 11261 on 2 August 2011 around a GOES M1.4 flare/CME (SOL2011-08-02T06:19). We compare coronal emission at (extreme) ultraviolet and X-ray wavelengths, using SDO AIA and RHESSI images, in order to identify the relative timing and locations of reconnection-related sources. We trace flare ribbon signatures at ultraviolet wavelengths, in order to pin down the intersection of previously reconnected flaring loops at the lower solar atmosphere. These locations are used to calculate field lines from 3D nonlinear force-free magnetic field models, established on the basis of SDO HMI photospheric vector magnetic field maps. With this procedure, we analyze the quasi-static time evolution of the coronal model magnetic field previously involved in magnetic reconnection. This allows us, for the first time, to estimate the elevation speed of the current sheet's lower tip during an on-disk observed flare, as a few kilometers per second. Comparison to pos...
A viable non-axisymmetric non-force-free field to represent solar active regions
Prasad, A
2016-01-01
A combination of analytical calculations and vectormagnetogram data are utilized to develop a non-axisymmetric non-force-free magnetic field and asses its viability in describing solar active regions. For the purpose, we construct a local spherical shell where a planar surface, tangential to the inner sphere, represents a Cartesian cutout of an active region. The magnetic field defined on the surface is then correlated with magnetograms. The analysis finds the non-axisymmetric non-force-free magnetic field, obtained by a superposition of two linear-force-free fields, correlates reasonably well with magnetograms.
Functional differential equations with unbounded delay in extrapolation spaces
Directory of Open Access Journals (Sweden)
Mostafa Adimy
2014-08-01
Full Text Available We study the existence, regularity and stability of solutions for nonlinear partial neutral functional differential equations with unbounded delay and a Hille-Yosida operator on a Banach space X. We consider two nonlinear perturbations: the first one is a function taking its values in X and the second one is a function belonging to a space larger than X, an extrapolated space. We use the extrapolation techniques to prove the existence and regularity of solutions and we establish a linearization principle for the stability of the equilibria of our equation.
Wavefield extrapolation in pseudodepth domain
Ma, Xuxin
2013-02-01
Wavefields are commonly computed in the Cartesian coordinate frame. Its efficiency is inherently limited due to spatial oversampling in deep layers, where the velocity is high and wavelengths are long. To alleviate this computational waste due to uneven wavelength sampling, we convert the vertical axis of the conventional domain from depth to vertical time or pseudodepth. This creates a nonorthognal Riemannian coordinate system. Isotropic and anisotropic wavefields can be extrapolated in the new coordinate frame with improved efficiency and good consistency with Cartesian domain extrapolation results. Prestack depth migrations are also evaluated based on the wavefield extrapolation in the pseudodepth domain.© 2013 Society of Exploration Geophysicists. All rights reserved.
Self-Similar Force-Free Wind From an Accretion Disk
Narayan, R; Farmer, A J; Narayan, Ramesh; Kinney, Jonathan C. Mc; Farmer, Alison J.
2006-01-01
We consider a self-similar force-free wind flowing out of an infinitely thin disk located in the equatorial plane. On the disk plane, we assume that the magnetic stream function $P$ scales as $P\\propto R^\
Local theory of extrapolation methods
Kulikov, Gennady
2010-03-01
In this paper we discuss the theory of one-step extrapolation methods applied both to ordinary differential equations and to index 1 semi-explicit differential-algebraic systems. The theoretical background of this numerical technique is the asymptotic global error expansion of numerical solutions obtained from general one-step methods. It was discovered independently by Henrici, Gragg and Stetter in 1962, 1964 and 1965, respectively. This expansion is also used in most global error estimation strategies as well. However, the asymptotic expansion of the global error of one-step methods is difficult to observe in practice. Therefore we give another substantiation of extrapolation technique that is based on the usual local error expansion in a Taylor series. We show that the Richardson extrapolation can be utilized successfully to explain how extrapolation methods perform. Additionally, we prove that the Aitken-Neville algorithm works for any one-step method of an arbitrary order s, under suitable smoothness.
Force-free field modeling of twist and braiding-induced magnetic energy in an active-region corona
Thalmann, J K; Wiegelmann, T
2013-01-01
The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region corona, has been substantiated by high-resolution observations only recently. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. 2013 (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on vector SDO/HMI magnetograms. We deliver estimates of the free magnetic energy associated to a braided coronal structure. Our model results suggest (~100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the active-region corona being heated by field line braiding. We were able to assess the coronal free energy appropriately by using vector field measurements and attribute the lower energy...
On the extrapolation of band-limited signals
Chamzas, C. C.
1980-12-01
The determination of the Fourier Transform of a band-limited signal in terms of a finite segment is examined. The Papoulis' Extrapolation Algorithm is extended in a broader class of signals and its convergence is considerably improved by a multiplication with an adaptive constant, chosen to minimize the mean square error in the extrapolation interval. The discrete version of the iteration is examined and then modified in order to converge to the best linear mean square estimator of the unknown signal when noise is added to the given data. The problem of determining the frequencies, amplitudes and phases of a sinusoidal signal from incomplete noisy data, is considered and the extrapolation algorithm is properly modified to estimate these quantities. The obtained iteration is nonlinear and adaptively reduces the spectral components due to noise. The adaptive extrapolation technique is applied to the problem of image restoration for objects consisting of point or line sources, and to an ultrasonic problem.
Tadesse, Tilaye; Wiegelmann, T.; Gosain, S.; Macneice, P.; Pevtsov, Alexei A.
2013-01-01
The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently there are several modelling techniques being used to calculate three-dimension of the field lines into the solar atmosphere. For the ...
Non-Linear Force-Free Field Modelling of Solar Coronal Jets in Theoretical Configurations
Savcheva, Antonia
2017-08-01
Coronal jets occur frequently on the Sun, and may contribute significantly to the solar wind. With the suite of instruments avilable now, e.g. on IRIS, Hinode and SDO, we can observe these phenomena in greater detail than ever before. Modeling and simulations can assist further in understanding the dynamic processes involved, but previous studies tend to consider only one mechanism (e.g. emergence or rotation) for the origin of the jet. In this study we model a series of idealised archetypaljet configurations and follow the evolution of the coronal magnetic field. This is a step towards understanding these idealised situations before considering their observational counterparts. Several simple situations are set up for the evolution of the photospheric magnetic field: a single parasitic polarity rotating or moving in a circular path; as well as opposite polarity pairs involved in flyby (shearing), cancellation or emergence; all in the presence of a uniform, open background magneticfield. The coronal magnetic field is evolved in time using a magnetofrictional relaxation method. While magnetofriction cannot accurately reproduce the dynamics of an eruptive phase, the structure of the coronal magnetic field, as well as the build up of electric currents and free magnetic energy are instructive. Certain configurations and motions produce a flux rope and allow the significant build up of free energy, reminiscent of the progenitors of so-called blowout jets, whereas other, simpler configurations are more comparable to the standard jet model. The next stage is a comparison with observed coronal jet structures and their corresponding photospheric evolution.
Infrared extrapolations for atomic nuclei
Furnstahl, R J; Papenbrock, T; Wendt, K A
2014-01-01
Harmonic oscillator model-space truncations introduce systematic errors to the calculation of binding energies and other observables. We identify the relevant infrared scaling variable and give values for this nucleus-dependent quantity. We consider isotopes of oxygen computed with the coupled-cluster method from chiral nucleon-nucleon interactions at next-to-next-to-leading order and show that the infrared component of the error is sufficiently understood to permit controlled extrapolations. By employing oscillator spaces with relatively large frequencies, well above the energy minimum, the ultraviolet corrections can be suppressed while infrared extrapolations over tens of MeVs are accurate for ground-state energies. However, robust uncertainty quantification for extrapolated quantities that fully accounts for systematic errors is not yet developed.
Magnetic Helicity of Self-Similar Axisymmetric Force-free Fields
Zhang, Mei; Low, Boon Chye
2012-01-01
In this paper we continue our theoretical studies on addressing what are the possible consequences of magnetic helicity accumulation in the solar corona. Our previous studies suggest that coronal mass ejections (CMEs) are natural products of coronal evolution as a consequence of magnetic helicity accumulation and the triggering of CMEs by surface processes such as flux emergence also have their origin in magnetic helicity accumulation. Here we use the same mathematical approach to study the magnetic helicity of axisymmetric power-law force-free fields, but focus on a family whose surface flux distributions are defined by self-similar force-free fields. The semi-analytical solutions of the axisymmetric self-similar force-free fields enable us to discuss the properties of force-free fields possessing a huge amount of accumulated magnetic helicity. Our study suggests that there may be an absolute upper bound on the total magnetic helicity of all bipolar axisymmetric force-free fields. And with the increase of ac...
Extrapolation methods theory and practice
Brezinski, C
1991-01-01
This volume is a self-contained, exhaustive exposition of the extrapolation methods theory, and of the various algorithms and procedures for accelerating the convergence of scalar and vector sequences. Many subroutines (written in FORTRAN 77) with instructions for their use are provided on a floppy disk in order to demonstrate to those working with sequences the advantages of the use of extrapolation methods. Many numerical examples showing the effectiveness of the procedures and a consequent chapter on applications are also provided - including some never before published results and applicat
Force-free collisionless current sheet models with non-uniform temperature and density profiles
Wilson, F.; Neukirch, T.; Allanson, O.
2017-09-01
We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner [Phys. Plasmas 20, 102117 (2013)] to allow for non-uniform density and temperature profiles. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al. [Phys. Plasmas 22, 112902 (2015)]. In one limit of the parameters, we recover the model of Kolotkov et al. [Phys. Plasmas 22, 112902 (2015)], while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive and give expressions for the pressure, density, temperature, and bulk-flow velocities of the equilibrium, discussing the differences from previous models. We also present some illustrative plots of the distribution function in velocity space.
On the ill posedness of Force-Free Electrodynamics in Euler Potentials
Reula, Oscar A
2016-01-01
We prove that the initial value problem for Force-free Electrodynamics in Euler variables is not well posed. We establish this result showing that a well-posedness criterion provided by Kreiss fails to hold for this theory, using a theorem provided by Strang. To show the nature of the problem we display a particular bounded (in Sobolev norms) sequence of initial data for the Force-free equations such that at any given time as close to zero as one wishes, the corresponding evolution sequence is not bounded. Thus, the Force-free evolution is non continuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense.
UFOs: Observations, Studies and Extrapolations
Baer, T; Barnes, M J; Bartmann, W; Bracco, C; Carlier, E; Cerutti, F; Dehning, B; Ducimetière, L; Ferrari, A; Ferro-Luzzi, M; Garrel, N; Gerardin, A; Goddard, B; Holzer, E B; Jackson, S; Jimenez, J M; Kain, V; Zimmermann, F; Lechner, A; Mertens, V; Misiowiec, M; Nebot Del Busto, E; Morón Ballester, R; Norderhaug Drosdal, L; Nordt, A; Papotti, G; Redaelli, S; Uythoven, J; Velghe, B; Vlachoudis, V; Wenninger, J; Zamantzas, C; Zerlauth, M; Fuster Martinez, N
2012-01-01
UFOs (“ Unidentified Falling Objects”) could be one of the major performance limitations for nominal LHC operation. Therefore, in 2011, the diagnostics for UFO events were significantly improved, dedicated experiments and measurements in the LHC and in the laboratory were made and complemented by FLUKA simulations and theoretical studies. The state of knowledge is summarized and extrapolations for LHC operation in 2012 and beyond are presented. Mitigation strategies are proposed and related tests and measures for 2012 are specified.
Renyi extrapolation of Shannon entropy
Zyczkowski, K
2003-01-01
Relations between Shannon entropy and Renyi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Renyi entropies of order two and three are known, we provide an lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann entropy of a mixed quantum state, its linear entropy and traces.
Revisiting Chiral Extrapolation by Studying a Lattice Quark Propagator
Institute of Scientific and Technical Information of China (English)
ZHANG Yan-Bin; SUN Wei-Min; L(U) Xiao-Fu; ZONG Hong-Shi
2009-01-01
The quark propagator in the Landau gauge is studied on the lattice,including the quenched and the unquenched results.No obvious unquenched effects are found by comparing the quenched quark propagator with the dynamical one.For the quenched and unquenched configurations,the results with different quark masses have been computed.For the quark mass function,a nonlinear chiral extrapolating behavior is found in the in/tared region for both the quenched and dynamical results.
Extrapolation of acenocoumarol pharmacogenetic algorithms.
Jiménez-Varo, Enrique; Cañadas-Garre, Marisa; Garcés-Robles, Víctor; Gutiérrez-Pimentel, María José; Calleja-Hernández, Miguel Ángel
2015-11-01
Acenocoumarol (ACN) has a narrow therapeutic range that is especially difficult to control at the start of its administration. Various dosing pharmacogenetic-guided dosing algorithms have been developed, but further work on their external validation is required. The aim of this study was to evaluate the extrapolation of pharmacogenetic algorithms for ACN as an alternative to the development of a specific algorithm for a given population. The predictive performance, deviation, accuracy, and clinical significance of five pharmacogenetic algorithms (EU-PACT, Borobia, Rathore, Markatos, Krishna Kumar) were compared in 189 stable ACN patients representing all indications for anticoagulant treatment. The correlation between the dose predictions of the five pharmacogenetic models ranged from 7.7 to 70.6% and the percentage of patients with a correct prediction (deviation ≤20% from actual ACN dose) ranged from 5.9 to 40.7%. EU-PACT and Borobia pharmacogenetic dosing algorithms were the most accurate in our setting and evidenced the best clinical performance. Among the five models studied, the EU-PACT and Borobia pharmacogenetic dosing algorithms demonstrated the best potential for extrapolation. Copyright © 2015 Elsevier Inc. All rights reserved.
On the "force-free surface " of the magnetized celestial bodies
Epp, V
2015-01-01
The field of a uniformly magnetized rotating sphere is studied with special attention to the surface where the electric and magnetic fields are orthogonal to each other. The equation of this surface, valid at arbitrary distances from the rotating magnetized sphere, is obtained. Inside the light cylinder this surface can be considered as a force-free surface, i.e. as a place where the particles with strong radiation damping can be trapped due to their energy loss. Outside the light cylinder this surface makes just a geometric locus which moves with a superlight velocity around the axis of rotation. The 2- and 3-dimensional plots of the force-free surface are constructed. Estimation of influence of the centrifugal force on the particle dynamics is made. It is shown, that in case of strong magnetic field the centrifugal force is negligible small everywhere except a narrow neighbourhood of the light cylinder.
A New Formulation for General Relativistic Force-Free Electrodynamics and Its Applications
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We formulate the general relativistic force-free electrodynamics in a new 3+1 language. In this formulation, when we have properly defined electric and magnetic fields, the covariant Maxwell equations could be cast in the traditional form with new vacuum con stitutive constraint equations. The fundamental equation governing a stationary, axisymmet ric force-free black hole magnetosphere is derived using this formulation which recasts the Grad-Shafranov equation in a simpler way. Compared to the classic 3+1 system of Thorne and MacDonald, the new system of 3+1 equations is more suitable for numerical use for it keeps the hyperbolic structure of the electrodynamics and avoids the singularity at the event horizon. This formulation could be readily extended to non-relativistic limit and find applications in flat spacetime. We investigate its application to disk wind, black hole magnetosphere and solar physics in both flat and curved spacetime.
The Chiral Anomaly, Dirac and Weyl Semimetals, and Force-Free Magnetic Fields
Marsh, Gerald E
2016-01-01
The chiral anomaly is a purely quantum mechanical phenomenon that has a long history dating back to the late 1960s. Surprisingly, it has recently made a macroscopic appearance in condensed matter physics. A brief introduction to the relevant features of this anomaly is given and it is shown that its appearance in condensed matter systems must involve force-free magnetic fields, which may help explain the long current relaxation times in Dirac and Weyl semimetals.
Quantifying non-ergodic dynamics of force-free granular gases
Bodrova, Anna; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Metzler, Ralf
2015-01-01
Brownianmotion is ergodic in the Boltzmann–Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a...
Extrapolating future Arctic ozone losses
Directory of Open Access Journals (Sweden)
B. M. Knudsen
2004-06-01
Full Text Available Future increases in the concentration of greenhouse gases and water vapour are likely to cool the stratosphere further and to increase the amount of polar stratospheric clouds (PSCs. Future Arctic PSC areas have been extrapolated using the highly significant trends in the temperature record from 1958–2001. Using a tight correlation between PSC area and the total vortex ozone depletion and taking the decreasing amounts of ozone depleting substances into account we make empirical estimates of future ozone. The result is that Arctic ozone losses increase until 2010–2020 and only decrease slightly up to 2030. This approach is an alternative method of prediction to that based on the complex coupled chemistry-climate models (CCMs.
Magnetic Energy of Force-Free Fields with Detached Field Lines
Institute of Scientific and Technical Information of China (English)
Guo-Qiang Li; You-Qiu Hu
2003-01-01
Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasmaβ (the ratio between gas pressure and magnetic pressure) is taken to be so small (β = 10-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magnetic energy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magnetic energy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of the corresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as to whether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope.This gives an example showing that a force-free magnetic field may have an energylarger than the corresponding open field energy if part of the field lines is allowed to be detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.
Effect of the mass center shift for force-free flexible spacecraft
Meirovitch, L.; Juang, J.-N.
1975-01-01
For a spinning flexible spacecraft the mass center generally shifts relative to the nominal undeformed position. It is thought that this shift of center complicates spacecraft stability analysis. It is proved, on the basis of results achieved by Meirovitch and Calico (1972), that for the general class of force-free single-spin flexible spacecraft it is possible to ignore this shift of center without affecting the stability criteria in any significant way. A new theorem on inequalities for quadratic forms is proved to demonstrate the validity of the stability analysis.
Modeling of Gamma-Ray Pulsar Light Curves with Force-Free Magnetic Field
Bai, Xue-Ning
2009-01-01
(Abridged) Gamma-ray emission from pulsars has long been modeled using a vacuum dipole field. This approximation ignores changes in the field structure caused by the magnetospheric plasma and strong plasma currents. We present the first results of gamma-ray pulsar light curve modeling using the more realistic field taken from 3D force-free magnetospheric simulations. Having the geometry of the field, we apply several prescriptions for the location of the emission zone, comparing the light curves to observations. We find that the conventional two-pole caustic model fails to produce double-peak pulse profiles, mainly because the size of the polar cap in force-free magnetosphere is larger than the vacuum field polar cap. The conventional outer-gap model is capable of producing only one peak under general conditions, because a large fraction of open field lines does not cross the null charge surface. We propose a novel "annular gap" model, where the high-energy emission originates from a thin layer on the open fi...
Kinetic model of force-free current sheets with non-uniform temperature
Kolotkov, D. Y.; Vasko, I. Y.; Nakariakov, V. M.
2015-11-01
The kinetic model of a one-dimensional force-free current sheet (CS) developed recently by Harrison and Neukirch [Phys. Rev. Lett. 102(13), 135003 (2009)] predicts uniform distributions of the plasma temperature and density across the CS. However, in realistic physical systems, inhomogeneities of these plasma parameters may arise quite naturally due to the boundary conditions or local plasma heating. Moreover, as the CS spatial scale becomes larger than the characteristic kinetic scales (the regime often referred to as the MHD limit), it should be possible to set arbitrary density and temperature profiles. Thus, an advanced model has to allow for inhomogeneities of the macroscopic plasma parameters across the CS, to be consistent with the MHD limit. In this paper, we generalise the kinetic model of a force-free current sheet, taking into account the inhomogeneity of the density and temperature across the CS. In the developed model, the density may either be enhanced or depleted in the CS central region. The temperature profile is prescribed by the density profile, keeping the plasma pressure uniform across the CS. All macroscopic parameters, as well as the distribution functions for the protons and electrons, are determined analytically. Applications of the developed model to current sheets observed in space plasmas are discussed.
Accurate Simulations of Binary Black-Hole Mergers in Force-Free Electrodynamics
Alic, Daniela; Rezzolla, Luciano; Zanotti, Olindo; Jaramillo, Jose Luis
2012-01-01
We provide additional information on our recent study of the electromagnetic emission produced during the inspiral and merger of supermassive black holes when these are immersed in a force-free plasma threaded by a uniform magnetic field. As anticipated in a recent letter, our results show that although a dual-jet structure is present, the associated luminosity is ~ 100 times smaller than the total one, which is predominantly quadrupolar. We here discuss the details of our implementation of the equations in which the force-free condition is not implemented at a discrete level, but rather obtained via a damping scheme which drives the solution to satisfy the correct condition. We show that this is important for a correct and accurate description of the current sheets that can develop in the course of the simulation. We also study in greater detail the three-dimensional charge distribution produced as a consequence of the inspiral and show that during the inspiral it possesses a complex but ordered structure wh...
Force-free Field Modeling of Twist and Braiding-induced Magnetic Energy in an Active-region Corona
Thalmann, J. K.; Tiwari, S. K.; Wiegelmann, T.
2014-01-01
The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region (AR) corona has only recently been substantiated by high-resolution observations. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We deliver estimates of the free magnetic energy associated with a braided coronal structure. Our model results suggest (~100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the AR corona being heated by field line braiding. We were able to appropriately assess the coronal free energy by using vector field measurements and we attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase in the overall twist of a flare-related flux rope that was noted by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within 12 minutes. Unlike another method to which we compare our results, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal three-dimensional field line geometry. To our knowledge, this is done for the first time here.
Force-free field modeling of twist and braiding-induced magnetic energy in an active-region corona
Energy Technology Data Exchange (ETDEWEB)
Thalmann, J. K. [Institute of Physics/IGAM, University of Graz, Universitätsplatz 5, A-8010 Graz (Austria); Tiwari, S. K.; Wiegelmann, T., E-mail: julia.thalmann@uni-graz.at [Max Plank Institute for Solar System Research, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau (Germany)
2014-01-01
The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region (AR) corona has only recently been substantiated by high-resolution observations. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We deliver estimates of the free magnetic energy associated with a braided coronal structure. Our model results suggest (∼100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the AR corona being heated by field line braiding. We were able to appropriately assess the coronal free energy by using vector field measurements and we attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase in the overall twist of a flare-related flux rope that was noted by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within 12 minutes. Unlike another method to which we compare our results, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal three-dimensional field line geometry. To our knowledge, this is done for the first time here.
Efficient Wavefield Extrapolation In Anisotropic Media
Alkhalifah, Tariq
2014-07-03
Various examples are provided for wavefield extrapolation in anisotropic media. In one example, among others, a method includes determining an effective isotropic velocity model and extrapolating an equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. The effective isotropic velocity model can be based upon a kinematic geometrical representation of an anisotropic, poroelastic or viscoelastic wavefield. Extrapolating the equivalent propagation can use isotopic, acoustic or elastic operators based upon the determined effective isotropic velocity model. In another example, non-transitory computer readable medium stores an application that, when executed by processing circuitry, causes the processing circuitry to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. In another example, a system includes processing circuitry and an application configured to cause the system to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield.
Builtin vs. auxiliary detection of extrapolation risk.
Energy Technology Data Exchange (ETDEWEB)
Munson, Miles Arthur; Kegelmeyer, W. Philip,
2013-02-01
A key assumption in supervised machine learning is that future data will be similar to historical data. This assumption is often false in real world applications, and as a result, prediction models often return predictions that are extrapolations. We compare four approaches to estimating extrapolation risk for machine learning predictions. Two builtin methods use information available from the classification model to decide if the model would be extrapolating for an input data point. The other two build auxiliary models to supplement the classification model and explicitly model extrapolation risk. Experiments with synthetic and real data sets show that the auxiliary models are more reliable risk detectors. To best safeguard against extrapolating predictions, however, we recommend combining builtin and auxiliary diagnostics.
Ideal MHD(-Einstein) Solutions Obeying The Force-Free Condition
Chu, Yi-Zen
2016-01-01
We find two families of analytic solutions to the ideal magnetohydrodynamics (iMHD) equations, in a class of 4-dimensional (4D) curved spacetimes. The plasma current is null, and as a result, the stress-energy tensor of the plasma itself can be chosen to take a cosmological-constant-like form. Despite the presence of a plasma, the force-free condition - where the electromagnetic current is orthogonal to the Maxwell tensor - continues to be maintained. Moreover, a special case of one of these two families leads us to a fully self-consistent solution to the Einstein-iMHD equations: we obtain the Vaidya-(anti-)de Sitter metric sourced by the plasma and a null electromagnetic stress tensor. We also provide a Mathematica code that researchers may use to readily verify analytic solutions to these iMHD equations in any curved 4D geometry.
A Two-Fluid Study of Oblique Tearing Modes in a Force-Free Current Sheet
Akcay, Cihan; Lukin, Vyacheslav S; Liu, Yi-Hsin
2016-01-01
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Since kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless tearing instability in a force-free current sheet with a two-fluid model and fully kinetic simulations. Our results indicate that the most unstable modes are oblique for guide fields larger than the reconnecting field, in agreement with the kinetic results. The standard two-fluid tearing theory is extended to address the tearing instability at oblique angles. The resulting theory yields a flat oblique spectrum and underest...
Expanded solutions of force-free electrodynamics on general Kerr black holes
Li, Huiquan; Wang, Jiancheng
2017-07-01
In this work, expanded solutions of force-free magnetospheres on general Kerr black holes are derived through a radial distance expansion method. From the regular conditions both at the horizon and at spatial infinity, two previously known asymptotical solutions (one of them is actually an exact solution) are identified as the only solutions that satisfy the same conditions at the two boundaries. Taking them as initial conditions at the boundaries, expanded solutions up to the first few orders are derived by solving the stream equation order by order. It is shown that our extension of the exact solution can (partially) cure the problems of the solution: it leads to magnetic domination and a mostly timelike current for restricted parameters.
Signal extrapolation based on wavelet representation
Xia, Xiang-Gen; Kuo, C.-C. Jay; Zhang, Zhen
1993-11-01
The Papoulis-Gerchberg (PG) algorithm is well known for band-limited signal extrapolation. We consider the generalization of the PG algorithm to signals in the wavelet subspaces in this research. The uniqueness of the extrapolation for continuous-time signals is examined, and sufficient conditions on signals and wavelet bases for the generalized PG (GPG) algorithm to converge are given. We also propose a discrete GPG algorithm for discrete-time signal extrapolation, and investigate its convergence. Numerical examples are given to illustrate the performance of the discrete GPG algorithm.
One-step lowrank wave extrapolation
Sindi, Ghada Atif
2014-01-01
Wavefield extrapolation is at the heart of modeling, imaging, and Full waveform inversion. Spectral methods gained well deserved attention due to their dispersion free solutions and their natural handling of anisotropic media. We propose a scheme a modified one-step lowrank wave extrapolation using Shanks transform in isotropic, and anisotropic media. Specifically, we utilize a velocity gradient term to add to the accuracy of the phase approximation function in the spectral implementation. With the higher accuracy, we can utilize larger time steps and make the extrapolation more efficient. Applications to models with strong inhomogeneity and considerable anisotropy demonstrates the utility of the approach.
Efficient extrapolation methods for electro- and magnetoquasistatic field simulations
Directory of Open Access Journals (Sweden)
M. Clemens
2003-01-01
Full Text Available In magneto- and electroquasi-static time domain simulations with implicit time stepping schemes the iterative solvers applied to the large sparse (non-linear systems of equations are observed to converge faster if more accurate start solutions are available. Different extrapolation techniques for such new time step solutions are compared in combination with the preconditioned conjugate gradient algorithm. Simple extrapolation schemes based on Taylor series expansion are used as well as schemes derived especially for multi-stage implicit Runge-Kutta time stepping methods. With several initial guesses available, a new subspace projection extrapolation technique is proven to produce an optimal initial value vector. Numerical tests show the resulting improvements in terms of computational efficiency for several test problems. In quasistatischen elektromagnetischen Zeitbereichsimulationen mit impliziten Zeitschrittverfahren zeigt sich, dass die iterativen Lösungsverfahren für die großen dünnbesetzten (nicht-linearen Gleichungssysteme schneller konvergieren, wenn genauere Startlösungen vorgegeben werden. Verschiedene Extrapolationstechniken werden für jeweils neue Zeitschrittlösungen in Verbindung mit dem präkonditionierten Konjugierte Gradientenverfahren vorgestellt. Einfache Extrapolationsverfahren basierend auf Taylorreihenentwicklungen werden ebenso benutzt wie speziell für mehrstufige implizite Runge-Kutta-Verfahren entwickelte Verfahren. Sind verschiedene Startlösungen verfügbar, so erlaubt ein neues Unterraum-Projektion- Extrapolationsverfahren die Konstruktion eines optimalen neuen Startvektors. Numerische Tests zeigen die aus diesen Verfahren resultierenden Verbesserungen der numerischen Effizienz.
Extrapolation procedures in Mott electron polarimetry
Gay, T. J.; Khakoo, M. A.; Brand, J. A.; Furst, J. E.; Wijayaratna, W. M. K. P.; Meyer, W. V.; Dunning, F. B.
1992-01-01
In standard Mott electron polarimetry using thin gold film targets, extrapolation procedures must be used to reduce the experimentally measured asymmetries A to the values they would have for scattering from single atoms. These extrapolations involve the dependent of A on either the gold film thickness or the maximum detected electron energy loss in the target. A concentric cylindrical-electrode Mott polarimeter, has been used to study and compare these two types of extrapolations over the electron energy range 20-100 keV. The potential systematic errors which can result from such procedures are analyzed in detail, particularly with regard to the use of various fitting functions in thickness extrapolations, and the failure of perfect energy-loss discrimination to yield accurate polarizations when thick foils are used.
Local, Non-Geodesic, Timelike Currents in the Force-Free Magnetosphere of a Kerr Black Hole
Menon, Govind
2014-01-01
In this paper, we use previously developed exact solutions to present some of the curious features of a force-free magnetosphere in a Kerr background. More precisely, we obtain a hitherto unseen timelike current in the force-free magnetosphere that does not flow along a geodesic. The electromagnetic field in this case happens to be magnetically dominated. This too is a feature that has entered the literature for the first time. Changing the sign of a single parameter in our solutions generates a spacelike current that creates an electromagnetic field that is electrically dominated.
NLT and extrapolated DLT:3-D cinematography alternatives for enlarging the volume of calibration.
Hinrichs, R N; McLean, S P
1995-10-01
This study investigated the accuracy of the direct linear transformation (DLT) and non-linear transformation (NLT) methods of 3-D cinematography/videography. A comparison of standard DLT, extrapolated DLT, and NLT calibrations showed the standard (non-extrapolated) DLT to be the most accurate, especially when a large number of control points (40-60) were used. The NLT was more accurate than the extrapolated DLT when the level of extrapolation exceeded 100%. The results indicated that when possible one should use the DLT with a control object, sufficiently large as to encompass the entire activity being studied. However, in situations where the activity volume exceeds the size of one's DLT control object, the NLT method should be considered.
A two-fluid study of oblique tearing modes in a force-free current sheet
Energy Technology Data Exchange (ETDEWEB)
Akçay, Cihan, E-mail: akcay@lanl.gov; Daughton, William [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Lukin, Vyacheslav S. [National Science Foundation, Arlington, Virginia 22230 (United States); Liu, Yi-Hsin [NASA Goddard Space Flight Center, Greenbelt, Maryland 20771 (United States)
2016-01-15
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Since kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless tearing instability in a force-free current sheet with a two-fluid model and fully kinetic simulations. Our results indicate that the most unstable modes are oblique for guide fields larger than the reconnecting field, in agreement with the kinetic results. The standard two-fluid tearing theory is extended to address the tearing instability at oblique angles. The resulting theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.
Exact properties of force-free jets in the Kerr spacetime
Pan, Zhen
2015-01-01
The Blandford-Znajek (BZ) mechanism describes a process extracting rotation energy from a spinning black hole (BH) via magnetic field lines penetrating the event horizon of central BH. We report, for the first time, a general analytic approach to study force-free jets launched by the BZ mechanism, and its three immediate applications: (1) we present a high-order split monopole perturbation solution to the BZ mechanism, which accurately pins down the energy extraction rate $\\dot E$ and well describes the structure of BH magnetosphere for all range of BH spins ($0\\leq a\\leq 1$); (2) the approach yields an exact constraint for the monopole field configuration in the Kerr spacetime, $I = \\Omega (1-A_\\phi^2)$, where $A_\\phi$ is the $\\phi-$component of electromagnetic field potential, $\\Omega$ is the angular velocity of magnetic field lines and $I$ is the poloidal electric current. The constraint is of particular importance to benchmark the accuracy of numerical simulations; (3) we prove the uniqueness of solutions...
Quantifying non-ergodic dynamics of force-free granular gases.
Bodrova, Anna; Chechkin, Aleksei V; Cherstvy, Andrey G; Metzler, Ralf
2015-09-14
Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient ε. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of ε on the impact velocity of particles.
Cosmic Ray Acceleration by E-Parallel Reconnection of Force-Free Fields
Colgate, S A; Colgate, Stirling A.; Li, Hui
2004-01-01
We propose that nearly every accelerated CR was part of the parallel current that maintains all force-free (f-f) magnetic fields. Charged particles are accelerated by the E-parallel (to the magnetic filed B) produced by reconnection. The inferred total energy in extra-galactic cosmic rays is 10^(60) ergs per galaxy spacing volume, provided that acceleration mechanisms assumed do not preferentially only accelerate ultra high energy cosmic rays (UHECRs). This total energy is about 10^5 times the parent galactic CR or magnetic energy. The formation energy of supermassive black holes (SMBHs) at galaxy centers, 10^(62) ergs, becomes the only feasible source. An efficient dynamo process converts gravitational free energy into magnetic energy in an accretion disk around a SMBH. Aided by Keplerian winding, this dynamo converts a poloidal seed field into f-f fields, which are transported into the general inter-galactic medium (IGM). This magnetic energy is also efficiently converted into particle energies, as evidence...
On the Shape of Force-Free Field Lines in the Solar Corona
Prior, C.
2012-02-02
This paper studies the shape parameters of looped field lines in a linear force-free magnetic field. Loop structures with a sufficient amount of kinking are generally seen to form S or inverse S (Z) shapes in the corona (as viewed in projection). For a single field line, we can ask how much the field line is kinked (as measured by the writhe), and how much neighbouring flux twists about the line (as measured by the twist number). The magnetic helicity of a flux element surrounding the field line can be decomposed into these two quantities. We find that the twist helicity contribution dominates the writhe helicity contribution, for field lines of significant aspect ratio, even when their structure is highly kinked. These calculations shed light on some popular assumptions of the field. First, we show that the writhe of field lines of significant aspect ratio (the apex height divided by the footpoint width) can sometimes be of opposite sign to the helicity. Secondly, we demonstrate the possibility of field line structures which could be interpreted as Z-shaped, but which have a helicity value sign expected of an S-shaped structure. These results suggest that caution should be exercised in using two-dimensional images to draw conclusions on the helicity value of field lines and flux tubes. © 2012 Springer Science+Business Media B.V.
Time Evolution of Relativistic Force-Free Fields Connecting a Neutron Star and its Disk
Asano, E; Matsumoto, R; Asano, Eiji; Uchida, Toshio; Matsumoto, Ryoji
2005-01-01
We study the magnetic interaction between a neutron star and its disk by solving the time-dependent relativistic force-free equations. At the initial state, we assume that the dipole magnetic field of the neutron star connects the neutron star and its equatorial disk, which deeply enters into the magnetosphere of the neutron star. Magnetic fields are assumed to be frozen to the star and the disk. The rotation of the neutron star and the disk is imposed as boundary conditions. We apply Harten-Lax-van Leer (HLL) method to simulate the evolution of the star-disk system. We carry out simulations for (1) a disk inside the corotation radius, in which the disk rotates faster than the star, and (2) a disk outside the corotation radius, in which the neutron star rotates faster than the disk. Numerical results indicate that for both models, the magnetic field lines connecting the disk and the star inflate as they are twisted by the differential rotation between the disk and the star. When the twist angle exceeds pi rad...
The origins of Causality Violations in Force Free Simulations of Black Hole Magnetospheres
Punsly, B; Punsly, Brian; Bini, Donato
2004-01-01
Recent simulations of force-free, degenerate (ffde) black hole magnetospheres indicate that the fast mode radiated from (or near) the event horizon can modify the global potential difference in the poloidal direction orthogonal to the magnetic field, V, in a black hole magnetosphere. There is a fundamental contradiction in a wave that alters V coming from near the horizon. The background fields in ffde satisfy the ``ingoing wave condition'' near the horizon (that arises from the requirement that all matter is ingoing at the event horizon), yet outgoing waves are radiated from this region in the simulation. Studying the properties of the waves in the simulations are useful tools to this end. It is shown that regularity of the stress-energy tensor in a freely falling frame requires that the outgoing (as viewed globally) waves near the event horizon are redshifted away and are ineffectual at changing V. It is also concluded that waves in massless MHD (ffde) are extremely inaccurate depictions of waves in a tenuo...
Typical object velocity influences motion extrapolation.
Makin, Alexis D J; Stewart, Andrew J; Poliakoff, Ellen
2009-02-01
Previous work indicates that extrapolation of object motion during occlusion is affected by the velocity of the immediately preceding trial. Here we ask whether longer-term velocity representations can also influence motion extrapolation. Red, blue or green targets disappeared behind an occluder. Participants pressed a button when they thought the target had reached the other side. Red targets were slower (10-20 deg/s), blue targets moved at medium velocities (14-26 deg/s) and green targets were faster (20-30 deg/s). We compared responses on a subset of red and green trials which always travelled at 20 deg/s. Although trial velocities were identical, participants responded as if the green targets moved faster (M = 22.64 deg/s) then the red targets (M = 19.72 deg/s). This indicates that motion extrapolation is affected by longer-term information about the typical velocity of different categories of stimuli.
Chiral extrapolation of nucleon magnetic form factors
Energy Technology Data Exchange (ETDEWEB)
P. Wang; D. Leinweber; A. W. Thomas; R.Young
2007-04-01
The extrapolation of nucleon magnetic form factors calculated within lattice QCD is investigated within a framework based upon heavy baryon chiral effective-field theory. All one-loop graphs are considered at arbitrary momentum transfer and all octet and decuplet baryons are included in the intermediate states. Finite range regularization is applied to improve the convergence in the quark-mass expansion. At each value of the momentum transfer (Q{sup 2}), a separate extrapolation to the physical pion mass is carried out as a function of m{sub {pi}} alone. Because of the large values of Q{sup 2} involved, the role of the pion form factor in the standard pion-loop integrals is also investigated. The resulting values of the form factors at the physical pion mass are compared with experimental data as a function of Q{sup 2} and demonstrate the utility and accuracy of the chiral extrapolation methods presented herein.
Wavefield extrapolation in pseudo-depth domain
Ma, Xuxin
2012-01-01
Extrapolating seismic waves in Cartesian coordinate is prone to uneven spatial sampling, because the seismic wavelength tends to grow with depth, as velocity increase. We transform the vertical depth axis to a pseudo one using a velocity weighted mapping, which can effectively mitigate this wavelength variation. We derive acoustic wave equations in this new domain based on the direct transformation of the Laplacian derivatives, which admits solutions that are more accurate and stable than those derived from the kinematic transformation. The anisotropic versions of these equations allow us to isolate the vertical velocity influence and reduce its impact on modeling and imaging. The major benefit of extrapolating wavefields in pseudo-depth space is its near uniform wavelength as opposed to the normally dramatic change of wavelength with the conventional approach. Time wavefield extrapolation on a complex velocity shows some of the features of this approach.
The optimizied expansion method for wavefield extrapolation
Wu, Zedong
2013-01-01
Spectral methods are fast becoming an indispensable tool for wave-field extrapolation, especially in anisotropic media, because of its dispersion and artifact free, as well as highly accurate, solutions of the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain operator.In this abstract, we propose an optimized expansion method that can approximate this operator with its low rank representation. The rank defines the number of inverse FFT required per time extrapolation step, and thus, a lower rank admits faster extrapolations. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its low rank representation.Thus,we obtain more accurate wave-fields using lower rank representation, and thus cheaper extrapolations. The optimization operation to define the low rank representation depends only on the velocity model, and this is done only once, and valid for a full reverse time migration (many shots) or one iteration of full waveform inversion. Applications on the BP model yielded superior results than those obtained using the decomposition approach. For transversely isotopic media, the solutions were free of the shear wave artifacts, and does not require that eta>0.
Array aperture extrapolation using sparse reconstruction
Anitori, L.; Rossum, W.L. van; Huizing, A.G.
2015-01-01
In this paper we present some preliminary results on antenna array extrapolation for Direction Of Arrival (DOA) estimation using Sparse Reconstruction (SR). The objective of this study is to establish wether it is possible to achieve with an array of a given physical length the performance (in terms
Efficient and stable extrapolation of prestack wavefields
Wu, Zedong
2013-09-22
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers and the image point, or in other words, prestack wavefields. Extrapolating such wavefields in time, nevertheless, is a big challenge because the radicand can be negative, thus reduce to a complex phase velocity, which will make the rank of the mixed domain matrix very high. Using the vertical offset between the sources and receivers, we introduce a method for deriving the DSR formulation, which gives us the opportunity to derive approximations for the mixed domain operator. The method extrapolates prestack wavefields by combining all data into one wave extrapolation procedure, allowing both upgoing and downgoing wavefields since the extrapolation is done in time, and doesn’t have the v(z) assumption in the offset axis of the media. Thus, the imaging condition is imposed by taking the zero-time and zero-offset slice from the multi-dimensional prestack wavefield. Unlike reverse time migration (RTM), no crosscorrelation is needed and we also have access to the subsurface offset information, which is important for migration velocity analysis. Numerical examples show the capability of this approach in dealing with complex velocity models and can provide a better quality image compared to RTM more efficiently.
Yuan, Yajie; Zrake, Jonathan; East, William E; Blandford, Roger D
2016-01-01
Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over very short time scales. These are likely due to rapid dissipation of electromagnetic energy in a highly magnetized, relativistic plasma. In order to understand the generic features of such processes, we have investigated simple models based on relaxation of unstable force-free magnetostatic equilibria. In this work, we make the connection between the corresponding plasma dynamics and the expected radiation signal, using 2D particle-in-cell simulations that self-consistently include synchrotron radiation reaction. We focus on the lowest order unstable force-free equilibrium in a 2D periodic box. We find that rapid variability, with modest apparent radiation efficiency as perceived by a fixed observer, can be produced during the evolution of the instability. The "flares" are accompanied by an increased pol...
Universality of Mixed Action Extrapolation Formulae
Chen, Jiunn-Wei; Walker-Loud, Andre
2009-01-01
Mixed action theories with chirally symmetric valence fermions exhibit very desirable features both at the level of the lattice calculations as well as in the construction and implementation of the low energy mixed action effective field theory. In this work we show that when the mixed action effective field theory is projected onto the valence sector, both the Lagrangian and the extrapolation formulae become universal in form through next to leading order, for all variants of discretization methods used for the sea fermions. This implies that for all sea quark methods which are in the same universality class as QCD, the numerical values of the physical coefficients in the various mixed action chiral Lagrangians will be the same up to perturbative lattice spacing dependent corrections. This allows us to construct a prescription to determine the mixed action extrapolation formulae for a large class of hadronic correlation functions computed in partially quenched chiral perturbation theory at the one-loop level...
Extrapolation Method for System Reliability Assessment
DEFF Research Database (Denmark)
Qin, Jianjun; Nishijima, Kazuyoshi; Faber, Michael Havbro
2012-01-01
The present paper presents a new scheme for probability integral solution for system reliability analysis, which takes basis in the approaches by Naess et al. (2009) and Bucher (2009). The idea is to evaluate the probability integral by extrapolation, based on a sequence of MC approximations....... The scheme is extended so that it can be applied to cases where the asymptotic property may not be valid and/or the random variables are not normally distributed. The performance of the scheme is investigated by four principal series and parallel systems and some practical examples. The results indicate...... of integrals with scaled domains. The performance of this class of approximation depends on the approach applied for the scaling and the functional form utilized for the extrapolation. A scheme for this task is derived here taking basis in the theory of asymptotic solutions to multinormal probability integrals...
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
Extrapolating spatial layout in scene representations.
Castelhano, Monica S; Pollatsek, Alexander
2010-12-01
Can the visual system extrapolate spatial layout of a scene to new viewpoints after a single view? In the present study, we examined this question by investigating the priming of spatial layout across depth rotations of the same scene (Sanocki & Epstein, 1997). Participants had to indicate which of two dots superimposed on objects in the target scene appeared closer to them in space. There was as much priming from a prime with a viewpoint that was 10° different from the test image as from a prime that was identical to the target; however, there was no reliable priming from larger differences in viewpoint. These results suggest that a scene's spatial layout can be extrapolated, but only to a limited extent.
Effective orthorhombic anisotropic models for wavefield extrapolation
Ibanez-Jacome, W.
2014-07-18
Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models to reproduce wave propagation phenomena in the Earth\\'s subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, we generate effective isotropic inhomogeneous models that are capable of reproducing the firstarrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, we develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic ones, is represented by a sixth order polynomial equation with the fastest solution corresponding to outgoing P waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, and using them to explicitly evaluate the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. We extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.
Residual extrapolation operators for efficient wavefield construction
Alkhalifah, Tariq Ali
2013-02-27
Solving the wave equation using finite-difference approximations allows for fast extrapolation of the wavefield for modelling, imaging and inversion in complex media. It, however, suffers from dispersion and stability-related limitations that might hamper its efficient or proper application to high frequencies. Spectral-based time extrapolation methods tend to mitigate these problems, but at an additional cost to the extrapolation. I investigate the prospective of using a residual formulation of the spectral approach, along with utilizing Shanks transform-based expansions, that adheres to the residual requirements, to improve accuracy and reduce the cost. Utilizing the fact that spectral methods excel (time steps are allowed to be large) in homogeneous and smooth media, the residual implementation based on velocity perturbation optimizes the use of this feature. Most of the other implementations based on the spectral approach are focussed on reducing cost by reducing the number of inverse Fourier transforms required in every step of the spectral-based implementation. The approach here fixes that by improving the accuracy of each, potentially longer, time step.
Jiang, Chaowei
2015-01-01
In the solar corona, magnetic flux rope is believed to be a fundamental structure accounts for magnetic free energy storage and solar eruptions. Up to the present, the extrapolation of magnetic field from boundary data is the primary way to obtain fully three-dimensional magnetic information of the corona. As a result, the ability of reliable recovering coronal magnetic flux rope is important for coronal field extrapolation. In this paper, our coronal field extrapolation code (CESE-MHD-NLFFF, Jiang & Feng 2012) is examined with an analytical magnetic flux rope model proposed by Titov & Demoulin (1999), which consists of a bipolar magnetic configuration holding an semi-circular line-tied flux rope in force-free equilibrium. By using only the vector field in the bottom boundary as input, we test our code with the model in a representative range of parameter space and find that the model field is reconstructed with high accuracy. Especially, the magnetic topological interfaces formed between the flux rop...
Ardekani, Mohammad Ali; Nafisi, Vahid Reza; Farhani, Foad
2012-10-01
Hot-wire spirometer is a kind of constant temperature anemometer (CTA). The working principle of CTA, used for the measurement of fluid velocity and flow turbulence, is based on convective heat transfer from a hot-wire sensor to a fluid being measured. The calibration curve of a CTA is nonlinear and cannot be easily extrapolated beyond its calibration range. Therefore, a method for extrapolation of CTA calibration curve will be of great practical application. In this paper, a novel approach based on the conventional neural network and self-organizing map (SOM) method has been proposed to extrapolate CTA calibration curve for measurement of velocity in the range 0.7-30 m/seconds. Results show that, using this approach for the extrapolation of the CTA calibration curve beyond its upper limit, the standard deviation is about -0.5%, which is acceptable in most cases. Moreover, this approach for the extrapolation of the CTA calibration curve below its lower limit produces standard deviation of about 4.5%, which is acceptable in spirometry applications. Finally, the standard deviation on the whole measurement range (0.7-30 m/s) is about 1.5%.
On extrapolation blowups in the scale
Directory of Open Access Journals (Sweden)
Fiorenza Alberto
2006-01-01
Full Text Available Yano's extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive operator acting continuously in for close to and/or taking into as and/or with norms blowing up at speed and/or , . Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens if as . The study has been motivated by current investigations of convolution maximal functions in stochastic analysis, where the problem occurs for . We also touch the problem of comparison of results in various scales of spaces.
Extrapolating Solar Dynamo Models Throughout the Heliosphere
Cox, B. T.; Miesch, M. S.; Augustson, K.; Featherstone, N. A.
2014-12-01
There are multiple theories that aim to explain the behavior of the solar dynamo, and their associated models have been fiercely contested. The two prevailing theories investigated in this project are the Convective Dynamo model that arises from the pure solving of the magnetohydrodynamic equations, as well as the Babcock-Leighton model that relies on sunspot dissipation and reconnection. Recently, the supercomputer simulations CASH and BASH have formed models of the behavior of the Convective and Babcock-Leighton models, respectively, in the convective zone of the sun. These models show the behavior of the models within the sun, while much less is known about the effects these models may have further away from the solar surface. The goal of this work is to investigate any fundamental differences between the Convective and Babcock-Leighton models of the solar dynamo outside of the sun and extending into the solar system via the use of potential field source surface extrapolations implemented via python code that operates on data from CASH and BASH. The use of real solar data to visualize supergranular flow data in the BASH model is also used to learn more about the behavior of the Babcock-Leighton Dynamo. From the process of these extrapolations it has been determined that the Babcock-Leighton model, as represented by BASH, maintains complex magnetic fields much further into the heliosphere before reverting into a basic dipole field, providing 3D visualisations of the models distant from the sun.
Solutions of the Force-Free Duffing-van der Pol Oscillator Equation
Directory of Open Access Journals (Sweden)
Najeeb Alam Khan
2011-01-01
Full Text Available A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution.
Schroedinger's radial equation - Solution by extrapolation
Goorvitch, D.; Galant, D. C.
1992-01-01
A high-accuracy numerical method for the solution of a 1D Schroedinger equation that is suitable for a diatomic molecule, obtained by combining a finite-difference method with iterative extrapolation to the limit, is presently shown to have several advantages over more conventional methods. Initial guesses for the term values are obviated, and implementation of the algorithm is straightforward. The method is both less sensitive to round-off error, and faster than conventional methods for equivalent accuracy. These advantages are illustrated through the solution of Schroedinger's equation for a Morse potential function suited for HCl and a numerically derived Rydberg-Klein-Rees potential function for the X 1Sigma(+) state of CO.
Universal properties of infrared oscillator basis extrapolations
More, S N; Furnstahl, R J; Hagen, G; Papenbrock, T
2013-01-01
Recent work has shown that a finite harmonic oscillator basis in nuclear many-body calculations effectively imposes a hard-wall boundary condition in coordinate space, motivating infrared extrapolation formulas for the energy and other observables. Here we further refine these formulas by studying two-body models and the deuteron. We accurately determine the box size as a function of the model space parameters, and compute scattering phase shifts in the harmonic oscillator basis. We show that the energy shift can be well approximated in terms of the asymptotic normalization coefficient and the bound-state momentum, discuss higher-order corrections for weakly bound systems, and illustrate this universal property using unitarily equivalent calculations of the deuteron.
Extrapolation methods for dynamic partial differential equations
Turkel, E.
1978-01-01
Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. Computational results are presented confirming the analytic discussions.
Full waveform inversion with extrapolated low frequency data
Li, Yunyue Elita
2016-01-01
The availability of low frequency data is an important factor in the success of full waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data below 2 or 3 Hz from the field is a challenging and expensive task. In this paper we explore the possibility of synthesizing the low frequencies computationally from high-frequency data, and use the resulting prediction of the missing data to seed the frequency sweep of FWI. As a signal processing problem, bandwidth extension is a very nonlinear and delicate operation. It requires a high-level interpretation of bandlimited seismic records into individual events, each of which is extrapolable to a lower (or higher) frequency band from the non-dispersive nature of the wave propagation model. We propose to use the phase tracking method for the event separation task. The...
Frequency extrapolation by nonconvex compressive sensing
Energy Technology Data Exchange (ETDEWEB)
Chartrand, Rick [Los Alamos National Laboratory; Sidky, Emil Y [UNIV OF CHICAGO; Pan, Xiaochaun [UNIV OF CHICAGO
2010-12-03
Tomographic imaging modalities sample subjects with a discrete, finite set of measurements, while the underlying object function is continuous. Because of this, inversion of the imaging model, even under ideal conditions, necessarily entails approximation. The error incurred by this approximation can be important when there is rapid variation in the object function or when the objects of interest are small. In this work, we investigate this issue with the Fourier transform (FT), which can be taken as the imaging model for magnetic resonance imaging (MRl) or some forms of wave imaging. Compressive sensing has been successful for inverting this data model when only a sparse set of samples are available. We apply the compressive sensing principle to a somewhat related problem of frequency extrapolation, where the object function is represented by a super-resolution grid with many more pixels than FT measurements. The image on the super-resolution grid is obtained through nonconvex minimization. The method fully utilizes the available FT samples, while controlling aliasing and ringing. The algorithm is demonstrated with continuous FT samples of the Shepp-Logan phantom with additional small, high-contrast objects.
Bandlimited image extrapolation with faster convergence
Cahana, D.; Stark, H.
1981-08-01
Techniques for increasing the convergence rate of the extrapolation algorithm proposed by Gerchberg (1974) and Papoulis (1975) for image restoration applications are presented. The techniques involve the modification of the Gerchberg-Papoulis algorithm to include additional a priori data such as the low-pass projection of the image either by the inclusion of the data at the start of the recursion to reduce the starting-point error, or by use of the low-pass image in each iteration to correct twice in the frequency domain. The performance of the GP algorithm and the two modifications presented in the restorations of a signal consisting of widely separated spectral components of equal magnitude and a signal with spectral components grouped in passbands is compared, and it is found that while both modifications reduced the starting point error, the convergence rate of the second technique was not substantially greater than that of the first despite the additional iterative frequency-plane correction. A significant improvement in the starting-point errors and convergence rates of both modified algorithms is obtained, however, when they are combined with adaptive thresholding in the presence of low noise levels and a signal with relatively well spaced impulse-type spectral components.
Force-free Currents and the Newman-Penrose Tetrad of a Kerr Black Hole: Exact Local Solutions
Menon, Govind
2015-01-01
In a previous article we derived a class of solutions to the force-free magnetosphere in a Kerr background. Here, the streaming surface, defined by constant values of the toriodal component of the electromagnetic vector potential $A$, were generated by constant values of $\\theta$. The electromagnetic current vector flowed along the in-falling principle null geodesic vector of the geometry. Subsequently, we generalized this to obtain an out-going principle null geodesic vector as well. In this article, we derive solutions that are complimentary to the above mentioned criteria. Namely, here the solution has a streaming surface generated by spheres of constant radial coordinate $r$, and the current vector is generated by linear combinations of $m$ and $m^\\star$, the remaining bases vectors in the Newman-Penrose null tetrad.
A Family of One-Dimensional Vlasov-Maxwell Equilibria for the Force-Free Harris Sheet
Wilson, Fiona
2011-01-01
A family of self-consistent collisionless distribution functions for the force-free Harris sheet is presented. This family includes the distribution function recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)] as well as distribution functions with a different dependence on the particle energy, but with the same dependence on the canonical momenta. It is shown generally that the other distribution functions in the family give rise to the same pressure function and thus to the same current density and magnetic field as the known distribution function, provided certain conditions on the parameters are satisfied. A number of examples of distribution functions from the new family are given, which illustrate the use of the general method.
Force-Free Magnetic Fields on AN Extreme Reissner-Nordström Spacetime and the Meissner Effect
Takamori, Yousuke; Ken-Ichi, Nakao; Hideki, Ishihara; Masashi, Kimura; Chul-Moon, Yoo
It is known that the Meissner effect of black holes is seen in the vacuum solutions of blackhole magnetosphere: no non-monopole component of magnetic flux penetrates the event horizon if the black hole is extreme. In this article, in order to see the effects of charge currents, we study the force-free magnetic field on the extreme Reissner-Nordström background. In this case, we should solve one elliptic differential equation called the Grad-Shafranov equation which has singular points called light surfaces. In order to see the Meissner effect, we consider the region near the event horizon and try to solve the equation by Taylor expansion about the event horizon. Moreover, we assume that the small rotational velocity of the magnetic field, and then, we construct a perturbative method to solve the Grad-Shafranov equation considering the efftect of the inner light surface and study the behavior of the magnetic field near the event horizon.
Timokhin, Andrey
2007-01-01
In this paper we consider stationary force-free magnetosphere of an aligned rotator when plasma in the open field line region rotates differentially due to presence of a zone with the accelerating electric field in the polar cap of pulsar. We study the impact of differential rotation on the current density distribution in the magnetosphere. Using split-monopole approximation we obtain analytical expressions for physical parameters of differentially rotating magnetosphere. We find the range of admitted current density distributions under the requirement that the potential drop in the polar cap is less than the vacuum potential drop. We show that the current density distribution could deviate significantly from the ``classical'' Michel distribution and could be made almost constant over the polar cap even when the potential drop in the accelerating zone is of the order of 10 per cents of the vacuum potential drop. We argue that differential rotation of the open magnetic field lines could play an important role ...
Gong, Xiaobo; Xu, Zhaoyi
2016-01-01
Based on the Lagrangian of the steady axisymmetric force-free magnetosphere (FFM) equation around Kerr black holes(KBHs), we find that the FFM equation can be rewritten in a new form as $f_{,rr} / (1-\\mu^{2}) + f_{,\\mu\\mu} / \\Delta + K(f(r,\\mu),r,\\mu) = 0$, where $\\mu = -\\cos\\theta$. By coordinate transformation, the form of the above equation can be given by $s_{,yy} + s_{,zz} + D(s(y,z),y,z) = 0$. Based on the form, we prove finally that the Meissner effect is not possessed by a KBH-FFM with the condition where $d\\omega/d A_{\\phi} \\leqslant 0$ and $H_{\\phi}(dH_{\\phi}/dA_{\\phi}) \\geqslant 0$, here $A_{\\phi}$ is the $\\phi$ component of the vector potential $\\vec{A}$, $\\omega$ is the angular velocity of magnetic fields and ${H_{\\phi}}$ corresponds to twice the poloidal electric current.
Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan; East, William E.; Blandford, Roger D.
2016-09-01
Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over very short timescales. These are likely due to the rapid dissipation of electromagnetic energy in a highly magnetized, relativistic plasma. In order to understand the generic features of such processes, we have investigated simple models based on the relaxation of unstable force-free magnetostatic equilibria. In this work, we make the connection between the corresponding plasma dynamics and the expected radiation signal, using 2D particle-in-cell simulations that self-consistently include synchrotron radiation reactions. We focus on the lowest order unstable force-free equilibrium in a 2D periodic box. We find that rapid variability, with modest apparent radiation efficiency as perceived by a fixed observer, can be produced during the evolution of the instability. The “flares” are accompanied by an increased polarization degree in the high energy band, with rapid variation in the polarization angle. Furthermore, the separation between the acceleration sites and the synchrotron radiation sites for the highest energy particles facilitates acceleration beyond the synchrotron radiation reaction limit. We also discuss the dynamical consequences of the radiation reaction, and some astrophysical applications of this model. Our current simulations with numerically tractable parameters are not yet able to reproduce the most dramatic gamma-ray flares, e.g., from the Crab Nebula. Higher magnetization studies are promising and will be carried out in the future.
Uncertainties of Euclidean Time Extrapolation in Lattice Effective Field Theory
Lähde, Timo A; Krebs, Hermann; Lee, Dean; Meißner, Ulf-G; Rupak, Gautam
2014-01-01
Extrapolations in Euclidean time form a central part of Nuclear Lattice Effective Field Theory (NLEFT) calculations using the Projection Monte Carlo method, as the sign problem in many cases prevents simulations at large Euclidean time. We review the next-to-next-to-leading order NLEFT results for the alpha nuclei up to $^{28}$Si, with emphasis on the Euclidean time extrapolations, their expected accuracy and potential pitfalls. We also discuss possible avenues for improving the reliability of Euclidean time extrapolations in NLEFT.
Analysis of extrapolation cascadic multigrid method(EXCMG)
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on an asymptotic expansion of finite element,a new extrapolation formula and extrapolation cascadic multigrid method(EXCMG)are proposed,in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid.In the case of triple grids,the error of the new initial value is analyzed in detail.A larger scale computation is completed in PC.
Varying self-inductance and energy storage in a sheared force-free arcade. [of coronal loops
Zuccarello, F.; Burm, H.; Kuperus, M.; Raadu, M.; Spicer, D. S.
1987-01-01
An electric circuit analogy is used to model the build-up and storage of magnetic energy in the coronal loops known to exist in the atmosphere of the sun. The present parameterization of magnetic energy storage in an electric circuit analog uses a bulk current I flowing in the circuit and a self-inductance L. Because the self-inductance is determined by the geometry of the magnetic configuration any change in its dimensions will change L. If L is increased, the amount of magnetic energy stored and the rate at which magnetic energy is stored are both increased. One way of increasing L is to shear the magnetic field lines and increase their effective geometrical length. Using the force-free field approximation for a magnetic arcade whose field lines are sheared by photospheric motions, it is demonstrated that the increase of magnetic energy is initially due to the increase of the current intensity I and later mainly due to the increase of the self-inductance.
Nandy, Dibyendu; Calhoun, A.; Windschitl, J.; Canfield, R. C.; Linton, M. G.
2007-05-01
The twist component of magnetic helicity in solar active regions is known to be an important indicator of sub-photospheric flux tube dynamics and solar eruptive activity. Traditionally, estimates of the parameter alpha -- appearing in the force-free-field equation -- has been used to infer the twist of photospheric active regions. However, the photosphere is not force-free and this has lead to recent concerns on the validity of using the alpha parameter for determining photospheric active region twist. We have devised a new flux-tube-fitting technique for determining the twist of active regions without recourse to the force-free-field equation. This method assumes that the underlying active region flux system is cylindrically symmetric and uniformly twisted. By using this new technique, on a statistically compelling number of photospheric active region vector magnetograms, we re-confirm the hemispheric helicity rule independent of the force-free-field assumption. This research has been supported in parts by a NASA Living With a Star grant NNG05GE47G. A.C. and J.W. were supported by a NSF Research Experience for Undergraduates grant ATM-0243923 to Montana State University. M.G.L. acknowledges support from NASA and the Office of Naval Research.
3D Hail Size Distribution Interpolation/Extrapolation Algorithm
Lane, John
2013-01-01
Radar data can usually detect hail; however, it is difficult for present day radar to accurately discriminate between hail and rain. Local ground-based hail sensors are much better at detecting hail against a rain background, and when incorporated with radar data, provide a much better local picture of a severe rain or hail event. The previous disdrometer interpolation/ extrapolation algorithm described a method to interpolate horizontally between multiple ground sensors (a minimum of three) and extrapolate vertically. This work is a modification to that approach that generates a purely extrapolated 3D spatial distribution when using a single sensor.
The chemistry side of AOP: implications for toxicity extrapolation
An adverse outcome pathway (AOP) is a structured representation of the biological events that lead to adverse impacts following a molecular initiating event caused by chemical interaction with a macromolecule. AOPs have been proposed to facilitate toxicity extrapolation across s...
Multidimensional signal restoration and band-limited extrapolation, 2
Sanz, J. L. C.; Huang, T. S.
1982-12-01
This technical report consists of three parts. The central problem is the extrapolation of band-limited signals. In part 1, several existing algorithms for band-limited extrapolation are compared: Two-step procedures appeared to give better reconstructions and require less computing time than iterative algorithms. In part 2, five basic procedures for iterative restoration are unified using a Hilbert Space approach. In particular, all known interative algorithms for extrapolation of band-limited signals are shown to be special cases of Bialy's iteration. The authors also obtained faster algorithms than that of Papoulis-Gerchberg. In part 3, the extrapolation problem is presented in a more general setting: Continuation of certain analytic functions. Presented are two steps procedures for finding the continuation of these functions. Some new procedures for band-limited continuation are also discussed as well as the case in which the signal is contaminated with noise.
Extrapolating demography with climate, proximity and phylogeny: approach with caution.
Coutts, Shaun R; Salguero-Gómez, Roberto; Csergő, Anna M; Buckley, Yvonne M
2016-12-01
Plant population responses are key to understanding the effects of threats such as climate change and invasions. However, we lack demographic data for most species, and the data we have are often geographically aggregated. We determined to what extent existing data can be extrapolated to predict population performance across larger sets of species and spatial areas. We used 550 matrix models, across 210 species, sourced from the COMPADRE Plant Matrix Database, to model how climate, geographic proximity and phylogeny predicted population performance. Models including only geographic proximity and phylogeny explained 5-40% of the variation in four key metrics of population performance. However, there was poor extrapolation between species and extrapolation was limited to geographic scales smaller than those at which landscape scale threats typically occur. Thus, demographic information should only be extrapolated with caution. Capturing demography at scales relevant to landscape level threats will require more geographically extensive sampling. © 2016 John Wiley & Sons Ltd/CNRS.
Biosimilar monoclonal antibodies : The scientific basis for extrapolation
Schellekens, Huub; Lietzan, Erika; Faccin, Freddy; Venema, Jaap
2015-01-01
Introduction: Biosimilars are biologic products that receive authorization based on an abbreviated regulatory application containing comparative quality and nonclinical and clinical data that demonstrate similarity to a licensed biologic product. Extrapolation of safety and efficacy has emerged as a
Image reconstruction: a unifying model for resolution enhancement and data extrapolation. Tutorial
Shieh, Hsin M.; Byrne, Charles L.; Fiddy, Michael A.
2006-02-01
In reconstructing an object function F(r) from finitely many noisy linear-functional values ∫F(r)Gn(r)dr we face the problem that finite data, noisy or not, are insufficient to specify F(r) uniquely. Estimates based on the finite data may succeed in recovering broad features of F(r), but may fail to resolve important detail. Linear and nonlinear, model-based data extrapolation procedures can be used to improve resolution, but at the cost of sensitivity to noise. To estimate linear-functional values of F(r) that have not been measured from those that have been, we need to employ prior information about the object F(r), such as support information or, more generally, estimates of the overall profile of F(r). One way to do this is through minimum-weighted-norm (MWN) estimation, with the prior information used to determine the weights. The MWN approach extends the Gerchberg-Papoulis band-limited extrapolation method and is closely related to matched-filter linear detection, the approximation of the Wiener filter, and to iterative Shannon-entropy-maximization algorithms. Nonlinear versions of the MWN method extend the noniterative, Burg, maximum-entropy spectral-estimation procedure.
Wildlife toxicity extrapolations: Allometry versus physiologically-based toxicokinetics
Energy Technology Data Exchange (ETDEWEB)
Fairbrother, A. [Ecological Planning and Toxicology Inc., Corvallis, OR (United States); Berg, M. van den [Univ. of Utrecht (Netherlands). Research Inst. of Toxicology
1995-12-31
Ecotoxicological assessments must rely on the extrapolation of toxicity data from a few indicator species to many species of concern. Data are available from laboratory studies (e.g., quail, mallards, rainbow trout, fathead minnow) and some planned or serendipitous field studies of a broader, but by no means comprehensive, suite of species. Yet all ecological risk assessments begin with an estimate of risk based on information gleaned from the literature. The authors are then confronted with the necessity of extrapolating toxicity information from a limited number of indicator species to all organisms of interest. This is a particularly acute problem when trying to estimate hazards to wildlife in terrestrial systems as there is an extreme paucity of data for most chemicals in all but a handful of species. The question arises of how interspecific extrapolations should be made. Should extrapolations be limited to animals within the same class, order, family or genus? Alteratively, should extrapolations be made along trophic levels or physiologic similarities rather than by taxonomic classification? In other words, is an avian carnivore more like a mammalian carnivore or an avian granivore in its response to a toxic substance? Can general rules be set or does the type of extrapolation depend upon the class of chemical and its mode of uptake and toxicologic effect?
Implicit extrapolation methods for multilevel finite element computations
Energy Technology Data Exchange (ETDEWEB)
Jung, M.; Ruede, U. [Technische Universitaet Chemnitz-Zwickau (Germany)
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
Do common systems control eye movements and motion extrapolation?
Makin, Alexis D J; Poliakoff, Ellen
2011-07-01
People are able to judge the current position of occluded moving objects. This operation is known as motion extrapolation. It has previously been suggested that motion extrapolation is independent of the oculomotor system. Here we revisited this question by measuring eye position while participants completed two types of motion extrapolation task. In one task, a moving visual target travelled rightwards, disappeared, then reappeared further along its trajectory. Participants discriminated correct reappearance times from incorrect (too early or too late) with a two-alternative forced-choice button press. In the second task, the target travelled rightwards behind a visible, rectangular occluder, and participants pressed a button at the time when they judged it should reappear. In both tasks, performance was significantly different under fixation as compared to free eye movement conditions. When eye movements were permitted, eye movements during occlusion were related to participants' judgements. Finally, even when participants were required to fixate, small changes in eye position around fixation (<2°) were influenced by occluded target motion. These results all indicate that overlapping systems control eye movements and judgements on motion extrapolation tasks. This has implications for understanding the mechanism underlying motion extrapolation.
Tadesse, Tilaye; MacNeice, Peter
2014-01-01
The solar coronal magnetic field produces solar activity, including extremely energetic solar flares and coronal mass ejections (CMEs). Knowledge of the structure and evolution of the magnetic field of the solar corona is important for investigating and understanding the origins of space weather. Although the coronal field remains difficult to measure directly, there is considerable interest in accurate modeling of magnetic fields in and around sunspot regions on the Sun using photospheric vector magnetograms as boundary data. In this work, we investigate effects of the size of the domain chosen for coronal magnetic field modeling on resulting model solution. We apply spherical Optimization procedure to vector magnetogram data of Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) with four Active Region observed on 09 March 2012 at 20:55UT. The results imply that quantities like magnetic flux density, electric current density and free magnetic energy density of ARs of interest are...
Lowrank seismic-wave extrapolation on a staggered grid
Fang, Gang
2014-05-01
© 2014 Society of Exploration Geophysicists. We evaluated a new spectral method and a new finite-difference (FD) method for seismic-wave extrapolation in time. Using staggered temporal and spatial grids, we derived a wave-extrapolation operator using a lowrank decomposition for a first-order system of wave equations and designed the corresponding FD scheme. The proposed methods extend previously proposed lowrank and lowrank FD wave extrapolation methods from the cases of constant density to those of variable density. Dispersion analysis demonstrated that the proposed methods have high accuracy for a wide wavenumber range and significantly reduce the numerical dispersion. The method of manufactured solutions coupled with mesh refinement was used to verify each method and to compare numerical errors. Tests on 2D synthetic examples demonstrated that the proposed method is highly accurate and stable. The proposed methods can be used for seismic modeling or reverse-time migration.
Chiral extrapolation beyond the power-counting regime
Hall, J M M; Leinweber, D B; Liu, K F; Mathur, N; Young, R D; Zhang, J B
2011-01-01
Chiral effective field theory can provide valuable insight into the chiral physics of hadrons when used in conjunction with non-perturbative schemes such as lattice QCD. In this discourse, the attention is focused on extrapolating the mass of the rho meson to the physical pion mass in quenched QCD (QQCD). With the absence of a known experimental value, this serves to demonstrate the ability of the extrapolation scheme to make predictions without prior bias. By using extended effective field theory developed previously, an extrapolation is performed using quenched lattice QCD data that extends outside the chiral power-counting regime (PCR). The method involves an analysis of the renormalization flow curves of the low energy coefficients in a finite-range regularized effective field theory. The analysis identifies an optimal regulator, which is embedded in the lattice QCD data themselves. This optimal regulator is the regulator value at which the renormalization of the low energy coefficients is approximately i...
Submarine Magnetic Field Extrapolation Based on Boundary Element Method
Institute of Scientific and Technical Information of China (English)
GAO Jun-ji; LIU Da-ming; YAO Qiong-hui; ZHOU Guo-hua; YAN Hui
2007-01-01
In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine, a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method (BEM). An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine. The data in differentheights above the model submarine are obtained by use of tri-axial magnetometers. The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data. Moreover, the model can reflect the submarine magnetic field distribution in the air exactly, and is valuable in practical engineering.
Rubio de Francia's extrapolation theory: estimates for the distribution function
Carro, María J; Torres, Rodolfo H
2010-01-01
Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \\infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution function of $Tf$ with respect to any weight $u$ can be essentially majorized by the distribution function of $Mf$ with respect to $u$ (plus an integral term easy to control). As a consequence, well-known extrapolation results, including results in a multilinear setting, can be obtained with very simple proofs. New applications in extrapolation for two-weight problems and estimates on rearrangement invariant spaces are established too.
Splitting extrapolation based on domain decomposition for finite element approximations
Institute of Scientific and Technical Information of China (English)
吕涛; 冯勇
1997-01-01
Splitting extrapolation based on domain decomposition for finite element approximations is a new technique for solving large scale scientific and engineering problems in parallel. By means of domain decomposition, a large scale multidimensional problem is turned to many discrete problems involving several grid parameters The multi-variate asymptotic expansions of finite element errors on independent grid parameters are proved for linear and nonlin ear second order elliptic equations as well as eigenvalue problems. Therefore after solving smaller problems with similar sizes in parallel, a global fine grid approximation with higher accuracy is computed by the splitting extrapolation method.
Extrapolation of scattering data to the negative-energy region
Blokhintsev, L D; Mukhamedzhanov, A M; Savin, D A
2016-01-01
Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negative-energy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.
Weights, Extrapolation and the Theory of Rubio de Francia
Cruz-Uribe, David; Perez, Carlos
2011-01-01
This book provides a systematic development of the Rubio de Francia theory of extrapolation, its many generalizations and its applications to one and two-weight norm inequalities. The book is based upon a new and elementary proof of the classical extrapolation theorem that fully develops the power of the Rubio de Francia iteration algorithm. This technique allows us to give a unified presentation of the theory and to give important generalizations to Banach function spaces and to two-weight inequalities. We provide many applications to the classical operators of harmonic analysis to illustrate
Panel discussion on Chiral extrapolation of physical observables
Bernard, C; Leinweber, D B; Lepage, P; Pallante, E; Sharpe, S R; Wittig, H; Bernard, Claude; Hashimoto, Shoji; Leinweber, Derek B.; Lepage, Peter; Pallante, Elisabetta; Sharpe, Stephen R.; Wittig, Hartmut
2002-01-01
This is an approximate reconstruction of the panel discussion on chiral extrapolation of physical observables. The session consisted of brief presentations from panelists, followed by responses from the panel, and concluded with questions and comments from the floor with answers from panelists. In the following, the panelists have summarized their statements, and the ensuing discussion has been approximately reconstructed from notes.
Biosimilars and the extrapolation of indications for inflammatory conditions
Tesser, John RP; Furst, Daniel E; Jacobs, Ira
2017-01-01
Extrapolation is the approval of a biosimilar for use in an indication held by the originator biologic not directly studied in a comparative clinical trial with the biosimilar. Extrapolation is a scientific rationale that bridges all the data collected (ie, totality of the evidence) from one indication for the biosimilar product to all the indications originally approved for the originator. Regulatory approval and marketing authorization of biosimilars in inflammatory indications are made on a case-by-case and agency-by-agency basis after evaluating the totality of evidence from the entire development program. This totality of the evidence comprises extensive comparative analytical, functional, nonclinical, and clinical pharmacokinetic/pharmacodynamic, efficacy, safety, and immunogenicity studies used by regulators when evaluating whether a product can be considered a biosimilar. Extrapolation reduces or eliminates the need for duplicative clinical studies of the biosimilar but must be justified scientifically with appropriate data. Understanding the concept, application, and regulatory decisions based on the extrapolation of data is important since biosimilars have the potential to significantly impact patient care in inflammatory diseases. PMID:28255229
Panel discussion on chiral extrapolation of physical observables
Bernard, Claude; Hashimoto, Shoji; Leinweber, Derek B.; Lepage, Peter; Pallante, Elisabetta; Sharpe, Stephen R.; Wittig, Hartmut
2003-01-01
This is an approximate reconstruction of the panel discussion on chiral extrapolation of physical observables. The session consisted of brief presentations from panelists, followed by responses from the panel, and concluded with questions and comments from the floor with answers from panelists. In t
Assessment of Load Extrapolation Methods for Wind Turbines
DEFF Research Database (Denmark)
Toft, Henrik Stensgaard; Sørensen, John Dalsgaard
2010-01-01
In the present paper methods for statistical load extrapolation of wind turbine response are studied using a stationary Gaussian process model which has approximately the same spectral properties as the response for the flap bending moment of a wind turbine blade. For a Gaussian process an approx...
How accurate are infrared luminosities from monochromatic photometric extrapolation?
Lin, Zesen; Kong, Xu
2016-01-01
Template-based extrapolations from only one photometric band can be a cost-effective method to estimate the total infrared (IR) luminosities ($L_{\\mathrm{IR}}$) of galaxies. By utilizing multi-wavelength data that covers across 0.35--500\\,$\\mathrm{\\mu m}$ in GOODS-North and GOODS-South fields, we investigate the accuracy of this monochromatic extrapolated $L_{\\mathrm{IR}}$ based on three IR spectral energy distribution (SED) templates (\\citealt[CE01]{Chary2001}; \\citealt[DH02]{Dale2002}; \\citealt[W08]{Wuyts2008a}) out to $z\\sim 3.5$. We find that the CE01 template provides the best estimate of $L_{\\mathrm{IR}}$ in {\\it Herschel}/PACS bands, while the DH02 template performs best in {\\it Herschel}/SPIRE bands. To estimate $L_{\\mathrm{IR}}$, we suggest that extrapolations from the available longest wavelength PACS band based on the CE01 template can be a good estimator. Moreover, if PACS measurement is unavailable, extrapolations from SPIRE observations but based on the \\cite{Dale2002} template can also provide ...
Panel discussion on chiral extrapolation of physical observables
Bernard, Claude; Hashimoto, Shoji; Leinweber, Derek B.; Lepage, Peter; Pallante, Elisabetta; Sharpe, Stephen R.; Wittig, Hartmut
2003-01-01
This is an approximate reconstruction of the panel discussion on chiral extrapolation of physical observables. The session consisted of brief presentations from panelists, followed by responses from the panel, and concluded with questions and comments from the floor with answers from panelists. In t
Genetic effects of radiation. [Extrapolation of mouse data to man
Energy Technology Data Exchange (ETDEWEB)
Selby, P.B.
1976-01-01
Data are reviewed from studies on the genetic effects of x radiation in mice and the extrapolation of the findings for estimating genetic hazards in man is discussed. Data are included on the frequency of mutation induction following acute or chronic irradiation of male or female mice at various doses and dose rates.
Extrapolations of nuclear binding energies from new linear mass relations
DEFF Research Database (Denmark)
Hove, D.; Jensen, A. S.; Riisager, K.
2013-01-01
We present a method to extrapolate nuclear binding energies from known values for neighboring nuclei. We select four specific mass relations constructed to eliminate smooth variation of the binding energy as function nucleon numbers. The fast odd-even variations are avoided by comparing nuclei...
Proposition of Improved Methodology in Creep Life Extrapolation
Energy Technology Data Exchange (ETDEWEB)
Kim, Woo Gon; Park, Jae Young; Jang, Jin Sung [KAERI, Daejeon (Korea, Republic of)
2016-05-15
To design SFRs for a 60-year operation, it is desirable to have the experimental creep-rupture data for Gr. 91 steel close to 20 y, or at least rupture lives significantly higher than 10{sup 5} h. This requirement arises from the fact that, for the creep design, a factor of 3 times for extrapolation is considered to be appropriate. However, obtaining experimental data close to 20 y would be expensive and also take considerable time. Therefore, reliable creep life extrapolation techniques become necessary for a safe design life of 60 y. In addition, it is appropriate to obtain experimental longterm creep-rupture data in the range 10{sup 5} ∼ 2x10{sup 5} h to improve the reliability of extrapolation. In the present investigation, a new function of a hyperbolic sine ('sinh') form for a master curve in time-temperature parameter (TTP) methods, was proposed to accurately extrapolate the long-term creep rupture stress of Gr. 91 steel. Constant values used for each parametric equation were optimized on the basis of the creep rupture data. Average stress values predicted for up to 60 y were evaluated and compared with those of French Nuclear Design Code, RCC-MRx. The results showed that the master curve of the 'sinh' function was a wider acceptance with good flexibility in the low stress ranges beyond the experimental data. It was clarified clarified that the 'sinh' function was reasonable in creep life extrapolation compared with polynomial forms, which have been used conventionally until now.
Effective wavefield extrapolation in anisotropic media: Accounting for resolvable anisotropy
Alkhalifah, Tariq Ali
2014-04-30
Spectral methods provide artefact-free and generally dispersion-free wavefield extrapolation in anisotropic media. Their apparent weakness is in accessing the medium-inhomogeneity information in an efficient manner. This is usually handled through a velocity-weighted summation (interpolation) of representative constant-velocity extrapolated wavefields, with the number of these extrapolations controlled by the effective rank of the original mixed-domain operator or, more specifically, by the complexity of the velocity model. Conversely, with pseudo-spectral methods, because only the space derivatives are handled in the wavenumber domain, we obtain relatively efficient access to the inhomogeneity in isotropic media, but we often resort to weak approximations to handle the anisotropy efficiently. Utilizing perturbation theory, I isolate the contribution of anisotropy to the wavefield extrapolation process. This allows us to factorize as much of the inhomogeneity in the anisotropic parameters as possible out of the spectral implementation, yielding effectively a pseudo-spectral formulation. This is particularly true if the inhomogeneity of the dimensionless anisotropic parameters are mild compared with the velocity (i.e., factorized anisotropic media). I improve on the accuracy by using the Shanks transformation to incorporate a denominator in the expansion that predicts the higher-order omitted terms; thus, we deal with fewer terms for a high level of accuracy. In fact, when we use this new separation-based implementation, the anisotropy correction to the extrapolation can be applied separately as a residual operation, which provides a tool for anisotropic parameter sensitivity analysis. The accuracy of the approximation is high, as demonstrated in a complex tilted transversely isotropic model. © 2014 European Association of Geoscientists & Engineers.
Energy Technology Data Exchange (ETDEWEB)
Dowding, Kevin J.; Hills, Richard Guy (New Mexico State University, Las Cruces, NM)
2005-04-01
Numerical models of complex phenomena often contain approximations due to our inability to fully model the underlying physics, the excessive computational resources required to fully resolve the physics, the need to calibrate constitutive models, or in some cases, our ability to only bound behavior. Here we illustrate the relationship between approximation, calibration, extrapolation, and model validation through a series of examples that use the linear transient convective/dispersion equation to represent the nonlinear behavior of Burgers equation. While the use of these models represents a simplification relative to the types of systems we normally address in engineering and science, the present examples do support the tutorial nature of this document without obscuring the basic issues presented with unnecessarily complex models.
Suppression of MRI Truncation Artifacts Using Total Variation Constrained Data Extrapolation
Directory of Open Access Journals (Sweden)
Kai Tobias Block
2008-01-01
Full Text Available The finite sampling of k-space in MRI causes spurious image artifacts, known as Gibbs ringing, which result from signal truncation at the border of k-space. The effect is especially visible for acquisitions at low resolution and commonly reduced by filtering at the expense of image blurring. The present work demonstrates that the simple assumption of a piecewise-constant object can be exploited to extrapolate the data in k-space beyond the measured part. The method allows for a significant reduction of truncation artifacts without compromising resolution. The assumption translates into a total variation minimization problem, which can be solved with a nonlinear optimization algorithm. In the presence of substantial noise, a modified approach offers edge-preserving denoising by allowing for slight deviations from the measured data in addition to supplementing data. The effectiveness of these methods is demonstrated with simulations as well as experimental data for a phantom and human brain in vivo.
Phase unwrapping using an extrapolation-projection algorithm
Marendic, Boris; Yang, Yongyi; Stark, Henry
2006-08-01
We explore an approach to the unwrapping of two-dimensional phase functions using a robust extrapolation-projection algorithm. Phase unwrapping is essential for imaging systems that construct the image from phase information. Unlike some existing methods where unwrapping is performed locally on a pixel-by-pixel basis, this work approaches the unwrapping problem from a global point of view. The unwrapping is done iteratively by a modification of the Gerchberg-Papoulis extrapolation algorithm, and the solution is refined by projecting onto the available global data at each iteration. Robustness of the algorithm is demonstrated through its performance in a noisy environment, and in comparison with a least-squares algorithm well-known in the literature.
Assessment of Load Extrapolation Methods for Wind Turbines
DEFF Research Database (Denmark)
Toft, Henrik Stensgaard; Sørensen, John Dalsgaard; Veldkamp, Dick
2011-01-01
In the present paper, methods for statistical load extrapolation of wind-turbine response are studied using a stationary Gaussian process model, which has approximately the same spectral properties as the response for the out-of-plane bending moment of a wind-turbine blade. For a Gaussian process......, an approximate analytical solution for the distribution of the peaks is given by Rice. In the present paper, three different methods for statistical load extrapolation are compared with the analytical solution for one mean wind speed. The methods considered are global maxima, block maxima, and the peak over....... By considering Gaussian processes for 12 mean wind speeds, the "fitting before aggregation" and "aggregation before fitting" approaches are studied. The results show that the fitting before aggregation approach gives the best results. [DOI: 10.1115/1.4003416]...
Outlier robustness for wind turbine extrapolated extreme loads
DEFF Research Database (Denmark)
Natarajan, Anand; Verelst, David Robert
2012-01-01
Methods for extrapolating extreme loads to a 50 year probability of exceedance, which display robustness to the presence of outliers in simulated loads data set, are described. Case studies of isolated high extreme out-of-plane loads are discussed to emphasize their underlying physical reasons....... Stochastic identification of numerical artifacts in simulated loads is demonstrated using the method of principal component analysis. The extrapolation methodology is made robust to outliers through a weighted loads approach, whereby the eigenvalues of the correlation matrix obtained using the loads with its...... simulation is demonstrated and compared with published results. Further effects of varying wind inflow angles and shear exponent is brought out. Parametric fitting techniques that consider all extreme loads including ‘outliers’ are proposed, and the physical reasons that result in isolated high extreme loads...
Temperature extrapolation of multicomponent grand canonical free energy landscapes
Mahynski, Nathan A.; Errington, Jeffrey R.; Shen, Vincent K.
2017-08-01
We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid.
A regularization method for extrapolation of solar potential magnetic fields
Gary, G. A.; Musielak, Z. E.
1992-01-01
The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.
Interpolation and Extrapolation of Precipitation Quantities in Serbia
Directory of Open Access Journals (Sweden)
Rastislav Stojsavljević
2013-01-01
Full Text Available The aim of this paper is to indicate the problems with filling the missing data in precipitation database using interpolation and extrapolation methods. Investigated periods were from 1981 to 2010 for Northern (Autonomous Province of Vojvodina and Proper Serbia and from 1971 to 2000 for Southern Serbia (Autonomous Province of Kosovo and Metohia. Database included time series from 78 meteorological stations that had less than 20% of missing data. Interpolation was performed if station had missing data for five consecutive months or less. If station had missing data for six consecutive months or more, extrapolation was performed. For every station with mising data correlation with at least three surrounding stations was performed. The lowest acceptable value of correlation coefficient for precipitation was set at 0,300
An efficient extrapolation to the (T)/CBS limit
Ranasinghe, Duminda S.; Barnes, Ericka C.
2014-05-01
We extrapolate to the perturbative triples (T)/complete basis set (CBS) limit using double ζ basis sets without polarization functions (Wesleyan-1-Triples-2ζ or "Wes1T-2Z") and triple ζ basis sets with a single level of polarization functions (Wesleyan-1-Triples-3ζ or "Wes1T-3Z"). These basis sets were optimized for 102 species representing the first two rows of the Periodic Table. The species include the entire set of neutral atoms, positive and negative atomic ions, as well as several homonuclear diatomic molecules, hydrides, rare gas dimers, polar molecules, such as oxides and fluorides, and a few transition states. The extrapolated Wes1T-(2,3)Z triples energies agree with (T)/CBS benchmarks to within ±0.65 mEh, while the rms deviations of comparable model chemistries W1, CBS-APNO, and CBS-QB3 for the same test set are ±0.23 mEh, ±2.37 mEh, and ±5.80 mEh, respectively. The Wes1T-(2,3)Z triples calculation time for the largest hydrocarbon in the G2/97 test set, C6H5Me+, is reduced by a factor of 25 when compared to W1. The cost-effectiveness of the Wes1T-(2,3)Z extrapolation validates the usefulness of the Wes1T-2Z and Wes1T-3Z basis sets which are now available for a more efficient extrapolation of the (T) component of any composite model chemistry.
An efficient extrapolation to the (T)/CBS limit.
Ranasinghe, Duminda S; Barnes, Ericka C
2014-05-14
We extrapolate to the perturbative triples (T)/complete basis set (CBS) limit using double ζ basis sets without polarization functions (Wesleyan-1-Triples-2ζ or "Wes1T-2Z") and triple ζ basis sets with a single level of polarization functions (Wesleyan-1-Triples-3ζ or "Wes1T-3Z"). These basis sets were optimized for 102 species representing the first two rows of the Periodic Table. The species include the entire set of neutral atoms, positive and negative atomic ions, as well as several homonuclear diatomic molecules, hydrides, rare gas dimers, polar molecules, such as oxides and fluorides, and a few transition states. The extrapolated Wes1T-(2,3)Z triples energies agree with (T)/CBS benchmarks to within ±0.65 mEh, while the rms deviations of comparable model chemistries W1, CBS-APNO, and CBS-QB3 for the same test set are ±0.23 mEh, ±2.37 mEh, and ±5.80 mEh, respectively. The Wes1T-(2,3)Z triples calculation time for the largest hydrocarbon in the G2/97 test set, C6H5Me(+), is reduced by a factor of 25 when compared to W1. The cost-effectiveness of the Wes1T-(2,3)Z extrapolation validates the usefulness of the Wes1T-2Z and Wes1T-3Z basis sets which are now available for a more efficient extrapolation of the (T) component of any composite model chemistry.
An efficient extrapolation to the (T)/CBS limit
Energy Technology Data Exchange (ETDEWEB)
Ranasinghe, Duminda S. [Hall-Atwater Laboratories of Chemistry, Wesleyan University, Middletown, Connecticut 06459-0180 (United States); Barnes, Ericka C., E-mail: barnese8@southernct.edu [Department of Chemistry, Southern Connecticut State University, 501 Crescent Street, New Haven, Connecticut 06515-1355 (United States)
2014-05-14
We extrapolate to the perturbative triples (T)/complete basis set (CBS) limit using double ζ basis sets without polarization functions (Wesleyan-1-Triples-2ζ or “Wes1T-2Z”) and triple ζ basis sets with a single level of polarization functions (Wesleyan-1-Triples-3ζ or “Wes1T-3Z”). These basis sets were optimized for 102 species representing the first two rows of the Periodic Table. The species include the entire set of neutral atoms, positive and negative atomic ions, as well as several homonuclear diatomic molecules, hydrides, rare gas dimers, polar molecules, such as oxides and fluorides, and a few transition states. The extrapolated Wes1T-(2,3)Z triples energies agree with (T)/CBS benchmarks to within ±0.65 mE{sub h}, while the rms deviations of comparable model chemistries W1, CBS-APNO, and CBS-QB3 for the same test set are ±0.23 mE{sub h}, ±2.37 mE{sub h}, and ±5.80 mE{sub h}, respectively. The Wes1T-(2,3)Z triples calculation time for the largest hydrocarbon in the G2/97 test set, C{sub 6}H{sub 5}Me{sup +}, is reduced by a factor of 25 when compared to W1. The cost-effectiveness of the Wes1T-(2,3)Z extrapolation validates the usefulness of the Wes1T-2Z and Wes1T-3Z basis sets which are now available for a more efficient extrapolation of the (T) component of any composite model chemistry.
Effective Orthorhombic Anisotropic Models for Wave field Extrapolation
Ibanez Jacome, Wilson
2013-05-01
Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models, to reproduce wave propagation phenomena in the Earth\\'s subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, I generate effective isotropic inhomogeneous models that are capable of reproducing the first-arrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, I develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic one, is represented by a sixth order polynomial equation that includes the fastest solution corresponding to outgoing P-waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, which is done by explicitly solving the isotropic eikonal equation for the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. I extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the
Line-of-sight extrapolation noise in dust polarization
Energy Technology Data Exchange (ETDEWEB)
Poh, Jason; Dodelson, Scott
2017-05-19
The B-modes of polarization at frequencies ranging from 50-1000 GHz are produced by Galactic dust, lensing of primordial E-modes in the cosmic microwave background (CMB) by intervening large scale structure, and possibly by primordial B-modes in the CMB imprinted by gravitational waves produced during inflation. The conventional method used to separate the dust component of the signal is to assume that the signal at high frequencies (e.g., 350 GHz) is due solely to dust and then extrapolate the signal down to lower frequency (e.g., 150 GHz) using the measured scaling of the polarized dust signal amplitude with frequency. For typical Galactic thermal dust temperatures of about 20K, these frequencies are not fully in the Rayleigh-Jeans limit. Therefore, deviations in the dust cloud temperatures from cloud to cloud will lead to different scaling factors for clouds of different temperatures. Hence, when multiple clouds of different temperatures and polarization angles contribute to the integrated line-of-sight polarization signal, the relative contribution of individual clouds to the integrated signal can change between frequencies. This can cause the integrated signal to be decorrelated in both amplitude and direction when extrapolating in frequency. Here we carry out a Monte Carlo analysis on the impact of this line-of-sight extrapolation noise, enabling us to quantify its effect. Using results from the Planck experiment, we find that this effect is small, more than an order of magnitude smaller than the current uncertainties. However, line-of-sight extrapolation noise may be a significant source of uncertainty in future low-noise primordial B-mode experiments. Scaling from Planck results, we find that accounting for this uncertainty becomes potentially important when experiments are sensitive to primordial B-mode signals with amplitude r < 0.0015 .
Biosimilars in Inflammatory Bowel Disease: Facts and Fears of Extrapolation.
Ben-Horin, Shomron; Vande Casteele, Niels; Schreiber, Stefan; Lakatos, Peter Laszlo
2016-12-01
Biologic drugs such as infliximab and other anti-tumor necrosis factor monoclonal antibodies have transformed the treatment of immune-mediated inflammatory conditions such as Crohn's disease and ulcerative colitis (collectively known as inflammatory bowel disease [IBD]). However, the complex manufacturing processes involved in producing these drugs mean their use in clinical practice is expensive. Recent or impending expiration of patents for several biologics has led to development of biosimilar versions of these drugs, with the aim of providing substantial cost savings and increased accessibility to treatment. Biosimilars undergo an expedited regulatory process. This involves proving structural, functional, and biological biosimilarity to the reference product (RP). It is also expected that clinical equivalency/comparability will be demonstrated in a clinical trial in one (or more) sensitive population. Once these requirements are fulfilled, extrapolation of biosimilar approval to other indications for which the RP is approved is permitted without the need for further clinical trials, as long as this is scientifically justifiable. However, such justification requires that the mechanism(s) of action of the RP in question should be similar across indications and also comparable between the RP and the biosimilar in the clinically tested population(s). Likewise, the pharmacokinetics, immunogenicity, and safety of the RP should be similar across indications and comparable between the RP and biosimilar in the clinically tested population(s). To date, most anti-tumor necrosis factor biosimilars have been tested in trials recruiting patients with rheumatoid arthritis. Concerns have been raised regarding extrapolation of clinical data obtained in rheumatologic populations to IBD indications. In this review, we discuss the issues surrounding indication extrapolation, with a focus on extrapolation to IBD.
Statistically extrapolated nowcasting of summertime precipitation over the Eastern Alps
Chen, Min; Bica, Benedikt; Tüchler, Lukas; Kann, Alexander; Wang, Yong
2017-07-01
This paper presents a new multiple linear regression (MLR) approach to updating the hourly, extrapolated precipitation forecasts generated by the INCA (Integrated Nowcasting through Comprehensive Analysis) system for the Eastern Alps. The generalized form of the model approximates the updated precipitation forecast as a linear response to combinations of predictors selected through a backward elimination algorithm from a pool of predictors. The predictors comprise the raw output of the extrapolated precipitation forecast, the latest radar observations, the convective analysis, and the precipitation analysis. For every MLR model, bias and distribution correction procedures are designed to further correct the systematic regression errors. Applications of the MLR models to a verification dataset containing two months of qualified samples, and to one-month gridded data, are performed and evaluated. Generally, MLR yields slight, but definite, improvements in the intensity accuracy of forecasts during the late evening to morning period, and significantly improves the forecasts for large thresholds. The structure-amplitude-location scores, used to evaluate the performance of the MLR approach, based on its simulation of morphological features, indicate that MLR typically reduces the overestimation of amplitudes and generates similar horizontal structures in precipitation patterns and slightly degraded location forecasts, when compared with the extrapolated nowcasting.
Effective ellipsoidal models for wavefield extrapolation in tilted orthorhombic media
Waheed, Umair Bin
2016-04-22
Wavefield computations using the ellipsoidally anisotropic extrapolation operator offer significant cost reduction compared to that for the orthorhombic case, especially when the symmetry planes are tilted and/or rotated. However, ellipsoidal anisotropy does not provide accurate wavefield representation or imaging for media of orthorhombic symmetry. Therefore, we propose the use of ‘effective ellipsoidally anisotropic’ models that correctly capture the kinematic behaviour of wavefields for tilted orthorhombic (TOR) media. We compute effective velocities for the ellipsoidally anisotropic medium using kinematic high-frequency representation of the TOR wavefield, obtained by solving the TOR eikonal equation. The effective model allows us to use the cheaper ellipsoidally anisotropic wave extrapolation operators. Although the effective models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The proposed methodology offers a much better cost versus accuracy trade-off for wavefield computations in TOR media, particularly for media of low to moderate anisotropic strength. Furthermore, the computed wavefield solution is free from shear-wave artefacts as opposed to the conventional finite-difference based TOR wave extrapolation scheme. We demonstrate applicability and usefulness of our formulation through numerical tests on synthetic TOR models. © 2016 Institute of Geophysics of the ASCR, v.v.i
An efficient wave extrapolation method for anisotropic media with tilt
Waheed, Umair bin
2015-03-23
Wavefield extrapolation operators for elliptically anisotropic media offer significant cost reduction compared with that for the transversely isotropic case, particularly when the axis of symmetry exhibits tilt (from the vertical). However, elliptical anisotropy does not provide accurate wavefield representation or imaging for transversely isotropic media. Therefore, we propose effective elliptically anisotropic models that correctly capture the kinematic behaviour of wavefields for transversely isotropic media. Specifically, we compute source-dependent effective velocities for the elliptic medium using kinematic high-frequency representation of the transversely isotropic wavefield. The effective model allows us to use cheaper elliptic wave extrapolation operators. Despite the fact that the effective models are obtained by matching kinematics using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy trade-off for wavefield computations in transversely isotropic media, particularly for media of low to moderate complexity. In addition, the wavefield solution is free from shear-wave artefacts as opposed to the conventional finite-difference-based transversely isotropic wave extrapolation scheme. We demonstrate these assertions through numerical tests on synthetic tilted transversely isotropic models.
Efficient anisotropic wavefield extrapolation using effective isotropic models
Alkhalifah, Tariq Ali
2013-06-10
Isotropic wavefield extrapolation is more efficient than anisotropic extrapolation, and this is especially true when the anisotropy of the medium is tilted (from the vertical). We use the kinematics of the wavefield, appropriately represented in the high-frequency asymptotic approximation by the eikonal equation, to develop effective isotropic models, which are used to efficiently and approximately extrapolate anisotropic wavefields using the isotropic, relatively cheaper, operators. These effective velocity models are source dependent and tend to embed the anisotropy in the inhomogeneity. Though this isotropically generated wavefield theoretically shares the same kinematic behavior as that of the first arrival anisotropic wavefield, it also has the ability to include all the arrivals resulting from a complex wavefield propagation. In fact, the effective models reduce to the original isotropic model in the limit of isotropy, and thus, the difference between the effective model and, for example, the vertical velocity depends on the strength of anisotropy. For reverse time migration (RTM), effective models are developed for the source and receiver fields by computing the traveltime for a plane wave source stretching along our source and receiver lines in a delayed shot migration implementation. Applications to the BP TTI model demonstrates the effectiveness of the approach.
Tremblay, Benoit; Vincent, Alain
2017-01-01
We present a generalization of the resistive minimum-energy fit (MEF-R: Tremblay and Vincent, Solar Phys. 290, 437, 2015) for non-force-free (NFF) magnetic fields. In MEF-R, an extremum principle is used to infer two-dimensional maps of plasma motions [boldsymbol{v}(x,y)] and magnetic eddy diffusivity [η _{eddy}(x,y)] at the photosphere. These reconstructions could be used as boundary conditions in data-driven simulations or in data assimilation. The algorithm is validated using the analytical model of a resistive expanding spheromak by Rakowski, Laming, and Lyutikov ( Astrophys. J. 730, 30, 2011). We study the flaring Active Region AR 12158 using a series of magnetograms and Dopplergrams provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The results are discussed for a non-force-free magnetic-field reconstruction [boldsymbol{B}_{NFF}] (Hu and Dasgupta in Solar Phys. 247, 87, 2008). We found that the vertical plasma velocities [vz(x,y)] inferred using MEF-R are very similar to the observed Doppler velocities [vr(x,y)]. Finally, we study the potential spatial correlation between microturbulent velocities and significant values of η_{eddy}(x,y).
Timokhin, A. N.; Arons, J.
2013-01-01
We report the results of an investigation of particle acceleration and electron-positron plasma generation at low altitude in the polar magnetic flux tubes of rotation-powered pulsars, when the stellar surface is free to emit whatever charges and currents are demanded by the force-free magnetosphere. We apply a new 1D hybrid plasma simulation code to the dynamical problem, using Particle-in-Cell methods for the dynamics of the charged particles, including a determination of the collective electrostatic fluctuations in the plasma, combined with a Monte Carlo treatment of the high-energy gamma-rays that mediate the formation of the electron-positron pairs.We assume the electric current flowing through the pair creation zone is fixed by the much higher inductance magnetosphere, and adopt the results of force-free magnetosphere models to provide the currents which must be carried by the accelerator. The models are spatially one dimensional, and designed to explore the physics, although of practical relevance to young, high-voltage pulsars. We observe novel behaviour (a) When the current density j is less than the Goldreich-Julian value (0 1), the system develops high voltage drops (TV or greater), causing emission of curvature gamma-rays and intense bursts of pair creation. The bursts exhibit limit cycle behaviour, with characteristic time-scales somewhat longer than the relativistic fly-by time over distances comparable to the polar cap diameter (microseconds). (c) In return current regions, where j/j(sub GJ) rotating frame), finding that such steady flows can occupy only a small fraction of the current density parameter space exhibited by the force-free magnetospheric model. The generic polar flow dynamics and pair creation are strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage (with pair creation, when the voltage drops are sufficiently large; without, when they are
Smooth extrapolation of unknown anatomy via statistical shape models
Grupp, R. B.; Chiang, H.; Otake, Y.; Murphy, R. J.; Gordon, C. R.; Armand, M.; Taylor, R. H.
2015-03-01
Several methods to perform extrapolation of unknown anatomy were evaluated. The primary application is to enhance surgical procedures that may use partial medical images or medical images of incomplete anatomy. Le Fort-based, face-jaw-teeth transplant is one such procedure. From CT data of 36 skulls and 21 mandibles separate Statistical Shape Models of the anatomical surfaces were created. Using the Statistical Shape Models, incomplete surfaces were projected to obtain complete surface estimates. The surface estimates exhibit non-zero error in regions where the true surface is known; it is desirable to keep the true surface and seamlessly merge the estimated unknown surface. Existing extrapolation techniques produce non-smooth transitions from the true surface to the estimated surface, resulting in additional error and a less aesthetically pleasing result. The three extrapolation techniques evaluated were: copying and pasting of the surface estimate (non-smooth baseline), a feathering between the patient surface and surface estimate, and an estimate generated via a Thin Plate Spline trained from displacements between the surface estimate and corresponding vertices of the known patient surface. Feathering and Thin Plate Spline approaches both yielded smooth transitions. However, feathering corrupted known vertex values. Leave-one-out analyses were conducted, with 5% to 50% of known anatomy removed from the left-out patient and estimated via the proposed approaches. The Thin Plate Spline approach yielded smaller errors than the other two approaches, with an average vertex error improvement of 1.46 mm and 1.38 mm for the skull and mandible respectively, over the baseline approach.
Extrapolation of vertical target motion through a brief visual occlusion.
Zago, Myrka; Iosa, Marco; Maffei, Vincenzo; Lacquaniti, Francesco
2010-03-01
It is known that arbitrary target accelerations along the horizontal generally are extrapolated much less accurately than target speed through a visual occlusion. The extent to which vertical accelerations can be extrapolated through an occlusion is much less understood. Here, we presented a virtual target rapidly descending on a blank screen with different motion laws. The target accelerated under gravity (1g), decelerated under reversed gravity (-1g), or moved at constant speed (0g). Probability of each type of acceleration differed across experiments: one acceleration at a time, or two to three different accelerations randomly intermingled could be presented. After a given viewing period, the target disappeared for a brief, variable period until arrival (occluded trials) or it remained visible throughout (visible trials). Subjects were asked to press a button when the target arrived at destination. We found that, in visible trials, the average performance with 1g targets could be better or worse than that with 0g targets depending on the acceleration probability, and both were always superior to the performance with -1g targets. By contrast, the average performance with 1g targets was always superior to that with 0g and -1g targets in occluded trials. Moreover, the response times of 1g trials tended to approach the ideal value with practice in occluded protocols. To gain insight into the mechanisms of extrapolation, we modeled the response timing based on different types of threshold models. We found that occlusion was accompanied by an adaptation of model parameters (threshold time and central processing time) in a direction that suggests a strategy oriented to the interception of 1g targets at the expense of the interception of the other types of tested targets. We argue that the prediction of occluded vertical motion may incorporate an expectation of gravity effects.
Singularity-preserving image interpolation using wavelet transform extrema extrapolation
Zhai, Guangtao; Zhang, Yang; Zheng, Xiaoshi
2003-09-01
One common task of image interpolation is to enhance the resolution of the image, which means to magnify the image without loss in its clarity. Traditional methods often assume that the original images are smooth enough so as to possess continues derivatives, which tend to blur the edges of the interpolated image. A novel fast image interpolation algorithm based on wavelet transform and multi-resolution analysis is proposed in this paper. It uses interpolation and extrapolation polynomial to estimate the higher resolution informatoin of the image and generate a new sub-band of wavelet transform coefficients to get processed image with shaper edges and preserved singularities.
Novel Extrapolation Method in the Monte Carlo Shell Model
Shimizu, Noritaka; Mizusaki, Takahiro; Otsuka, Takaharu; Abe, Takashi; Honma, Michio
2010-01-01
We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model in order to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater determinants, which enables us to calculate the energy variance efficiently. The feasibility of the method is demonstrated for the full $pf$-shell calculation of $^{56}$Ni, and the applicability of the method to a system beyond current limit of exact diagonalization is shown for the $pf$+$g_{9/2}$-shell calculation of $^{64}$Ge.
Mass extrapolation of quarks and leptons to higher generations
Energy Technology Data Exchange (ETDEWEB)
Barik, N. (Utkal Univ., Bhubaneswar (India). Dept. of Physics)
1981-05-01
An empirical mass formula is tested for the basic fermion sequences of charged quarks and leptons. This relation is a generalization of Barut's mass formula for the lepton sequence (e, ..mu.., tau ....). It is found that successful mass extrapolation to the third and possibly to other higher generations (N > 2) can be obtained with the first and second generation masses as inputs, which predicts the top quark mass msub(t) to be around 20 GeV. This also leads to the mass ratios between members of two different sequences (i) and (i') corresponding to the same higher generations (N > 2).
QCD thermodynamics with continuum extrapolated dynamical overlap fermions
Borsanyi, Sz; Lippert, T; Nogradi, D; Pittler, F; Szabo, K K; Toth, B C
2015-01-01
We study the finite temperature transition in QCD with two flavors of dynamical fermions at a pseudoscalar pion mass of about 350 MeV. We use lattices with temporal extent of $N_t$=8, 10 and 12. For the first time in the literature a continuum limit is carried out for several observables with dynamical overlap fermions. These findings are compared with results obtained within the staggered fermion formalism at the same pion masses and extrapolated to the continuum limit. The presented results correspond to fixed topology and its effect is studied in the staggered case. Nice agreement is found between the overlap and staggered results.
Evidence for risk extrapolation in decision making by tadpoles
Crane, Adam L.; Ferrari, Maud C. O.
2017-01-01
Through time, the activity patterns, morphology, and development of both predators and prey change, which in turn alter the relative vulnerability of prey to their coexisting predators. Recognizing these changes can thus allow prey to make optimal decisions by projecting risk trends into the future. We used tadpoles (Lithobates sylvaticus) to test the hypothesis that tadpoles can extrapolate information about predation risk from past information. We exposed tadpoles to an odour that represented either a temporally consistent risk or an increasing risk. When tested for their response to the odour, the initial antipredator behaviour of tadpoles did not differ, appearing to approach the limit of their maximum response, but exposure to increasing risk induced longer retention of these responses. When repeating the experiment using lower risk levels, heightened responses occurred for tadpoles exposed to increasing risk, and the strongest responses were exhibited by those that received an abrupt increase compared to a steady increase. Our results indicate that tadpoles can assess risk trends through time and adjust their antipredator responses in a way consistent with an extrapolated trend. This is a sophisticated method for prey to avoid threats that are becoming more (or less) dangerous over part of their lifespan. PMID:28230097
Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media
Waheed, Umair bin
2014-05-01
Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.
Calculating excitation energies by extrapolation along adiabatic connections
Rebolini, Elisa; Teale, Andrew M; Helgaker, Trygve; Savin, Andreas
2015-01-01
In this paper, an alternative method to range-separated linear-response time-dependent density-functional theory and perturbation theory is proposed to improve the estimation of the energies of a physical system from the energies of a partially interacting system. Starting from the analysis of the Taylor expansion of the energies of the partially interacting system around the physical system, we use an extrapolation scheme to improve the estimation of the energies of the physical system at an intermediate point of the range-separated or linear adiabatic connection where either the electron--electron interaction is scaled or only the long-range part of the Coulomb interaction is included. The extrapolation scheme is first applied to the range-separated energies of the helium and beryllium atoms and of the hydrogen molecule at its equilibrium and stretched geometries. It improves significantly the convergence rate of the energies toward their exact limit with respect to the range-separation parameter. The range...
The solution of coupled Schroedinger equations using an extrapolation method
Goorvitch, D.; Galant, D. C.
1992-01-01
In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.
Nuclear Lattice Simulations using Symmetry-Sign Extrapolation
Lähde, Timo A; Lee, Dean; Meißner, Ulf-G; Epelbaum, Evgeny; Krebs, Hermann; Rupak, Gautam
2015-01-01
Projection Monte Carlo calculations of lattice Chiral Effective Field Theory suffer from sign oscillations to a varying degree dependent on the number of protons and neutrons. Hence, such studies have hitherto been concentrated on nuclei with equal numbers of protons and neutrons, and especially on the alpha nuclei where the sign oscillations are smallest. We now introduce the technique of "symmetry-sign extrapolation" which allows us to use the approximate Wigner SU(4) symmetry of the nuclear interaction to control the sign oscillations without introducing unknown systematic errors. We benchmark this method by calculating the ground-state energies of the $^{12}$C, $^6$He and $^6$Be nuclei, and discuss its potential for studies of neutron-rich halo nuclei and asymmetric nuclear matter.
Nuclear lattice simulations using symmetry-sign extrapolation
Energy Technology Data Exchange (ETDEWEB)
Laehde, Timo A.; Luu, Thomas [Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik, and Juelich Center for Hadron Physics, Juelich (Germany); Lee, Dean [North Carolina State University, Department of Physics, Raleigh, NC (United States); Meissner, Ulf G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik, and Juelich Center for Hadron Physics, Juelich (Germany); Forschungszentrum Juelich, JARA - High Performance Computing, Juelich (Germany); Epelbaum, Evgeny; Krebs, Hermann [Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik II, Bochum (Germany); Rupak, Gautam [Mississippi State University, Department of Physics and Astronomy, Mississippi State, MS (United States)
2015-07-15
Projection Monte Carlo calculations of lattice Chiral Effective Field Theory suffer from sign oscillations to a varying degree dependent on the number of protons and neutrons. Hence, such studies have hitherto been concentrated on nuclei with equal numbers of protons and neutrons, and especially on the alpha nuclei where the sign oscillations are smallest. Here, we introduce the ''symmetry-sign extrapolation'' method, which allows us to use the approximate Wigner SU(4) symmetry of the nuclear interaction to systematically extend the Projection Monte Carlo calculations to nuclear systems where the sign problem is severe. We benchmark this method by calculating the ground-state energies of the {sup 12}C, {sup 6}He and {sup 6}Be nuclei, and discuss its potential for studies of neutron-rich halo nuclei and asymmetric nuclear matter. (orig.)
UFOs in the LHC: Observations, studies and extrapolations
Baer, T; Cerutti, F; Ferrari, A; Garrel, N; Goddard, B; Holzer, EB; Jackson, S; Lechner, A; Mertens, V; Misiowiec, M; Nebot del Busto, E; Nordt, A; Uythoven, J; Vlachoudis, V; Wenninger, J; Zamantzas, C; Zimmermann, F; Fuster, N
2012-01-01
Unidentified falling objects (UFOs) are potentially a major luminosity limitation for nominal LHC operation. They are presumably micrometer sized dust particles which lead to fast beam losses when they interact with the beam. With large-scale increases and optimizations of the beam loss monitor (BLM) thresholds, their impact on LHC availability was mitigated from mid 2011 onwards. For higher beam energy and lower magnet quench limits, the problem is expected to be considerably worse, though. In 2011/12, the diagnostics for UFO events were significantly improved: dedicated experiments and measurements in the LHC and in the laboratory were made and complemented by FLUKA simulations and theoretical studies. The state of knowledge, extrapolations for nominal LHC operation and mitigation strategies are presented
The extrapolated successive overrelaxation (ESOR method for consistently ordered matrices
Directory of Open Access Journals (Sweden)
N. M. Missirlis
1984-01-01
Full Text Available This paper develops the theory of the Extrapolated Successive Overrelaxation (ESOR method as introduced by Sisler in [1], [2], [3] for the numerical solution of large sparse linear systems of the form Au=b, when A is a consistently ordered 2-cyclic matrix with non-vanishing diagonal elements and the Jacobi iteration matrix B possesses only real eigenvalues. The region of convergence for the ESOR method is described and the optimum values of the involved parameters are also determined. It is shown that if the minimum of the moduli of the eigenvalues of B, μ¯ does not vanish, then ESOR attains faster rate of convergence than SOR when 1−μ¯2<(1−μ¯212, where μ¯ denotes the spectral radius of B.
Spatial extrapolation of lysimeter results using thermal infrared imaging
Voortman, B. R.; Bosveld, F. C.; Bartholomeus, R. P.; Witte, J. P. M.
2016-12-01
Measuring evaporation (E) with lysimeters is costly and prone to numerous errors. By comparing the energy balance and the remotely sensed surface temperature of lysimeters with those of the undisturbed surroundings, we were able to assess the representativeness of lysimeter measurements and to quantify differences in evaporation caused by spatial variations in soil moisture content. We used an algorithm (the so called 3T model) to spatially extrapolate the measured E of a reference lysimeter based on differences in surface temperature, net radiation and soil heat flux. We tested the performance of the 3T model on measurements with multiple lysimeters (47.5 cm inner diameter) and micro lysimeters (19.2 cm inner diameter) installed in bare sand, moss and natural dry grass. We developed different scaling procedures using in situ measurements and remotely sensed surface temperatures to derive spatially distributed estimates of Rn and G and explored the physical soundness of the 3T model. Scaling of Rn and G considerably improved the performance of the 3T model for the bare sand and moss experiments (Nash-Sutcliffe efficiency (NSE) increasing from 0.45 to 0.89 and from 0.81 to 0.94, respectively). For the grass surface, the scaling procedures resulted in a poorer performance of the 3T model (NSE decreasing from 0.74 to 0.70), which was attributed to effects of shading and the difficulty to correct for differences in emissivity between dead and living biomass. The 3T model is physically unsound if the field scale average air temperature, measured at an arbitrarily chosen reference height, is used as input to the model. The proposed measurement system is relatively cheap, since it uses a zero tension (freely draining) lysimeter which results are extrapolated by the 3T model to the unaffected surroundings. The system is promising for bridging the gap between ground observations and satellite based estimates of E.
Balabin, Roman M; Smirnov, Sergey V
2012-04-07
Modern analytical chemistry of industrial products is in need of rapid, robust, and cheap analytical methods to continuously monitor product quality parameters. For this reason, spectroscopic methods are often used to control the quality of industrial products in an on-line/in-line regime. Vibrational spectroscopy, including mid-infrared (MIR), Raman, and near-infrared (NIR), is one of the best ways to obtain information about the chemical structures and the quality coefficients of multicomponent mixtures. Together with chemometric algorithms and multivariate data analysis (MDA) methods, which were especially created for the analysis of complicated, noisy, and overlapping signals, NIR spectroscopy shows great results in terms of its accuracy, including classical prediction error, RMSEP. However, it is unclear whether the combined NIR + MDA methods are capable of dealing with much more complex interpolation or extrapolation problems that are inevitably present in real-world applications. In the current study, we try to make a rather general comparison of linear, such as partial least squares or projection to latent structures (PLS); "quasi-nonlinear", such as the polynomial version of PLS (Poly-PLS); and intrinsically non-linear, such as artificial neural networks (ANNs), support vector regression (SVR), and least-squares support vector machines (LS-SVM/LSSVM), regression methods in terms of their robustness. As a measure of robustness, we will try to estimate their accuracy when solving interpolation and extrapolation problems. Petroleum and biofuel (biodiesel) systems were chosen as representative examples of real-world samples. Six very different chemical systems that differed in complexity, composition, structure, and properties were studied; these systems were gasoline, ethanol-gasoline biofuel, diesel fuel, aromatic solutions of petroleum macromolecules, petroleum resins in benzene, and biodiesel. Eighteen different sample sets were used in total. General
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Set Your Creative Forces Free!
DEFF Research Database (Denmark)
Meier Sørensen, Bent; Villadsen, Kaspar
Critical studies of new forms of flexible, delegating and even artistic forms of management demonstrate how power relations between employees and management do not dissolve but rather re-configure. This paper addresses this problematic by exploring how an artistic form of allegedly ‘non-hierarchi......Critical studies of new forms of flexible, delegating and even artistic forms of management demonstrate how power relations between employees and management do not dissolve but rather re-configure. This paper addresses this problematic by exploring how an artistic form of allegedly ‘non...... against managerial authority....
Wang, Yuming; Zhou, Zhenjun; Shen, Chenglong; Liu, Rui; Wang, S.
2015-03-01
Magnetic clouds (MCs) are the interplanetary counterparts of coronal mass ejections (CMEs), and usually modeled by a flux rope. By assuming the quasi-steady evolution and self-similar expansion, we introduce three types of global motion into a cylindrical force-free flux rope model and developed a new velocity-modified model for MCs. The three types of the global motion are the linear propagating motion away from the Sun, the expanding, and the poloidal motion with respect to the axis of the MC. The model is applied to 72 MCs observed by Wind spacecraft to investigate the properties of the plasma motion of MCs. First, we find that some MCs had a significant propagation velocity perpendicular to the radial direction, suggesting the direct evidence of the CME's deflected propagation and/or rotation in interplanetary space. Second, we confirm the previous results that the expansion speed is correlated with the radial propagation speed and most MCs did not expand self-similarly at 1 AU. In our statistics, about 62%/17% of MCs underwent a underexpansion/overexpansion at 1 AU and the expansion rate is about 0.6 on average. Third, most interestingly, we find that a significant poloidal motion did exist in some MCs. Three speculations about the cause of the poloidal motion are therefore proposed. These findings advance our understanding of the MC's properties at 1 AU and the dynamic evolution of CMEs from the Sun to interplanetary space.
Wang, Yuming; Shen, Chenglong; Liu, Rui; Wang, S
2015-01-01
Magnetic clouds (MCs) are the interplanetary counterparts of coronal mass ejections (CMEs), and usually modeled by a flux rope. By assuming the quasi-steady evolution and self-similar expansion, we introduce three types of global motion into a cylindrical force-free flux rope model, and developed a new velocity-modified model for MCs. The three types of the global motion are the linear propagating motion away from the Sun, the expanding and the poloidal motion with respect to the axis of the MC. The model is applied to 72 MCs observed by Wind spacecraft to investigate the properties of the plasma motion of MCs. First, we find that some MCs had a significant propagation velocity perpendicular to the radial direction, suggesting the direct evidence of the CME's deflected propagation and/or rotation in interplanetary space. Second, we confirm the previous results that the expansion speed is correlated with the radial propagation speed and most MCs did not expand self-similarly at 1 AU. In our statistics, about 6...
Border extrapolation using fractal attributes in remote sensing images
Cipolletti, M. P.; Delrieux, C. A.; Perillo, G. M. E.; Piccolo, M. C.
2014-01-01
In management, monitoring and rational use of natural resources the knowledge of precise and updated information is essential. Satellite images have become an attractive option for quantitative data extraction and morphologic studies, assuring a wide coverage without exerting negative environmental influence over the study area. However, the precision of such practice is limited by the spatial resolution of the sensors and the additional processing algorithms. The use of high resolution imagery (i.e., Ikonos) is very expensive for studies involving large geographic areas or requiring long term monitoring, while the use of less expensive or freely available imagery poses a limit in the geographic accuracy and physical precision that may be obtained. We developed a methodology for accurate border estimation that can be used for establishing high quality measurements with low resolution imagery. The method is based on the original theory by Richardson, taking advantage of the fractal nature of geographic features. The area of interest is downsampled at different scales and, at each scale, the border is segmented and measured. Finally, a regression of the dependence of the measured length with respect to scale is computed, which then allows for a precise extrapolation of the expected length at scales much finer than the originally available. The method is tested with both synthetic and satellite imagery, producing accurate results in both cases.
Delayed inhibition of an anticipatory action during motion extrapolation
Directory of Open Access Journals (Sweden)
Riek Stephan
2010-04-01
Full Text Available Abstract Background Continuous visual information is important for movement initiation in a variety of motor tasks. However, even in the absence of visual information people are able to initiate their responses by using motion extrapolation processes. Initiation of actions based on these cognitive processes, however, can demand more attentional resources than that required in situations in which visual information is uninterrupted. In the experiment reported we sought to determine whether the absence of visual information would affect the latency to inhibit an anticipatory action. Methods The participants performed an anticipatory timing task where they were instructed to move in synchrony with the arrival of a moving object at a determined contact point. On 50% of the trials, a stop sign appeared on the screen and it served as a signal for the participants to halt their movements. They performed the anticipatory task under two different viewing conditions: Full-View (uninterrupted and Occluded-View (occlusion of the last 500 ms prior to the arrival at the contact point. Results The results indicated that the absence of visual information prolonged the latency to suppress the anticipatory movement. Conclusion We suggest that the absence of visual information requires additional cortical processing that creates competing demand for neural resources. Reduced neural resources potentially causes increased reaction time to the inhibitory input or increased time estimation variability, which in combination would account for prolonged latency.
Institute of Scientific and Technical Information of China (English)
Qiumei Huang; Yidu Yang
2008-01-01
In this paper,we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms.Using this extrapolation formula,we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues.Some numerical experiments are carried out to demonstrate the effectiveness of OUr new method and to confirm our theoretical results.
Measurement of fatty acid oxidation: validation of isotopic equilibrium extrapolation
Energy Technology Data Exchange (ETDEWEB)
Robin, A.P.; Jeevanandam, M.; Elwyn, D.H.; Askanazi, J.; Kinney, J.M.
1989-01-01
Measurement of whole body substrate oxidation requires prolonged isotope infusion to attain plateau specific activity (SA) of expired CO/sub 2/. We have investigated in 13 hospitalized patients a technique whereby plateau /sup 14/CO/sub 2/ SA is extrapolated using computer curve fitting based upon the early exponential rise. A primed-constant infusion of albumin-bound 1-/sup 14/C-palmitate was continued for 260 minutes with isotope priming of the secondary bicarbonate pool at 70 minutes. Plasma free fatty acid (FFA) SA reached steady state by 40 minutes and was 91% +/- 4% (SE) of values obtained at 190 to 260 minutes. At 70 minutes /sup 14/CO/sub 2/ SA reached only 44% +/- 1% of the 190 to 260 minute values, which were consistently at plateau. The predicted steady state /sup 14/CO/sub 2/ SA from the 40 to 70 minute curves and the FFA oxidation rates calculated from those values were 94% +/- 2% and 102% +/- 4%, respectively, of values measured at steady state (190 to 260 minutes). The relationship between predicted and measured values approximated the line of identity for /sup 14/CO/sub 2/ SA (y = 0.90x + 0.14, r = .98, P less than .001) and FFA oxidation (y = 1.02x, r = .98, P less than .001). The results suggest that FFA oxidation can be accurately calculated using a short infusion of labeled FFA without bicarbonate pool priming, thus avoiding overpriming or underpriming and possibly allowing multiple studies and diminished radioisotope exposure.
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
NOLB: Nonlinear Rigid Block Normal Mode Analysis Method
Hoffmann, Alexandre; Grudinin, Sergei
2017-01-01
International audience; We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velo...
Extrapolating human judgments from skip-gram vector representations of word meaning.
Hollis, Geoff; Westbury, Chris; Lefsrud, Lianne
2017-08-01
There is a growing body of research in psychology that attempts to extrapolate human lexical judgments from computational models of semantics. This research can be used to help develop comprehensive norm sets for experimental research, it has applications to large-scale statistical modelling of lexical access and has broad value within natural language processing and sentiment analysis. However, the value of extrapolated human judgments has recently been questioned within psychological research. Of primary concern is the fact that extrapolated judgments may not share the same pattern of statistical relationship with lexical and semantic variables as do actual human judgments; often the error component in extrapolated judgments is not psychologically inert, making such judgments problematic to use for psychological research. We present a new methodology for extrapolating human judgments that partially addresses prior concerns of validity. We use this methodology to extrapolate human judgments of valence, arousal, dominance, and concreteness for 78,286 words. We also provide resources for users to extrapolate these human judgments for three million English words and short phrases. Applications for large sets of extrapolated human judgments are demonstrated and discussed.
Load extrapolations based on measurements from an offshore wind turbine at alpha ventus
Lott, Sarah; Cheng, Po Wen
2016-09-01
Statistical extrapolations of loads can be used to estimate the extreme loads that are supposed to occur on average once in a given return period. Load extrapolations of extreme loads recorded for a period of three years at different measurement positions of an offshore wind turbine at the alpha ventus offshore test field have been performed. The difficulties that arise when using measured instead of simulated extreme loads in order to determine 50-year return loads will be discussed in detail. The main challenge are outliers in the databases that have a significant influence on the extrapolated extreme loads. Results of the short- and longterm extreme load extrapolations, comprising different methods for the extreme load extraction, the choice of the statistical distribution function as well as the fitting method are presented. Generally, load extrapolation with measurement data is possible, but care should be taken in terms of the selection of the database and the choice of the distribution function and fitting method.
Can Pearlite form Outside of the Hultgren Extrapolation of the Ae3 and Acm Phase Boundaries?
Aranda, M. M.; Rementeria, R.; Capdevila, C.; Hackenberg, R. E.
2016-02-01
It is usually assumed that ferrous pearlite can form only when the average austenite carbon concentration C 0 lies between the extrapolated Ae3 ( γ/ α) and Acm ( γ/ θ) phase boundaries (the "Hultgren extrapolation"). This "mutual supersaturation" criterion for cooperative lamellar nucleation and growth is critically examined from a historical perspective and in light of recent experiments on coarse-grained hypoeutectoid steels which show pearlite formation outside the Hultgren extrapolation. This criterion, at least as interpreted in terms of the average austenite composition, is shown to be unnecessarily restrictive. The carbon fluxes evaluated from Brandt's solution are sufficient to allow pearlite growth both inside and outside the Hultgren Extrapolation. As for the feasibility of the nucleation events leading to pearlite, the only criterion is that there are some local regions of austenite inside the Hultgren Extrapolation, even if the average austenite composition is outside.
Strong, James Asa; Elliott, Michael
2017-03-15
The reporting of ecological phenomena and environmental status routinely required point observations, collected with traditional sampling approaches to be extrapolated to larger reporting scales. This process encompasses difficulties that can quickly entrain significant errors. Remote sensing techniques offer insights and exceptional spatial coverage for observing the marine environment. This review provides guidance on (i) the structures and discontinuities inherent within the extrapolative process, (ii) how to extrapolate effectively across multiple spatial scales, and (iii) remote sensing techniques and data sets that can facilitate this process. This evaluation illustrates that remote sensing techniques are a critical component in extrapolation and likely to underpin the production of high-quality assessments of ecological phenomena and the regional reporting of environmental status. Ultimately, is it hoped that this guidance will aid the production of robust and consistent extrapolations that also make full use of the techniques and data sets that expedite this process. Copyright © 2017 Elsevier Ltd. All rights reserved.
Fang, Jun; Song, Haifeng; Wang, Han
2016-01-01
Wavefunction extrapolation greatly reduces the number of self-consistent field (SCF) iterations and thus the overall computational cost of Born-Oppenheimer molecular dynamics (BOMD) that is based on the Kohn-Sham density functional theory. Going against the intuition that the higher order of extrapolation possesses a better accuracy, we demonstrate, from both theoretical and numerical perspectives, that the extrapolation accuracy firstly increases and then decreases with respect to the order, and an optimal extrapolation order in terms of minimal number of SCF iterations always exists. We also prove that the optimal order tends to be larger when using larger MD time steps or more strict SCF convergence criteria. By example BOMD simulations of a solid copper system, we show that the optimal extrapolation order covers a broad range when varying the MD time step or the SCF convergence criterion. Therefore, we suggest the necessity for BOMD simulation packages to open the user interface and to provide more choice...
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Chen, Yuan; Liu, Liling; Nguyen, Khanh; Fretland, Adrian J
2011-03-01
Reaction phenotyping using recombinant human cytochromes P450 (P450) has great utility in early discovery. However, to fully realize the advantages of using recombinant expressed P450s, the extrapolation of data from recombinant systems to human liver microsomes (HLM) is required. In this study, intersystem extrapolation factors (ISEFs) were established for CYP1A2, CYP2C8, CYP2C9, CYP2C19, CYP2D6, and CYP3A4 using 11 probe substrates, based on substrate depletion and/or metabolite formation kinetics. The ISEF values for CYP2C9, CYP2D6, and CYP3A4 determined using multiple substrates were similar across substrates. When enzyme kinetics of metabolite formation for CYP1A2, 2C9, 2D6, and 3A4 were used, the ISEFs determined were generally within 2-fold of that determined on the basis of substrate depletion. Validation of ISEFs was conducted using 10 marketed drugs by comparing the extrapolated data with published data. The major isoforms responsible for the metabolism were identified, and the contribution of the predominant P450s was similar to that of previously reported data. In addition, phenotyping data from internal compounds, extrapolated using the rhP450-ISEF method, were comparable to those obtained using an HLM-based inhibition assay approach. Moreover, the intrinsic clearance (CL(int)) calculated from extrapolated rhP450 data correlated well with measured HLM CL(int). The ISEF method established in our laboratory provides a convenient tool in early reaction phenotyping for situations in which the HLM-based inhibition approach is limited by low turnover and/or unavailable metabolite formation. Furthermore, this method allows for quantitative extrapolation of HLM intrinsic clearance from rhP450 phenotyping data simultaneously to obtaining the participating metabolizing enzymes.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
An extrapolation scheme for solid-state NMR chemical shift calculations
Nakajima, Takahito
2017-06-01
Conventional quantum chemical and solid-state physical approaches include several problems to accurately calculate solid-state nuclear magnetic resonance (NMR) properties. We propose a reliable computational scheme for solid-state NMR chemical shifts using an extrapolation scheme that retains the advantages of these approaches but reduces their disadvantages. Our scheme can satisfactorily yield solid-state NMR magnetic shielding constants. The estimated values have only a small dependence on the low-level density functional theory calculation with the extrapolation scheme. Thus, our approach is efficient because the rough calculation can be performed in the extrapolation scheme.
Chiral extrapolation of nucleon axial charge gA in effective field theory
Li, Hong-na; Wang, P.
2016-12-01
The extrapolation of nucleon axial charge gA is investigated within the framework of heavy baryon chiral effective field theory. The intermediate octet and decuplet baryons are included in the one loop calculation. Finite range regularization is applied to improve the convergence in the quark-mass expansion. The lattice data from three different groups are used for the extrapolation. At physical pion mass, the extrapolated gA are all smaller than the experimental value. Supported by National Natural Science Foundation of China (11475186) and Sino-German CRC 110 (NSFC 11621131001)
Frequency Extrapolation by Floating Genetic Algorithm Based on GTD Model for Radar Cross Section
Institute of Scientific and Technical Information of China (English)
YANG Zhenglong; FANG Dagang; SHENG Weixing; LIU Tiejun; ZHUANG Jing
2001-01-01
A frequency extrapolation scheme isdeveloped to effectively predict radar cross section us-ing floating genetic algorithm based on the GTD (ge-ometry theory of diffraction) model. The parameter-ized model to extrapolate the frequency response tohigher (or lower) frequency band is used and somepractical targets are calculated to test the effective-ness of the method. The influence of extrapolationon the range profile is studied. Furthermore, the re-lationship between the fitting precision and extrap-olation ability is considered. Different extrapolationprocedures are discussed.
Yurkin, Maxim A; Hoekstra, Alfons G
2006-01-01
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many different discretizations. The quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for one test case.
DEFF Research Database (Denmark)
Toft, Henrik Stensgaard; Naess, Arvid; Saha, Nilanjan;
2011-01-01
The paper explores a recently developed method for statistical response load (load effect) extrapolation for application to extreme response of wind turbines during operation. The extrapolation method is based on average conditional exceedance rates and is in the present implementation restricted......-of-plane bending moment and the tower mudline bending moment of a pitch-controlled wind turbine. In general, the results show that the method based on average conditional exceedance rates predicts the extrapolated characteristic response loads at the individual mean wind speeds well and results in more consistent...
Extrapolation from , vector-valued inequalities and applications in the Schrödinger settings
Tang, Lin
2014-04-01
In this paper, we generalize the A ∞ extrapolation theorem ( Cruz-Uribe-Martell-Pérez, Extrapolation from A ∞ weights and applications, J. Funct. Anal. 213 (2004), 412-439) and the A p extrapolation theorem of Rubio de Francia to Schrödinger settings. In addition, we also establish weighted vector-valued inequalities for Schrödinger-type maximal operators by using weights belonging to which includes A p . As applications, we establish weighted vector-valued inequalities for some Schrödinger-type operators.
Inertial Lévy Flight with Nonlinear Friction
Institute of Scientific and Technical Information of China (English)
L(U) Yan; BAO Jing-Dong
2011-01-01
Lévy Bight with nonlinear friction is studied. Due to the occurrence of extremely long jumps Levy flights often possess infinite variance and are physically problematic if describing the dynamics of a particle of finite mass. However, by introducing nonlinear friction, we show that the stochastic process subject to Levy noise exhibits finite variance, leading to a well-defined .kinetic energy. In the force-free fiIeld, normal diffusion behavior is observed and the diffusion coefficient decreases with Levy index μ. Furthermore, we find a kinetic resonance of the particle in the harmonic potential to the external oscillating field in the generally underdamped region and the value of the linear friction γo determines whether resonance occurs or not.%Lévy flight with nonlinear friction is studied.Due to the occurrence of extremely long jumps Lévy flights often possess infinite variance and are physically problematic if describing the dynamics of a particle of finite mass.However,by introducing nonlinear friction,we show that the stochastic process subject to Lévy noise exhibits finite variance,leading to a well-defined kinetic energy.In the force-free field,normal diffusion behavior is observed and the diffusion coefficient decreases with Lévy index μ.Furthermore,we find a kinetic resonance of the particle in the harmonic potential to the external oscillating field in the generally underdamped region and the value of the linear friction γ0 determines whether resonance occurs or not.The stable Lévy process,often called the Lévy flight,is used to model various phenomena such as self-diffusion in micelle systems,[1] special problems in reaction dynamics,[2] and even the flight of an albatross.
Refinement of approximated solution of nonlinear differential equation of second order
Energy Technology Data Exchange (ETDEWEB)
Zhidkov, E.P.; Sidorova, O.V.
1982-01-01
The boundary problem for nonlinear differential equation of the second order is considered. The problem is assumed to have a unique solution, stable over the right part. It was proved that if the step of the net is small, then the corresponding difference value problem has a unique solution, stable over the right part. Expansion over degrees of discrediting step for approximate solutions is established. The expansion allows one to apply the Richardson type extrapolation. Efficiency of extrapolation is illustrated by numerical example.
Cross-species extrapolation of toxicity data from limited surrogate test organisms to all wildlife with potential of chemical exposure remains a key challenge in ecological risk assessment. A number of factors affect extrapolation, including the chemical exposure, pharmacokinetic...
Melting of "non-magic" argon clusters and extrapolation to the bulk limit
Senn, Florian; Wiebke, Jonas; Schumann, Ole; Gohr, Sebastian; Schwerdtfeger, Peter; Pahl, Elke
2014-01-01
The melting of argon clusters ArN is investigated by applying a parallel-tempering Monte Carlo algorithm for all cluster sizes in the range from 55 to 309 atoms. Extrapolation to the bulk gives a melting temperature of 85.9 K in good agreement with the previous value of 88.9 K using only Mackay icosahedral clusters for the extrapolation [E. Pahl, F. Calvo, L. Koči, and P. Schwerdtfeger, "Accurate melting temperatures for neon and argon from ab initio Monte Carlo simulations," Angew. Chem., Int. Ed. 47, 8207 (2008)]. Our results for argon demonstrate that for the extrapolation to the bulk one does not have to restrict to magic number cluster sizes in order to obtain good estimates for the bulk melting temperature. However, the extrapolation to the bulk remains a problem, especially for the systematic selection of suitable cluster sizes.
[Effects of spatial heterogeneity on spatial extrapolation of sampling plot data].
Liang, Yu; He, Hong-Shi; Hu, Yuan-Man; Bu, Ren-Cang
2012-01-01
By using model combination method, this paper simulated the changes of response variable (tree species distribution area at landscape level under climate change) under three scenarios of environmental spatial heterogeneous level, analyzed the differentiation of simulated results under different scenarios, and discussed the effects of environmental spatial heterogeneity on the larger spatial extrapolation of the tree species responses to climate change observed in sampling plots. For most tree species, spatial heterogeneity had little effects on the extrapolation from plot scale to class scale; for the tree species insensitive to climate warming and the azonal species, spatial heterogeneity also had little effects on the extrapolation from plot-scale to zonal scale. By contrast, for the tree species sensitive to climate warming, spatial heterogeneity had effects on the extrapolation from plot scale to zonal scale, and the effects could be varied under different scenarios.
The extrapolation of creep rupture data by PD6605 - An independent case study
Energy Technology Data Exchange (ETDEWEB)
Bolton, J., E-mail: john.bolton@uwclub.net [65 Fisher Avenue, Rugby, Warks CV22 5HW (United Kingdom)
2011-04-15
The worked example presented in BSI document PD6605-1:1998, to illustrate the selection, validation and extrapolation of a creep rupture model using statistical analysis, was independently examined. Alternative rupture models were formulated and analysed by the same statistical methods, and were shown to represent the test data more accurately than the original model. Median rupture lives extrapolated from the original and alternative models were found to diverge widely under some conditions of practical interest. The tests prescribed in PD6605 and employed to validate the original model were applied to the better of the alternative models. But the tests were unable to discriminate between the two, demonstrating that these tests fail to ensure reliability in extrapolation. The difficulties of determining when a model is sufficiently reliable for use in extrapolation are discussed and some proposals are made.
Optimal channels of the Garvey-Kelson mass relations in extrapolation
Bao, Man; He, Zeng; Cheng, YiYuan; Zhao, YuMin; Arima, Akito
2017-02-01
Garvey-Kelson mass relations connect nuclear masses of neighboring nuclei within high accuracy, and provide us with convenient tools in predicting unknown masses by extrapolations from existent experimental data. In this paper we investigate optimal "channels" of the Garvey-Kelson relations in extrapolation to the unknown regions, and tabulate our predicted masses by using these optimized channels of the Garvey-Kelson relations.
Wadsworth, Ian; Jaki, Thomas; Sills, Graeme J; Appleton, Richard; Cross, J Helen; Marson, Anthony G; Martland, Tim; McLellan, Ailsa; Smith, Philip E. M.; Pellock, John M; Hampson, Lisa V.
2016-01-01
Data from clinical trials in adults, extrapolated to predict benefits in paediatric patients, could result in fewer or smaller trials being required to obtain a new drug licence for paediatrics. This article outlines the place of such extrapolation in the development of drugs for use in paediatric epilepsies. Based on consensus expert opinion, a proposal is presented for a new paradigm for the clinical development of drugs for focal epilepsies. Phase I data should continue to be collected in ...
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Bobin, C; Thiam, C; Bouchard, J
2016-03-01
At LNE-LNHB, a liquid scintillation (LS) detection setup designed for Triple to Double Coincidence Ratio (TDCR) measurements is also used in the β-channel of a 4π(LS)β-γ coincidence system. This LS counter based on 3 photomultipliers was first modeled using the Monte Carlo code Geant4 to enable the simulation of optical photons produced by scintillation and Cerenkov effects. This stochastic modeling was especially designed for the calculation of double and triple coincidences between photomultipliers in TDCR measurements. In the present paper, this TDCR-Geant4 model is extended to 4π(LS)β-γ coincidence counting to enable the simulation of the efficiency-extrapolation technique by the addition of a γ-channel. This simulation tool aims at the prediction of systematic biases in activity determination due to eventual non-linearity of efficiency-extrapolation curves. First results are described in the case of the standardization (59)Fe. The variation of the γ-efficiency in the β-channel due to the Cerenkov emission is investigated in the case of the activity measurements of (54)Mn. The problem of the non-linearity between β-efficiencies is featured in the case of the efficiency tracing technique for the activity measurements of (14)C using (60)Co as a tracer.
In situ LTE exposure of the general public: Characterization and extrapolation.
Joseph, Wout; Verloock, Leen; Goeminne, Francis; Vermeeren, Günter; Martens, Luc
2012-09-01
In situ radiofrequency (RF) exposure of the different RF sources is characterized in Reading, United Kingdom, and an extrapolation method to estimate worst-case long-term evolution (LTE) exposure is proposed. All electric field levels satisfy the International Commission on Non-Ionizing Radiation Protection (ICNIRP) reference levels with a maximal total electric field value of 4.5 V/m. The total values are dominated by frequency modulation (FM). Exposure levels for LTE of 0.2 V/m on average and 0.5 V/m maximally are obtained. Contributions of LTE to the total exposure are limited to 0.4% on average. Exposure ratios from 0.8% (LTE) to 12.5% (FM) are obtained. An extrapolation method is proposed and validated to assess the worst-case LTE exposure. For this method, the reference signal (RS) and secondary synchronization signal (S-SYNC) are measured and extrapolated to the worst-case value using an extrapolation factor. The influence of the traffic load and output power of the base station on in situ RS and S-SYNC signals are lower than 1 dB for all power and traffic load settings, showing that these signals can be used for the extrapolation method. The maximal extrapolated field value for LTE exposure equals 1.9 V/m, which is 32 times below the ICNIRP reference levels for electric fields.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Nonlinear dynamics by mode superposition
Energy Technology Data Exchange (ETDEWEB)
Nickell, R.E.
1976-01-01
A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly. The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matric half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Mueller, David S.
2013-04-01
Selection of the appropriate extrapolation methods for computing the discharge in the unmeasured top and bottom parts of a moving-boat acoustic Doppler current profiler (ADCP) streamflow measurement is critical to the total discharge computation. The software tool, extrap, combines normalized velocity profiles from the entire cross section and multiple transects to determine a mean profile for the measurement. The use of an exponent derived from normalized data from the entire cross section is shown to be valid for application of the power velocity distribution law in the computation of the unmeasured discharge in a cross section. Selected statistics are combined with empirically derived criteria to automatically select the appropriate extrapolation methods. A graphical user interface (GUI) provides the user tools to visually evaluate the automatically selected extrapolation methods and manually change them, as necessary. The sensitivity of the total discharge to available extrapolation methods is presented in the GUI. Use of extrap by field hydrographers has demonstrated that extrap is a more accurate and efficient method of determining the appropriate extrapolation methods compared with tools currently (2012) provided in the ADCP manufacturers' software.
Choice of order and extrapolation method in Aarseth-type N-body algorithms
Press, William H.; Spergel, David N.
1988-02-01
The force-versus-time history of a typical particle in a 50-body King model is taken as input data, and its 'extrapolatability' is measured. Extrapolatability means how far the force can be extrapolated, measured in units of a locally defined rate-of-change time scale, and still be within a specified fractional accuracy of the true values. Greater extrapolatability means larger step size, hence greater efficiency, in an Aarseth-type N-body code. Extrapolatability is found to depend systematically on the order of the extrapolation method, but it goes to a finite limit in the limit of large order. A formula for choosing the optimal (most efficient) order for any desired accuracy is given; higher orders than are presently in use are indicated. Neither rational function extrapolation nor a somewhat vector-regularized polynomial method is found to be systematically better than component-wise polynomial extrapolation, indicating that extrapolatability can be viewed as an intrinsic property of the underlying N-body forces, independent of the extrapolation method.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
The influence of an extrapolation chamber over the low energy X-ray beam radiation field
Energy Technology Data Exchange (ETDEWEB)
Tanuri de F, M. T.; Da Silva, T. A., E-mail: mttf@cdtn.br [Centro de Desenvolvimento da Tecnologia Nuclear / CNEN, Av. Pte. Antonio Carlos 6627, 31270-901 Pampulha, Belo Horizonte, Minas Gerais (Brazil)
2016-10-15
The extrapolation chambers are detectors whose sensitive volume can be modified by changing the distance between the electrodes and has been widely used for beta particles primary measurement system. In this work, was performed a PTW 23392 extrapolation chamber Monte Carlo simulation, by mean the MCNPX code. Although the sensitive volume of an extrapolation chamber can be reduced to very small size, their packaging is large enough to modify the radiation field and change the absorbed dose measurements values. Experiments were performed to calculate correction factors for this purpose. The validation of the Monte Carlo model was done by comparing the spectra obtained with a CdTe detector according to the ISO 4037 criteria. Agreements smaller than 5% for half value layers, 10% for spectral resolution and 1% for mean energy, were found. It was verified that the correction factors are dependent of the X-ray beam quality. (Author)
DEFF Research Database (Denmark)
Ambühl, Simon; Sterndorff, Martin; Sørensen, John Dalsgaard
2014-01-01
Mooring systems for floating wave energy converters (WECs) are a major cost driver. Failure of mooring systems often occurs due to extreme loads. This paper introduces an extrapolation method for extreme response which accounts for the control system of a WEC that controls the loads onto the stru......Mooring systems for floating wave energy converters (WECs) are a major cost driver. Failure of mooring systems often occurs due to extreme loads. This paper introduces an extrapolation method for extreme response which accounts for the control system of a WEC that controls the loads onto...... the structure and the harvested power of the device as well as the fact that extreme loads may occur during operation and not at extreme wave states when the device is in storm protection mode. The extrapolation method is based on shortterm load time series and applied to a case study where up-scaled surge load...
An extrapolation approach for aeroengine’s transient control law design
Institute of Scientific and Technical Information of China (English)
Kong Xiangxing; Wang Xi; Tan Daoliang; He Ai; Liu Yue
2013-01-01
Transient control law ensures that the aeroengine transits to the command operating state rapidly and reliably. Most of the existing approaches for transient control law design have complicated principle and arithmetic. As a result, those approaches are not convenient for applica-tion. This paper proposes an extrapolation approach based on the set-point parameters to construct the transient control law, which has a good practicability. In this approach, the transient main fuel control law for acceleration and deceleration process is designed based on the main fuel flow on steady operating state. In order to analyze the designing feature of the extrapolation approach, the simulation results of several different transient control laws designed by the same approach are compared together. The analysis indicates that the aeroengine has a good performance in the transient process and the designing feature of the extrapolation approach conforms to the elements of the turbofan aeroengine.
The optimized expansion based low-rank method for wavefield extrapolation
Wu, Zedong
2014-03-01
Spectral methods are fast becoming an indispensable tool for wavefield extrapolation, especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain extrapolation operator efficiently. To solve this problem, we evaluated an optimized expansion method that can approximate this operator with a low-rank variable separation representation. The rank defines the number of inverse Fourier transforms for each time extrapolation step, and thus, the lower the rank, the faster the extrapolation. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low-rank representation. As a result, we obtain lower rank representations compared with the standard low-rank method within reasonable accuracy and thus cheaper extrapolations. Additional bounds set on the range of propagated wavenumbers to adhere to the physical wave limits yield unconditionally stable extrapolations regardless of the time step. An application on the BP model provided superior results compared to those obtained using the decomposition approach. For transversely isotopic media, because we used the pure P-wave dispersion relation, we obtained solutions that were free of the shear wave artifacts, and the algorithm does not require that n > 0. In addition, the required rank for the optimization approach to obtain high accuracy in anisotropic media was lower than that obtained by the decomposition approach, and thus, it was more efficient. A reverse time migration result for the BP tilted transverse isotropy model using this method as a wave propagator demonstrated the ability of the algorithm.
Jaffrin, M Y; Maasrani, M; Le Gourrier, A; Boudailliez, B
1997-05-01
A method is presented for monitoring the relative variation of extracellular and intracellular fluid volumes using a multifrequency impedance meter and the Cole-Cole extrapolation technique. It is found that this extrapolation is necessary to obtain reliable data for the resistance of the intracellular fluid. The extracellular and intracellular resistances can be approached using frequencies of, respectively, 5 kHz and 1000 kHz, but the use of 100 kHz leads to unacceptable errors. In the conventional treatment the overall relative variation of intracellular resistance is found to be relatively small.
An Extrapolation Method of Vector Magnetic Field via Surface Integral Technique
Institute of Scientific and Technical Information of China (English)
YAN Hui; XIAO Chang-han; ZHOU Guo-hua
2009-01-01
According to the integral relationship between the vector magnetic flux density on a spatial point and that over a closed surface around magnetic sources, a technique for the extrapolation of vector magnetic field of a ferromagnetic object is given without computing scalar potential and its gradient. The vector magnetic flux density on a remote spatial point can be extrapolated by surface integral from the vector values over a closed measureed surface around the ferromagnetic object. The correctness of the technique testified by a special example and simulation. The experimented result shows that its accuracy is satisfying and the execution time is less than 1 second.
Zhao, Yi-Gong; Corsini, G.; Dalle Mese, E.
The method of extrapolation of frequency data based on the finite size property of the Gerchberg-Papoulis algorithm is used to address the problem of radar image enhancement. The rate of convergence of the algorithm and the behavior of noise-affected data are discussed. Simulation results show that the convergence rate can be very slow, depending on the ratio of the amount of extrapolated data to that of observed data. This behavior is due to the eigenvalues of the system matrix close to 1.
Extrapolation of Extreme Response for Wind Turbines based on FieldMeasurements
DEFF Research Database (Denmark)
Toft, Henrik Stensgaard; Sørensen, John Dalsgaard
2009-01-01
The characteristic loads on wind turbines during operation are among others dependent on the mean wind speed, the turbulence intensity and the type and settings of the control system. These parameters must be taken into account in the assessment of the characteristic load. The characteristic load...... extrapolation are presented. The first method is based on the same assumptions as the existing method but the statistical extrapolation is only performed for a limited number of mean wind speeds where the extreme load is likely to occur. For the second method the mean wind speeds are divided into storms which...
Extrapolation of neutron-rich isotope cross-sections from projectile fragmentation
Mocko, M; Sun, Z Y; Andronenko, L; Andronenko, M; Delaunay, F; Famiano, M; Friedman, W A; Henzl, V; Henzlova, D; Hui, H; Liu, X D; Lukyanov, S; Lynch, W G; Rogers, A M; Wallace, M S
2007-01-01
Using the measured fragmentation cross sections produced from the 48Ca and 64Ni beams at 140 MeV per nucleon on 9Be and 181Ta targets, we find that the cross sections of unmeasured neutron rich nuclei can be extrapolated using a systematic trend involving the average binding energy. The extrapolated cross-sections will be very useful in planning experiments with neutron rich isotopes produced from projectile fragmentation. The proposed method is general and could be applied to other fragmentation systems including those used in other radioactive ion beam facilities.
A least square extrapolation method for improving solution accuracy of PDE computations
Garbey, M
2003-01-01
Richardson extrapolation (RE) is based on a very simple and elegant mathematical idea that has been successful in several areas of numerical analysis such as quadrature or time integration of ODEs. In theory, RE can be used also on PDE approximations when the convergence order of a discrete solution is clearly known. But in practice, the order of a numerical method often depends on space location and is not accurately satisfied on different levels of grids used in the extrapolation formula. We propose in this paper a more robust and numerically efficient method based on the idea of finding automatically the order of a method as the solution of a least square minimization problem on the residual. We introduce a two-level and three-level least square extrapolation method that works on nonmatching embedded grid solutions via spline interpolation. Our least square extrapolation method is a post-processing of data produced by existing PDE codes, that is easy to implement and can be a better tool than RE for code v...
Uncertainty in vertical extrapolation of wind statistics: shear-exponent and WAsP/EWA methods
DEFF Research Database (Denmark)
Kelly, Mark C.
for uncertainties inherent in determination of (wind) shear exponents, and subsequent vertical extrapolation of wind speeds. The report further outlines application of the theory and results of Kelly & Troen (2014-6) for gauging the uncertainty inherent in use of the European Wind Atlas (EWA) / WAsP method...
Photon neutrino-production in a chiral EFT for nuclei and extrapolation to $E_{\
Zhang, Xilin
2013-01-01
We carry out a series of studies on pion and photon productions in neutrino/electron/photon--nucleus scatterings. The low energy region is investigated by using a chiral effective field theory for nuclei. The results for the neutral current induced photon production ($\\gamma$-NCP) are then extrapolated to neutrino energy $E_{\
Monte Carlo analysis: error of extrapolated thermal conductivity from molecular dynamics simulations
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiang-Yang [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Andersson, Anders David [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-11-07
In this short report, we give an analysis of the extrapolated thermal conductivity of UO2 from earlier molecular dynamics (MD) simulations [1]. Because almost all material properties are functions of temperature, e.g. fission gas release, the fuel thermal conductivity is the most important parameter from a model sensitivity perspective [2]. Thus, it is useful to perform such analysis.
Groeneveld, C.N.; Hakkert, B.C.; Bos, P.M.J.; Heer, C.de
2004-01-01
For human risk assessment, experimental data often have to be extrapolated for exposure duration, which is generally done by means of default values. The purpose of the present study was twofold. First, to derive a statistical distribution for differences in exposure duration that can be used in a p
Wu, G.; Skidmore, A.K.; Leeuw, de J.; Liu, X.; Prins, H.H.T.
2010-01-01
Measurements of photosynthetically active radiation (PAR), which are indispensable for simulating plant growth and productivity, are generally very scarce. This study aimed to compare two extrapolation and one interpolation methods for estimating daily PAR reaching the earth surface within the Poyan
Source-receiver two-way wave extrapolation for prestack exploding-reflector modelling and migration
Alkhalifah, Tariq Ali
2014-10-08
Most modern seismic imaging methods separate input data into parts (shot gathers). We develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield forward or backward in time. This approach has the potential for generating accurate images free of artiefacts associated with conventional approaches. We derive novel high-order partial differential equations in the source-receiver time domain. The fourth-order nature of the extrapolation in time leads to four solutions, two of which correspond to the incoming and outgoing P-waves and reduce to the zero-offset exploding-reflector solutions when the source coincides with the receiver. A challenge for implementing two-way time extrapolation is an essential singularity for horizontally travelling waves. This singularity can be avoided by limiting the range of wavenumbers treated in a spectral-based extrapolation. Using spectral methods based on the low-rank approximation of the propagation symbol, we extrapolate only the desired solutions in an accurate and efficient manner with reduced dispersion artiefacts. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach.
Senjean, Bruno; Alam, Md Mehboob; Knecht, Stefan; Fromager, Emmanuel
2015-01-01
The combination of a recently proposed linear interpolation method (LIM) [Senjean et al., Phys. Rev. A 92, 012518 (2015)], which enables the calculation of weight-independent excitation energies in range-separated ensemble density-functional approximations, with the extrapolation scheme of Savin [J. Chem. Phys. 140, 18A509 (2014)] is presented in this work. It is shown that LIM excitation energies vary quadratically with the inverse of the range-separation parameter mu when the latter is large. As a result, the extrapolation scheme, which is usually applied to long-range interacting energies, can be adapted straightforwardly to LIM. This extrapolated LIM (ELIM) has been tested on a small test set consisting of He, Be, H2 and HeH+. Relatively accurate results have been obtained for the first singlet excitation energies with the typical mu=0.4 value. The improvement of LIM after extrapolation is remarkable, in particular for the doubly-excited 2^1Sigma+g state in the stretched H2 molecule. Three-state ensemble ...
Scaling and chiral extrapolation of pion mass and decay constant with maximally twisted mass QCD
Dimopoulos, P; Herdoiza, G; Jansen, K; Michael, C; Urbach, C
2008-01-01
We present an update of the results for pion mass and pion decay constant as obtained by the ETM collaboration in large scale simulations with maximally twisted mass fermions and two mass degenerate flavours of light quarks. We discuss the continuum, chiral and infinite volume extrapolation of these quantities as well as the extraction of low energy constants, and investigate possible systematic uncertainties.
Kissling, Wilm Daniel; Dalby, Lars; Fløjgaard, Camilla; Lenoir, Jonathan; Sandel, Brody; Sandom, Christopher; Trøjelsgaard, Kristian; Svenning, Jens-Christian
2014-07-01
Ecological trait data are essential for understanding the broad-scale distribution of biodiversity and its response to global change. For animals, diet represents a fundamental aspect of species' evolutionary adaptations, ecological and functional roles, and trophic interactions. However, the importance of diet for macroevolutionary and macroecological dynamics remains little explored, partly because of the lack of comprehensive trait datasets. We compiled and evaluated a comprehensive global dataset of diet preferences of mammals ("MammalDIET"). Diet information was digitized from two global and cladewide data sources and errors of data entry by multiple data recorders were assessed. We then developed a hierarchical extrapolation procedure to fill-in diet information for species with missing information. Missing data were extrapolated with information from other taxonomic levels (genus, other species within the same genus, or family) and this extrapolation was subsequently validated both internally (with a jack-knife approach applied to the compiled species-level diet data) and externally (using independent species-level diet information from a comprehensive continentwide data source). Finally, we grouped mammal species into trophic levels and dietary guilds, and their species richness as well as their proportion of total richness were mapped at a global scale for those diet categories with good validation results. The success rate of correctly digitizing data was 94%, indicating that the consistency in data entry among multiple recorders was high. Data sources provided species-level diet information for a total of 2033 species (38% of all 5364 terrestrial mammal species, based on the IUCN taxonomy). For the remaining 3331 species, diet information was mostly extrapolated from genus-level diet information (48% of all terrestrial mammal species), and only rarely from other species within the same genus (6%) or from family level (8%). Internal and external
Nonlinear magnetohydrodynamics. Progress report, December 15, 1977--December 14, 1978
Energy Technology Data Exchange (ETDEWEB)
Vahala, G.
1978-01-01
Incompressible MHD turbulence is considered for both 2D and 3D plasmas in cylindrical geometry. It is found that for virtually all initial conditions (including quiescent ones) the plasma is nonlinearly unstable in that mean square turbulent velocity fields develop. However, there is a unique stable state of extremal magnetic helicity/energy ratio for which no turbulent fields develop (in 2D with B/sub z/ = const., it is the state of extremal mean square vector potential/energy). It is force free and is just the Taylor state. A conjecture can be put forward (based on a dual cascade argument for resistive MHD) to explain Taylor's hypothesis. In spherical geometry, the stable axisymmetric state is the spheromak.
Nonlinear stabilization of tokamak microturbulence by fast ions
Citrin, J; Garcia, J; Haverkort, J W; Hogeweij, G M D; Jenko, F; Johnson, T; Mantica, P; Pueschel, M J; Told, D; contributors, JET-EFDA
2013-01-01
Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic stabilization. Based on nonlinear gyrokinetic simulations investigating a set of ion heat transport experiments on the JET tokamak, described by Mantica et al. [Phys. Rev. Lett. 107 135004 (2011)], this result explains the experimentally observed ion heat flux and stiffness reduction. These findings are expected to improve the extrapolation of advanced tokamak scenarios to reactor relevant regimes.
Robust Designs for Three Commonly Used Nonlinear Models
Xu, Xiaojian; Chen, Arnold
2011-11-01
In this paper, we study the robust designs for a few nonlinear models, including an exponential model with an intercept, a compartmental model, and a Michaelis-Menten model, when these models are possibly misspecified. The minimax robust designs we considered in this paper are under consideration of not only minimizing the variances but also reducing the possible biases in estimation. Both prediction and extrapolation cases are discussed. The robust designs are found incorporating the approximation of these models with several situations such as homoscedasticity, and heteroscedasticity. Both ordinary and weighted nonlinear least squares methods are utilized.
Levy, Aharon; Cohen, Giora; Gilat, Eran; Kapon, Joseph; Dachir, Shlomit; Abraham, Shlomo; Herskovitz, Miriam; Teitelbaum, Zvi; Raveh, Lily
2007-05-01
The extrapolation from animal data to therapeutic effects in humans, a basic pharmacological issue, is especially critical in studies aimed to estimate the protective efficacy of drugs against nerve agent poisoning. Such efficacy can only be predicted by extrapolation of data from animal studies to humans. In pretreatment therapy against nerve agents, careful dose determination is even more crucial than in antidotal therapy, since excessive doses may lead to adverse effects or performance decrements. The common method of comparing dose per body weight, still used in some studies, may lead to erroneous extrapolation. A different approach is based on the comparison of plasma concentrations at steady state required to obtain a given pharmacodynamic endpoint. In the present study, this approach was applied to predict the prophylactic efficacy of the anticholinergic drug caramiphen in combination with pyridostigmine in man based on animal data. In two species of large animals, dogs and monkeys, similar plasma concentrations of caramiphen (in the range of 60-100 ng/ml) conferred adequate protection against exposure to a lethal-dose of sarin (1.6-1.8 LD(50)). Pharmacokinetic studies at steady state were required to achieve the correlation between caramiphen plasma concentrations and therapeutic effects. Evaluation of total plasma clearance values was instrumental in establishing desirable plasma concentrations and minimizing the number of animals used in the study. Previous data in the literature for plasma levels of caramiphen that do not lead to overt side effects in humans (70-100 ng/ml) enabled extrapolation to expected human protection. The method can be applied to other drugs and other clinical situations, in which human studies are impossible due to ethical considerations. When similar dose response curves are obtained in at least two animal models, the extrapolation to expected therapeutic effects in humans might be considered more reliable.
Directory of Open Access Journals (Sweden)
S. A. Banin
2016-01-01
Full Text Available Forecasting methods, extrapolation ones in particular, are used in health care for medical, biological and clinical research. The author, using accessible internet space, has not met a single publication devoted to extrapolation of financial parameters of health care activities. This determined the relevance of the material presented in the article: based on health care financing dynamics in Russia in 2000–2010 the author examined possibility of application of basic perspective extrapolation methods - moving average, exponential smoothing and least squares. It is hypothesized that all three methods can equally forecast actual public expenditures on health care in medium term in Russia’s current financial and economic conditions. The study result was evaluated in two time periods: within the studied interval and a five-year period. It was found that within the study period all methods have an average relative extrapolation error of 3–5%, which means high precision of the forecast. The study shown a specific feature of the least squares method which were gradually accumulating results so their economic interpretation became possible only in the end of the studied period. That is why the extrapolating results obtained by least squares method are not applicable in an entire study period and rather have a theoretical value. Beyond the study period, however, this feature was found to be the most corresponding to the real situation. It was the least squares method that proved to be the most appropriate for economic interpretation of the forecast results of actual public expenditures on health care. The hypothesis was not confirmed, the author received three differently directed results, while each method had independent significance and its application depended on evaluation study objectives and real social, economic and financial situation in Russian health care system.
How to Appropriately Extrapolate Costs and Utilities in Cost-Effectiveness Analysis.
Bojke, Laura; Manca, Andrea; Asaria, Miqdad; Mahon, Ronan; Ren, Shijie; Palmer, Stephen
2017-05-03
Costs and utilities are key inputs into any cost-effectiveness analysis. Their estimates are typically derived from individual patient-level data collected as part of clinical studies the follow-up duration of which is often too short to allow a robust quantification of the likely costs and benefits a technology will yield over the patient's entire lifetime. In the absence of long-term data, some form of temporal extrapolation-to project short-term evidence over a longer time horizon-is required. Temporal extrapolation inevitably involves assumptions regarding the behaviour of the quantities of interest beyond the time horizon supported by the clinical evidence. Unfortunately, the implications for decisions made on the basis of evidence derived following this practice and the degree of uncertainty surrounding the validity of any assumptions made are often not fully appreciated. The issue is compounded by the absence of methodological guidance concerning the extrapolation of non-time-to-event outcomes such as costs and utilities. This paper considers current approaches to predict long-term costs and utilities, highlights some of the challenges with the existing methods, and provides recommendations for future applications. It finds that, typically, economic evaluation models employ a simplistic approach to temporal extrapolation of costs and utilities. For instance, their parameters (e.g. mean) are typically assumed to be homogeneous with respect to both time and patients' characteristics. Furthermore, costs and utilities have often been modelled to follow the dynamics of the associated time-to-event outcomes. However, cost and utility estimates may be more nuanced, and it is important to ensure extrapolation is carried out appropriately for these parameters.
Bližňák, Vojtěch; Sokol, Zbyněk; Zacharov, Petr
2017-02-01
An evaluation of convective cloud forecasts performed with the numerical weather prediction (NWP) model COSMO and extrapolation of cloud fields is presented using observed data derived from the geostationary satellite Meteosat Second Generation (MSG). The present study focuses on the nowcasting range (1-5 h) for five severe convective storms in their developing stage that occurred during the warm season in the years 2012-2013. Radar reflectivity and extrapolated radar reflectivity data were assimilated for at least 6 h depending on the time of occurrence of convection. Synthetic satellite imageries were calculated using radiative transfer model RTTOV v10.2, which was implemented into the COSMO model. NWP model simulations of IR10.8 μm and WV06.2 μm brightness temperatures (BTs) with a horizontal resolution of 2.8 km were interpolated into the satellite projection and objectively verified against observations using Root Mean Square Error (RMSE), correlation coefficient (CORR) and Fractions Skill Score (FSS) values. Naturally, the extrapolation of cloud fields yielded an approximately 25% lower RMSE, 20% higher CORR and 15% higher FSS at the beginning of the second forecasted hour compared to the NWP model forecasts. On the other hand, comparable scores were observed for the third hour, whereas the NWP forecasts outperformed the extrapolation by 10% for RMSE, 15% for CORR and up to 15% for FSS during the fourth forecasted hour and 15% for RMSE, 27% for CORR and up to 15% for FSS during the fifth forecasted hour. The analysis was completed by a verification of the precipitation forecasts yielding approximately 8% higher RMSE, 15% higher CORR and up to 45% higher FSS when the NWP model simulation is used compared to the extrapolation for the first hour. Both the methods yielded unsatisfactory level of precipitation forecast accuracy from the fourth forecasted hour onward.
SU-D-204-02: BED Consistent Extrapolation of Mean Dose Tolerances
Energy Technology Data Exchange (ETDEWEB)
Perko, Z; Bortfeld, T; Hong, T; Wolfgang, J; Unkelbach, J [Massachusetts General Hospital, Boston, MA (United States)
2016-06-15
Purpose: The safe use of radiotherapy requires the knowledge of tolerable organ doses. For experimental fractionation schemes (e.g. hypofractionation) these are typically extrapolated from traditional fractionation schedules using the Biologically Effective Dose (BED) model. This work demonstrates that using the mean dose in the standard BED equation may overestimate tolerances, potentially leading to unsafe treatments. Instead, extrapolation of mean dose tolerances should take the spatial dose distribution into account. Methods: A formula has been derived to extrapolate mean physical dose constraints such that they are mean BED equivalent. This formula constitutes a modified BED equation where the influence of the spatial dose distribution is summarized in a single parameter, the dose shape factor. To quantify effects we analyzed 14 liver cancer patients previously treated with proton therapy in 5 or 15 fractions, for whom also photon IMRT plans were available. Results: Our work has two main implications. First, in typical clinical plans the dose distribution can have significant effects. When mean dose tolerances are extrapolated from standard fractionation towards hypofractionation they can be overestimated by 10–15%. Second, the shape difference between photon and proton dose distributions can cause 30–40% differences in mean physical dose for plans having the same mean BED. The combined effect when extrapolating proton doses to mean BED equivalent photon doses in traditional 35 fraction regimens resulted in up to 7–8 Gy higher doses than when applying the standard BED formula. This can potentially lead to unsafe treatments (in 1 of the 14 analyzed plans the liver mean dose was above its 32 Gy tolerance). Conclusion: The shape effect should be accounted for to avoid unsafe overestimation of mean dose tolerances, particularly when estimating constraints for hypofractionated regimens. In addition, tolerances established for a given treatment modality cannot
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Sun, Shuyu
2013-06-01
This paper introduces an efficient technique to generate new molecular simulation Markov chains for different temperature and density conditions, which allow for rapid extrapolation of canonical ensemble averages at a range of temperatures and densities different from the original conditions where a single simulation is conducted. Obtained information from the original simulation are reweighted and even reconstructed in order to extrapolate our knowledge to the new conditions. Our technique allows not only the extrapolation to a new temperature or density, but also the double extrapolation to both new temperature and density. The method was implemented for Lennard-Jones fluid with structureless particles in single-gas phase region. Extrapolation behaviors as functions of extrapolation ranges were studied. Limits of extrapolation ranges showed a remarkable capability especially along isochors where only reweighting is required. Various factors that could affect the limits of extrapolation ranges were investigated and compared. In particular, these limits were shown to be sensitive to the number of particles used and starting point where the simulation was originally conducted.
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Source‐receiver two‐way wave extrapolation for prestack exploding‐reflector modeling and migration
Alkhalifah, Tariq Ali
2010-10-17
While most of the modern seismic imaging methods perform imaging by separating input data into parts (shot gathers), we develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield backward in time. While computationally extensive, this approach has the potential of generating accurate images, free of artifacts associated with conventional approaches. We derive novel high‐order partial differential equations in source‐receiver‐time domain. The fourth order nature of the extrapolation in time has four solutions two of which correspond to the ingoing and outgoing P‐waves and reduces to the zero‐offset exploding‐reflector solutions when the source coincides with the receiver. Using asymptotic approximations, we develop an approach to extrapolating the full prestack wavefield forward or backward in time.
Variational procedure for nuclear shell-model calculations and energy-variance extrapolation
Shimizu, Noritaka; Mizusaki, Takahiro; Honma, Michio; Tsunoda, Yusuke; Otsuka, Takaharu
2012-01-01
We discuss a variational calculation for nuclear shell-model calculations and propose a new procedure for the energy-variance extrapolation (EVE) method using a sequence of the approximated wave functions obtained by the variational calculation. The wave functions are described as linear combinations of the parity, angular-momentum projected Slater determinants, the energy of which is minimized by the conjugate gradient method obeying the variational principle. The EVE generally works well using the wave functions, but we found some difficult cases where the EVE gives a poor estimation. We discuss the origin of the poor estimation concerning shape coexistence. We found that the appropriate reordering of the Slater determinants allows us to overcome this difficulty and to reduce the uncertainty of the extrapolation.
{sup 131}I-CRTX internal dosimetry: animal model and human extrapolation
Energy Technology Data Exchange (ETDEWEB)
Andrade, Henrique Martins de; Ferreira, Andrea Vidal; Soares, Marcella Araugio; Silveira, Marina Bicalho; Santos, Raquel Gouvea dos [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN-CNEN-MG), Belo Horizonte, MG (Brazil)], e-mail: hma@cdtn.br
2009-07-01
Snake venoms molecules have been shown to play a role not only in the survival and proliferation of tumor cells but also in the processes of tumor cell adhesion, migration and angiogenesis. {sup 125}I-Crtx, a radiolabeled version of a peptide derived from Crotalus durissus terrificus snake venom, specifically binds to tumor and triggers apoptotic signalling. At the present work, {sup 125}I-Crtx biokinetic data (evaluated in mice bearing Erlich tumor) were treated by MIRD formalism to perform Internal Dosimetry studies. Doses in several organs of mice were determinate, as well as in implanted tumor, for {sup 131}I-Crtx. Doses results obtained for animal model were extrapolated to humans assuming a similar concentration ratio among various tissues between mouse and human. In the extrapolation, it was used human organ masses from Cristy/Eckerman phantom. Both penetrating and non-penetrating radiation from {sup 131}I in the tissue were considered in dose calculations. (author)
Energy Technology Data Exchange (ETDEWEB)
Latychevskaia, Tatiana; Fink, Hans-Werner [Physics Department, University of Zurich, Winterthurerstrasse 190, 8057 Zurich (Switzerland)
2015-01-12
Previously reported crystalline structures obtained by an iterative phase retrieval reconstruction of their diffraction patterns seem to be free from displaying any irregularities or defects in the lattice, which appears to be unrealistic. We demonstrate here that the structure of a nanocrystal including its atomic defects can unambiguously be recovered from its diffraction pattern alone by applying a direct phase retrieval procedure not relying on prior information of the object shape. Individual point defects in the atomic lattice are clearly apparent. Conventional phase retrieval routines assume isotropic scattering. We show that when dealing with electrons, the quantitatively correct transmission function of the sample cannot be retrieved due to anisotropic, strong forward scattering specific to electrons. We summarize the conditions for this phase retrieval method and show that the diffraction pattern can be extrapolated beyond the original record to even reveal formerly not visible Bragg peaks. Such extrapolated wave field pattern leads to enhanced spatial resolution in the reconstruction.
Usage of Empirical-Statical-Dynamical (ESD method for data extrapolation in Tunnel Construction
Directory of Open Access Journals (Sweden)
Zafirovski Zlatko
2016-01-01
Full Text Available This article describes a methodology that shows how it is possible to integrate all these approaches in a problem for extrapolation of the parameters for hydrotechical tunnels. During the design process for tunnels in hydrotechics, one of the main problems is how to extrapolate the deformability and shear strentgh rock mass parameters from the zone of testing to the whole area (volume of interes for interaction analyses between structure abd natural environments. Computers development in recent decades has contributed to the development of numerical calculation method in rock mechanics which enabled new and wider possibilities of stress and deformation calculation. This had significantly stimulated the development of rock mechanics and tunneling as scientific and technical discipline as well as the wider application of research results into practice.
The immunogenicity of biosimilar infliximab: can we extrapolate the data across indications?
Ben-Horin, Shomron; Heap, Graham A; Ahmad, Tariq; Kim, HoUng; Kwon, TaekSang; Chowers, Yehuda
2015-01-01
Biopharmaceuticals or 'biologics' have revolutionized the treatment of many diseases. However, some patients generate an immune response to such drugs, potentially limiting clinical efficacy and safety. Infliximab (Remicade(®)) is a monoclonal antibody used to treat several immune-mediated inflammatory disorders. A biosimilar of infliximab, CT-P13 (Remsima(®), Inflectra(®)), has recently been approved in Europe for all indications in which infliximab is approved. Approval of CT-P13 was based in part on extrapolation of clinical trial data from two indications (rheumatoid arthritis and ankylosing spondylitis) to all other indications, including inflammatory bowel disease. This review discusses the validity of extrapolating immunogenicity data across indications - a process adopted by the EMA as part of their biosimilar approval process - with a focus on CT-P13.
{sup 131}I-SPGP internal dosimetry: animal model and human extrapolation
Energy Technology Data Exchange (ETDEWEB)
Andrade, Henrique Martins de; Ferreira, Andrea Vidal; Soprani, Juliana; Santos, Raquel Gouvea dos [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN-CNEN-MG), Belo Horizonte, MG (Brazil)], e-mail: hma@cdtn.br; Figueiredo, Suely Gomes de [Universidade Federal do Espirito Santo, (UFES), Vitoria, ES (Brazil). Dept. de Ciencias Fisiologicas. Lab. de Quimica de Proteinas
2009-07-01
Scorpaena plumieri is commonly called moreia-ati or manganga and is the most venomous and one of the most abundant fish species of the Brazilian coast. Soprani 2006, demonstrated that SPGP - an isolated protein from S. plumieri fish- possess high antitumoral activity against malignant tumours and can be a source of template molecules for the development (design) of antitumoral drugs. In the present work, Soprani's {sup 125}ISPGP biokinetic data were treated by MIRD formalism to perform Internal Dosimetry studies. Absorbed doses due to the {sup 131}I-SPGP uptake were determinate in several organs of mice, as well as in the implanted tumor. Doses obtained for animal model were extrapolated to humans assuming a similar ratio for various mouse and human tissues. For the extrapolation, it was used human organ masses from Cristy/Eckerman phantom. Both penetrating and non-penetrating radiation from {sup 131}I were considered. (author)
Improving Predictions with Reliable Extrapolation Schemes and Better Understanding of Factorization
More, Sushant N
2016-01-01
We investigate two distinct sources of uncertainty in low-energy nuclear physics calculations and develop ways to account for them. Harmonic oscillator basis expansions are widely used in ab-initio nuclear structure calculations. Finite computational resources usually require that the basis be truncated before observables are fully converged, necessitating reliable extrapolation schemes. We show that a finite oscillator basis effectively imposes a hard-wall boundary condition. We accurately determine the position of the hard-wall as a function of oscillator space parameters, derive extrapolation formulas for the energy and other observables, and discuss the extension of this approach to higher angular momentum. Nucleon knockout reactions have been widely used to study and understand nuclear properties. Such an analysis implicitly assumes that the effects of the probe can be separated from the physics of the target nucleus. This factorization between nuclear structure and reaction components depends on the ren...
Extrapolation modeling of aerosol deposition in human and laboratory rat lungs
Energy Technology Data Exchange (ETDEWEB)
Martonen, T.B.; Zhang, Z.; Yang, Y.
1992-01-01
Laboratory test animals are often used as surrogates in exposure studies to assess the potential threat to human health following inhalation of airborne contaminants. To aid in the interpretation and extrapolation of data to man, dosimetric considerations need to be addressed. Therefore, a mathematical model describing the behavior and fate of inhaled particulate matter within the respiratory tracts of man and rats has been developed. In the computer simulations, the CO2 concentrations of inhalation exposure chamber atmospheres are controlled to produce desired breathing patterns in the rat which mimic human breathing patterns as functions of physical activity levels. Herein, deposition patterns in human and rat lung airways are specifically examined as functions of respiratory intensities and particle parameters. The model provides a basis for the re-evaluation of data from past experiments, and, perhaps most importantly, permits new inhalation exposure tests to be designed and conducted in a sound scientific manner regarding this endpoint: the extrapolation of results to human conditions.
Agarwal, Amit B; McBride, Ali
2016-08-01
The World Health Organization defines a biosimilar as "a biotherapeutic product which is similar in terms of quality, safety and efficacy to an already licensed reference biotherapeutic product." Biosimilars are biologic medical products that are very distinct from small-molecule generics, as their active substance is a biological agent derived from a living organism. Approval processes are highly regulated, with guidance issued by the European Medicines Agency and US Food and Drug Administration. Approval requires a comparability exercise consisting of extensive analytical and preclinical in vitro and in vivo studies, and confirmatory clinical studies. Extrapolation of biosimilars from their original indication to another is a feasible but highly stringent process reliant on rigorous scientific justification. This review focuses on the processes involved in gaining biosimilar approval and extrapolation and details the comparability exercise undertaken in the European Union between originator erythropoietin-stimulating agent, Eprex(®), and biosimilar, Retacrit™.
New allometric scaling relationships and applications for dose and toxicity extrapolation.
Cao, Qiming; Yu, Jimmy; Connell, Des
2014-01-01
Allometric scaling between metabolic rate, size, body temperature, and other biological traits has found broad applications in ecology, physiology, and particularly in toxicology and pharmacology. Basal metabolic rate (BMR) was observed to scale with body size and temperature. However, the mass scaling exponent was increasingly debated whether it should be 2/3, 3/4, or neither, and scaling with body temperature also attracted recent attention. Based on thermodynamic principles, this work reports 2 new scaling relationships between BMR, size, temperature, and biological time. Good correlations were found with the new scaling relationships, and no universal scaling exponent can be obtained. The new scaling relationships were successfully validated with external toxicological and pharmacological studies. Results also demonstrated that individual extrapolation models can be built to obtain scaling exponent specific to the interested group, which can be practically applied for dose and toxicity extrapolations.
Infrared length scale and extrapolations for the no-core shell model
Wendt, K A; Papenbrock, T; Sääf, D
2015-01-01
We precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the $A$-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of $A$ nucleons in the NCSM space to that of $A$ nucleons in a $3(A-1)$-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for $^{6}$Li. We apply our result and perform accurate IR extrapolations for bound states of $^{4}$He, $^{6}$He, $^{6}$Li, $^{7}$Li. We also attempt to extrapolate NCSM results for $^{10}$B and $^{16}$O with bare interactions from chiral effective field theory over tens of MeV.
Yi, Grace Y; He, Wenqing
2012-05-01
It has been well known that ignoring measurement error may result in substantially biased estimates in many contexts including linear and nonlinear regressions. For survival data with measurement error in covariates, there has been extensive discussion in the literature with the focus on proportional hazards (PH) models. Recently, research interest has extended to accelerated failure time (AFT) and additive hazards (AH) models. However, the impact of measurement error on other models, such as the proportional odds model, has received relatively little attention, although these models are important alternatives when PH, AFT, or AH models are not appropriate to fit data. In this paper, we investigate this important problem and study the bias induced by the naive approach of ignoring covariate measurement error. To adjust for the induced bias, we describe the simulation-extrapolation method. The proposed method enjoys a number of appealing features. Its implementation is straightforward and can be accomplished with minor modifications of existing software. More importantly, the proposed method does not require modeling the covariate process, which is quite attractive in practice. As the precise values of error-prone covariates are often not observable, any modeling assumption on such covariates has the risk of model misspecification, hence yielding invalid inferences if this happens. The proposed method is carefully assessed both theoretically and empirically. Theoretically, we establish the asymptotic normality for resulting estimators. Numerically, simulation studies are carried out to evaluate the performance of the estimators as well as the impact of ignoring measurement error, along with an application to a data set arising from the Busselton Health Study. Sensitivity of the proposed method to misspecification of the error model is studied as well.
Hsieh, T C; Chao, Anne
2017-01-01
Measures of phylogenetic diversity are basic tools in many studies of systematic biology. Faith’s PD (sum of branch lengths of a phylogenetic tree connecting all focal species) is the most widely used phylogenetic measure. Like species richness, Faith’s PD based on sampling data is highly dependent on sample size and sample completeness. The sample-size- and sample-coverage-based integration of rarefaction and extrapolation of Faith’s PD was recently developed to make fair comparison across multiple assemblages. However, species abundances are not considered in Faith’s PD. Based on the framework of Hill numbers, Faith’s PD was generalized to a class of phylogenetic diversity measures that incorporates species abundances. In this article, we develop both theoretical formulae and analytic estimators for seamless rarefaction and extrapolation for this class of abundance-sensitive phylogenetic measures, which includes simple transformations of phylogenetic entropy and of quadratic entropy. This work generalizes the previous rarefaction/extrapolation model of Faith’s PD to incorporate species abundance, and also extends the previous rarefaction/extrapolation model of Hill numbers to include phylogenetic differences among species. Thus a unified approach to assessing and comparing species/taxonomic diversity and phylogenetic diversity can be established. A bootstrap method is suggested for constructing confidence intervals around the phylogenetic diversity, facilitating the comparison of multiple assemblages. Our formulation and estimators can be extended to incidence data collected from multiple sampling units. We also illustrate the formulae and estimators using bacterial sequence data from the human distal esophagus and phyllostomid bat data from three habitats.
On the problem of discrete extrapolation of a band-limited signal
Vincenti, Graziano; Volpi, Aldo
1992-01-01
Si considera il sistema lineare equivalente al problema della estrapolazione discreta di un segnale a banda limitata. Si dimostra che la matrice di iterazione del metodo di Gerchberg-Papoulis, metodo iterativo applicato a questo sistema, è una matrice convergente. Si verifica inoltre che la convergenza di tale metodo è cosi lenta da rendere tale metodo praticamente inutilizzabile. We consider the linear system equivalent to the problem of discrete extrapolation of a band-limited signal. We...
Precise Numerical Results of IR-vertex and box integration with Extrapolation Method
Yuasa, F; Fujimoro, J; Hamaguchi, N; Ishikawa, T; Shimizu, Y
2007-01-01
We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an appropriate numerical integration routine with an extrapolation method, together with a multi-precision library, we have obtained integration results which agree with the analytic results to 10 digits even for such a very small photon mass as $10^{-150}$ GeV in the infrared vertex diagram.
On the problem of discrete extrapolation of a band-limited signal
Vincenti, Graziano; Volpi, Aldo
1992-01-01
Si considera il sistema lineare equivalente al problema della estrapolazione discreta di un segnale a banda limitata. Si dimostra che la matrice di iterazione del metodo di Gerchberg-Papoulis, metodo iterativo applicato a questo sistema, è una matrice convergente. Si verifica inoltre che la convergenza di tale metodo è cosi lenta da rendere tale metodo praticamente inutilizzabile. We consider the linear system equivalent to the problem of discrete extrapolation of a band-limited signal. We...
Multi-State Extrapolation of Uv/vis Absorption Spectra with Qm/qm Hybrid Methods
Ren, Sijin; Caricato, Marco
2017-06-01
In this work, we present a simple approach to obtain absorption spectra from hybrid QM/QM calculations. The goal is to obtain reliable spectra for compounds that are too large to be treated entirely at a high level of theory. The approach is based on the extrapolation of the entire absorption spectrum obtained by individual subcalculations. Our program locates the main spectral features in each subcalculation, e.g. band peaks and shoulders, and fits them to Gaussian functions. Each Gaussian is then extrapolated with a formula similar to that of ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics). However, information about individual excitations is not necessary so that difficult state-matching across subcalculations is avoided. This multi-state extrapolation thus requires relatively low implementation effort while affording maximum flexibility in the choice of methods to be combined in the hybrid approach. The test calculations show the efficacy and robustness of this methodology in reproducing the spectrum computed for the entire molecule at a high level of theory.
A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems
Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong
2017-09-01
In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.
Entropy Rate Estimates for Natural Language—A New Extrapolation of Compressed Large-Scale Corpora
Directory of Open Access Journals (Sweden)
Ryosuke Takahira
2016-10-01
Full Text Available One of the fundamental questions about human language is whether its entropy rate is positive. The entropy rate measures the average amount of information communicated per unit time. The question about the entropy of language dates back to experiments by Shannon in 1951, but in 1990 Hilberg raised doubt regarding a correct interpretation of these experiments. This article provides an in-depth empirical analysis, using 20 corpora of up to 7.8 gigabytes across six languages (English, French, Russian, Korean, Chinese, and Japanese, to conclude that the entropy rate is positive. To obtain the estimates for data length tending to infinity, we use an extrapolation function given by an ansatz. Whereas some ansatzes were proposed previously, here we use a new stretched exponential extrapolation function that has a smaller error of fit. Thus, we conclude that the entropy rates of human languages are positive but approximately 20% smaller than without extrapolation. Although the entropy rate estimates depend on the script kind, the exponent of the ansatz function turns out to be constant across different languages and governs the complexity of natural language in general. In other words, in spite of typological differences, all languages seem equally hard to learn, which partly confirms Hilberg’s hypothesis.
A model for the data extrapolation of greenhouse gas emissions in the Brazilian hydroelectric system
Pinguelli Rosa, Luiz; Aurélio dos Santos, Marco; Gesteira, Claudio; Elias Xavier, Adilson
2016-06-01
Hydropower reservoirs are artificial water systems and comprise a small proportion of the Earth’s continental territory. However, they play an important role in the aquatic biogeochemistry and may affect the environment negatively. Since the 90s, as a result of research on organic matter decay in manmade flooded areas, some reports have associated greenhouse gas emissions with dam construction. Pioneering work carried out in the early period challenged the view that hydroelectric plants generate completely clean energy. Those estimates suggested that GHG emissions into the atmosphere from some hydroelectric dams may be significant when measured per unit of energy generated and should be compared to GHG emissions from fossil fuels used for power generation. The contribution to global warming of greenhouse gases emitted by hydropower reservoirs is currently the subject of various international discussions and debates. One of the most controversial issues is the extrapolation of data from different sites. In this study, the extrapolation from a site sample where measurements were made to the complete set of 251 reservoirs in Brazil, comprising a total flooded area of 32 485 square kilometers, was derived from the theory of self-organized criticality. We employed a power law for its statistical representation. The present article reviews the data generated at that time in order to demonstrate how, with the help of mathematical tools, we can extrapolate values from one reservoir to another without compromising the reliability of the results.
Parallel difference schemes with interface extrapolation terms for quasi-linear parabolic systems
Institute of Scientific and Technical Information of China (English)
Guang-wei YUAN; Xu-deng HANG; Zhi-qiang SHENG
2007-01-01
In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed.Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.
Directory of Open Access Journals (Sweden)
Bressler B
2015-06-01
Full Text Available Brian Bressler,1 Theo Dingermann2 1St Paul’s Hospital, University of British Columbia, Vancouver, BC, Canada; 2Institute of Pharmaceutical Biology, Frankfurt, Germany Abstract: Despite their enormous value for our health care system, biopharmaceuticals have become a serious threat to the system itself due to their high cost. Costs may be warranted if the medicine is new and innovative; however, it is no longer an innovation when its patent protection expires. As patents and exclusivities expire on biological drugs, biosimilar products defined as highly similar to reference biologics are being marketed. The goal of biosimilar development is to establish a high degree of biosimilarity, not to reestablish clinical efficacy and safety. Current sophisticated analytical methods allow the detection of even small changes in quality attributes and can therefore enable sensitive monitoring of the batch-to-batch consistency and variability of the manufacturing process. The European Medicines Agency (EMA, US Food and Drug Administration (FDA, and Health Canada have determined that a reduced number of nonclinical and clinical comparative studies can be sufficient for approval with clinical data from the most sensitive indication extrapolated to other indications. Extrapolation of data is a scientifically based principle, guided by specific criteria, and if approved by the EMA, FDA, and/or Health Canada is appropriate. Enablement of extrapolation of data is a core principle of biosimilar development, based on principles of comparability and necessary to fully realize cost savings for these drugs. Keywords: biosimilars, Inflectra, infliximab, pharmacoeconomics, Canada, Europe
Ilieva, T.; Iliev, I.; Pashov, A.
2016-12-01
In the traditional description of electronic states of diatomic molecules by means of molecular constants or Dunham coefficients, one of the important fitting parameters is the value of the zero point energy - the minimum of the potential curve or the energy of the lowest vibrational-rotational level - E00 . Their values are almost always the result of an extrapolation and it may be difficult to estimate their uncertainties, because they are connected not only with the uncertainty of the experimental data, but also with the distribution of experimentally observed energy levels and the particular realization of set of Dunham coefficients. This paper presents a comprehensive analysis based on Monte Carlo simulations, which aims to demonstrate the influence of all these factors on the uncertainty of the extrapolated minimum of the potential energy curve U (Re) and the value of E00 . The very good extrapolation properties of the Dunham coefficients are quantitatively confirmed and it is shown that for a proper estimate of the uncertainties, the ambiguity in the composition of the Dunham coefficients should be taken into account.
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Karslı, Hakan
2006-08-01
Seismic data have still no enough temporal resolution because of band-limited nature of available data even if it is deconvolved. However, lower and higher frequency information belonging to seismic data is missing and it is not directly recovered from seismic data. In this paper, a method originally applied by Honarvar et al. [Honarvar, F., Sheikhzadeh, H., Moles, M., Sinclair, A.N., 2004. Improving the time-resolution and signal-noise ratio of ultrasonic NDE signals. Ultrasonics 41, 755-763.] which is the combination of the most widely used Wiener deconvolution and AR spectral extrapolation in frequency domain is briefly reviewed and is applied to seismic data to improve temporal resolution further. The missing frequency information is optimally recovered by forward and backward extrapolation based on the selection of a high signal-noise ratio (SNR) of signal spectrum deconvolved in signal processing technique. The combination of the two methods is firstly tested on a variety of synthetic examples and then applied to a stacked real trace. The selection of necessary parameters in Wiener filtering and in extrapolation are discussed in detail. It is used an optimum frequency windows between 3 and 10 dB drops by comparing results from these drops, while frequency windows are used as standard between 2.8 and 3.2 dB drops in study of Honarvar et al. [Honarvar, F., Sheikhzadeh, H., Moles, M., Sinclair, A.N., 2004. Improving the time-resolution and signal-noise ratio of ultrasonic NDE signals. Ultrasonics 41, 755-763.]. The results obtained show that the application of the purposed signal processing technique considerably improves temporal resolution of seismic data when compared with the original seismic data. Furthermore, AR based spectral extrapolated data can be almost considered as reflectivity sequence of layered medium. Consequently, the combination of Wiener deconvolution and AR spectral extrapolation can reveal some details of seismic data that cannot be
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
Mirus, Benjamin B.; Halford, Keith; Sweetkind, Don; Fenelon, Joe
2016-08-01
The suitability of geologic frameworks for extrapolating hydraulic conductivity ( K) to length scales commensurate with hydraulic data is difficult to assess. A novel method is presented for evaluating assumed relations between K and geologic interpretations for regional-scale groundwater modeling. The approach relies on simultaneous interpretation of multiple aquifer tests using alternative geologic frameworks of variable complexity, where each framework is incorporated as prior information that assumes homogeneous K within each model unit. This approach is tested at Pahute Mesa within the Nevada National Security Site (USA), where observed drawdowns from eight aquifer tests in complex, highly faulted volcanic rocks provide the necessary hydraulic constraints. The investigated volume encompasses 40 mi3 (167 km3) where drawdowns traversed major fault structures and were detected more than 2 mi (3.2 km) from pumping wells. Complexity of the five frameworks assessed ranges from an undifferentiated mass of rock with a single unit to 14 distinct geologic units. Results show that only four geologic units can be justified as hydraulically unique for this location. The approach qualitatively evaluates the consistency of hydraulic property estimates within extents of investigation and effects of geologic frameworks on extrapolation. Distributions of transmissivity are similar within the investigated extents irrespective of the geologic framework. In contrast, the extrapolation of hydraulic properties beyond the volume investigated with interfering aquifer tests is strongly affected by the complexity of a given framework. Testing at Pahute Mesa illustrates how this method can be employed to determine the appropriate level of geologic complexity for large-scale groundwater modeling.
Mirus, Benjamin B.; Halford, Keith J.; Sweetkind, Donald; Fenelon, Joseph M.
2016-01-01
The suitability of geologic frameworks for extrapolating hydraulic conductivity (K) to length scales commensurate with hydraulic data is difficult to assess. A novel method is presented for evaluating assumed relations between K and geologic interpretations for regional-scale groundwater modeling. The approach relies on simultaneous interpretation of multiple aquifer tests using alternative geologic frameworks of variable complexity, where each framework is incorporated as prior information that assumes homogeneous K within each model unit. This approach is tested at Pahute Mesa within the Nevada National Security Site (USA), where observed drawdowns from eight aquifer tests in complex, highly faulted volcanic rocks provide the necessary hydraulic constraints. The investigated volume encompasses 40 mi3 (167 km3) where drawdowns traversed major fault structures and were detected more than 2 mi (3.2 km) from pumping wells. Complexity of the five frameworks assessed ranges from an undifferentiated mass of rock with a single unit to 14 distinct geologic units. Results show that only four geologic units can be justified as hydraulically unique for this location. The approach qualitatively evaluates the consistency of hydraulic property estimates within extents of investigation and effects of geologic frameworks on extrapolation. Distributions of transmissivity are similar within the investigated extents irrespective of the geologic framework. In contrast, the extrapolation of hydraulic properties beyond the volume investigated with interfering aquifer tests is strongly affected by the complexity of a given framework. Testing at Pahute Mesa illustrates how this method can be employed to determine the appropriate level of geologic complexity for large-scale groundwater modeling.
Scotcher, Daniel; Jones, Christopher; Posada, Maria; Galetin, Aleksandra; Rostami-Hodjegan, Amin
2016-09-01
It is envisaged that application of mechanistic models will improve prediction of changes in renal disposition due to drug-drug interactions, genetic polymorphism in enzymes and transporters and/or renal impairment. However, developing and validating mechanistic kidney models is challenging due to the number of processes that may occur (filtration, secretion, reabsorption and metabolism) in this complex organ. Prediction of human renal drug disposition from preclinical species may be hampered by species differences in the expression and activity of drug metabolising enzymes and transporters. A proposed solution is bottom-up prediction of pharmacokinetic parameters based on in vitro-in vivo extrapolation (IVIVE), mediated by recent advances in in vitro experimental techniques and application of relevant scaling factors. This review is a follow-up to the Part I of the report from the 2015 AAPS Annual Meeting and Exhibition (Orlando, FL; 25th-29th October 2015) which focuses on IVIVE and mechanistic prediction of renal drug disposition. It describes the various mechanistic kidney models that may be used to investigate renal drug disposition. Particular attention is given to efforts that have attempted to incorporate elements of IVIVE. In addition, the use of mechanistic models in prediction of renal drug-drug interactions and potential for application in determining suitable adjustment of dose in kidney disease are discussed. The need for suitable clinical pharmacokinetics data for the purposes of delineating mechanistic aspects of kidney models in various scenarios is highlighted.
Linear extrapolation for prediction of tensile creep compliance of polyvinyl chloride
Institute of Scientific and Technical Information of China (English)
XIE Gang
2005-01-01
The universal creep equation is successful in relating the creep (ε) to the aging time (te), coefficient of retardation time (β), and intrinsic time (to ). This relation was used to treat the creep experimental data for polyvinyl chloride (PVC) specimens at a given stress and different aging times. The βgs found by the "polynomial fitting" method in this work instead of the "middle -point" method reported in the literature. The unified master line was constructed with the treated data and curves according to the universal equation. The master line can be used to predict the long -term creep behavior and lifetime by extrapolating.
Sur l'Extrapolation des Signoux d'Energie Finie a Band Limitee
Charbonniaud, A. L.; Crouzet, J-F.; Gay, R.
1996-01-01
We show that both Papoulis' method and Aizenberg's method for extrapolating finite energy and band limited signals are related to each other, provided that the same setting is used to describe both methods. We study such a setting and give some examples we comment. On montre que les méthodes d'Exploration de signaux d'énergie finie et à bande limitée de Papoulis et d'Aizenberg peuvent être reliées dans un cadre d'étude commun. On étudie ce cadre de travail et on donne quelques exemples com...
Challenges for In vitro to in Vivo Extrapolation of Nanomaterial Dosimetry for Human Risk Assessment
Energy Technology Data Exchange (ETDEWEB)
Smith, Jordan N.
2013-11-01
The proliferation in types and uses of nanomaterials in consumer products has led to rapid application of conventional in vitro approaches for hazard identification. Unfortunately, assumptions pertaining to experimental design and interpretation for studies with chemicals are not generally appropriate for nanomaterials. The fate of nanomaterials in cell culture media, cellular dose to nanomaterials, cellular dose to nanomaterial byproducts, and intracellular fate of nanomaterials at the target site of toxicity all must be considered in order to accurately extrapolate in vitro results to reliable predictions of human risk.
Making the most of what we have: application of extrapolation approaches in wildlife transfer models
Energy Technology Data Exchange (ETDEWEB)
Beresford, Nicholas A.; Barnett, Catherine L.; Wells, Claire [NERC Centre for Ecology and Hydrology, Lancaster Environment Center, Library Av., Bailrigg, Lancaster, LA1 4AP (United Kingdom); School of Environment and Life Sciences, University of Salford, Manchester, M4 4WT (United Kingdom); Wood, Michael D. [School of Environment and Life Sciences, University of Salford, Manchester, M4 4WT (United Kingdom); Vives i Batlle, Jordi [Belgian Nuclear Research Centre, Boeretang 200, 2400 Mol (Belgium); Brown, Justin E.; Hosseini, Ali [Norwegian Radiation Protection Authority, P.O. Box 55, N-1332 Oesteraas (Norway); Yankovich, Tamara L. [International Atomic Energy Agency, Vienna International Centre, 1400, Vienna (Austria); Bradshaw, Clare [Department of Ecology, Environment and Plant Sciences, Stockholm University, SE-10691 (Sweden); Willey, Neil [Centre for Research in Biosciences, University of the West of England, Coldharbour Lane, Frenchay, Bristol BS16 1QY (United Kingdom)
2014-07-01
Radiological environmental protection models need to predict the transfer of many radionuclides to a large number of organisms. There has been considerable development of transfer (predominantly concentration ratio) databases over the last decade. However, in reality it is unlikely we will ever have empirical data for all the species-radionuclide combinations which may need to be included in assessments. To provide default values for a number of existing models/frameworks various extrapolation approaches have been suggested (e.g. using data for a similar organism or element). This paper presents recent developments in two such extrapolation approaches, namely phylogeny and allometry. An evaluation of how extrapolation approaches have performed and the potential application of Bayesian statistics to make best use of available data will also be given. Using a Residual Maximum Likelihood (REML) mixed-model regression we initially analysed a dataset comprising 597 entries for 53 freshwater fish species from 67 sites to investigate if phylogenetic variation in transfer could be identified. The REML analysis generated an estimated mean value for each species on a common scale after taking account of the effect of the inter-site variation. Using an independent dataset, we tested the hypothesis that the REML model outputs could be used to predict radionuclide activity concentrations in other species from the results of a species which had been sampled at a specific site. The outputs of the REML analysis accurately predicted {sup 137}Cs activity concentrations in different species of fish from 27 lakes. Although initially investigated as an extrapolation approach the output of this work is a potential alternative to the highly site dependent concentration ratio model. We are currently applying this approach to a wider range of organism types and different ecosystems. An initial analysis of these results will be presented. The application of allometric, or mass
Institute of Scientific and Technical Information of China (English)
秦开怀; 范刚; 等
1994-01-01
The new algorithms for finding B-Spline or Bezier curves and surfaces intersections using recursive subdivision techniques are presented,which use extrapolating acceleration technique,and have convergent precision of order 2.Matrix method is used to subdivide the curves or surfaces which makes the subdivision more concise and intuitive.Dividing depths of Bezier curves and surfaces are used to subdivide the curves or surfaces adaptively.Therefore the convergent precision and the computing efficiency of finding the intersections of curves and surfaces have been improved by the methods proposed in the paper.
Study of an extrapolation chamber in a standard diagnostic radiology beam by Monte Carlo simulation
Energy Technology Data Exchange (ETDEWEB)
Vedovato, Uly Pita; Silva, Rayre Janaina Vieira; Neves, Lucio Pereira; Santos, William S.; Perini, Ana Paula, E-mail: anapaula.perini@ufu.br [Universidade Federal de Uberlandia (INFIS/UFU), MG (Brazil). Instituto de Fisica; Caldas, Linda V.E. [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil); Belinato, Walmir [Instituto Federal de Educacao, Ciencia e Tecnologia da Bahia (IFBA), Vitoria da Conquista, BA (Brazil)
2016-07-01
In this work, we studied the influence of the components of an extrapolation ionization chamber in its response. This study was undertaken using the MCNP-5 Monte Carlo code, and the standard diagnostic radiology quality for direct beams (RQR5). Using tally F6 and 2.1 x 10{sup 9} simulated histories, the results showed that the chamber design and material not alter significantly the energy deposited in its sensitive volume. The collecting electrode and support board were the components with more influence on the chamber response. (author)
Alessandria, F; Ardito, R; Arnaboldi, C; Avignone, F T; Balata, M; Bandac, I; Banks, T I; Bari, G; Beeman, J W; Bellini, F; Bersani, A; Biassoni, M; Bloxham, T; Brofferio, C; Bryant, A; Bucci, C; Cai, X Z; Canonica, L; Capelli, S; Carbone, L; Cardani, L; Carrettoni, M; Chott, N; Clemenza, M; Cosmelli, C; Cremonesi, O; Creswick, R J; Dafinei, I; Dally, A; De Biasi, A; Decowski, M P; Deninno, M M; de Waard, A; Di Domizio, S; Ejzak, L; Faccini, R; Fang, D Q; Farach, H; Ferri, E; Ferroni, F; Fiorini, E; Foggetta, L; Freedman, S; Frossati, G; Giachero, A; Gironi, L; Giuliani, A; Gorla, P; Gotti, C; Guardincerri, E; Gutierrez, T D; Haller, E E; Han, K; Heeger, K M; Huang, H Z; Ichimura, K; Kadel, R; Kazkaz, K; Keppel, G; Kogler, L; Kolomensky, Y G; Kraft, S; Lenz, D; Li, Y L; Liu, X; Longo, E; Ma, Y G; Maiano, C; Maier, G; Martinez, C; Martinez, M; Maruyama, R H; Moggi, N; Morganti, S; Newman, S; Nisi, S; Nones, C; Norman, E B; Nucciotti, A; Orio, F; Orlandi, D; Ouellet, J; Pallavicini, M; Palmieri, V; Pattavina, L; Pavan, M; Pedretti, M; Pessina, G; Pirro, S; Previtali, E; Rampazzo, V; Rimondi, F; Rosenfeld, C; Rusconi, C; Salvioni, C; Sangiorgio, S; Schaeffer, D; Scielzo, N D; Sisti, M; Smith, A R; Stivanello, F; Taffarello, L; Terenziani, G; Tian, W D; Tomei, C; Trentalange, S; Ventura, G; Vignati, M; Wang, B; Wang, H W; Whitten, C A; Wise, T; Woodcraft, A; Xu, N; Zanotti, L; Zarra, C; Zhu, B X; Zucchelli, S
2011-01-01
The CUORE Crystal Validation Runs (CCVRs) have been carried out since the end of 2008 at the Gran Sasso National Laboratories, in order to test the performances and the radiopurity of the TeO$_2$ crystals produced at SICCAS (Shanghai Institute of Ceramics, Chinese Academy of Sciences) for the CUORE experiment. In this work the results of the first 5 validation runs are presented. Results have been obtained for bulk contaminations and surface contaminations from several nuclides. An extrapolation to the CUORE background has been performed.
Model of a realistic InP surface quantum dot extrapolated from atomic force microscopy results.
Barettin, Daniele; De Angelis, Roberta; Prosposito, Paolo; Auf der Maur, Matthias; Casalboni, Mauro; Pecchia, Alessandro
2014-05-16
We report on numerical simulations of a zincblende InP surface quantum dot (QD) on In₀.₄₈Ga₀.₅₂ buffer. Our model is strictly based on experimental structures, since we extrapolated a three-dimensional dot directly by atomic force microscopy results. Continuum electromechanical, [Formula: see text] bandstructure and optical calculations are presented for this realistic structure, together with benchmark calculations for a lens-shape QD with the same radius and height of the extrapolated dot. Interesting similarities and differences are shown by comparing the results obtained with the two different structures, leading to the conclusion that the use of a more realistic structure can provide significant improvements in the modeling of QDs fact, the remarkable splitting for the electron p-like levels of the extrapolated dot seems to prove that a realistic experimental structure can reproduce the right symmetry and a correct splitting usually given by atomistic calculations even within the multiband [Formula: see text] approach. Moreover, the energy levels and the symmetry of the holes are strongly dependent on the shape of the dot. In particular, as far as we know, their wave function symmetries do not seem to resemble to any results previously obtained with simulations of zincblende ideal structures, such as lenses or truncated pyramids. The magnitude of the oscillator strengths is also strongly dependent on the shape of the dot, showing a lower intensity for the extrapolated dot, especially for the transition between the electrons and holes ground state, as a result of a relevant reduction of the wave functions overlap. We also compare an experimental photoluminescence spectrum measured on an homogeneous sample containing about 60 dots with a numerical ensemble average derived from single dot calculations. The broader energy range of the numerical spectrum motivated us to perform further verifications, which have clarified some aspects of the experimental
DEFF Research Database (Denmark)
Storhaug, Gaute; Andersen, Ingrid Marie Vincent
2015-01-01
Whipping can contribute to increased fatigue and extreme loading of container ships, and guidelines have been made available by the leading class societies. Reports concerning the hogging collapse of MSC Napoli and MOL Comfort suggest that whipping contributed. The accidents happened in moderate...... to small storms. Model tests of three container ships have been carried out in different sea states under realistic assumptions. Preliminary extrapolation of the measured data suggested that moderate storms are dimensioning when whipping is included due to higher maximum speed in moderate storms...
Kaltenboeck, Rudolf; Kerschbaum, Markus; Hennermann, Karin; Mayer, Stefan
2013-04-01
Nowcasting of precipitation events, especially thunderstorm events or winter storms, has high impact on flight safety and efficiency for air traffic management. Future strategic planning by air traffic control will result in circumnavigation of potential hazardous areas, reduction of load around efficiency hot spots by offering alternatives, increase of handling capacity, anticipation of avoidance manoeuvres and increase of awareness before dangerous areas are entered by aircraft. To facilitate this rapid update forecasts of location, intensity, size, movement and development of local storms are necessary. Weather radar data deliver precipitation analysis of high temporal and spatial resolution close to real time by using clever scanning strategies. These data are the basis to generate rapid update forecasts in a time frame up to 2 hours and more for applications in aviation meteorological service provision, such as optimizing safety and economic impact in the context of sub-scale phenomena. On the basis of tracking radar echoes by correlation the movement vectors of successive weather radar images are calculated. For every new successive radar image a set of ensemble precipitation fields is collected by using different parameter sets like pattern match size, different time steps, filter methods and an implementation of history of tracking vectors and plausibility checks. This method considers the uncertainty in rain field displacement and different scales in time and space. By validating manually a set of case studies, the best verification method and skill score is defined and implemented into an online-verification scheme which calculates the optimized forecasts for different time steps and different areas by using different extrapolation ensemble members. To get information about the quality and reliability of the extrapolation process additional information of data quality (e.g. shielding in Alpine areas) is extrapolated and combined with an extrapolation
3D Drop Size Distribution Extrapolation Algorithm Using a Single Disdrometer
Lane, John
2012-01-01
Determining the Z-R relationship (where Z is the radar reflectivity factor and R is rainfall rate) from disdrometer data has been and is a common goal of cloud physicists and radar meteorology researchers. The usefulness of this quantity has traditionally been limited since radar represents a volume measurement, while a disdrometer corresponds to a point measurement. To solve that problem, a 3D-DSD (drop-size distribution) method of determining an equivalent 3D Z-R was developed at the University of Central Florida and tested at the Kennedy Space Center, FL. Unfortunately, that method required a minimum of three disdrometers clustered together within a microscale network (.1-km separation). Since most commercial disdrometers used by the radar meteorology/cloud physics community are high-cost instruments, three disdrometers located within a microscale area is generally not a practical strategy due to the limitations of these kinds of research budgets. A relatively simple modification to the 3D-DSD algorithm provides an estimate of the 3D-DSD and therefore, a 3D Z-R measurement using a single disdrometer. The basis of the horizontal extrapolation is mass conservation of a drop size increment, employing the mass conservation equation. For vertical extrapolation, convolution of a drop size increment using raindrop terminal velocity is used. Together, these two independent extrapolation techniques provide a complete 3DDSD estimate in a volume around and above a single disdrometer. The estimation error is lowest along a vertical plane intersecting the disdrometer position in the direction of wind advection. This work demonstrates that multiple sensors are not required for successful implementation of the 3D interpolation/extrapolation algorithm. This is a great benefit since it is seldom that multiple sensors in the required spatial arrangement are available for this type of analysis. The original software (developed at the University of Central Florida, 1998.- 2000) has
Increased identification of veterinary pharmaceutical contaminants in aquatic environments has raised concerns regarding potential adverse effects of these chemicals on non-target organisms. The purpose of this work was to develop a method for predictive species extrapolation ut...
Increased identification of veterinary pharmaceutical contaminants in aquatic environments has raised concerns regarding potential adverse effects of these chemicals on non-target organisms. The purpose of this work was to develop a method for predictive species extrapolation ut...
Application of Two-Parameter Extrapolation for Solution of Boundary-Value Problem on Semi-Axis
Zhidkov, E P
2000-01-01
A method for refining approximate eigenvalues and eigenfunctions for a boundary-value problem on a half-axis is suggested. To solve the problem numerically, one has to solve a problem on a finite segment [0,R] instead of the original problem on the interval [0,\\infty). This replacement leads to eigenvalues' and eigenfunctions' errors. To choose R beforehand for obtaining their required accuracy is often impossible. Thus, one has to resolve the problem on [0,R] with larger R. If there are two eigenvalues or two eigenfunctions that correspond to different segments, the suggested method allows one to improve the accuracy of the eigenvalue and the eigenfunction for the original problem by means of extrapolation along the segment. This approach is similar to Richardson's method. Moreover, a two-parameter extrapolation is described. It is combination of the extrapolation along the segment and Richardson's extrapolation along a discretization step.
Direct activity determination of Mn-54 and Zn-65 by a non-extrapolation liquid scintillation method
CSIR Research Space (South Africa)
Simpson, BRS
2004-02-01
Full Text Available The measurement of Mn-54 and Zn-65 by liquid scintillation coincidence counting results in low detection efficiencies. The activity obtained from the extrapolation of efficiency data can therefore become problematic if curvature is present...
Spackman, Peter R.; Karton, Amir
2015-05-01
Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/Lα two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol-1. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol-1.
Energy Technology Data Exchange (ETDEWEB)
Spackman, Peter R.; Karton, Amir, E-mail: amir.karton@uwa.edu.au [School of Chemistry and Biochemistry, The University of Western Australia, Perth, WA 6009 (Australia)
2015-05-15
Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/L{sup α} two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol{sup –1}. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol{sup –1}.
Yamamoto, Tetsuya
2007-06-01
A novel test fixture operating at a millimeter-wave band using an extrapolation range measurement technique was developed at the National Metrology Institute of Japan (NMIJ). Here I describe the measurement system using a Q-band test fixture. I measured the relative insertion loss as a function of antenna separation distance and observed the effects of multiple reflections between the antennas. I also evaluated the antenna gain at 33 GHz using the extrapolation technique.
Amir, Sahar Z.
2013-05-01
We introduce an efficient thermodynamically consistent technique to extrapolate and interpolate normalized Canonical NVT ensemble averages like pressure and energy for Lennard-Jones (L-J) fluids. Preliminary results show promising applicability in oil and gas modeling, where accurate determination of thermodynamic properties in reservoirs is challenging. The thermodynamic interpolation and thermodynamic extrapolation schemes predict ensemble averages at different thermodynamic conditions from expensively simulated data points. The methods reweight and reconstruct previously generated database values of Markov chains at neighboring temperature and density conditions. To investigate the efficiency of these methods, two databases corresponding to different combinations of normalized density and temperature are generated. One contains 175 Markov chains with 10,000,000 MC cycles each and the other contains 3000 Markov chains with 61,000,000 MC cycles each. For such massive database creation, two algorithms to parallelize the computations have been investigated. The accuracy of the thermodynamic extrapolation scheme is investigated with respect to classical interpolation and extrapolation. Finally, thermodynamic interpolation benefiting from four neighboring Markov chains points is implemented and compared with previous schemes. The thermodynamic interpolation scheme using knowledge from the four neighboring points proves to be more accurate than the thermodynamic extrapolation from the closest point only, while both thermodynamic extrapolation and thermodynamic interpolation are more accurate than the classical interpolation and extrapolation. The investigated extrapolation scheme has great potential in oil and gas reservoir modeling.That is, such a scheme has the potential to speed up the MCMC thermodynamic computation to be comparable with conventional Equation of State approaches in efficiency. In particular, this makes it applicable to large-scale optimization of L
The role of strange sea quarks in chiral extrapolations on the lattice
Descotes-Genon, S
2004-01-01
Since the strange quark has a light mass of order Lambda_QCD, fluctuations of sea s-s bar pairs may play a special role in the low-energy dynamics of QCD by inducing significantly different patterns of chiral symmetry breaking in the chiral limits N_f=2 (m_u=m_d=0, m_s physical) and N_f=3 (m_u=m_d=m_s=0). This effect of vacuum fluctuations of s-s bar pairs is related to the violation of the Zweig rule in the scalar sector, described through the two O(p^4) low-energy constants L_4 and L_6 of the three-flavour strong chiral lagrangian. In the case of significant vacuum fluctuations, three-flavour chiral expansions might exhibit a numerical competition between leading- and next-to-leading-order terms according to the chiral counting, and chiral extrapolations should be handled with a special care. We investigate the impact of the fluctuations of s-s bar pairs on chiral extrapolations in the case of lattice simulations with three dynamical flavours in the isospin limit. Information on the size of the vacuum fluct...
$
Abbasi, R U
2016-01-01
Recent measurements at the LHC of the p-p total cross section have reduced the uncertainty in simulations of cosmic ray air showers. In particular of the depth of shower maximum, called $X_{max}$. However, uncertainties of other important parameters, in particular the multiplicity and elasticity of high energy interactions, have not improved, and there is a remaining uncertainty due to the total cross section. Uncertainties due to extrapolations from accelerator data, at a maximum energy of $\\sim$ one TeV in the p-p center of mass, to 250 TeV ($3\\times10^{19}$ eV in a cosmic ray proton's lab frame) introduce significant uncertainties in predictions of $$. In this paper we estimate a lower limit on these uncertainties. The result is that the uncertainty in $$ is larger than the difference among the modern models being used in the field. At the full energy of the LHC, which is equivalent to $\\sim 1\\times10^{17}$ eV in the cosmic ray lab frame, the extrapolation is not as extreme, and the uncertainty is approxim...
Waheed, Umair bin
2014-08-01
The wavefield extrapolation operator for ellipsoidally anisotropic (EA) media offers significant cost reduction compared to that for the orthorhombic case, especially when the symmetry planes are tilted and/or rotated. However, ellipsoidal anisotropy does not provide accurate focusing for media of orthorhombic anisotropy. Therefore, we develop effective EA models that correctly capture the kinematic behavior of the wavefield for tilted orthorhombic (TOR) media. Specifically, we compute effective source-dependent velocities for the EA model using kinematic high-frequency representation of the TOR wavefield. The effective model allows us to use the cheaper EA wavefield extrapolation operator to obtain approximate wavefield solutions for a TOR model. Despite the fact that the effective EA models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TOR media, particularly for media of low to moderate complexity. We demonstrate applicability of the proposed approach on a layered TOR model.
Counter-extrapolation method for conjugate interfaces in computational heat and mass transfer.
Le, Guigao; Oulaid, Othmane; Zhang, Junfeng
2015-03-01
In this paper a conjugate interface method is developed by performing extrapolations along the normal direction. Compared to other existing conjugate models, our method has several technical advantages, including the simple and straightforward algorithm, accurate representation of the interface geometry, applicability to any interface-lattice relative orientation, and availability of the normal gradient. The model is validated by simulating the steady and unsteady convection-diffusion system with a flat interface and the steady diffusion system with a circular interface, and good agreement is observed when comparing the lattice Boltzmann results with respective analytical solutions. A more general system with unsteady convection-diffusion process and a curved interface, i.e., the cooling process of a hot cylinder in a cold flow, is also simulated as an example to illustrate the practical usefulness of our model, and the effects of the cylinder heat capacity and thermal diffusivity on the cooling process are examined. Results show that the cylinder with a larger heat capacity can release more heat energy into the fluid and the cylinder temperature cools down slower, while the enhanced heat conduction inside the cylinder can facilitate the cooling process of the system. Although these findings appear obvious from physical principles, the confirming results demonstrates the application potential of our method in more complex systems. In addition, the basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems.
Electric form factors of the octet baryons from lattice QCD and chiral extrapolation
Energy Technology Data Exchange (ETDEWEB)
Shanahan, P.E.; Thomas, A.W.; Young, R.D.; Zanotti, J.M. [Adelaide Univ., SA (Australia). ARC Centre of Excellence in Particle Physics at the Terascale and CSSM; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe, Hyogo (Japan); Pleiter, D. [Forschungszentrum Juelich (Germany). JSC; Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Stueben, H. [Hamburg Univ. (Germany). Regionales Rechenzentrum; Collaboration: CSSM and QCDSF/UKQCD Collaborations
2014-03-15
We apply a formalism inspired by heavy baryon chiral perturbation theory with finite-range regularization to dynamical 2+1-flavor CSSM/QCDSF/UKQCD Collaboration lattice QCD simulation results for the electric form factors of the octet baryons. The electric form factor of each octet baryon is extrapolated to the physical pseudoscalar masses, after finite-volume corrections have been applied, at six fixed values of Q{sup 2} in the range 0.2-1.3 GeV{sup 2}. The extrapolated lattice results accurately reproduce the experimental form factors of the nucleon at the physical point, indicating that omitted disconnected quark loop contributions are small. Furthermore, using the results of a recent lattice study of the magnetic form factors, we determine the ratio μ{sub p}G{sub E}{sup p}/G{sub M}{sup p}. This quantity decreases with Q{sup 2} in a way qualitatively consistent with recent experimental results.
The Impacts of Atmospheric Stability on the Accuracy of Wind Speed Extrapolation Methods
Directory of Open Access Journals (Sweden)
Jennifer F. Newman
2014-01-01
Full Text Available The building of utility-scale wind farms requires knowledge of the wind speed climatology at hub height (typically 80–100 m. As most wind speed measurements are taken at 10 m above ground level, efforts are being made to relate 10-m measurements to approximate hub-height wind speeds. One common extrapolation method is the power law, which uses a shear parameter to estimate the wind shear between a reference height and hub height. The shear parameter is dependent on atmospheric stability and should ideally be determined independently for different atmospheric stability regimes. In this paper, data from the Oklahoma Mesonet are used to classify atmospheric stability and to develop stability-dependent power law fits for a nearby tall tower. Shear exponents developed from one month of data are applied to data from different seasons to determine the robustness of the power law method. In addition, similarity theory-based methods are investigated as possible alternatives to the power law. Results indicate that the power law method performs better than similarity theory methods, particularly under stable conditions, and can easily be applied to wind speed data from different seasons. In addition, the importance of using co-located near-surface and hub-height wind speed measurements to develop extrapolation fits is highlighted.
Energy Technology Data Exchange (ETDEWEB)
Kim, B.H.; Velas, J.P.; Lee, K.Y [Pennsylvania State Univ., University Park, PA (United States). Dept. of Electrical Engineering
2006-07-01
This paper presented a mathematical method that power plant operators can use to estimate rotational mass unbalance, which is the most common source of vibration in turbine generators. An unbalanced rotor or driveshaft causes vibration and stress in the rotating part and in its supporting structure. As such, balancing the rotating part is important to minimize structural stress, minimize operator annoyance and fatigue, increase bearing life, or minimize power loss. The newly proposed method for estimating vibration on a turbine generator uses mass unbalance extrapolation based on a modified system-type neural network architecture, notably the semigroup theory used to study differential equations, partial differential equations and their combinations. Rather than relying on inaccurate vibration measurements, this method extrapolates a set of reliable mass unbalance readings from a common source of vibration. Given a set of empirical data with no analytic expression, the authors first developed an analytic description and then extended that model along a single axis. The algebraic decomposition which was used to obtain the analytic description of empirical data in the semigroup form involved the product of a coefficient vector and a basis set of vectors. The proposed approach was simulated on empirical data. The concept can also be tested in many other engineering and non-engineering problems. 23 refs., 11 figs.
Counter-extrapolation method for conjugate interfaces in computational heat and mass transfer
Le, Guigao; Oulaid, Othmane; Zhang, Junfeng
2015-03-01
In this paper a conjugate interface method is developed by performing extrapolations along the normal direction. Compared to other existing conjugate models, our method has several technical advantages, including the simple and straightforward algorithm, accurate representation of the interface geometry, applicability to any interface-lattice relative orientation, and availability of the normal gradient. The model is validated by simulating the steady and unsteady convection-diffusion system with a flat interface and the steady diffusion system with a circular interface, and good agreement is observed when comparing the lattice Boltzmann results with respective analytical solutions. A more general system with unsteady convection-diffusion process and a curved interface, i.e., the cooling process of a hot cylinder in a cold flow, is also simulated as an example to illustrate the practical usefulness of our model, and the effects of the cylinder heat capacity and thermal diffusivity on the cooling process are examined. Results show that the cylinder with a larger heat capacity can release more heat energy into the fluid and the cylinder temperature cools down slower, while the enhanced heat conduction inside the cylinder can facilitate the cooling process of the system. Although these findings appear obvious from physical principles, the confirming results demonstrates the application potential of our method in more complex systems. In addition, the basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems.
Classification of future 5 MW turbines by extrapolation of current trends
Energy Technology Data Exchange (ETDEWEB)
Thakoer, R.; Van Kuik, G.A.M.; Van Leeuwen, H.L.
1999-09-01
This report is part of the STABTOOL project. The goals of the STABTOOL project can be summarised as follows: (1) first establish the elastic configuration of the present megawatt scaled wind turbines, and making an inventory of the present design trends and trends for future wind turbine developments w.r.t changes in the elastic configuration; (2) to make an inventory of the different types of instabilities which can occur for the present and next generation wind turbines for both onshore and offshore applications; (3) to make an inventory of analysis and design methods and development or adjustment of calculation methods. The final objective of the STABTOOL project is to create STABility TOOLs: a simple set of calculation models and methods for specific forms of aeroelastic instabilities and vibration problems which are applicable for both present and future large wind turbines. This report concerns the up scaling of the selected elastic configurations described in ST-NW-1-004: 2-blade, (active)pitch controlled, fixed speed (Kvaerner WTS 80M); 3-blade, (active)stall controlled, fixed speed (Nedwind 62 ); 3-blade, pitch controlled variable speed (Lagerwey 50/1000). Based on scaling rules and extrapolation of trend figures, the characteristics of the future 5MW class of wind turbines is estimated. The Nedwind based extrapolation is considered to be an onshore turbine, whereas the others are offshore. 5 refs.
On Extrapolating Past the Range of Observed Data When Making Statistical Predictions in Ecology.
Directory of Open Access Journals (Sweden)
Paul B Conn
Full Text Available Ecologists are increasingly using statistical models to predict animal abundance and occurrence in unsampled locations. The reliability of such predictions depends on a number of factors, including sample size, how far prediction locations are from the observed data, and similarity of predictive covariates in locations where data are gathered to locations where predictions are desired. In this paper, we propose extending Cook's notion of an independent variable hull (IVH, developed originally for application with linear regression models, to generalized regression models as a way to help assess the potential reliability of predictions in unsampled areas. Predictions occurring inside the generalized independent variable hull (gIVH can be regarded as interpolations, while predictions occurring outside the gIVH can be regarded as extrapolations worthy of additional investigation or skepticism. We conduct a simulation study to demonstrate the usefulness of this metric for limiting the scope of spatial inference when conducting model-based abundance estimation from survey counts. In this case, limiting inference to the gIVH substantially reduces bias, especially when survey designs are spatially imbalanced. We also demonstrate the utility of the gIVH in diagnosing problematic extrapolations when estimating the relative abundance of ribbon seals in the Bering Sea as a function of predictive covariates. We suggest that ecologists routinely use diagnostics such as the gIVH to help gauge the reliability of predictions from statistical models (such as generalized linear, generalized additive, and spatio-temporal regression models.
Determination of the true null electrode spacing of an extrapolation chamber for X-ray dosimetry
Energy Technology Data Exchange (ETDEWEB)
Figueiredo, M.T.T.; Bastos, F.M.; Silva, T.A. da, E-mail: mttf@cdtn.br, E-mail: fmb@cdtn.br, E-mail: silvata@cdtn.br [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil). Pos-Graduacao em Ciencia e Tecnologia da Radiacao, Minerais e Materiais
2015-07-01
An accurate determination of the actual null distance is critical for the establishment of primary measurement method for absorbed dose in tissue, since the concept of the true null electrode spacing is used to define the sensitive volume of an extrapolation chamber. In this paper, a critical analysis of two methodologies for determining the true null electrode spacing of an extrapolation chamber was done. Firstly, the ionization current as a function of electrode spacing was measured in ISO 4037 low energy X-ray beams. In the second procedure, a LC Bridge was used to measure the capacitance between the electrodes of a 23392 Böhm model PTW ionization chamber and a reliable relationship between capacitance and relative distance was established. Results showed that the true null spacing values varied from 0.0015 to 0.38 mm. Since capacitance meters with high resolution are not always available in calibration laboratories, the second method showed values with large uncertainties. The first method proved to be highly sensitive to the quality of the X-ray beams used. (author)
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind P. Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications,the Raman amplification being only one of the recent examples. In this tutorial I review the vario us nonlinear effects occurring in optical fibers from both standpoints..
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind; P.; Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Poppe, L. J.; Eliason, A. E.; Hastings, M. E.
2004-05-01
Methods that describe and summarize grain-size distributions are important to geologists because of the large amount of information contained in textural data sets. Therefore, to facilitate reduction of sedimentologic data, we have written a computer program (GSSTAT) to generate grain-size statistics and extrapolate particle distributions. Our program is written in Microsoft Visual Basic 6.0, runs on Windows 95/98/ME/NT/2000/XP computers, provides a window to facilitate execution, and allows users to select options with mouse-click events or through interactive dialogue boxes. The program permits users to select output in either inclusive graphics or moment statistics, to extrapolate distributions to the colloidal-clay boundary by three methods, and to convert between frequency and cumulative frequency percentages. Detailed documentation is available within the program. Input files to the program must be comma-delimited ASCII text and have 20 fields that include: sample identifier, latitude, longitude, and the frequency or cumulative frequency percentages of the whole-phi fractions from 11 phi through -5 phi. Individual fields may be left blank, but the sum of the phi fractions must total 100% (+/- 0.2%). The program expects the first line of the input file to be a header showing attribute names; no embedded commas are allowed in any of the fields. Error messages warn the user of potential problems. The program generates an output file in the requested destination directory and allows the user to view results in a display window to determine the occurrence of errors. The output file has a header for its first line, but now has 34 fields; the original descriptor fields plus percentages of gravel, sand, silt and clay, statistics, classification, verbal descriptions, frequency or cumulative frequency percentages of the whole- phi fractions from 13 phi through -5 phi, and a field for error messages. If the user has selected extrapolation, the two additional phi
Mackie, Iain D.; DiLabio, Gino A.
2011-10-01
The first-principles calculation of non-covalent (particularly dispersion) interactions between molecules is a considerable challenge. In this work we studied the binding energies for ten small non-covalently bonded dimers with several combinations of correlation methods (MP2, coupled-cluster single double, coupled-cluster single double (triple) (CCSD(T))), correlation-consistent basis sets (aug-cc-pVXZ, X = D, T, Q), two-point complete basis set energy extrapolations, and counterpoise corrections. For this work, complete basis set results were estimated from averaged counterpoise and non-counterpoise-corrected CCSD(T) binding energies obtained from extrapolations with aug-cc-pVQZ and aug-cc-pVTZ basis sets. It is demonstrated that, in almost all cases, binding energies converge more rapidly to the basis set limit by averaging the counterpoise and non-counterpoise corrected values than by using either counterpoise or non-counterpoise methods alone. Examination of the effect of basis set size and electron correlation shows that the triples contribution to the CCSD(T) binding energies is fairly constant with the basis set size, with a slight underestimation with CCSD(T)/aug-cc-pVDZ compared to the value at the (estimated) complete basis set limit, and that contributions to the binding energies obtained by MP2 generally overestimate the analogous CCSD(T) contributions. Taking these factors together, we conclude that the binding energies for non-covalently bonded systems can be accurately determined using a composite method that combines CCSD(T)/aug-cc-pVDZ with energy corrections obtained using basis set extrapolated MP2 (utilizing aug-cc-pVQZ and aug-cc-pVTZ basis sets), if all of the components are obtained by averaging the counterpoise and non-counterpoise energies. With such an approach, binding energies for the set of ten dimers are predicted with a mean absolute deviation of 0.02 kcal/mol, a maximum absolute deviation of 0.05 kcal/mol, and a mean percent
Sato, A.; Yomogida, K.
2014-12-01
The early warning system operated by Japan Meteorological Agency (JMA) has been available in public since October 2007.The present system is still not effective in cases, that we cannot assume a nearly circular wavefront expansion from a source. We propose a new approach based on the extrapolation of the early observed wavefield alone without estimating its epicenter. The idea is similar to the migration method in exploration seismology, but we use not only the information of wave field at an early stage (i.e., at time T2 in Figure, but also its normal derivatives the difference between T1 and T2), that is, we utilize the apparent velocity and direction of early-stage wave propagation to predict the wavefield later (at T3 in Fig.). For the extrapolation of wavefield, we need a reliable Green's function from the observed point to a target point at which the wave arrives later. Since the complete 3-D wave propagation is extremely complex, particularly in and around Japan of highly heterogeneous structures, we shall consider a phenomenological 2-D Green's function, that is, a wavefront propagates on the surface with a certain apparent velocity and direction of P wave. This apparent velocity and direction may vary significantly depending on, for example, event depth and an area of propagation, so we examined those of P wave propagating in Japan in various situations. For example, the velocity of shallow events in Hokkaido is 7.1km/s while that in Nagano prefecture is about 5.5km/s. In addition, the apparent velocity depends on event depth, 7.1km/s for the depth of 10km and 8.9km/s for 100km in Hokkaido. We also conducted f-k array analyses of adjacent five or six stations where we can accurately estimate the apparent velocity and direction of P wave. For deep events with relatively simple waveforms, they are easily obtained, but we may need site corrections to enhance correlations of waveforms among stations for shallow ones. In the above extrapolation scheme, we can
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Verloock, Leen; Joseph, Wout; Gati, Azeddine; Varsier, Nadège; Flach, Björn; Wiart, Joe; Martens, Luc
2013-06-01
An experimental validation of a low-cost method for extrapolation and estimation of the maximal electromagnetic-field exposure from long-term evolution (LTE) radio base station installations are presented. No knowledge on downlink band occupation or service characteristics is required for the low-cost method. The method is applicable in situ. It only requires a basic spectrum analyser with appropriate field probes without the need of expensive dedicated LTE decoders. The method is validated both in laboratory and in situ, for a single-input single-output antenna LTE system and a 2×2 multiple-input multiple-output system, with low deviations in comparison with signals measured using dedicated LTE decoders.
Removal of lipid artifacts in 1H spectroscopic imaging by data extrapolation.
Haupt, C I; Schuff, N; Weiner, M W; Maudsley, A A
1996-05-01
Proton MR spectroscopic imaging (MRSI) of human cerebral cortex is complicated by the presence of an intense signal from subcutaneous lipids, which, if not suppressed before Fourier reconstruction, causes ringing and signal contamination throughout the metabolite images as a result of limited k-space sampling. In this article, an improved reconstruction of the lipid region is obtained using the Papoulis-Gerchberg algorithm. This procedure makes use of the narrow-band-limited nature of the subcutaneous lipid signal to extrapolate to higher k-space values without alteration of the metabolite signal region. Using computer simulations and in vivo experimental studies, the implementation and performance of this algorithm were examined. This method was found to permit MRSI brain spectra to be obtained without applying any lipid suppression during data acquisition, at echo times of 50 ms and longer. When applied together with optimized acquisition methods, this provides an effective procedure for imaging metabolite distributions in cerebral cortical surface regions.
DEFF Research Database (Denmark)
Thorndahl, Søren Liedtke; Grum, M.; Rasmussen, Michael R.;
2011-01-01
in a small urban catchment has been developed. The forecast is based on application of radar rainfall data, which by a correlation based technique, is extrapolated with a lead time up to two hours. The runoff forecast in the drainage system is based on a fully distributed MOUSE model which is auto......Forecasting of flows, overflow volumes, water levels, etc. in drainage systems can be applied in real time control of drainage systems in the future climate in order to fully utilize system capacity and thus save possible construction costs. An online system for forecasting flows and water levels......-calibrated on flow measurements in order to produce the best possible forecast for the drainage system at all times. The system shows great potential for the implementation of real time control in drainage systems and forecasting flows and water levels....
Polanco, Carlos; Buhse, Thomas; Vizcaíno, Gloria; Picciotto, Jacobo Levy
2017-01-01
This paper addresses the polar profile of ancient proteins using a comparative study of amino acids found in 25 000 000-year-old shells described in Abelson's work. We simulated the polar profile with a computer platform that represented an evolutionary computational toy model that mimicked the generation of small proteins starting from a pool of monomeric amino acids and that included several dynamic properties, such as self-replication and fragmentation-recombination of the proteins. The simulations were taken up to 15 generations and produced a considerable number of proteins of 25 amino acids in length. The computational model included the amino acids found in the ancient shells, the thermal degradation factor, and the relative abundance of the amino acids observed in the Miller-Urey experimental simulation of the prebiotic amino acid formation. We found that the amino acid polar profiles of the ancient shells and those simulated and extrapolated from the Miller-Urey abundances are coincident.
Continuum extrapolation of finite temperature meson correlation functions in quenched lattice QCD
Francis, Anthony
2010-01-01
We explore the continuum limit $a\\rightarrow 0$ of meson correlation functions at finite temperature. In detail we analyze finite volume and lattice cut-off effects in view of possible consequences for continuum physics. We perform calculations on quenched gauge configurations using the clover improved Wilson fermion action. We present and discuss simulations on isotropic $N_\\sigma^3\\times 16$ lattices with $N_\\sigma=32,48,64,128$ and $128^3 \\times N_\\tau$ lattices with $N_\\tau=16,24,32,48$ corresponding to lattice spacings in the range of $0.01 fm \\lsim a \\lsim\\ 0.031 fm$ at $T\\simeq1.45T_c$. Continuum limit extrapolations of vector meson and pseudo scalar correlators are performed and their large distance expansion in terms of thermal moments is introduced. We discuss consequences of this analysis for the calculation of the electrical conductivity of the QGP at this temperature.
Extrapolation of lattice QCD results beyond the power-counting regime
Leinweber, D B; Young, R D
2005-01-01
Resummation of the chiral expansion is necessary to make accurate contact with current lattice simulation results of full QCD. Resummation techniques including relativistic formulations of chiral effective field theory and finite-range regularization (FRR) techniques are reviewed, with an emphasis on using lattice simulation results to constrain the parameters of the chiral expansion. We illustrate how the chiral extrapolation problem has been solved and use FRR techniques to identify the power-counting regime (PCR) of chiral perturbation theory. To fourth-order in the expansion at the 1% tolerance level, we find $0 \\le m_\\pi \\le 0.18$ GeV for the PCR, extending only a small distance beyond the physical pion mass.
Variance reduction technique in a beta radiation beam using an extrapolation chamber.
Polo, Ivón Oramas; Souza Santos, William; de Lara Antonio, Patrícia; Caldas, Linda V E
2017-10-01
This paper aims to show how the variance reduction technique "Geometry splitting/Russian roulette" improves the statistical error and reduces uncertainties in the determination of the absorbed dose rate in tissue using an extrapolation chamber for beta radiation. The results show that the use of this technique can increase the number of events in the chamber cavity leading to a closer approximation of simulation result with the physical problem. There was a good agreement among the experimental measurements, the certificate of manufacture and the simulation results of the absorbed dose rate values and uncertainties. The absorbed dose rate variation coefficient using the variance reduction technique "Geometry splitting/Russian roulette" was 2.85%. Copyright © 2017 Elsevier Ltd. All rights reserved.
Prediction of long-term creep behaviour and lifetime of polystyrene by linear extrapolation
Institute of Scientific and Technical Information of China (English)
胡立江; 赵树山
2002-01-01
The universal creep function derived from the kinetic equations is successful in relating the creep (ε) to the aging time (ta), coefficient of retardation time (β), and intrinsic time (t0). The relation was used to treat the creep experimental data for polystyrene (PS) specimens which were aged at a given temperature and different times (short-term) and tested at a certain temperature and different stress levels. Then unified master lines were constructed with the treated data and curves according to the universal equation. The master lines can be used to predict the long-term creep behaviour and lifetime by extrapolating to a required ultimate strain. The verifications of results obtained with this method were shown as well.
Prediction of long-term creep behavior and lifetime of PPC pipe materials by linear extrapolation
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The universal creep equation relates creep behavior(ε/εo)to aging time(ta),coefficient of retardation time(β),and intrinsic time(to).The relation was used to treat the creep experimental data for pipe specimens of polypropylene block copelymer(PPC),which were aged for different days(short-term)and tested under different stress levels at a certain temperature.Then unified master lines were constructed with the treated data and curves according to the universal equation.The master straight lines can be used for extrapolation to predict the long-term creep behavior and lifetime of the pipe materials of PPC in the same way as plate materials.
Top Background Extrapolation for $H \\to WW$ Searches at the LHC
Kauer, N
2004-01-01
A leading order (LO) analysis is presented that demonstrates that key top backgrounds to H -> W^+W^- -> l^\\pm l^\\mp \\sla{p}_T decays in weak boson fusion (WBF) and gluon fusion (GF) at the CERN Large Hadron Collider can be extrapolated from experimental data with an accuracy of order 5% to 10%. If LO scale variation is accepted as proxy for the theoretical error, parton level results indicate that the tt~j background to the H -> WW search in WBF can be determined with a theoretical error of about 5%, while the tt~ background to the H -> WW search in GF can be determined with a theoretical error of better than 1%. Uncertainties in the parton distribution functions contribute an estimated 3% to 10% to the total error.
DEFF Research Database (Denmark)
Kissling, W. Daniel; Dalby, Lars; Fløjgaard, Camilla
2014-01-01
, the importance of diet for macroevolutionary and macroecological dynamics remains little explored, partly because of the lack of comprehensive trait datasets. We compiled and evaluated a comprehensive global dataset of diet preferences of mammals (“MammalDIET”). Diet information was digitized from two global......, we grouped mammal species into trophic levels and dietary guilds, and their species richness as well as their proportion of total richness were mapped at a global scale for those diet categories with good validation results. The success rate of correctly digitizing data was 94%, indicating...... that the consistency in data entry among multiple recorders was high. Data sources provided species-level diet information for a total of 2033 species (38% of all 5364 terrestrial mammal species, based on the IUCN taxonomy). For the remaining 3331 species, diet information was mostly extrapolated from genus-level diet...
de Sitter limit of inflation and nonlinear perturbation theory
Jarnhus, Philip R
2007-01-01
We study the fourth order action of comoving curvature perturbations in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbations to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of comoving curvature perturbations and discuss the slow-roll order of the n-point correlation function.
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
Antonio, Patrícia L.; Xavier, Marcos; Caldas, Linda V. E.
2014-11-01
The Calibration Laboratory (LCI) at the Instituto de Pesquisas Energéticas e Nucleares (IPEN) is going to establish a Böhm extrapolation chamber as a primary standard system for the dosimetry and calibration of beta radiation sources and detectors. This chamber was already tested in beta radiation beams with an aluminized Mylar entrance window, and now, it was characterized with an original Hostaphan entrance window. A comparison between the results of the extrapolation chamber with the two entrance windows was performed. The results showed that this extrapolation chamber presents the same effectiveness in beta radiation fields as a primary standard system with both entrance windows, showing that any one of them may be utilized.
Energy Technology Data Exchange (ETDEWEB)
Rothe, R.E.
1997-12-01
Sixty-nine critical configurations of up to 186 kg of uranium are reported from very early experiments (1960s) performed at the Rocky Flats Critical Mass Laboratory near Denver, Colorado. Enriched (93%) uranium metal spherical and hemispherical configurations were studied. All were thick-walled shells except for two solid hemispheres. Experiments were essentially unreflected; or they included central and/or external regions of mild steel. No liquids were involved. Critical parameters are derived from extrapolations beyond subcritical data. Extrapolations, rather than more precise interpolations between slightly supercritical and slightly subcritical configurations, were necessary because experiments involved manually assembled configurations. Many extrapolations were quite long; but the general lack of curvature in the subcritical region lends credibility to their validity. In addition to delayed critical parameters, a procedure is offered which might permit the determination of prompt critical parameters as well for the same cases. This conjectured procedure is not based on any strong physical arguments.
Tang, Lin
2011-01-01
In this paper, we generalize the $A_\\fz$ extrapolation theorem in \\cite{cmp} and the $A_p$ extrapolation theorem of Rubio de Francia to Schr\\"odinger settings. In addition, we also establish the weighted vector-valued inequalities for Schr\\"odinger type maximal operators by using weights belonging to $ A_p^{\\rho,\\tz}$ which includes $A_p$. As their applications, we establish the weighted vector-valued inequalities for some Sch\\"odinger type operators and pseudo-differential operators.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Ionescu, Tudor C.; Scherpen, Jacquelien M. A.
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Nonlinear Electrodynamics and QED
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
Improving Predictions with Reliable Extrapolation Schemes and Better Understanding of Factorization
More, Sushant N.
New insights into the inter-nucleon interactions, developments in many-body technology, and the surge in computational capabilities has led to phenomenal progress in low-energy nuclear physics in the past few years. Nonetheless, many calculations still lack a robust uncertainty quantification which is essential for making reliable predictions. In this work we investigate two distinct sources of uncertainty and develop ways to account for them. Harmonic oscillator basis expansions are widely used in ab-initio nuclear structure calculations. Finite computational resources usually require that the basis be truncated before observables are fully converged, necessitating reliable extrapolation schemes. It has been demonstrated recently that errors introduced from basis truncation can be taken into account by focusing on the infrared and ultraviolet cutoffs induced by a truncated basis. We show that a finite oscillator basis effectively imposes a hard-wall boundary condition in coordinate space. We accurately determine the position of the hard-wall as a function of oscillator space parameters, derive infrared extrapolation formulas for the energy and other observables, and discuss the extension of this approach to higher angular momentum and to other localized bases. We exploit the duality of the harmonic oscillator to account for the errors introduced by a finite ultraviolet cutoff. Nucleon knockout reactions have been widely used to study and understand nuclear properties. Such an analysis implicitly assumes that the effects of the probe can be separated from the physics of the target nucleus. This factorization between nuclear structure and reaction components depends on the renormalization scale and scheme, and has not been well understood. But it is potentially critical for interpreting experiments and for extracting process-independent nuclear properties. We use a class of unitary transformations called the similarity renormalization group (SRG) transformations to
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinearity-reduced interferometer
Wu, Chien-ming
2007-12-01
Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.
An Explicit High Resolution Scheme for Nonlinear Shallow Water Equations
Institute of Scientific and Technical Information of China (English)
FANG Ke-zhao; ZOU Zhi-li; WANG Yan
2005-01-01
The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations (NSWE) for the wave run-up on a beach. The finite volume method (FVM) is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe's flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws (MUSCL) variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.
DEFF Research Database (Denmark)
Stadtmann, Georg; Rülke; Reitz
2012-01-01
or not regressive and extrapolative expectations themselves exhibit significant nonlinear dynamics. The empirical results are based on a new data set from the European Central Bank Survey of Professional Forecasters on oil price expectations. In particular, we find that forecasters form destabilizing expectations...... in the neighborhood of the fundamental value, whereas expectations tend to be stabilizing in the presence of substantial oil price misalignment.......Chartist and fundamentalist models have proven to be capable of replicating stylized facts on speculative markets. In general, this is achieved by specifying nonlinear interactions of otherwise linear asset price expectations of the respective trader groups. This paper investigates whether...
Spatial extrapolation of light use efficiency model parameters to predict gross primary production
Directory of Open Access Journals (Sweden)
Karsten Schulz
2011-12-01
Full Text Available To capture the spatial and temporal variability of the gross primary production as a key component of the global carbon cycle, the light use efficiency modeling approach in combination with remote sensing data has shown to be well suited. Typically, the model parameters, such as the maximum light use efficiency, are either set to a universal constant or to land class dependent values stored in look-up tables. In this study, we employ the machine learning technique support vector regression to explicitly relate the model parameters of a light use efficiency model calibrated at several FLUXNET sites to site-specific characteristics obtained by meteorological measurements, ecological estimations and remote sensing data. A feature selection algorithm extracts the relevant site characteristics in a cross-validation, and leads to an individual set of characteristic attributes for each parameter. With this set of attributes, the model parameters can be estimated at sites where a parameter calibration is not possible due to the absence of eddy covariance flux measurement data. This will finally allow a spatially continuous model application. The performance of the spatial extrapolation scheme is evaluated with a cross-validation approach, which shows the methodology to be well suited to recapture the variability of gross primary production across the study sites.
Caldwell, J.; Shakibi, B.; Moles, M.; Sinclair, A. N.
2013-01-01
Phased array inspection was conducted on a V-butt welded steel sample with multiple shallow flaws of varying depths. The inspection measurements were processed using Wiener filtering and Autoregressive Spectral Extrapolation (AS) to enhance the signals. Phased array inspections were conducted using multiple phased array probes of varying nominal central frequencies (2.25, 4, 5 and 10 MHz). This paper describes the measured results, which show high accuracy, typically in the range of 0.1-0.2 mm. The results concluded that: 1. There was no statistical difference between the calculated flaw depths from phased array inspections at different flaw tip angles. 2. There was no statistical difference in flaw depths calculated using phased array data collected from either side of the weld. 3. Flaws with depths less than the estimated probe signal shear wavelength could not be sized. 4. Finally, there was no statistical difference in the calculated flaw depths using phased array probes with different sampling frequencies and destructive measurements of the flaws.
Mass, Measurement, Materials, and Mathematical Modeling: The Nuts and Bolts of Extrapolation
Directory of Open Access Journals (Sweden)
Scott A Sinex
2011-12-01
Full Text Available A simple activity is described which is appropriate for any class dealing with measurement. It introduces students to the important scientific process of mathematical modeling and online collaboration. Students, working in groups, determine the mass of a bolt indirectly by extrapolation from massing the bolt with one to five nuts on it and determining the equation of the line; the y-intercept being the mass of the bolt. Students gain experience with using a balance, graphing data, and analyzing results using algebraic skills. They calculate percent error after measuring the bolt’s mass directly and can compare this with the error limits from the least squares fit. Groups enter data into a web-based form and the data is examined by the class using Google Docs in a collaborative manner. After entering data in Google Docs, the students use an interactive Excel spreadsheet to compare their results to the best-fit line obtained by linear regression (pre-built into the spreadsheet for novices. In the spreadsheet, they further explore the model to gain an understanding and examine the influence of scatter (error in the data and material density.
Octet baryon masses and sigma terms from an SU(3) chiral extrapolation
Energy Technology Data Exchange (ETDEWEB)
Young, Ross; Thomas, Anthony
2009-01-01
We analyze the consequences of the remarkable new results for octet baryon masses calculated in 2+1- avour lattice QCD using a low-order expansion about the SU(3) chiral limit. We demonstrate that, even though the simulation results are clearly beyond the power-counting regime, the description of the lattice results by a low-order expansion can be significantly improved by allowing the regularisation scale of the effective field theory to be determined by the lattice data itself. The model dependence of our analysis is demonstrated to be small compared with the present statistical precision. In addition to the extrapolation of the absolute values of the baryon masses, this analysis provides a method to solve the difficult problem of fine-tuning the strange-quark mass. We also report a determination of the sigma terms for all of the octet baryons, including an accurate value of the pion-nucleon sigma term and the first determination of the strangeness sigma term based on 2+1-flavour l
The risk of extrapolation in neuroanatomy: the case of the mammalian vomeronasal system
Directory of Open Access Journals (Sweden)
Ignacio Salazar
2009-10-01
Full Text Available The sense of smell plays a crucial role in mammalian social and sexual behaviour, identification of food, and detection of predators. Nevertheless, mammals vary in their olfactory ability. One reason for this concerns the degree of development of their pars basalis rhinencephali, an anatomical feature that has has been considered in classifying this group of animals as macrosmatic, microsmatic or anosmatic. In mammals, different structures are involved in detecting odours: the main olfactory system, the vomeronasal system (VNS, and two subsystems, namely the ganglion of Grüneberg and the septal organ. Here, we review and summarise some aspects of the comparative anatomy of the VNS and its putative relationship to other olfactory structures. Even in the macrosmatic group, morphological diversity is an important characteristic of the VNS, specifically of the vomeronasal organ and the accessory olfactory bulb. We conclude that it is a big mistake to extrapolate anatomical data of the VNS from species to species, even in the case of relatively close evolutionary proximity between them. We propose to study other mammalian VNS than those of rodents in depth as a way to clarify its exact role in olfaction. Our experience in this field leads us to hypothesise that the VNS, considered for all mammalian species, could be a system undergoing involution or regression, and could serve as one more integrated olfactory subsystem.
Yang, X; Zhou, Y-F; Yu, Y; Zhao, D-H; Shi, W; Fang, B-H; Liu, Y-H
2015-02-01
A multi-compartment physiologically based pharmacokinetic (PBPK) model to describe the disposition of cyadox (CYX) and its metabolite quinoxaline-2-carboxylic acid (QCA) after a single oral administration was developed in rats (200 mg/kg b.w. of CYX). Considering interspecies differences in physiology and physiochemistry, the model efficiency was validated by pharmacokinetic data set in swine. The model included six compartments that were blood, muscle, liver, kidney, adipose, and a combined compartment for the rest of tissues. The model was parameterized using rat plasma and tissue concentration data that were generated from this study. Model simulations were achieved using a commercially available software program (ACSLXL ibero version 3.0.2.1). Results supported the validity of the model with simulated tissue concentrations within the range of the observations. The correlation coefficients of the predicted and experimentally determined values for plasma, liver, kidney, adipose, and muscles in rats were 0.98, 0.98, 0.98, 0.99, and 0.95, respectively. The rat model parameters were then extrapolated to pigs to estimate QCA disposition in tissues and validated by tissue concentration of QCA in swine. The correlation coefficients between the predicted and observed values were over 0.90. This model could provide a foundation for developing more reliable pig models once more data are available.
Cui, Jie; Li, Zhiying; Krems, Roman V
2015-10-21
We consider a problem of extrapolating the collision properties of a large polyatomic molecule A-H to make predictions of the dynamical properties for another molecule related to A-H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A-X. We assume that the effect of the -H →-X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can be used to produce an interval of the observable values which corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C6H5CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He - C6H6 collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C6H5CN with He.
Montiel, Ariadna; Sendra, Irene; Escamilla-Rivera, Celia; Salzano, Vincenzo
2014-01-01
In this work we present a nonparametric approach, which works on minimal assumptions, to reconstruct the cosmic expansion of the Universe. We propose to combine a locally weighted scatterplot smoothing method and a simulation-extrapolation method. The first one (Loess) is a nonparametric approach that allows to obtain smoothed curves with no prior knowledge of the functional relationship between variables nor of the cosmological quantities. The second one (Simex) takes into account the effect of measurement errors on a variable via a simulation process. For the reconstructions we use as raw data the Union2.1 Type Ia Supernovae compilation, as well as recent Hubble parameter measurements. This work aims to illustrate the approach, which turns out to be a self-sufficient technique in the sense we do not have to choose anything by hand. We examine the details of the method, among them the amount of observational data needed to perform the locally weighted fit which will define the robustness of our reconstructio...
Extrapolation of Galactic Dust Emission at 100 Microns to CMBR Frequencies Using FIRAS
Finkbeiner, D; Schlegel, D J; Finkbeiner, Douglas P.; Davis, Marc; Schlegel, David J.
1999-01-01
We present predicted full-sky maps of submillimeter and microwave emission from the diffuse interstellar dust in the Galaxy. These maps are extrapolated from the 100 micron emission and 100/240 micron flux ratio maps that Schlegel, Finkbeiner, & Davis (1998; SFD98) generated from IRAS and COBE/DIRBE data. Results are presented for a number of physically plausible emissivity models. We find that no power law emissivity function fits the FIRAS data from 200 - 2100 GHz. In this paper we provide a formalism for a multi-component model for the dust emission. A two-component model with a mixture of silicate and carbon-dominated grains (motivated by Pollack et al., 1994}) provides a fit to an accuracy of about 15% to all the FIRAS data over the entire high-latitude sky. Small systematic differences are found between the atomic and molecular phases of the ISM. Our predictions for the thermal (vibrational) emission from Galactic dust at made at the DIRBE resolution of 40' or at the higher resolution of 6.1 arcmin ...
Caution warranted in extrapolating from Boston Naming Test item gradation construct.
Beattey, Robert A; Murphy, Hilary; Cornwell, Melinda; Braun, Thomas; Stein, Victoria; Goldstein, Martin; Bender, Heidi Allison
2017-01-01
The Boston Naming Test (BNT) was designed to present items in order of difficulty based on word frequency. Changes in word frequencies over time, however, would frustrate extrapolation in clinical and research settings based on the theoretical construct because performance on the BNT might reflect changes in ecological frequency of the test items, rather than performance across items of increasing difficulty. This study identifies the ecological frequency of BNT items at the time of publication using the American Heritage Word Frequency Book and determines changes in frequency over time based on the frequency distribution of BNT items across a current corpus, the Corpus of Contemporary American English. Findings reveal an uneven distribution of BNT items across 2 corpora and instances of negligible differentiation in relative word frequency across test items. As BNT items are not presented in order from least to most frequent, clinicians and researchers should exercise caution in relying on the BNT as presenting items in increasing order of difficulty. A method is proposed for distributing confrontation-naming items to be explicitly measured against test items that are normally distributed across the corpus of a given language.
Chenglin, L.; Charpentier, R.R.
2010-01-01
The U.S. Geological Survey procedure for the estimation of the general form of the parent distribution requires that the parameters of the log-geometric distribution be calculated and analyzed for the sensitivity of these parameters to different conditions. In this study, we derive the shape factor of a log-geometric distribution from the ratio of frequencies between adjacent bins. The shape factor has a log straight-line relationship with the ratio of frequencies. Additionally, the calculation equations of a ratio of the mean size to the lower size-class boundary are deduced. For a specific log-geometric distribution, we find that the ratio of the mean size to the lower size-class boundary is the same. We apply our analysis to simulations based on oil and gas pool distributions from four petroleum systems of Alberta, Canada and four generated distributions. Each petroleum system in Alberta has a different shape factor. Generally, the shape factors in the four petroleum systems stabilize with the increase of discovered pool numbers. For a log-geometric distribution, the shape factor becomes stable when discovered pool numbers exceed 50 and the shape factor is influenced by the exploration efficiency when the exploration efficiency is less than 1. The simulation results show that calculated shape factors increase with those of the parent distributions, and undiscovered oil and gas resources estimated through the log-geometric distribution extrapolation are smaller than the actual values. ?? 2010 International Association for Mathematical Geology.
Directory of Open Access Journals (Sweden)
Trevor G. Jones
2014-07-01
Full Text Available Information derived from high spatial resolution remotely sensed data is critical for the effective management of forested ecosystems. However, high spatial resolution data-sets are typically costly to acquire and process and usually provide limited geographic coverage. In contrast, moderate spatial resolution remotely sensed data, while not able to provide the spectral or spatial detail required for certain types of products and applications, offer inexpensive, comprehensive landscape-level coverage. This study assessed using an object-based approach to extrapolate detailed tree species heterogeneity beyond the extent of hyperspectral/LiDAR flightlines to the broader area covered by a Landsat scene. Using image segments, regression trees established ecologically decipherable relationships between tree species heterogeneity and the spectral properties of Landsat segments. The spectral properties of Landsat bands 4 (i.e., NIR: 0.76–0.90 µm, 5 (i.e., SWIR: 1.55–1.75 µm and 7 (SWIR: 2.08–2.35 µm were consistently selected as predictor variables, explaining approximately 50% of variance in richness and diversity. Results have important ramifications for ongoing management initiatives in the study area and are applicable to wide range of applications.
Comparison of Coronal Extrapolation Methods for Cycle 24 Using HMI Data
Arden, William M; Sun, Xudong; Zhao, Xuepu
2016-01-01
Two extrapolation models of the solar coronal magnetic field are compared using magnetogram data from the SDO/HMI instrument. The two models, a horizontal current-current sheet-source surface (HCCSSS) model and a potential field-source surface (PFSS) model differ in their treatment of coronal currents. Each model has its own critical variable, respectively the radius of a cusp surface and a source surface, and it is found that adjusting these heights over the period studied allows better fit between the models and the solar open flux at 1 AU as calculated from the Interplanetary Magnetic Field (IMF). The HCCSSS model provides the better fit for the overall period from 2010 November to 2015 May as well as for two subsets of the period - the minimum/rising part of the solar cycle, and the recently-identified peak in the IMF from mid-2014 to mid-2015 just after solar maximum. It is found that a HCCSSS cusp surface height of 1.7 Rsun provides the best fit to the IMF for the overall period, while 1.7 & 1.9 Rsu...
Latychevskaia, Tatiana
2015-01-01
In coherent diffractive imaging (CDI) the resolution with which the reconstructed object can be obtained is limited by the numerical aperture of the experimental setup. We present here a theoretical and numerical study for achieving super-resolution by post-extrapolation of coherent diffraction images, such as diffraction patterns or holograms. We proof that a diffraction pattern can unambiguously be extrapolated from just a fraction of the entire pattern and that the ratio of the extrapolated signal to the originally available signal, is linearly proportional to the oversampling ratio. While there could be in principle other methods to achieve extrapolation, we devote our discussion to employing phase retrieval methods and demonstrate their limits. We present two numerical studies; namely the extrapolation of diffraction patterns of non-binary and that of phase objects together with a discussion of the optimal extrapolation procedure.
Macsween, A
2001-09-01
While the accepted measure of aerobic power remains the VO2max this test is extremely demanding even for athletes. There are serious practical and ethical concerns in attempting such testing in non-athletic or patient populations. An alternative method of measuring aerobic power in such populations is required. A limited body of work exists evaluating the accuracy of the Astrand-Ryhming nomogram and linear extrapolation of the heart rate/oxygen uptake plot. Issues exist in terms of both equipment employed and sample numbers. Twenty-five normal subjects (mean age 28.6, range 22-50) completed 52 trials (Bruce treadmill protocol) meeting stringent criteria for VO2max performance. Respiratory gases were measured with a portable gas analyser on a five-sec sample period. The data was analysed to allow comparison of the reliability and validity of linear extrapolations to three estimates of heart rate maximum with the Astrand nomogram prediction. Extrapolation was preferable yielding intraclass correlation co-efficients (ICC) of 0.9433 comparable to that of the observed VO2max at 0.9443 and a bias of -1.1 ml x min(-1) x kg(-1) representing a 2.19 percent underestimate. This study provides empirical evidence that extrapolation of submaximal data can be employed with confidence for both clinical monitoring and research purposes. With the use of portable equipment and submaximal testing the scope for future research in numerous populations and non-laboratory environments is considerably increased.
Mueller, David S.
2013-01-01
Selection of the appropriate extrapolation methods for computing the discharge in the unmeasured top and bottom parts of a moving-boat acoustic Doppler current proﬁler (ADCP) streamﬂow measurement is critical to the total discharge computation. The software tool, extrap, combines normalized velocity
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Ionescu, T. C.; Scherpen, J. M. A.; Korytowski, A; Malanowski, K; Mitkowski, W; Szymkat, M
2009-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Mangrove litter fall: Extrapolation from traps to a large tropical macrotidal harbour
Metcalfe, Kristin N.; Franklin, Donald C.; McGuinness, Keith A.
2011-11-01
Mangrove litter is a major source of organic matter for detrital food chains in many tropical coastal ecosystems, but scant attention has been paid to the substantial challenges in sampling and extrapolation of rates of litter fall. The challenges arise due to within-stand heterogeneity including incomplete canopy cover, and canopy that is below the high tide mark. We sampled litter monthly for three years at 35 sites across eight mapped communities in the macrotidal Darwin Harbour, northern Australia. Totals were adjusted for mean community canopy cover and the occurrence of canopy below the high tide mark. The mangroves of Darwin Harbour generate an estimated average of 5.0 t ha -1 yr -1 of litter. This amount would have been overestimated by 32% had we not corrected for limited canopy cover and underestimated by 11% had we not corrected for foliage that is below the high tide mark. Had we made neither correction, we would have overestimated litter fall by 17%. Among communities, rates varied 2.6-fold per unit area of canopy, and 3.9-fold among unit area of community. Seaward fringe mangroves were the most productive per unit of canopy area but the canopy was relatively open; Tidal creek forest was the most productive per unit area of community. Litter fall varied 1.1-fold among years and 2.0-fold among months though communities exhibited a range of seasonalities. Our study may be the most extensively stratified and sampled evaluation of mangrove litter fall in a tropical estuary. We believe our study is also the first such assessment to explicitly deal with canopy discontinuities and demonstrates that failure to do so can result in considerable overestimation of mangrove productivity.
Measurement of absorbed dose with a bone-equivalent extrapolation chamber.
DeBlois, François; Abdel-Rahman, Wamied; Seuntjens, Jan P; Podgorsak, Ervin B
2002-03-01
A hybrid phantom-embedded extrapolation chamber (PEEC) made of Solid Water and bone-equivalent material was used for determining absorbed dose in a bone-equivalent phantom irradiated with clinical radiation beams (cobalt-60 gamma rays; 6 and 18 MV x rays; and 9 and 15 MeV electrons). The dose was determined with the Spencer-Attix cavity theory, using ionization gradient measurements and an indirect determination of the chamber air-mass through measurements of chamber capacitance. The collected charge was corrected for ionic recombination and diffusion in the chamber air volume following the standard two-voltage technique. Due to the hybrid chamber design, correction factors accounting for scatter deficit and electrode composition were determined and applied in the dose equation to obtain absorbed dose in bone for the equivalent homogeneous bone phantom. Correction factors for graphite electrodes were calculated with Monte Carlo techniques and the calculated results were verified through relative air cavity dose measurements for three different polarizing electrode materials: graphite, steel, and brass in conjunction with a graphite collecting electrode. Scatter deficit, due mainly to loss of lateral scatter in the hybrid chamber, reduces the dose to the air cavity in the hybrid PEEC in comparison with full bone PEEC by 0.7% to approximately 2% depending on beam quality and energy. In megavoltage photon and electron beams, graphite electrodes do not affect the dose measurement in the Solid Water PEEC but decrease the cavity dose by up to 5% in the bone-equivalent PEEC even for very thin graphite electrodes (<0.0025 cm). In conjunction with appropriate correction factors determined with Monte Carlo techniques, the uncalibrated hybrid PEEC can be used for measuring absorbed dose in bone material to within 2% for high-energy photon and electron beams.
Birgand, F.; Etheridge, J. R.; Burchell, M. R.
2013-12-01
Tidal marshes are among the most dynamic aquatic systems in the world. While astronomical and wind driven tides are the major driver to displace water volumes, rainfall events and evapotranspiration move the overall balance towards water export or import, respectively. Until now, only glimpses of the associated biogeochemical functioning could be obtained, usually at one or several tidal cycles scale, because there was no obvious method to obtain long term water quality data at a high temporal frequency. We have successfully managed, using UV-Vis spectrophotometers in the field, to obtain water quality and flow data on a 15-min frequency for over 20 months in a restored brackish marsh in North Carolina. This marsh was designed to intercept water generated by subsurface drainage of adjacent agricultural land before discharge to the nearby estuary. It is particularly tempting in tidal systems where tides may look very similar from one to the next, to extrapolate results obtained possibly over several days or weeks to a ';seasonal biogeochemical functioning'. The lessons learned from high frequency data at the tidal scale are fascinating, but in the longer term, we have learned that a few and inherently rare rainfall events drove the overall nutrient balance in the marsh. Continuous water quality monitoring is thus essential for two reasons: 1) to observe the short term dynamics, as they are the key to unveil possibly misunderstood biogeochemical processes, and 2) to capture the rare yet essential events which drive the system's response. However, continuous water quality monitoring on a long term basis in harsh coastal environments is not without challenges.
The cerebellum and visual perceptual learning: evidence from a motion extrapolation task.
Deluca, Cristina; Golzar, Ashkan; Santandrea, Elisa; Lo Gerfo, Emanuele; Eštočinová, Jana; Moretto, Giuseppe; Fiaschi, Antonio; Panzeri, Marta; Mariotti, Caterina; Tinazzi, Michele; Chelazzi, Leonardo
2014-09-01
Visual perceptual learning is widely assumed to reflect plastic changes occurring along the cerebro-cortical visual pathways, including at the earliest stages of processing, though increasing evidence indicates that higher-level brain areas are also involved. Here we addressed the possibility that the cerebellum plays an important role in visual perceptual learning. Within the realm of motor control, the cerebellum supports learning of new skills and recalibration of motor commands when movement execution is consistently perturbed (adaptation). Growing evidence indicates that the cerebellum is also involved in cognition and mediates forms of cognitive learning. Therefore, the obvious question arises whether the cerebellum might play a similar role in learning and adaptation within the perceptual domain. We explored a possible deficit in visual perceptual learning (and adaptation) in patients with cerebellar damage using variants of a novel motion extrapolation, psychophysical paradigm. Compared to their age- and gender-matched controls, patients with focal damage to the posterior (but not the anterior) cerebellum showed strongly diminished learning, in terms of both rate and amount of improvement over time. Consistent with a double-dissociation pattern, patients with focal damage to the anterior cerebellum instead showed more severe clinical motor deficits, indicative of a distinct role of the anterior cerebellum in the motor domain. The collected evidence demonstrates that a pure form of slow-incremental visual perceptual learning is crucially dependent on the intact cerebellum, bearing the notion that the human cerebellum acts as a learning device for motor, cognitive and perceptual functions. We interpret the deficit in terms of an inability to fine-tune predictive models of the incoming flow of visual perceptual input over time. Moreover, our results suggest a strong dissociation between the role of different portions of the cerebellum in motor versus
Song, Yang; Hamtaei, Ehsan; Sethi, Sean K; Yang, Guang; Xie, Haibin; Mark Haacke, E
2017-09-01
To introduce a new approach to reconstruct high definition vascular images using COnstrained Data Extrapolation (CODE) and evaluate its capability in estimating vessel area and stenosis. CODE is based on the constraint that the full width half maximum of a vessel can be accurately estimated and, since it represents the best estimate for the width of the object, higher k-space data can be generated from this information. To demonstrate the potential of extracting high definition vessel edges using low resolution data, both simulated and human data were analyzed to better visualize the vessels and to quantify both area and stenosis measurements. The results from CODE using one-fourth of the fully sampled k-space data were compared with a compressed sensing (CS) reconstruction approach using the same total amount of data but spread out between the center of k-space and the outer portions of the original k-space to accelerate data acquisition by a factor of four. For a sufficiently high signal-to-noise ratio (SNR) such as 16 (8), we found that objects as small as 3 voxels in the 25% under-sampled data (6 voxels when zero-filled) could be used for CODE and CS and provide an estimate of area with an error 200 (30) times faster for CODE compared to CS in the simulated (human) data. CODE was capable of producing sharp sub-voxel edges and accurately estimating stenosis to within 5% for clinically relevant studies of vessels with a width of at least 3pixels in the low resolution images. Copyright © 2017 Elsevier Inc. All rights reserved.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Agrawal, Govind P
2001-01-01
The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Nonlinear graphene metamaterial
Nikolaenko, Andrey E; Atmatzakis, Evangelos; Luo, Zhiqiang; Shen, Ze Xiang; De Angelis, Francesco; Boden, Stuart A; Di Fabrizio, Enzo; Zheludev, Nikolay I
2012-01-01
We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.
Energy Technology Data Exchange (ETDEWEB)
Silva, Eric A.B. da; Caldas, Linda V.E., E-mail: ebrito@usp.b [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2011-10-26
The extrapolation chamber is a ionization chamber used for detection low energy radiation and can be used as an standard instrument for beta radiation beams. This type of ionization chamber have as main characteristic the variation of sensible volume. This paper performs a study of characterization of a PTW commercial extrapolation chamber, in the energy interval of the qualities of conventional radiodiagnostic
Martín-Jiménez, Tomás; Baynes, Ronald E; Craigmill, Arthur; Riviere, Jim E
2002-08-01
The extralabel use of drugs can be defined as the use of drugs in a manner inconsistent with their FDA-approved labeling. The passage of the Animal Medicinal Drug Use Clarification Act (AMDUCA) in 1994 and its implementation by the FDA-Center for Veterinary Medicine in 1996 has allowed food animal veterinarians to use drugs legally in an extralabel manner, as long as an appropriate withdrawal period is established. The present study introduces and validates with simulated and experimental data the Extrapolated Withdrawal-Period Estimator (EWE) Algorithm, a procedure aimed at predicting extralabel withdrawal intervals (WDIs) based on the label and pharmacokinetic literature data contained in the Food Animal Residue Avoidance Databank (FARAD). This is the initial and first attempt at consistently obtaining WDI estimates that encompass a reasonable degree of statistical soundness. Data on the determination of withdrawal times after the extralabel use of the antibiotic oxytetracycline were obtained both with simulated disposition data and from the literature. A withdrawal interval was computed using the EWE Algorithm for an extralabel dose of 25 mg/kg (simulation study) and for a dose of 40 mg/kg (literature data). These estimates were compared with the withdrawal times computed with the simulated data and with the literature data, respectively. The EWE estimates of WDP for a simulated extralabel dose of 25 mg/kg was 39 days. The withdrawal time (WDT) obtained for this dose on a tissue depletion study was 39 days. The EWE estimate of WDP for an extralabel intramuscular dose of 40 mg/kg in cattle, based on the kinetic data contained in the FARAD database, was 48 days. The withdrawal time experimentally obtained for similar use of this drug was 49 days. The EWE Algorithm can obtain WDI estimates that encompass the same degree of statistical soundness as the WDT estimates, provided that the assumptions of the approved dosage regimen hold for the extralabel dosage regimen
Multipolar nonlinear nanophotonics
Smirnova, Daria
2016-01-01
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. Thus, both modal and multipolar analyses are widely exploited for engineering nonlinear scattering from resonant nanoscale elements, in particular for enhancing the near-field interaction, tailoring the far-field multipolar interference, and optimization of the radiation directionality. Here, we review the recent advances in this recently emerged research field ranging from metallic structures exhibiting localized plasmonic resonances to hybrid metal-dielectric and all-dielectric...
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Directory of Open Access Journals (Sweden)
Shakeeb Bin Hasan
2014-12-01
Full Text Available Contrary to traditional optical elements, plasmonic antennas made from nanostructured metals permit the localization of electromagnetic fields on length scales much smaller than the wavelength of light. This results in huge amplitudes for the electromagnetic field close to the antenna being conducive for the observation of nonlinear effects already at moderate pump powers. Thus, these antennas exhibit a promising potential to achieve optical frequency conversion and all-optical control of light at the nano-scale. This opens unprecedented opportunities for ultrafast nonlinear spectroscopy, sensing devices, on-chip optical frequency conversion, nonlinear optical metamaterials, and novel photon sources. Here, we review some of the recent advances in exploiting the potential of plasmonic antennas to realize robust nonlinear applications.
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE......) is a good solution to solve the problems associated with the use of real nonlinear sources in testing phases. However, a recent technical survey conducted during this work shows that most existing NSEs have only been concerned with simulating nonlinear systems in terrestrial applications. Furthermore......, their dynamic performance were not fast enough in order to imitate how a real nonlinear energy source would react under extreme conditions and operation modes. Particularly, a system in the sky can experience a step change of sunlight irradiation. Moreover, operation modes may include load step between nominal...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
DEFF Research Database (Denmark)
Thorndahl, Søren Liedtke; Rasmussen, Michael R.
2013-01-01
Model based short-term forecasting of urban storm water runoff can be applied in realtime control of drainage systems in order to optimize system capacity during rain and minimize combined sewer overflows, improve wastewater treatment or activate alarms if local flooding is impending. A novel...... online system, which forecasts flows and water levels in real-time with inputs from extrapolated radar rainfall data, has been developed. The fully distributed urban drainage model includes auto-calibration using online in-sewer measurements which is seen to improve forecast skills significantly....... The radar rainfall extrapolation (nowcast) limits the lead time of the system to two hours. In this paper, the model set-up is tested on a small urban catchment for a period of 1.5 years. The 50 largest events are presented....
Monte Carlo based approach to the LS–NaI 4πβ–γ anticoincidence extrapolation and uncertainty.
Fitzgerald, R
2016-03-01
The 4πβ–γ anticoincidence method is used for the primary standardization of β−, β+, electron capture (EC), α, and mixed-mode radionuclides. Efficiency extrapolation using one or more γ ray coincidence gates is typically carried out by a low-order polynomial fit. The approach presented here is to use a Geant4-based Monte Carlo simulation of the detector system to analyze the efficiency extrapolation. New code was developed to account for detector resolution, direct γ ray interaction with the PMT, and implementation of experimental β-decay shape factors. The simulation was tuned to 57Co and 60Co data, then tested with 99mTc data, and used in measurements of 18F, 129I, and 124I. The analysis method described here offers a more realistic activity value and uncertainty than those indicated from a least-squares fit alone.
Lee, Jung-Won; Choi, Jeung-Yoon; Kang, Hong-Goo
2012-02-01
Knowledge-based speech recognition systems extract acoustic cues from the signal to identify speech characteristics. For channel-deteriorated telephone speech, acoustic cues, especially those for stop consonant place, are expected to be degraded or absent. To investigate the use of knowledge-based methods in degraded environments, feature extrapolation of acoustic-phonetic features based on Gaussian mixture models is examined. This process is applied to a stop place detection module that uses burst release and vowel onset cues for consonant-vowel tokens of English. Results show that classification performance is enhanced in telephone channel-degraded speech, with extrapolated acoustic-phonetic features reaching or exceeding performance using estimated Mel-frequency cepstral coefficients (MFCCs). Results also show acoustic-phonetic features may be combined with MFCCs for best performance, suggesting these features provide information complementary to MFCCs.
Exl, Lukas; Mauser, Norbert J.; Schrefl, Thomas; Suess, Dieter
2017-10-01
A practical and efficient scheme for the higher order integration of the Landau-Lifschitz-Gilbert (LLG) equation is presented. The method is based on extrapolation of the two-step explicit midpoint rule and incorporates adaptive time step and order selection. We make use of a piecewise time-linear stray field approximation to reduce the necessary work per time step. The approximation to the interpolated operator is embedded into the extrapolation process to keep in step with the hierarchic order structure of the scheme. We verify the approach by means of numerical experiments on a standardized NIST problem and compare with a higher order embedded Runge-Kutta formula. The efficiency of the presented approach increases when the stray field computation takes a larger portion of the costs for the effective field evaluation.
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
Nonlinear Optics and Turbulence
1992-10-01
currently at Queen Mary College, London Patrick Dunne, (Ph.D., 1987, M.I.T., Hydrodynamic Stability, Nonlinear Waves), 1987-1988. Alecsander Dyachenko...U I I I U I I 3 9 3 V. BIOGRAPHIES A. FACULTY BRUCE BAYLY, 31, Ph.D. 1986, Princeton University. Postdoctoral visiting member 1986-88 at Courant...Caputo, A. C. Newell, and M. Shelley , "Nonlinear Wave Propagation Through a Random Medium and Soliton Tunneling", Integrable Systems and
Wang, Z.; Kwok, KWH; Lui, GCS; Zhou, G; Lee, JS; Lam, MHW; Leung, KMY
2015-01-01
Due to a lack of saltwater toxicity data in tropical regions, toxicity data generated from temperate or cold water species endemic to North America and Europe are often adopted to derive water quality guidelines (WQG) for protecting tropical marine ecosystems. Given the differences in species composition and environmental attributes between tropical and temperate saltwater ecosystems, there are conceivable uncertainties in such ‘temperate-to-tropic’ extrapolations. This ...
Xia, Hong; Luo, Zhendong
2017-01-01
In this study, we devote ourselves to establishing a stabilized mixed finite element (MFE) reduced-order extrapolation (SMFEROE) model holding seldom unknowns for the two-dimensional (2D) unsteady conduction-convection problem via the proper orthogonal decomposition (POD) technique, analyzing the existence and uniqueness and the stability as well as the convergence of the SMFEROE solutions and validating the correctness and dependability of the SMFEROE model by means of numerical simulations.
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Handbook of nonlinear optical crystals
Dmitriev, Valentin G; Nikogosyan, David N
1991-01-01
This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics
Fallou, Hélène; Cimetière, Nicolas; Giraudet, Sylvain; Wolbert, Dominique; Le Cloirec, Pierre
2016-01-15
Activated carbon fiber cloths (ACFC) have shown promising results when applied to water treatment, especially for removing organic micropollutants such as pharmaceutical compounds. Nevertheless, further investigations are required, especially considering trace concentrations, which are found in current water treatment. Until now, most studies have been carried out at relatively high concentrations (mg L(-1)), since the experimental and analytical methodologies are more difficult and more expensive when dealing with lower concentrations (ng L(-1)). Therefore, the objective of this study was to validate an extrapolation procedure from high to low concentrations, for four compounds (Carbamazepine, Diclofenac, Caffeine and Acetaminophen). For this purpose, the reliability of the usual adsorption isotherm models, when extrapolated from high (mg L(-1)) to low concentrations (ng L(-1)), was assessed as well as the influence of numerous error functions. Some isotherm models (Freundlich, Toth) and error functions (RSS, ARE) show weaknesses to be used as an adsorption isotherms at low concentrations. However, from these results, the pairing of the Langmuir-Freundlich isotherm model with Marquardt's percent standard of deviation was evidenced as the best combination model, enabling the extrapolation of adsorption capacities by orders of magnitude.
Ketcheson, David I.
2014-06-13
We compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge–Kutta pairs. We consider orders four through twelve, including both serial and parallel implementations. We cast extrapolation and deferred correction methods as fixed-order Runge–Kutta methods, providing a natural framework for the comparison. The stability and accuracy properties of the methods are analyzed by theoretical measures, and these are compared with the results of numerical tests. In serial, the eighth-order pair of Prince and Dormand (DOP8) is most efficient. But other high-order methods can be more efficient than DOP8 when implemented in parallel. This is demonstrated by comparing a parallelized version of the wellknown ODEX code with the (serial) DOP853 code. For an N-body problem with N = 400, the experimental extrapolation code is as fast as the tuned Runge–Kutta pair at loose tolerances, and is up to two times as fast at tight tolerances.
Energy Technology Data Exchange (ETDEWEB)
Reynaldo, S. R. [Development Centre of Nuclear Technology, Posgraduate Course in Science and Technology of Radiations, Minerals and Materials / CNEN, Av. Pte. Antonio Carlos 6627, 31270-901 Belo Horizonte, Minas Gerais (Brazil); Benavente C, J. A.; Da Silva, T. A., E-mail: sirr@cdtn.br [Development Centre of Nuclear Technology / CNEN, Av. Pte. Antonio Carlos 6627, 31270-901 Belo Horizonte, Minas Gerais (Brazil)
2015-10-15
Beta Secondary Standard 2 (Bss 2) provides beta radiation fields with certified values of absorbed dose to tissue and the derived operational radiation protection quantities. As part of the quality assurance, metrology laboratories are required to verify the reliability of the Bss-2 system by performing additional verification measurements. In the CDTN Calibration Laboratory, the absorbed dose rates and their angular variation in the {sup 90}Sr/{sup 90}Y and {sup 85}Kr beta radiation fields were studied. Measurements were done with a 23392 model PTW extrapolation chamber and with Gafchromic radiochromic films on a PMMA slab phantom. In comparison to the certificate values provided by the Bss-2, absorbed dose rates measured with the extrapolation chamber differed from -1.4 to 2.9% for the {sup 90}Sr/{sup 90}Y and -0.3% for the {sup 85}Kr fields; their angular variation showed differences lower than 2% for incidence angles up to 40-degrees and it reached 11% for higher angles, when compared to ISO values. Measurements with the radiochromic film showed an asymmetry of the radiation field that is caused by a misalignment. Differences between the angular variations of absorbed dose rates determined by both dosimetry systems suggested that some correction factors for the extrapolation chamber that were not considered should be determined. (Author)
Scott, Bradley J; Klein, Agnes V; Wang, Jian
2015-03-01
Monoclonal antibodies have become mainstays of treatment for many diseases. After more than a decade on the Canadian market, a number of authorized monoclonal antibody products are facing patent expiry. Given their success, most notably in the areas of oncology and autoimmune disease, pharmaceutical and biotechnology companies are eager to produce their own biosimilar versions and have begun manufacturing and testing for a variety of monoclonal antibody products. In October of 2013, the first biosimilar monoclonal antibody products were approved by the European Medicines Agency (Remsima™ and Inflectra™). These products were authorized by Health Canada shortly after; however, while the EMA allowed for extrapolation to all of the indications held by the reference product, Health Canada limited extrapolation to a subset of the indications held by the reference product, Remicade®. The purpose of this review is to discuss the Canadian regulatory framework for the authorization of biosimilar mAbs with specific discussion around the clinical requirements for establishing (bio)-similarity and to present the principles that are used in the clinical assessment of New Drug Submissions for intended biosimilar monoclonal antibodies. Health Canada's current views regarding indication extrapolation, product interchangeability, and post-market surveillance are discussed as well.
Ground state energy of the δ-Bose and Fermi gas at weak coupling from double extrapolation
Prolhac, Sylvain
2017-04-01
We consider the ground state energy of the Lieb–Liniger gas with δ interaction in the weak coupling regime γ \\to 0 . For bosons with repulsive interaction, previous studies gave the expansion {{e}\\text{B}}≤ft(γ \\right)≃ γ -4{γ3/2}/3π +≤ft(1/6-1/{π2}\\right){γ2} . Using a numerical solution of the Lieb–Liniger integral equation discretized with M points and finite strength γ of the interaction, we obtain very accurate numerics for the next orders after extrapolation on M and γ. The coefficient of {γ5/2} in the expansion is found to be approximately equal to -0.001 587 699 865 505 944 989 29 , accurate within all digits shown. This value is supported by a numerical solution of the Bethe equations with N particles, followed by extrapolation on N and γ. It was identified as ≤ft(3\\zeta (3)/8-1/2\\right)/{π3} by G Lang. The next two coefficients are also guessed from the numerics. For balanced spin 1/2 fermions with attractive interaction, the best result so far for the ground state energy has been {{e}\\text{F}}≤ft(γ \\right)≃ {π2}/12-γ /2+{γ2}/6 . An analogue double extrapolation scheme leads to the value -\\zeta (3)/{π4} for the coefficient of {γ3} .
Eliav, Ephraim; Vilkas, Marius J; Ishikawa, Yasuyuki; Kaldor, Uzi
2005-06-08
The intermediate Hamiltonian (IH) coupled-cluster method makes possible the use of very large model spaces in coupled-cluster calculations without running into intruder states. This is achieved at the cost of approximating some of the IH matrix elements, which are not taken at their rigorous effective Hamiltonian (EH) value. The extrapolated intermediate Hamiltonian (XIH) approach proposed here uses a parametrized IH and extrapolates it to the full EH, with model spaces larger by several orders of magnitude than those possible in EH coupled-cluster methods. The flexibility and resistance to intruders of the IH approach are thus combined with the accuracy of full EH. Various extrapolation schemes are described. A pilot application to the electron affinities (EAs) of alkali atoms is presented, where converged EH results are obtained by XIH for model spaces of approximately 20,000 determinants; direct EH calculations converge only for a one-dimensional model space. Including quantum electrodynamic effects, the average XIH error for the EAs is 0.6 meV and the largest error is 1.6 meV. A new reference estimate for the EA of Fr is proposed at 486+/-2 meV.
Directory of Open Access Journals (Sweden)
Alexander Pechenkin
2015-10-01
Full Text Available The article is concerned with the philosophical talks which became popular in the 1980s and have kept their popularity till now–the philosophical essays about self-organization. The author attempts to find out as to which extent are these essays founded on the scientific theory to which they regularly refer, that is, Ilya Prigogine’s non-linear thermodynamics. The author insists that the equivalent of self-organization in Prigogine’s theoretical physics is the concept of dissipative structure. The concept of selforganization, as it is used in philosophical literature, presupposes a sequence of extrapolations, the first extrapolation being conducted by Prigogine and his coauthors. They became to use the concept of dissipative structure beyond the rigorous theory of this phenomenon. The subsequent step was that the scientific term “dissipative structure” was replaced by the vague concept “self-organization” in many popular and semi-popular books and papers. The author also emphasizes that by placing the concept of self-organization into the framework of philosophical concepts (the picture of the world, the ideals of scientific thought, the contemporary scientific revolution, etc. a philosopher conducts the extrapolation of extrapolation and comes to a kind of what Edmund Husserl called Weltanschauung (‘worldview’ philosophy.
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Patient-bounded extrapolation using low-dose priors for volume-of-interest imaging in C-arm CT
Energy Technology Data Exchange (ETDEWEB)
Xia, Y.; Maier, A.; Berger, M.; Hornegger, J. [Pattern Recognition Lab, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen 91058 (Germany); Bauer, S. [Siemens AG, Healthcare Sector, Forchheim 91301 (Germany)
2015-04-15
Purpose: Three-dimensional (3D) volume-of-interest (VOI) imaging with C-arm systems provides anatomical information in a predefined 3D target region at a considerably low x-ray dose. However, VOI imaging involves laterally truncated projections from which conventional reconstruction algorithms generally yield images with severe truncation artifacts. Heuristic based extrapolation methods, e.g., water cylinder extrapolation, typically rely on techniques that complete the truncated data by means of a continuity assumption and thus appear to be ad-hoc. It is our goal to improve the image quality of VOI imaging by exploiting existing patient-specific prior information in the workflow. Methods: A necessary initial step prior to a 3D acquisition is to isocenter the patient with respect to the target to be scanned. To this end, low-dose fluoroscopic x-ray acquisitions are usually applied from anterior–posterior (AP) and medio-lateral (ML) views. Based on this, the patient is isocentered by repositioning the table. In this work, we present a patient-bounded extrapolation method that makes use of these noncollimated fluoroscopic images to improve image quality in 3D VOI reconstruction. The algorithm first extracts the 2D patient contours from the noncollimated AP and ML fluoroscopic images. These 2D contours are then combined to estimate a volumetric model of the patient. Forward-projecting the shape of the model at the eventually acquired C-arm rotation views gives the patient boundary information in the projection domain. In this manner, we are in the position to substantially improve image quality by enforcing the extrapolated line profiles to end at the known patient boundaries, derived from the 3D shape model estimate. Results: The proposed method was evaluated on eight clinical datasets with different degrees of truncation. The proposed algorithm achieved a relative root mean square error (rRMSE) of about 1.0% with respect to the reference reconstruction on
Energy Technology Data Exchange (ETDEWEB)
Croom, Edward L.; Shafer, Timothy J.; Evans, Marina V.; Mundy, William R.; Eklund, Chris R.; Johnstone, Andrew F.M.; Mack, Cina M.; Pegram, Rex A., E-mail: pegram.rex@epa.gov
2015-02-15
Approaches for extrapolating in vitro toxicity testing results for prediction of human in vivo outcomes are needed. The purpose of this case study was to employ in vitro toxicokinetics and PBPK modeling to perform in vitro to in vivo extrapolation (IVIVE) of lindane neurotoxicity. Lindane cell and media concentrations in vitro, together with in vitro concentration-response data for lindane effects on neuronal network firing rates, were compared to in vivo data and model simulations as an exercise in extrapolation for chemical-induced neurotoxicity in rodents and humans. Time- and concentration-dependent lindane dosimetry was determined in primary cultures of rat cortical neurons in vitro using “faux” (without electrodes) microelectrode arrays (MEAs). In vivo data were derived from literature values, and physiologically based pharmacokinetic (PBPK) modeling was used to extrapolate from rat to human. The previously determined EC{sub 50} for increased firing rates in primary cultures of cortical neurons was 0.6 μg/ml. Media and cell lindane concentrations at the EC{sub 50} were 0.4 μg/ml and 7.1 μg/ml, respectively, and cellular lindane accumulation was time- and concentration-dependent. Rat blood and brain lindane levels during seizures were 1.7–1.9 μg/ml and 5–11 μg/ml, respectively. Brain lindane levels associated with seizures in rats and those predicted for humans (average = 7 μg/ml) by PBPK modeling were very similar to in vitro concentrations detected in cortical cells at the EC{sub 50} dose. PBPK model predictions matched literature data and timing. These findings indicate that in vitro MEA results are predictive of in vivo responses to lindane and demonstrate a successful modeling approach for IVIVE of rat and human neurotoxicity. - Highlights: • In vitro to in vivo extrapolation for lindane neurotoxicity was performed. • Dosimetry of lindane in a micro-electrode array (MEA) test system was assessed. • Cell concentrations at the MEA EC
Directory of Open Access Journals (Sweden)
J. J. Vélez
2009-02-01
Full Text Available A Regional Water Resources study was performed at basins within and draining to the Basque Country Region (N of Spain, with a total area of approximately 8500 km^{2}. The objective was to obtain daily and monthly long-term discharges in 567 points, most of them ungauged, with basin areas ranging from 0.25 to 1850 km^{2}. In order to extrapolate the calibrations at gauged points to the ungauged ones, a distributed and conceptually based model called TETIS was used. In TETIS the runoff production is modelled using five linked tanks at the each cell with different outflow relationships at each tank, which represents the main hydrological processes as snowmelt, evapotranspiration, overland flow, interflow and base flow. The routing along the channels' network couples its geomorphologic characteristics with the kinematic wave approach. The parameter estimation methodology tries to distinguish between the effective parameter used in the model at the cell scale, and the watershed characteristic estimated from the available information, being the best estimation without losing its physical meaning. The relationship between them can be considered as a correction function or, in its simple form, a correction factor. The correction factor can take into account the model input errors, the temporal and spatial scale effects and the watershed characteristics. Therefore, it is reasonable to assume the correction factor is the same for each parameter to all cells within the watershed. This approach reduces drastically the number of parameter to be calibrated, because only the common correction factors are calibrated instead of parameter maps (number of parameters times the number of cells. In this way, the calibration can be performed using automatic methodologies. In this work, the Shuffled Complex Evolution – University of Arizona, SCE-UA algorithm was used. The available recent year's data was used to calibrate the model in 20 of
Energy Technology Data Exchange (ETDEWEB)
Davis, C.G.
1990-01-01
The advent of nonlinear pulsation theory really coincides with the development of the large computers after the second world war. Christy and Stobbie were the first to make use of finite difference techniques on computers to model the bumps'' observed in the classical Cepheid light and velocity curves, the so-called Hertzsprung'' sequence. Following this work a more sophisticated analysis of the light and velocity curves from the models was made by Simon and Davis using Fourier techniques. Recently a simpler amplitude equation formalism has been developed that helps explain this resonance mechanism. The determination of Population I Cepheid masses by nonlinear methods will be discussed. For the lower mass objects, such as RR Lyrae and BL Her. stars, we find general agreement using evolutionary masses and nonlinear pulsation theory. An apparent difficulty of nonlinear pulsation theory occurs in the understanding of double'' mode pulsation, which will also be discussed. Recent studies in nonlinear pulsation theory have dealt with the question of mode selection, period doubling and the trends towards chaotic behavior such as is observed in the transition from W Virginis to RV Tauri-like stars. 10 refs., 1 fig., 2 tabs.
Nonlinear optics response of semiconductor quantum wells under high magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Chemla, D.S.
1993-07-01
Recent investigations on the nonlinear optical response of semiconductor quantum wells in a strong perpendicular magnetic field, H, are reviewed. After some introductory material the evolution of the linear optical properties of GaAs QW`s as a function of H is discussed; an examination is made of how the magneto-excitons (MX) extrapolate continuously between quasi-2D QW excitons (X) when H = 0, and pairs of Landau levels (LL) when H {yields} {infinity}. Next, femtosecond time resolved investigations of their nonlinear optical response are presented; the evolution of MX-MX interactions with increasing H is stressed. Finally, how, as the dimensionality is reduced by application of H, the number of scattering channels is limited and relaxation of electron-hole pairs is affected. How nonlinear optical spectroscopy can be exploited to access the relaxation of angular momentum within magneto-excitons is also discussed.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear optomechanical paddle nanocavities
Kaviani, Hamidreza; Wu, Marcelo; Ghobadi, Roohollah; Barclay, Paul E
2014-01-01
A photonic crystal optomechanical system combining strong nonlinear optomechanical coupling, low effective mass and large optical mode spacing is introduced. This nanoscale "paddle nanocavity" device supports mechanical resonances with effective mass of 300--600 fg which couple nonlinearly to co-localized optical modes with a quadratic optomechanical coupling coefficient $g^{(2)} > 2\\pi\\times400$ MHz/nm$^2$, and a two phonon to single photon optomechanical coupling rate $\\Delta \\omega_0 > 2\\pi\\times 16$ Hz. This coupling relies on strong phonon-photon interactions in a structure whose optical mode spectrum is highly non--degenerate. Simulations indicate that nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T $> 50 $ mK, and that measurement of phonon shot noise is achievable.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Nonlinear Photonic Crystal Fibers
DEFF Research Database (Denmark)
Hansen, Kim Per
2004-01-01
, leading to reduced mode confinement and dispersion flexibility. In this thesis, we treat the nonlinear photonic crystal fiber – a special sub-class of photonic crystal fibers, the core of which has a diameter comparable to the wavelength of the light guided in the fiber. The small core results in a large...... nonlinear coefficient and in various applications, it is therefore possible to reduce the required fiber lengths quite dramatically, leading to increased stability and efficiency. Furthermore, it is possible to design these fibers with zero-dispersion at previously unreachable wavelengths, paving the way...... for completely new applications, especially in and near the visible wavelength region. One such application is supercontinuum generation. Supercontinuum generation is extreme broadening of pulses in a nonlinear medium (in this case a small-core fiber), and depending on the dispersion of the fiber, it is possible...
Schmidt, Bruno E; Ernotte, Guilmot; Clerici, Matteo; Morandotti, Roberto; Ibrahim, Heide; Legare, Francois
2016-01-01
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new dipole radiation whose amplitude, frequency and phase differ from the incoming fields. Such high fields are typically achieved with ultra-short, femtosecond (1fs = 10-15 sec.) laser pulses containing very broad frequency spectra. Here, the matter not only couples incoming and outgoing fields but also causes different spectral components to interact and mix through a convolution process. In this contribution, we describe how frequency domain nonlinear optics overcomes the shortcomings arising from this convolution in conventional time domain nonlinear optics1. We generate light fields with previously inaccessible properties because the uncontrolled coupling of amplitudes and phases is turned off. For example, arbitrary phase functions are transferred linearly to the second har...
Nonlinear optomechanics with graphene
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Nonlinear Analysis of Buckling
Directory of Open Access Journals (Sweden)
Psotný Martin
2014-06-01
Full Text Available The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
Nonlinear airship aeroelasticity
Bessert, N.; Frederich, O.
2005-12-01
The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.
Agrawal, Govind
2012-01-01
Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Fundamentals of nonlinear optics
Powers, Peter E
2011-01-01
Peter Powers's rigorous but simple description of a difficult field keeps the reader's attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author's writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become pop
Tunable nonlinear graphene metasurfaces
Smirnova, Daria A; Kivshar, Yuri S; Khanikaev, Alexander B
2015-01-01
We introduce the concept of nonlinear graphene metasurfaces employing the controllable interaction between a graphene layer and a planar metamaterial. Such hybrid metasurfaces support two types of subradiant resonant modes, asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. High tunability of graphene plasmons facilitates strong interaction between the subradiant modes, modifying the spectral position and lifetime of the associated Fano resonances. We demonstrate that strong resonant interaction, combined with the subwavelength localization of plasmons, leads to the enhanced nonlinear response and high efficiency of the second-harmonic generation.
Nonlinear effects in optical fibers
Ferreira, Mario F
2011-01-01
Cutting-edge coverage of nonlinear phenomena occurring inside optical fibers Nonlinear fiber optics is a specialized part of fiber optics dealing with optical nonlinearities and their applications. As fiber-optic communication systems have become more advanced and complex, the nonlinear effects in optical fibers have increased in importance, as they adversely affect system performance. Paradoxically, the same nonlinear phenomena also offer the promise of addressing the bandwidth bottleneck for signal processing for future ultra-high speed optical networks. Nonlinear Effects in Optical Fiber
Directory of Open Access Journals (Sweden)
Orien M W Richmond
Full Text Available Species distribution models (SDMs are increasingly used for extrapolation, or predicting suitable regions for species under new geographic or temporal scenarios. However, SDM predictions may be prone to errors if species are not at equilibrium with climatic conditions in the current range and if training samples are not representative. Here the controversial "Pleistocene rewilding" proposal was used as a novel example to address some of the challenges of extrapolating modeled species-climate relationships outside of current ranges. Climatic suitability for three proposed proxy species (Asian elephant, African cheetah and African lion was extrapolated to the American southwest and Great Plains using Maxent, a machine-learning species distribution model. Similar models were fit for Oryx gazella, a species native to Africa that has naturalized in North America, to test model predictions. To overcome biases introduced by contracted modern ranges and limited occurrence data, random pseudo-presence points generated from modern and historical ranges were used for model training. For all species except the oryx, models of climatic suitability fit to training data from historical ranges produced larger areas of predicted suitability in North America than models fit to training data from modern ranges. Four naturalized oryx populations in the American southwest were correctly predicted with a generous model threshold, but none of these locations were predicted with a more stringent threshold. In general, the northern Great Plains had low climatic suitability for all focal species and scenarios considered, while portions of the southern Great Plains and American southwest had low to intermediate suitability for some species in some scenarios. The results suggest that the use of historical, in addition to modern, range information and randomly sampled pseudo-presence points may improve model accuracy. This has implications for modeling range shifts of
Richmond, Orien M W; McEntee, Jay P; Hijmans, Robert J; Brashares, Justin S
2010-09-22
Species distribution models (SDMs) are increasingly used for extrapolation, or predicting suitable regions for species under new geographic or temporal scenarios. However, SDM predictions may be prone to errors if species are not at equilibrium with climatic conditions in the current range and if training samples are not representative. Here the controversial "Pleistocene rewilding" proposal was used as a novel example to address some of the challenges of extrapolating modeled species-climate relationships outside of current ranges. Climatic suitability for three proposed proxy species (Asian elephant, African cheetah and African lion) was extrapolated to the American southwest and Great Plains using Maxent, a machine-learning species distribution model. Similar models were fit for Oryx gazella, a species native to Africa that has naturalized in North America, to test model predictions. To overcome biases introduced by contracted modern ranges and limited occurrence data, random pseudo-presence points generated from modern and historical ranges were used for model training. For all species except the oryx, models of climatic suitability fit to training data from historical ranges produced larger areas of predicted suitability in North America than models fit to training data from modern ranges. Four naturalized oryx populations in the American southwest were correctly predicted with a generous model threshold, but none of these locations were predicted with a more stringent threshold. In general, the northern Great Plains had low climatic suitability for all focal species and scenarios considered, while portions of the southern Great Plains and American southwest had low to intermediate suitability for some species in some scenarios. The results suggest that the use of historical, in addition to modern, range information and randomly sampled pseudo-presence points may improve model accuracy. This has implications for modeling range shifts of organisms in response
Energy Technology Data Exchange (ETDEWEB)
Miyazawa, J., E-mail: miyazawa@LHD.nifs.ac.jp [National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292 (Japan); Goto, T.; Morisaki, T.; Goto, M.; Sakamoto, R.; Motojima, G.; Peterson, B.J.; Suzuki, C.; Ida, K.; Yamada, H.; Sagara, A. [National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292 (Japan)
2011-12-15
Highlights: Black-Right-Pointing-Pointer The DPE method predicts temperature and density profiles in a fusion reactor. Black-Right-Pointing-Pointer This method is based on the gyro-Bohm type parameter dependence. Black-Right-Pointing-Pointer The size of fusion reactor is determined to fulfill the power balance. Black-Right-Pointing-Pointer The reactor size is proportional to a factor and -4/3 power of the magnetic field. Black-Right-Pointing-Pointer This factor can be a measure of plasma performance like the fusion triple product. - Abstract: A new method named direct profile extrapolation (DPE) has been developed to estimate the radial profiles of temperature and density in a fusion reactor. This method directly extrapolates the radial profiles observed in present experiments to the fusion reactor condition assuming gyro-Bohm type parameter dependence. The magnetohydrodynamic equilibrium that fits the experimental profile data is used to determine the plasma volume. Four enhancement factors for the magnetic field strength, the density, the plasma beta, and the energy confinement are assumed. Then, the plasma size is determined so as to fulfill the power balance in the reactor plasma. The plasma performance can be measured by an index, C{sub exp}, introduced in the DPE method. The minimum magnetic stored energy of the fusion reactor to achieve self-ignition is shown to be proportional to the cube of C{sub exp} and inversely proportional to the square of magnetic field strength. Using this method, the design window of a self-ignited fusion reactor that can be extrapolated from recent experimental results in the Large Helical Device (LHD) is considered. Also discussed is how large an enhancement is needed for the LHD experiment to ensure the helical reactor design of FFHR2m2.
Barman, Stephen L; Jean, Gary W; Dinsfriend, William M; Gerber, David E
2016-02-01
The treatment of adults who present with rare pediatric tumors is not characterized well in the literature. We report an instance of a 40-year-old African American woman with a diagnosis of choroid plexus carcinoma admitted to the intensive care unit for severe sepsis seven days after receiving chemotherapy consisting of carboplatin (350 mg/m(2) on Days 1 and 2 plus etoposide 100 mg/m(2) on Days 1-5). Her laboratory results were significant for an absolute neutrophil count of 0/µL and blood cultures positive for Capnocytophagia species. She was supported with broad spectrum antibiotics and myeloid growth factors. She eventually recovered and was discharged in stable condition. The management of adults with malignancies most commonly seen in pediatric populations presents substantial challenges. There are multiple age-specific differences in renal and hepatic function that explain the need for higher dosing in pediatric patients without increasing the risk of toxicity. Furthermore, differences in pharmacokinetic parameters such as absorption, distribution, and clearance are present but are less likely to affect patients. It is expected that the pediatric population will have more bone marrow reserve and, therefore, less susceptible to myelosuppression. The extrapolation of pediatric dosing to an adult presents a problematic situation in treating adults with malignancies that primarily effect pediatric patients. We recommend extrapolating from adult treatment regimens with similar agents rather than extrapolating from pediatric treatment regimens to reduce the risk of toxicity. We also recommend the consideration of adding myeloid growth factors. If the treatment is tolerated without significant toxicity, dose escalation can be considered.
Directory of Open Access Journals (Sweden)
Ravichandran R
2009-01-01
Full Text Available The objective of the present study is to establish radiation standards for absorbed doses, for clinical high energy linear accelerator beams. In the nonavailability of a cobalt-60 beam for arriving at Nd, water values for thimble chambers, we investigated the efficacy of perspex mounted extrapolation chamber (EC used earlier for low energy x-rays and beta dosimetry. Extrapolation chamber with facility for achieving variable electrode separations 10.5mm to 0.5mm using micrometer screw was used for calibrations. Photon beams 6 MV and 15 MV and electron beams 6 MeV and 15 MeV from Varian Clinac linacs were calibrated. Absorbed Dose estimates to Perspex were converted into dose to solid water for comparison with FC 65 ionisation chamber measurements in water. Measurements made during the period December 2006 to June 2008 are considered for evaluation. Uncorrected ionization readings of EC for all the radiation beams over the entire period were within 2% showing the consistency of measurements. Absorbed doses estimated by EC were in good agreement with in-water calibrations within 2% for photons and electron beams. The present results suggest that extrapolation chambers can be considered as an independent measuring system for absorbed dose in addition to Farmer type ion chambers. In the absence of standard beam quality (Co-60 radiations as reference Quality for Nd,water the possibility of keeping EC as Primary Standards for absorbed dose calibrations in high energy radiation beams from linacs should be explored. As there are neither Standard Laboratories nor SSDL available in our country, we look forward to keep EC as Local Standard for hospital chamber calibrations. We are also participating in the IAEA mailed TLD intercomparison programme for quality audit of existing status of radiation dosimetry in high energy linac beams. The performance of EC has to be confirmed with cobalt-60 beams by a separate study, as linacs are susceptible for minor
Directory of Open Access Journals (Sweden)
Ezekiel Uba Nwose
2010-04-01
Full Text Available Background: There are many different methods for the assessment of whole blood viscosity, but not every pathology unit has equipment for any of the methods. However, a validated arithmetic method exists whereby whole blood viscosity can be extrapolated from haematocrit and total serum proteins. Aims: The objective of this work is to develop an algorithm in the form of a chart by which clinicians can easily extrapolate whole blood viscosity values in their consulting rooms or on the ward. Another objective is to suggest normal, subnormal and critical reference ranges applicable to this method. Materials and Methods: Whole blood viscosity at high shear stress was determined, from various possible pairs of haematocrit and total proteins. A chart was formulated so that whole blood viscosity can be extrapolated. After determination of two standard deviations from the mean and ascertainment of symmetric distribution, normal and abnormal reference ranges were defined. Results: The clinicians’ user-friendly chart is presented. Considering presumptive lower and upper limits, the continuum of ≤14.28, 14.29 – 15.00, 15.01 – 19.01, 19.02 – 19.39 and ≥19.40 (208 Sec-1 is obtained as reference ranges for critically low, subnormal low, normal, subnormal high and critically high whole blood viscosity levels respectively. Conclusion: This article advances a validated method to provide a user-friendly chart that would enable clinicians to assess whole blood viscosity for any patients who has results for full blood count and total proteins. It would make the assessment of whole blood viscosity costless and the neglect of a known cardiovascular risk factor less excusable.
Energy Technology Data Exchange (ETDEWEB)
Sussmann, R.; Homburg, F.; Freudenthaler, V.; Jaeger, H. [Frauenhofer Inst. fuer Atmosphaerische Umweltforschung, Garmisch-Partenkirchen (Germany)
1997-12-31
The CCD image of a persistent contrail and the coincident LIDAR measurement are presented. To extrapolate the LIDAR derived optical thickness to the video field of view an anisotropy correction and calibration has to be performed. Observed bright halo components result from highly regular oriented hexagonal crystals with sizes of 200 {mu}m-2 mm. This explained by measured ambient humidities below the formation threshold of natural cirrus. Optical thickness from LIDAR shows significant discrepancies to the result from coincident NOAA-14 data. Errors result from anisotropy correction and parameterized relations between AVHRR channels and optical properties. (author) 28 refs.
Cruz Uribe, David; Pérez Moreno, Carlos
2000-01-01
We give several extrapolation theorems for pairs of weights of the form (w, Mkw) and (w, (Mw/w)r w), where w is any non-negative function, r>1, and Mk is the kth iterate of the Hardy–Littlewood maximal operator. As an application we show that our results can be used to extend and sharpen results for square functions and singular integral operators by Chang et al. (1985, Comment. Math. Helv.60, 217–246), Chanillo and Wheeden (1987, Indiana Univ. Math. J.36, 277–294), Wilson (1987, Duke Math. J...
Reynaldo, S R; Benavente, J A; Da Silva, T A
2016-11-01
Beta Secondary Standard 2 (BSS 2) provides beta radiation fields with certified values of absorbed dose to tissue and the derived operational radiation protection quantities. As part of the quality assurance, the reliability of the CDTN BSS2 system was verified through measurements in the (90)Sr/(90)Y and (85)Kr beta radiation fields. Absorbed dose rates and their angular variation were measured with a 23392 model PTW extrapolation chamber and with Gafchromic radiochromic films on a PMMA slab phantom. The feasibility of using both methods was analyzed.
Rong, Lu; Latychevskaia, Tatiana; Wang, Dayong; Zhou, Xun; Huang, Haochong; Li, Zeyu; Wang, Yunxin
2014-07-14
We report here on terahertz (THz) digital holography on a biological specimen. A continuous-wave (CW) THz in-line holographic setup was built based on a 2.52 THz CO(2) pumped THz laser and a pyroelectric array detector. We introduced novel statistical method of obtaining true intensity values for the pyroelectric array detector's pixels. Absorption and phase-shifting images of a dragonfly's hindwing were reconstructed simultaneously from single in-line hologram. Furthermore, we applied phase retrieval routines to eliminate twin image and enhanced the resolution of the reconstructions by hologram extrapolation beyond the detector area. The finest observed features are 35 μm width cross veins.
Nonlinear elliptic systems with exponential nonlinearities
Directory of Open Access Journals (Sweden)
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Ritz, Christian; Parmigiani, Giovanni
2009-01-01
R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Trirefringence in nonlinear metamaterials
De Lorenci, Vitorio A
2012-01-01
We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
Nonlinear fibre optics overview
DEFF Research Database (Denmark)
Travers, J. C.; Frosz, Michael Henoch; Dudley, J. M.
2010-01-01
, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers...
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Leitao, J C; Gerlach, M; Altmann, E G
2016-01-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\\sim x^\\beta, \\beta \
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Nonlinearities in Microwave Superconductivity
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2012-01-01
The research is focused on the modeling of nonlinear properties of High Temperature Superconducting (HTS) thin films, using Bardeen, Cooper, Schrieffer and Lumped Element Circuit theories, with purpose to enhance microwave power handling capabilities of microwave filters and optimize design of microwave circuits in micro- and nano- electronics.
Nonlinear tsunami generation mechanism
Directory of Open Access Journals (Sweden)
M. A. Nosov
2001-01-01
Full Text Available The nonlinear mechanism of long gravitational surface water wave generation by high-frequency bottom oscillations in a water layer of constant depth is investigated analytically. The connection between the surface wave amplitude and the parameters of bottom oscillations and source length is investigated.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...
Method and system for non-linear motion estimation
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Nonlinear analysis of doubly curved shells: An analytical approach
Indian Academy of Sciences (India)
Y Nath; K Sandeep
2000-08-01
Dynamic analogues of vin Karman-Donnell type shell equations for doubly curved, thin isotropic shells in rectangular planform are formulated and expressed in displacement components. These nonlinear partial differential equations of motion are linearized by using a quadratic extrapolation technique. The spatial and temporal discretization of differential equatoins have been carried out by finite-degree Chebyshev polynomials and implicit Houbolt time-marching techniques respectively. Multiple regression besed on the least square error norm is employed to eliminate the incompatability generated due to spatial discretization (equations > unknowns). Spatial convergence study revealed that nine term expansion of each displacement in and respectively, is sufficient to yield fairly accurate results. Clamped and simply supported immovable doubly curved shallow shells are analysed. Results have been compared with those obtained by other numerical methods. Considering uniformly distributed normal loading, the results of static and dynamic analyses are presented.
Nonlinear Optical Terahertz Technology Project
National Aeronautics and Space Administration — Our approach is based on high-Q optical WGM resonators made with a nonlinear crystal. Such resonators have been demonstrated to dramatically enhance nonlinear...
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.