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Sample records for saddle point approximation

Approximate Dual Averaging Method for Multiagent Saddle-Point Problems with Stochastic Subgradients

Directory of Open Access Journals (Sweden)

Deming Yuan

2014-01-01

Full Text Available This paper considers the problem of solving the saddle-point problem over a network, which consists of multiple interacting agents. The global objective function of the problem is a combination of local convex-concave functions, each of which is only available to one agent. Our main focus is on the case where the projection steps are calculated approximately and the subgradients are corrupted by some stochastic noises. We propose an approximate version of the standard dual averaging method and show that the standard convergence rate is preserved, provided that the projection errors decrease at some appropriate rate and the noises are zero-mean and have bounded variance.
'Saddle-point' ionization

International Nuclear Information System (INIS)

Gay, T.J.; Hale, E.B.; Irby, V.D.; Olson, R.E.; Missouri Univ., Rolla; Berry, H.G.

1988-01-01

We have studied the ionization of rare gases by protons at intermediate energies, i.e., energies at which the velocities of the proton and the target-gas valence electrons are comparable. A significant channel for electron production in the forward direction is shown to be 'saddle-point' ionization, in which electrons are stranded on or near the saddle-point of electric potential between the receding projectile and the ionized target. Such electrons yield characteristic energy spectra, and contribute significantly to forward-electron-production cross sections. Classical trajectory Monte Carlo calculations are found to provide qualitative agreement with our measurements and the earlier measurements of Rudd and coworkers, and reproduce, in detail, the features of the general ionization spectra. (orig.)
Acceleration of saddle-point searches with machine learning

Energy Technology Data Exchange (ETDEWEB)

Peterson, Andrew A., E-mail: andrew-peterson@brown.edu [School of Engineering, Brown University, Providence, Rhode Island 02912 (United States)

2016-08-21

In atomistic simulations, the location of the saddle point on the potential-energy surface (PES) gives important information on transitions between local minima, for example, via transition-state theory. However, the search for saddle points often involves hundreds or thousands of ab initio force calls, which are typically all done at full accuracy. This results in the vast majority of the computational effort being spent calculating the electronic structure of states not important to the researcher, and very little time performing the calculation of the saddle point state itself. In this work, we describe how machine learning (ML) can reduce the number of intermediate ab initio calculations needed to locate saddle points. Since machine-learning models can learn from, and thus mimic, atomistic simulations, the saddle-point search can be conducted rapidly in the machine-learning representation. The saddle-point prediction can then be verified by an ab initio calculation; if it is incorrect, this strategically has identified regions of the PES where the machine-learning representation has insufficient training data. When these training data are used to improve the machine-learning model, the estimates greatly improve. This approach can be systematized, and in two simple example problems we demonstrate a dramatic reduction in the number of ab initio force calls. We expect that this approach and future refinements will greatly accelerate searches for saddle points, as well as other searches on the potential energy surface, as machine-learning methods see greater adoption by the atomistics community.
Acceleration of saddle-point searches with machine learning

International Nuclear Information System (INIS)

Peterson, Andrew A.

2016-01-01

In atomistic simulations, the location of the saddle point on the potential-energy surface (PES) gives important information on transitions between local minima, for example, via transition-state theory. However, the search for saddle points often involves hundreds or thousands of ab initio force calls, which are typically all done at full accuracy. This results in the vast majority of the computational effort being spent calculating the electronic structure of states not important to the researcher, and very little time performing the calculation of the saddle point state itself. In this work, we describe how machine learning (ML) can reduce the number of intermediate ab initio calculations needed to locate saddle points. Since machine-learning models can learn from, and thus mimic, atomistic simulations, the saddle-point search can be conducted rapidly in the machine-learning representation. The saddle-point prediction can then be verified by an ab initio calculation; if it is incorrect, this strategically has identified regions of the PES where the machine-learning representation has insufficient training data. When these training data are used to improve the machine-learning model, the estimates greatly improve. This approach can be systematized, and in two simple example problems we demonstrate a dramatic reduction in the number of ab initio force calls. We expect that this approach and future refinements will greatly accelerate searches for saddle points, as well as other searches on the potential energy surface, as machine-learning methods see greater adoption by the atomistics community.
Acceleration of saddle-point searches with machine learning.

Science.gov (United States)

Peterson, Andrew A

2016-08-21

In atomistic simulations, the location of the saddle point on the potential-energy surface (PES) gives important information on transitions between local minima, for example, via transition-state theory. However, the search for saddle points often involves hundreds or thousands of ab initio force calls, which are typically all done at full accuracy. This results in the vast majority of the computational effort being spent calculating the electronic structure of states not important to the researcher, and very little time performing the calculation of the saddle point state itself. In this work, we describe how machine learning (ML) can reduce the number of intermediate ab initio calculations needed to locate saddle points. Since machine-learning models can learn from, and thus mimic, atomistic simulations, the saddle-point search can be conducted rapidly in the machine-learning representation. The saddle-point prediction can then be verified by an ab initio calculation; if it is incorrect, this strategically has identified regions of the PES where the machine-learning representation has insufficient training data. When these training data are used to improve the machine-learning model, the estimates greatly improve. This approach can be systematized, and in two simple example problems we demonstrate a dramatic reduction in the number of ab initio force calls. We expect that this approach and future refinements will greatly accelerate searches for saddle points, as well as other searches on the potential energy surface, as machine-learning methods see greater adoption by the atomistics community.
The Antitriangular Factorization of Saddle Point Matrices

KAUST Repository

Pestana, J.

2014-01-01

Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners. © 2014 Society for Industrial and Applied Mathematics.
Complex saddle points and the sign problem in complex Langevin simulation

International Nuclear Information System (INIS)

Hayata, Tomoya; Hidaka, Yoshimasa; Tanizaki, Yuya

2016-01-01

We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.
Complex saddle points in QCD at finite temperature and density

Science.gov (United States)

Nishimura, Hiromichi; Ogilvie, Michael C.; Pangeni, Kamal

2014-08-01

The sign problem in QCD at finite temperature and density leads naturally to the consideration of complex saddle points of the action or effective action. The global symmetry CK of the finite-density action, where C is charge conjugation and K is complex conjugation, constrains the eigenvalues of the Polyakov loop operator P at a saddle point in such a way that the action is real at a saddle point, and net color charge is zero. The values of TrFP and TrFP† at the saddle point are real but not identical, indicating the different free energy cost associated with inserting a heavy quark versus an antiquark into the system. At such complex saddle points, the mass matrix associated with Polyakov loops may have complex eigenvalues, reflecting oscillatory behavior in color-charge densities. We illustrate these properties with a simple model which includes the one-loop contribution of gluons and two flavors of massless quarks moving in a constant Polyakov loop background. Confinement-deconfinement effects are modeled phenomenologically via an added potential term depending on the Polyakov loop eigenvalues. For sufficiently large temperature T and quark chemical potential μ, the results obtained reduce to those of perturbation theory at the complex saddle point. These results may be experimentally relevant for the compressed baryonic matter experiment at FAIR.
Electrons at the monkey saddle: A multicritical Lifshitz point

Science.gov (United States)

Shtyk, A.; Goldstein, G.; Chamon, C.

2017-01-01

We consider two-dimensional interacting electrons at a monkey saddle with dispersion ∝px3-3 pxpy2 . Such a dispersion naturally arises at the multicritical Lifshitz point when three Van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior Em∝(Bm ) 3 /2 and related oscillations in thermodynamic and transport properties, such as de Haas-Van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the noninteracting electron fixed point is unstable to interactions under the renormalization-group flow, developing either a superconducting instability or non-Fermi-liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the K and K' points, exhibits an interplay of competing many-body instabilities, namely, s -wave superconductivity, ferromagnetism, and spin- and charge-density waves.
The Sun-Earth saddle point: characterization and opportunities to test general relativity

Science.gov (United States)

Topputo, Francesco; Dei Tos, Diogene A.; Rasotto, Mirco; Nakamiya, Masaki

2018-04-01

The saddle points are locations where the net gravitational accelerations balance. These regions are gathering more attention within the astrophysics community. Regions about the saddle points present clean, close-to-zero background acceleration environments where possible deviations from General Relativity can be tested and quantified. Their location suggests that flying through a saddle point can be accomplished by leveraging highly nonlinear orbits. In this paper, the geometrical and dynamical properties of the Sun-Earth saddle point are characterized. A systematic approach is devised to find ballistic orbits that experience one or multiple passages through this point. A parametric analysis is performed to consider spacecraft initially on L_{1,2} Lagrange point orbits. Sun-Earth saddle point ballistic fly-through trajectories are evaluated and classified for potential use. Results indicate an abundance of short-duration, regular solutions with a variety of characteristics.
Assessment of saddle-point-mass predictions for astrophysical applications

Energy Technology Data Exchange (ETDEWEB)

Kelic, A.; Schmidt, K.H.

2005-07-01

Using available experimental data on fission barriers and ground-state masses, a detailed study on the predictions of different models concerning the isospin dependence of saddle-point masses is performed. Evidence is found that several macroscopic models yield unrealistic saddle-point masses for very neutron-rich nuclei, which are relevant for the r-process nucleosynthesis. (orig.)
Natural Preconditioning and Iterative Methods for Saddle Point Systems

KAUST Repository

Pestana, Jennifer

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness - in terms of rapidity of convergence - is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends.
Approximating chaotic saddles for delay differential equations.

Science.gov (United States)

Taylor, S Richard; Campbell, Sue Ann

2007-04-01

Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.
Approximating chaotic saddles for delay differential equations

Science.gov (United States)

Taylor, S. Richard; Campbell, Sue Ann

2007-04-01

Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a “logistic” delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.
Effect of saddle-point anisotropy on point-defect drift-diffusion into straight dislocations

International Nuclear Information System (INIS)

Skinner, B.C.; Woo, C.H.

1983-02-01

Effects on point-defect drift-diffusion in the strain fields of edge or screw dislocations, due to the anisotropy of the point defect in its saddle-point configuration, are investigated. Expressions for sink strength and bias that include the saddle-point shape effect are derived, both in the absence and presence of an externally applied stress. These are found to depend on intrinsic parameters such as the relaxation volume and the saddle-point shape of the point defects, and extrinsic parameters such as temperature and the magnitude and direction of the externally applied stress with respect to the line direction and Burgers vector direction of the dislocation. The theory is applied to fcc copper and bcc iron. It is found that screw dislocations are biased sinks and that the stress-induced bias differential for the edge dislocations depends much more on the line direction than the Burgers vector direction. Comparison with the stress-induced bias differential due to the usual SIPA effect is made. It is found that the present effect causes a bias differential that is more than an order of magnitude larger
Preconditioners for regularized saddle point matrices

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe

2011-01-01

Roč. 19, č. 2 (2011), s. 91-112 ISSN 1570-2820 Institutional research plan: CEZ:AV0Z30860518 Keywords : saddle point matrices * preconditioning * regularization * eigenvalue clustering Subject RIV: BA - General Mathematics Impact factor: 0.533, year: 2011 http://www.degruyter.com/view/j/jnma.2011.19.issue-2/jnum.2011.005/jnum.2011.005. xml
Recent progress in fission at saddle point and scission point

International Nuclear Information System (INIS)

Blons, J.; Paya, D.; Signarbieux, C.

High resolution measurements of 230 Th and 232 Th fission cross sections for neutrons exhibit a fine structure. Such a structure is interpreted as a superposition of two rotational bands in the third, asymmetric, well of the fission barrier. The fragment mass distribution in the thermal fission of 235 U and 233 U does not show any even-odd effect, even at the highest kinetic energies. This is the mark of a strong viscosity in the descent from saddle point to scission point [fr
Use and Subtleties of Saddlepoint Approximation for Minimum Mean-Square Error Estimation

DEFF Research Database (Denmark)

Beierholm, Thomas; Nuttall, Albert H.; Hansen, Lars Kai

2008-01-01

integral representation. However, the examples also demonstrate that when two saddle points are close or coalesce, then saddle-point approximation based on isolated saddle points is not valid. A saddle-point approximation based on two close or coalesced saddle points is derived and in the examples......, the validity and accuracy of the derivation is demonstrated...
Natural Preconditioning and Iterative Methods for Saddle Point Systems

KAUST Repository

Pestana, Jennifer; Wathen, Andrew J.

2015-01-01

or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example
Maximum Attainable Accuracy of Inexact Saddle Point Solvers

Czech Academy of Sciences Publication Activity Database

Jiránek, P.; Rozložník, Miroslav

2008-01-01

Roč. 29, č. 4 (2008), s. 1297-1321 ISSN 0895-4798 R&D Projects: GA MŠk 1M0554; GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : saddle point problems * Schur complement reduction * null-space projection method * rounding error analysis Subject RIV: BA - General Mathematics Impact factor: 1.328, year: 2008

Generalized saddle point condition for ignition in a tokamak reactor with temperature and density profiles

International Nuclear Information System (INIS)

Mitari, O.; Hirose, A.; Skarsgard, H.M.

1989-01-01

In this paper, the concept of a generalized ignition contour map, is extended to the realistic case of a plasma with temperature and density profiles in order to study access to ignition in a tokamak reactor. The generalized saddle point is found to lie between the Lawson and ignition conditions. If the height of the operation path with Goldston L-mode scaling is higher than the generalized saddle point, a reactor can reach ignition with this scaling for the case with no confinement degradation effect due to alpha-particle heating. In this sense, the saddle point given in a general form is a new criterion for reaching ignition. Peaking the profiles for the plasma temperature and density can lower the height of the generalized saddle point and help a reactor to reach ignition. With this in mind, the authors can judge whether next-generation tokamaks, such as Compact Ignition Tokamak, Tokamak Ignition/Burn Experimental Reactor, Next European Torus, Fusion Experimental Reactor, International Tokamak Reactor, and AC Tokamak Reactor, can reach ignition with realistic profile parameters and an L-mode scaling law
Unified analysis of preconditioning methods for saddle point matrices

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe

2015-01-01

Roč. 22, č. 2 (2015), s. 233-253 ISSN 1070-5325 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : saddle point problems * preconditioning * spectral properties Subject RIV: BA - General Mathematics Impact factor: 1.431, year: 2015 http://onlinelibrary.wiley.com/doi/10.1002/nla.1947/pdf
Localized saddle-point search and application to temperature-accelerated dynamics

Energy Technology Data Exchange (ETDEWEB)

Shim, Yunsic; Amar, Jacques G. [Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606 (United States); Callahan, Nathan B. [Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606 (United States); Department of Physics, Indiana University, Bloomington, Indiana 47405 (United States)

2013-03-07

We present a method for speeding up temperature-accelerated dynamics (TAD) simulations by carrying out a localized saddle-point (LSAD) search. In this method, instead of using the entire system to determine the energy barriers of activated processes, the calculation is localized by only including a small chunk of atoms around the atoms directly involved in the transition. Using this method, we have obtained N-independent scaling for the computational cost of the saddle-point search as a function of system size N. The error arising from localization is analyzed using a variety of model systems, including a variety of activated processes on Ag(100) and Cu(100) surfaces, as well as multiatom moves in Cu radiation damage and metal heteroepitaxial growth. Our results show significantly improved performance of TAD with the LSAD method, for the case of Ag/Ag(100) annealing and Cu/Cu(100) growth, while maintaining a negligibly small error in energy barriers.
Measuring the distance from saddle points and driving to locate them over quantum control landscapes

International Nuclear Information System (INIS)

Sun, Qiuyang; Riviello, Gregory; Rabitz, Herschel; Wu, Re-Bing

2015-01-01

Optimal control of quantum phenomena involves the introduction of a cost functional J to characterize the degree of achieving a physical objective by a chosen shaped electromagnetic field. The cost functional dependence upon the control forms a control landscape. Two theoretically important canonical cases are the landscapes associated with seeking to achieve either a physical observable or a unitary transformation. Upon satisfaction of particular assumptions, both landscapes are analytically known to be trap-free, yet possess saddle points at precise suboptimal J values. The presence of saddles on the landscapes can influence the effort needed to find an optimal field. As a foundation to future algorithm development and analyzes, we define metrics that identify the ‘distance’ from a given saddle based on the sufficient and necessary conditions for the existence of the saddles. Algorithms are introduced utilizing the metrics to find a control such that the dynamics arrive at a targeted saddle. The saddle distance metric and saddle-seeking methodology is tested numerically in several model systems. (paper)
Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning

Czech Academy of Sciences Publication Activity Database

Rozložník, Miroslav; Simoncini, V.

2002-01-01

Roč. 24, č. 2 (2002), s. 368-391 ISSN 0895-4798 R&D Projects: GA ČR GA101/00/1035; GA ČR GA201/00/0080 Institutional research plan: AV0Z1030915 Keywords : saddle point problems * preconditioning * indefinite linear systems * finite precision arithmetic * conjugate gradients Subject RIV: BA - General Mathematics Impact factor: 0.753, year: 2002
On Signed Incomplete Cholesky Factorization Preconditioners for Saddle-Point Systems

Czech Academy of Sciences Publication Activity Database

Scott, J.; Tůma, Miroslav

2014-01-01

Roč. 36, č. 6 (2014), A2984-A3010 ISSN 1064-8275 R&D Projects: GA ČR GA13-06684S Grant - others:EPSRC(GB) EP/I013067/1 Program:GA Institutional support: RVO:67985807 Keywords : sparse matrices * sparse linear systems * indefinite symmetric systems * saddle-point systems * iterative solvers * preconditioning * incomplete Cholesky factorization Subject RIV: BA - General Mathematics Impact factor: 1.854, year: 2014
Compound nucleus decay: Comparison between saddle point and scission point barriers

Energy Technology Data Exchange (ETDEWEB)

Santos, T. J.; Carlson, B. V. [Depto. de Física, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (Brazil)

2014-11-11

One of the principal characteristics of nuclear multifragmentation is the emission of complex fragments of intermediate mass. An extension of the statistical multifragmentation model has been developed, in which the process can be interpreted as the near simultaneous limit of a series of sequential binary decays. In this extension, intermediate mass fragment emissions are described by expressions almost identical to those of light particle emission. At lower temperatures, similar expressions have been shown to furnish a good description of very light intermediate mass fragment emission but not of the emission of heavier fragments, which seems to be determined by the transition density at the saddle-point rather than at the scission point. Here, we wish to compare these different formulations of intermediate fragmment emission and analyze the extent to which they remain distinguishable at high excitation energy.
Comparison between cross sections, saddle point and scission point barriers for the 32S+24Mg reaction

Directory of Open Access Journals (Sweden)

Santos T. J.

2014-04-01

Full Text Available One of the principal characteristics of nuclear multifragmentation is the emission of complex fragments of intermediate mass. The statistical multifragmentation model has been used for many years to describe the distribution of these fragments. An extension of the statistical multifragmentation model to include partial widths and lifetimes for emission, interprets the fragmentation process as the near simultaneous limit of a series of sequential binary decays. In this extension, the expression describing intermediate mass fragment emission is almost identical to that of light particle emission. At lower temperatures, similar expressions have been shown to furnish a good description of very light intermediate mass fragment emission. However, this is usually not considered a good approximation to the emission of heavier fragments. These emissions seem to be determined by the characteristics of the system at the saddle-point and its subsequent dynamical evolution rather than by the scission point. Here, we compare the barriers and decay widths of these different formulations of intermediate fragment emission and analyze the extent to which they remain distinguishable at high excitation energy.
Saddle-points of a two dimensional random lattice theory

International Nuclear Information System (INIS)

Pertermann, D.

1985-07-01

A two dimensional random lattice theory with a free massless scalar field is considered. We analyse the field theoretic generating functional for any given choice of positions of the lattice sites. Asking for saddle-points of this generating functional with respect to the positions we find the hexagonal lattice and a triangulated version of the hypercubic lattice as candidates. The investigation of the neighbourhood of a single lattice site yields triangulated rectangles and regular polygons extremizing the above generating functional on the local level. (author)
Regularization of the Boundary-Saddle-Node Bifurcation

Directory of Open Access Journals (Sweden)

Xia Liu

2018-01-01

Full Text Available In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.
Limiting Accuracy of Segregated Solution Methods for Nonsymmetric Saddle Point Problems

Czech Academy of Sciences Publication Activity Database

Jiránek, P.; Rozložník, Miroslav

Roc. 215, c. 1 (2008), s. 28-37 ISSN 0377-0427 R&D Projects: GA MŠk 1M0554; GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : saddle point problems * Schur complement reduction method * null-space projection method * rounding error analysis Subject RIV: BA - General Mathematics Impact factor: 1.048, year: 2008
Model reduction method using variable-separation for stochastic saddle point problems

Science.gov (United States)

Jiang, Lijian; Li, Qiuqi

2018-02-01

In this paper, we consider a variable-separation (VS) method to solve the stochastic saddle point (SSP) problems. The VS method is applied to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs) in a mixed formulation. The aim of such a technique is to construct a reduced basis approximation of the solution of the SSP problems. The VS method attempts to get a low rank separated representation of the solution for SSP in a systematic enrichment manner. No iteration is performed at each enrichment step. In order to satisfy the inf-sup condition in the mixed formulation, we enrich the separated terms for the primal system variable at each enrichment step. For the SSP problems by regularization or penalty, we propose a more efficient variable-separation (VS) method, i.e., the variable-separation by penalty method. This can avoid further enrichment of the separated terms in the original mixed formulation. The computation of the variable-separation method decomposes into offline phase and online phase. Sparse low rank tensor approximation method is used to significantly improve the online computation efficiency when the number of separated terms is large. For the applications of SSP problems, we present three numerical examples to illustrate the performance of the proposed methods.
Classical generalized transition-state theory. Application to a collinear reaction with two saddle points

International Nuclear Information System (INIS)

Garrett, B.C.; Truhlar, D.G.; Grev, R.S.

1981-01-01

Accurate classical dynamical fixed-energy reaction probabilities and fixed-temperature rate constants are calculated for the collinear reaction H + FH on a low-barrier model potential energy surface. The calculations cover energies from 0.1 to 100 kcal/mol above threshold and temperatures of 100 to 10,000 K. The accurate results are used to test five approximate theories: conventional transition-state theory (TST), canonical variational theory (CVT), improved canonical variational theory (ICVT), microcanonical variational theory (μVT), and the unified statistical model (US). The first four of these theories involve a single dividing surface in phase space, and the US theory involves three dividing surfaces. The tests are particularly interesting because the potential energy surface has two identical saddle points. At temperatures from 100 to 2000 K, the μVt is the most accurate theory, with errors in the range 11 to 14%; for temperatures from 2000 to 10,000 K, the US theory is the most successful, with errors in the range 3 to 14%. Over the whole range, a factor of 100 in temperature, both theories have errors of 35% or less. Even TST has errors of 47% or less over the whole factor-of-100 temperature range. Although the US model should become exact at threshold for this system, it already underestimates the reaction probability by a factor of 0.64 at 0.1 kcal/mol above threshold. TST and μVT agree with each other within 12% up to an energy 13 kcal/mol above the saddle point energy. 3 figures, 2 tables
Comparison between cross sections, saddle point and scission point barriers for the {sup 32}S+{sup 24}Mg reaction

Energy Technology Data Exchange (ETDEWEB)

Santos, T.J.; Carlson, B.V., E-mail: nztiago@gmail.com [Instituto Tecnologia de Aeronautica (ITA), Sao Jose dos Campos, SP (Brazil)

2014-07-01

One of the principal characteristics of nuclear multifragmentation is the emission of complex fragments of intermediate mass. The statistical multifragmentation model has been used for many years to describe the distribution of these fragments. An extension of the statistical multifragmentation model to include partial widths and lifetimes for emission, interprets the fragmentation process as the near simultaneous limit of a series of sequential binary decays. In this extension, the expression describing intermediate mass fragment emission is almost identical to that of light particle emission. At lower temperatures, similar expressions have been shown to furnish a good description of very light intermediate mass fragment emission. However, this is usually not considered a good approximation to the emission of heavier fragments. These emissions seem to be determined by the characteristics of the system at the saddle-point and its subsequent dynamical evolution rather than by the scission point. Here, we compare the barriers and decay widths of these different formulations of intermediate fragment emission and analyze the extent to which they remain distinguishable at high excitation energy. (author)
The Antitriangular Factorization of Saddle Point Matrices

KAUST Repository

Pestana, J.; Wathen, A. J.

2014-01-01

Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle
On preconditioner updates for sequences of saddle-point linear systems

Directory of Open Access Journals (Sweden)

Simone Valentina De

2018-02-01

Full Text Available Updating preconditioners for the solution of sequences of large and sparse saddle- point linear systems via Krylov methods has received increasing attention in the last few years, because it allows to reduce the cost of preconditioning while keeping the efficiency of the overall solution process. This paper provides a short survey of the two approaches proposed in the literature for this problem: updating the factors of a preconditioner available in a block LDLT form, and updating a preconditioner via a limited-memory technique inspired by quasi-Newton methods.
Triangular preconditioners for saddle point problems with a penalty term

Energy Technology Data Exchange (ETDEWEB)

Klawonn, A. [Westfaelische Wilhelms-Universitaet, Muenster (Germany)

1996-12-31

Triangular preconditioners for a class of saddle point problems with a penalty term are considered. An important example is the mixed formulation of the pure displacement problem in linear elasticity. It is shown that the spectrum of the preconditioned system is contained in a real, positive interval, and that the interval bounds can be made independent of the discretization and penalty parameters. This fact is used to construct bounds of the convergence rate of the GMRES method used with an energy norm. Numerical results are given for GMRES and BI-CGSTAB.
Feature-Based Retinal Image Registration Using D-Saddle Feature

Directory of Open Access Journals (Sweden)

Roziana Ramli

2017-01-01

Full Text Available Retinal image registration is important to assist diagnosis and monitor retinal diseases, such as diabetic retinopathy and glaucoma. However, registering retinal images for various registration applications requires the detection and distribution of feature points on the low-quality region that consists of vessels of varying contrast and sizes. A recent feature detector known as Saddle detects feature points on vessels that are poorly distributed and densely positioned on strong contrast vessels. Therefore, we propose a multiresolution difference of Gaussian pyramid with Saddle detector (D-Saddle to detect feature points on the low-quality region that consists of vessels with varying contrast and sizes. D-Saddle is tested on Fundus Image Registration (FIRE Dataset that consists of 134 retinal image pairs. Experimental results show that D-Saddle successfully registered 43% of retinal image pairs with average registration accuracy of 2.329 pixels while a lower success rate is observed in other four state-of-the-art retinal image registration methods GDB-ICP (28%, Harris-PIIFD (4%, H-M (16%, and Saddle (16%. Furthermore, the registration accuracy of D-Saddle has the weakest correlation (Spearman with the intensity uniformity metric among all methods. Finally, the paired t-test shows that D-Saddle significantly improved the overall registration accuracy of the original Saddle.
Saddle point solutions in Yang-Mills-dilaton theory

International Nuclear Information System (INIS)

Bizon, P.

1992-01-01

The coupling of a dilaton to the SU(2)-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analytical and numerical methods. In the abelian sector of the theory there are finite-energy magnetic and electric monopole solutions which saturate the Bogomol'nyi bound. In the nonabelian sector there exist a countable family of globally regular solutions which are purely magnetic but have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is bounded from above by the energy of the abelian magnetic monopole with unit magnetic charge. The stability analysis demonstrates that the solutions are saddle points of the energy functional with increasing number of unstable modes. The existence and instability of these solutions are 'explained' by the Morse-theory argument recently proposed by Sudarsky and Wald. (author)
Stable discretization of poroelasticity problems and efficient preconditioners for arising saddle point type matrices

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Blaheta, Radim; Byczanski, Petr

2012-01-01

Roč. 15, č. 4 (2012), s. 191-207 ISSN 1432-9360 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : poroelasticity * saddle point matrices * preconditioning * stability of discretization Subject RIV: BA - General Mathematics http://link.springer.com/article/10.1007/s00791-013-0209-0

Quasar Microlensing at High Magnification and the Role of Dark Matter: Enhanced Fluctuations and Suppressed Saddle Points

Science.gov (United States)

Schechter, Paul L.; Wambsganss, Joachim

2002-12-01

Contrary to naive expectation, diluting the stellar component of the lensing galaxy in a highly magnified system with smoothly distributed ``dark'' matter increases rather than decreases the microlensing fluctuations caused by the remaining stars. For a bright pair of images straddling a critical curve, the saddle point (of the arrival time surface) is much more strongly affected than the associated minimum. With a mass ratio of smooth matter to microlensing matter of 4:1, a saddle point with a macromagnification of μ=9.5 will spend half of its time more than a magnitude fainter than predicted. The anomalous flux ratio observed for the close pair of images in MG 0414+0534 is a factor of 5 more likely than computed by Witt, Mao, & Schechter, if the smooth matter fraction is as high as 93%. The magnification probability histograms for macroimages exhibit a distinctly different structure that varies with the smooth matter content, providing a handle on the smooth matter fraction. Enhanced fluctuations can manifest themselves either in the temporal variations of a light curve or as flux ratio anomalies in a single epoch snapshot of a multiply imaged system. While the millilensing simulations of Metcalf & Madau also give larger anomalies for saddle points than for minima, the effect appears to be less dramatic for extended subhalos than for point masses. Moreover, microlensing is distinguishable from millilensing because it will produce noticeable changes in the magnification on a timescale of a decade or less.
Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Blaheta, Radim; Byczanski, Petr; Karátson, J.; Ahmad, B.

2015-01-01

Roč. 280, č. 280 (2015), s. 141-157 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : preconditioners * heterogeneous coefficients * regularized saddle point Inner–outer iterations * Darcy flow Subject RIV: BA - General Mathematics Impact factor: 1.328, year: 2015 http://www.sciencedirect.com/science/article/pii/S0377042714005238
A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

Science.gov (United States)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.
FABRICATION OF WINDOW SADDLES FOR NIF CRYOGENIC HOHLRAUMS

International Nuclear Information System (INIS)

GIRALDEZ, E; KAAE, J.L

2003-09-01

OAK-B135 A planar diagnostic viewing port attached to the cylindrical wall of the NIF cryogenic hohlraum requires a saddle-like transition piece. While the basic design of this window saddle is straightforward, its fabrication is not, given the scale and precision of the component. They solved the problem through the use of a two segment copper mandrel to electroform the gold window saddle. The segments were micro-machined using a combination of single-point diamond turning and single point diamond milling. These processes as well as the electroplating conditions, final machining and mandrel removal are described in this paper
Sums over geometries and improvements on the mean field approximation

International Nuclear Information System (INIS)

Sacksteder, Vincent E. IV

2007-01-01

The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels
Determination of shell correction energies at saddle point using pre-scission neutron multiplicities

International Nuclear Information System (INIS)

Golda, K.S.; Saxena, A.; Mittal, V.K.; Mahata, K.; Sugathan, P.; Jhingan, A.; Singh, V.; Sandal, R.; Goyal, S.; Gehlot, J.; Dhal, A.; Behera, B.R.; Bhowmik, R.K.; Kailas, S.

2013-01-01

Pre-scission neutron multiplicities have been measured for 12 C + 194, 198 Pt systems at matching excitation energies at near Coulomb barrier region. Statistical model analysis with a modified fission barrier and level density prescription have been carried out to fit the measured pre-scission neutron multiplicities and the available evaporation residue and fission cross sections simultaneously to constrain statistical model parameters. Simultaneous fitting of the pre-scission neutron multiplicities and cross section data requires shell correction at the saddle point
A computational/directional solidification method to establish saddle points on the Mg-Al-Ca liquidus

International Nuclear Information System (INIS)

Cao Hongbo; Zhang Chuan; Zhu Jun; Cao Guoping; Kou Sindo; Schmid-Fetzer, Rainer; Chang, Y. Austin

2008-01-01

We established two saddle point maxima, L + α(Mg) + C14 and L + α(Mg) + C36, on the monovariant liquidus, calculated from a previously presented thermodynamic description, by characterizing the microstructures of several directionally solidified alloys in the near-solidification front zone, the mushy zone, and the steady-state zone using optical microscopy, scanning electron microscopy and transmission electron microscopy
Corrigendum to Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Blaheta, Radim

2016-01-01

Roč. 298, May 2016 (2016), s. 252-255 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : saddle point systems * conditions of nonsingularity * spectrum of preconditioned systems Subject RIV: BA - General Mathematics Impact factor: 1.357, year: 2016 http://www.sciencedirect.com/science/article/pii/S0377042715005889
On the many saddle points description of quantum black holes

Energy Technology Data Exchange (ETDEWEB)

Germani, Cristiano, E-mail: cristiano.germani@physik.uni-muenchen.de

2014-06-02

Considering two dimensional gravity coupled to a CFT, we show that a semiclassical black hole can be described in terms of two Liouville theories matched at the horizon. The black hole exterior corresponds to a space-like while the interior to a time-like Liouville theory. This matching automatically implies that a semiclassical black hole has an infinite entropy. The path integral description of the time-like Liouville theory (the Black Hole interior) is studied and it is found that the correlation functions of the coupled CFT-gravity system are dominated by two (complex) saddle points, even in the semiclassical limit. We argue that this system can be interpreted as two interacting Bose–Einstein condensates constructed out of two degenerate quantum states. In AdS/CFT context, the same system is mapped into two interacting strings intersecting inside a three-dimensional BTZ black hole.
Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties

DEFF Research Database (Denmark)

Christensen, Max la Cour; Vassilevski, Panayot S.; Villa, Umberto

2017-01-01

discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar...... to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow...
Integrability and Linearizability of the Lotka-Volterra System with a Saddle Point with Rational Hyperbolicity Ratio

Science.gov (United States)

Gravel, Simon; Thibault, Pierre

In this paper, we consider normalizability, integrability and linearizability properties of the Lotka-Volterra system in the neighborhood of a singular point with eigenvalues 1 and - λ. The results are obtained by generalizing and expanding two methods already known: the power expansion of the first integral or of the linearizing transformation and the transformation of the saddle into a node. With these methods we find conditions that are valid for λ∈ R+ or λ∈ Q. These conditions will allow us to find all the integrable and linearizable systems for λ= {p}/{2} and {2}/{p} with p∈ N+.
A saddle-point for data verification and materials accountancy to control nuclear material

International Nuclear Information System (INIS)

Beedgen, R.

1983-01-01

Materials accountancy is one of the main elements in international safeguards to determine whether or not nuclear material has been diverted in nuclear plants. The inspector makes independent measurements to verify the plant-operator's data before closing the materials balance with the operator's data. All inspection statements are in principle probability statements because of random errors in measuring the material and verification on a random sampling basis. Statistical test procedures help the inspector to decide under this uncertainty. In this paper a statistical test procedure representing a saddle-point is presented that leads to the highest guaranteed detection probability taking all concealing strategies into account. There are arguments favoring a separate statistical evaluation of data verification and materials accountancy. Following these considerations, a bivariate test procedure is explained that evaluates verification and accountancy separately. (orig.) [de
27 CFR 9.203 - Saddle Rock-Malibu.

Science.gov (United States)

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Saddle Rock-Malibu. 9.203... Saddle Rock-Malibu. (a) Name. The name of the viticultural area described in this section is “Saddle Rock-Malibu”. For purposes of part 4 of this chapter, “Saddle Rock-Malibu” is a term of viticultural...
A smooth landscape: ending saddle point inflation requires features to be shallow

International Nuclear Information System (INIS)

Battefeld, Diana; Battefeld, Thorsten

2013-01-01

We consider inflation driven near a saddle point in a higher dimensional field space, which is the most likely type of slow roll inflation on the string theoretical landscape; anthropic arguments need to be invoked in order to find a sufficiently flat region. To give all inflatons large masses after inflation and yield a small but positive cosmological constant, the trajectory in field space needs to terminate in a hole on the inflationary plateau, introducing a curved end-of-inflation hypersurface. We compute non-Gaussianities (bi- and tri-spectrum) caused by this curved hyper-surface and find a negative, potentially large, local non-linearity parameter. To be consistent with current observational bounds, the hole needs to be shallow, i.e. considerably wider than deep in natural units. To avoid singling out our vacuum as special (i.e. more special than a positive cosmological constant entails), we deduce that all features on field space should be similarly shallow, severely limiting the type of landscapes one may use for inflationary model building. We justify the use of a truncated Fourier series with random coefficients, which are suppressed the higher the frequency, to model such a smooth landscape by a random potential, as is often done in the literature without a good a priory reason
36 CFR 34.10 - Saddle and pack animals.

Science.gov (United States)

2010-07-01

... 36 Parks, Forests, and Public Property 1 2010-07-01 2010-07-01 false Saddle and pack animals. 34... INTERIOR EL PORTAL ADMINISTRATIVE SITE REGULATIONS § 34.10 Saddle and pack animals. The use of saddle and pack animals is prohibited without a permit from the Superintendent. ...
Detecting Change-Point via Saddlepoint Approximations

Institute of Scientific and Technical Information of China (English)

Zhaoyuan LI; Maozai TIAN

2017-01-01

It's well-known that change-point problem is an important part of model statistical analysis.Most of the existing methods are not robust to criteria of the evaluation of change-point problem.In this article,we consider "mean-shift" problem in change-point studies.A quantile test of single quantile is proposed based on saddlepoint approximation method.In order to utilize the information at different quantile of the sequence,we further construct a "composite quantile test" to calculate the probability of every location of the sequence to be a change-point.The location of change-point can be pinpointed rather than estimated within a interval.The proposed tests make no assumptions about the functional forms of the sequence distribution and work sensitively on both large and small size samples,the case of change-point in the tails,and multiple change-points situation.The good performances of the tests are confirmed by simulations and real data analysis.The saddlepoint approximation based distribution of the test statistic that is developed in the paper is of independent interest and appealing.This finding may be of independent interest to the readers in this research area.
Complex economic dynamics: Chaotic saddle, crisis and intermittency

International Nuclear Information System (INIS)

Chian, Abraham C.-L.; Rempel, Erico L.; Rogers, Colin

2006-01-01

Complex economic dynamics is studied by a forced oscillator model of business cycles. The technique of numerical modeling is applied to characterize the fundamental properties of complex economic systems which exhibit multiscale and multistability behaviors, as well as coexistence of order and chaos. In particular, we focus on the dynamics and structure of unstable periodic orbits and chaotic saddles within a periodic window of the bifurcation diagram, at the onset of a saddle-node bifurcation and of an attractor merging crisis, and in the chaotic regions associated with type-I intermittency and crisis-induced intermittency, in non-linear economic cycles. Inside a periodic window, chaotic saddles are responsible for the transient motion preceding convergence to a periodic or a chaotic attractor. The links between chaotic saddles, crisis and intermittency in complex economic dynamics are discussed. We show that a chaotic attractor is composed of chaotic saddles and unstable periodic orbits located in the gap regions of chaotic saddles. Non-linear modeling of economic chaotic saddle, crisis and intermittency can improve our understanding of the dynamics of financial intermittency observed in stock market and foreign exchange market. Characterization of the complex dynamics of economic systems is a powerful tool for pattern recognition and forecasting of business and financial cycles, as well as for optimization of management strategy and decision technology
The Taylor saddle effacement: a new technique for correction of saddle nose deformity.

Science.gov (United States)

Taylor, S Mark; Rigby, Matthew H

2008-02-01

To describe a novel technique, the Taylor saddle effacement (TSE), for correction of saddle nose deformity using autologous grafts from the lower lateral cartilages. A prospective evaluation of six patients, all of whom had the TSE performed. Photographs were taken in combination with completion of a rhinoplasty outcomes questionnaire preoperatively and at 6 months. The questionnaire included a visual analogue scale (VAS) of nasal breathing and a rhinoplasty outcomes evaluation (ROE) of nasal function and esthetics. All six patients had improvement in both their global nasal airflow on the VAS and on their ROE that was statistically significant. The mean preoperative VAS score was 5.8 compared with our postoperative mean of 8.5 of a possible 10. Mean ROE scores improved from 34.7 to 85.5. At 6 months, all patients felt that their nasal appearance had improved. The TSE is a simple and reliable technique for correction of saddle nose deformity. This prospective study has demonstrated improvement in both nasal function and esthetics when it is employed.
Sequential function approximation on arbitrarily distributed point sets

Science.gov (United States)

Wu, Kailiang; Xiu, Dongbin

2018-02-01

We present a randomized iterative method for approximating unknown function sequentially on arbitrary point set. The method is based on a recently developed sequential approximation (SA) method, which approximates a target function using one data point at each step and avoids matrix operations. The focus of this paper is on data sets with highly irregular distribution of the points. We present a nearest neighbor replacement (NNR) algorithm, which allows one to sample the irregular data sets in a near optimal manner. We provide mathematical justification and error estimates for the NNR algorithm. Extensive numerical examples are also presented to demonstrate that the NNR algorithm can deliver satisfactory convergence for the SA method on data sets with high irregularity in their point distributions.
Solar saddle bags. Solar-Fahrradpacktaschen

Energy Technology Data Exchange (ETDEWEB)

Willems, M

1991-09-12

The invention consists of the arrangement of solar cells on the upper side of saddle bags of every design (handle bar pocket, bicycle saddle bag etc.) which charge the accumulators in the pack pocket. One can drive the alternator of the bicycle, a transistor radio, a cassette tape recorder, or similar, with the power from the accumulators. The lamp and the taillight of the bicycle can still be used. The solar cells can be attached firmly to the pack pocket. However, they can also be assembled detachably, e.g. by push-buttons or zip-fasteners.

Euclidean scalar field theory in the bilocal approximation

Science.gov (United States)

Nagy, S.; Polonyi, J.; Steib, I.

2018-04-01

The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean ϕ6 model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.
Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties

DEFF Research Database (Denmark)

Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter

The paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on unstructured meshes has the ability to be as powerful/successful as FAS on geometrically refined meshes. For comparison, Newton’s method and Picard iterations with an inner state-of-the-art linear solver...... are compared to FAS on a nonlinear saddle point problem with applications to porous media flow. It is demonstrated that FAS is faster than Newton’s method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate...
The effect of saddle design on stresses in the perineum during cycling.

Science.gov (United States)

Spears, Iain R; Cummins, Neil K; Brenchley, Zoe; Donohue, Claire; Turnbull, Carli; Burton, Shona; Macho, Gabrielle A

2003-09-01

Repetitive internal stress in the perineum has been associated with soft-tissue trauma in bicyclists. Using an engineering approach, the purpose of this study was to quantify the amount of compression exerted in the perineum for a range of saddle widths and orientations. Computer tomography was used to create a three-dimensional voxel-based finite element model of the right side of the male perineum-pelvis. For the creation of the saddle model, a commercially available saddle was digitized and the surface manipulated to represent a variety of saddle widths and orientations. The two models were merged, and a static downward load of 189 N was applied to the model at the region representing the sacroiliac joint. For validation purposes, external stresses along the perineum-saddle interface were compared with the results of pressure sensitive film. Good agreement was found for these external stresses. The saddles were then stretched and rotated, and the magnitude and location of maximum stresses within the perineum were both recorded. In all cases, the model of the pelvis-perineum was held in an upright position. Stresses within the perineum were reduced when the saddle was sufficiently wide to support both ischial tuberosities. This supporting mechanism was best achieved when the saddle was at least two times wider than the bi-ischial width of the cyclist. Stresses in the anterior of the perineum were reduced when the saddle was tilted downward, whereas stresses in the posterior were reduced when the saddle was tilted upward. Recommendations that saddles should be sufficiently wide to support the ischial tuberosities appear to be well founded. Recommendations that saddles be tilted downward (i.e., nose down) are supported by the model, but with caution, given the limitations of the model.
Identifying Septal Support Reconstructions for Saddle Nose Deformity: The Cakmak Algorithm.

Science.gov (United States)

Cakmak, Ozcan; Emre, Ismet Emrah; Ozkurt, Fazil Emre

2015-01-01

The saddle nose deformity is one of the most challenging problems in nasal surgery with a less predictable and reproducible result than other nasal procedures. The main feature of this deformity is loss of septal support with both functional and aesthetic implications. Most reports on saddle nose have focused on aesthetic improvement and neglected the reestablishment of septal support to improve airway. To explain how the Cakmak algorithm, an algorithm that describes various fixation techniques and grafts in different types of saddle nose deformities, aids in identifying saddle nose reconstructions that restore supportive nasal framework and provide the aesthetic improvements typically associated with procedures to correct saddle nose deformities. This algorithm presents septal support reconstruction of patients with saddle nose deformity based on the experience of the senior author in 206 patients with saddle nose deformity. Preoperative examination, intraoperative assessment, reconstruction techniques, graft materials, and patient evaluation of aesthetic success were documented, and 4 different types of saddle nose deformities were defined. The Cakmak algorithm classifies varying degrees of saddle nose deformity from type 0 to type 4 and helps identify the most appropriate surgical procedure to restore the supportive nasal framework and aesthetic dorsum. Among the 206 patients, 110 women and 96 men, mean (range) age was 39.7 years (15-68 years), and mean (range) of follow-up was 32 months (6-148 months). All but 12 patients had a history of previous nasal surgeries. Application of the Cakmak algorithm resulted in 36 patients categorized with type 0 saddle nose deformities; 79, type 1; 50, type 2; 20, type 3a; 7, type 3b; and 14, type 4. Postoperative photographs showed improvement of deformities, and patient surveys revealed aesthetic improvement in 201 patients and improvement in nasal breathing in 195 patients. Three patients developed postoperative infection
Fission along the mass asymmetry coordinate: an experimental evaluation of the conditional saddle masses and of the Businaro-Gallone point

International Nuclear Information System (INIS)

Moretto, L.G.; McMahan, M.A.; Sobotka, L.G.; Wozniak, G.J.

1984-12-01

The importance of empirically determining the ridge line of conditional saddle points is discussed in view of the recent liquid drop model refinements, like diffuseness and finite range. Two series of experiments are presented. The first series involves the complex fragment emission from compound nuclei resulting from the 3 He + Ag reaction. Kinetic energy distributions and excitation functions are shown, and the conditional barriers are obtained over a range of atomic numbers. In the second series, reverse kinematic reactions like Ge, Nb, La + Be, C are studied. The fragments emitted cover the entire Z range, from Z = 1 to symmetric splitting. Their origin from a full momentum transfer intermediate is shown. From the complete charge distributions it is possible to conclude that the Businaro-Gallone transition is observed. 15 references
On the Use of the Main-sequence Knee (Saddle) to Measure Globular Cluster Ages

Science.gov (United States)

Saracino, S.; Dalessandro, E.; Ferraro, F. R.; Lanzoni, B.; Origlia, L.; Salaris, M.; Pietrinferni, A.; Geisler, D.; Kalirai, J. S.; Correnti, M.; Cohen, R. E.; Mauro, F.; Villanova, S.; Moni Bidin, C.

2018-06-01

In this paper, we review the operational definition of the so-called main-sequence knee (MS-knee), a feature in the color-magnitude diagram (CMD) occurring at the low-mass end of the MS. The magnitude of this feature is predicted to be independent of age at fixed chemical composition. For this reason, its difference in magnitude with respect to the MS turn-off (MS-TO) point has been suggested as a possible diagnostic to estimate absolute globular cluster (GC) ages. We first demonstrate that the operational definition of the MS-knee currently adopted in the literature refers to the inflection point of the MS (which we here more appropriately named MS-saddle), a feature that is well distinct from the knee and which cannot be used as its proxy. The MS-knee is only visible in near-infrared CMDs, while the MS-saddle can be also detected in optical–NIR CMDs. By using different sets of isochrones, we then demonstrate that the absolute magnitude of the MS-knee varies by a few tenths of a dex from one model to another, thus showing that at the moment stellar models may not capture the full systematic error in the method. We also demonstrate that while the absolute magnitude of the MS-saddle is almost coincident in different models, it has a systematic dependence on the adopted color combinations which is not predicted by stellar models. Hence, it cannot be used as a reliable reference for absolute age determination. Moreover, when statistical and systematic uncertainties are properly taken into account, the difference in magnitude between the MS-TO and the MS-saddle does not provide absolute ages with better accuracy than other methods like the MS-fitting.
MIT-Skywalker: Evaluating comfort of bicycle/saddle seat.

Science.gov (United States)

Goncalves, Rogerio S; Hamilton, Taya; Daher, Ali R; Hirai, Hiroaki; Krebs, Hermano I

2017-07-01

The MIT-Skywalker is a robotic device developed for the rehabilitation of gait and balance after a neurological injury. This device has been designed based on the concept of a passive walker and provides three distinct training modes: discrete movement, rhythmic movement, and balance training. In this paper, we present our efforts to evaluate the comfort of a bicycle/saddle seat design for the system's novel actuated body weight support device. We employed different bicycle and saddle seats and evaluated comfort using objective and subjective measures. Here we will summarize the results obtained from a study of fifteen healthy subjects and one stroke patient that led to the selection of a saddle seat design for the MIT-Skywalker.
Approximate solutions of common fixed-point problems

CERN Document Server

Zaslavski, Alexander J

2016-01-01

This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space · dynamic string-averaging version of the proximal...
Geology of the Saddle Mountains between Sentinel Gap and 119030' longitude

International Nuclear Information System (INIS)

Reidel, S.P.

1978-09-01

Members and flows of the Grande Ronde, Wanapum, and Saddle Mountains basalts of the Columbia River Basalt Group were mapped in the Saddle Mountains between Sentinel Gap and the eastern edge of Smyrna Bench. The Grande Ronde Basalt consists of the Schwana (low-MgO) and Sentinel Bluffs (high-MgO) members (informal names). The Wanapum Basalt consists of the aphyric and phyric units of the Frenchman Springs Member, the Roza-Like Member, and the Priest Rapids Member. The Saddle Mountains Basalt consists of the Wahluke, Huntzinger, Pomona, Mattawa, and Elephant Mountain basalts. The Wanapum and Saddle Mountains basalts are unevenly distributed across the Saddle Mountains. The Wanapum Basalt thins from south to north and across a northwest-southeast-trending axis at the west end of Smyrna Bench. The Priest Rapids, Roza-Like, and aphyric Frenchman Springs units are locally missing across this zone. The Saddle Mountains basalt has a more irregular distribution and, within an area between Sentinel Gap and Smyrna Bench, is devoid of the basalt. The Wahluke, Huntzinger, and Mattawa flows are locally present, but the Pomona is restricted to the southern flank west of Smyrna Bench, and the Elephant Mountain Basalt only occurs on the flanks and in three structurally controlled basins on the northwest side. The structure of the Saddle Mountains is dominated by an east-west trend and, to a lesser degree, controlled by a northwest-southeast and northeast-southwest trend. The geomorphological expression of the Saddle Mountains results from the east-west fold set and the Saddle Mountains fault along the north side. The oldest structures follow the northwest-southeast trend. The distribution of the flows, combined with the structural features, indicates a complex geologic history for the Saddel Mountains
Effect of bicycle saddle designs on the pressure to the perineum of the bicyclist.

Science.gov (United States)

Lowe, Brian D; Schrader, Steven M; Breitenstein, Michael J

2004-06-01

Increasing awareness of an association between bicycling and male sexual dysfunction has led to the appearance of a variety of bicycle saddles that share the design objective of reducing pressure in the groin of the cyclist by removal of the narrow protruding nose of the saddle. This study compared three of these saddle designs to a traditional sport/road racing saddle with a narrow protruding nose in terms of pressure in the region of the perineum (groin) of the cyclist. Saddle, pedal, and handlebar contact pressure were measured from 33 bicycle police patrol officers pedaling a stationary bicycle at a controlled cadence and workload. Pressure was characterized over the saddle as a whole and over a region of the saddle assumed to represent pressure on the cyclist's perineum located anteriorly to the ischial tuberosities. The traditional sport/racing saddle was associated with more than two times the pressure in the perineal region than the saddles without a protruding nose (P perineum of the bicyclist.
Large N saddle formulation of quadratic building block theories

International Nuclear Information System (INIS)

Halpern, M.B.

1980-01-01

I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)
Geometric convergence of some two-point Pade approximations

International Nuclear Information System (INIS)

Nemeth, G.

1983-01-01

The geometric convergences of some two-point Pade approximations are investigated on the real positive axis and on certain infinite sets of the complex plane. Some theorems concerning the geometric convergence of Pade approximations are proved, and bounds on geometric convergence rates are given. The results may be interesting considering the applications both in numerical computations and in approximation theory. As a specific case, the numerical calculations connected with the plasma dispersion function may be performed. (D.Gy.)
Time delays across saddles as a test of modified gravity

International Nuclear Information System (INIS)

Magueijo, João; Mozaffari, Ali

2013-01-01

Modified gravity theories can produce strong signals in the vicinity of the saddles of the total gravitational potential. In a sub-class of these models, this translates into diverging time delays for echoes crossing the saddles. Such models arise from the possibility that gravity might be infrared divergent or confined, and if suitably designed they are very difficult to rule out. We show that Lunar Laser Ranging during an eclipse could probe the time-delay effect within metres of the saddle, thereby proving or excluding these models. Very Large Baseline Interferometry, instead, could target delays across the Jupiter–Sun saddle. Such experiments would shed light on the infrared behaviour of gravity and examine the puzzling possibility that there might be well-hidden regions of strong gravity and even singularities inside the solar system. (fast track communication)
Divided Saddle Theory: A New Idea for Rate Constant Calculation.

Science.gov (United States)

Daru, János; Stirling, András

2014-03-11

We present a theory of rare events and derive an algorithm to obtain rates from postprocessing the numerical data of a free energy calculation and the corresponding committor analysis. The formalism is based on the division of the saddle region of the free energy profile of the rare event into two adjacent segments called saddle domains. The method is built on sampling the dynamics within these regions: auxiliary rate constants are defined for the saddle domains and the absolute forward and backward rates are obtained by proper reweighting. We call our approach divided saddle theory (DST). An important advantage of our approach is that it requires only standard computational techniques which are available in most molecular dynamics codes. We demonstrate the potential of DST numerically on two examples: rearrangement of alanine-dipeptide (CH3CO-Ala-NHCH3) conformers and the intramolecular Cope reaction of the fluxional barbaralane molecule.
GEODESIC RECONSTRUCTION, SADDLE ZONES & HIERARCHICAL SEGMENTATION

Directory of Open Access Journals (Sweden)

Serge Beucher

2011-05-01

Full Text Available The morphological reconstruction based on geodesic operators, is a powerful tool in mathematical morphology. The general definition of this reconstruction supposes the use of a marker function f which is not necessarily related to the function g to be built. However, this paper deals with operations where the marker function is defined from given characteristic regions of the initial function f, as it is the case, for instance, for the extrema (maxima or minima but also for the saddle zones. Firstly, we show that the intuitive definition of a saddle zone is not easy to handle, especially when digitised images are involved. However, some of these saddle zones (regional ones also called overflow zones can be defined, this definition providing a simple algorithm to extract them. The second part of the paper is devoted to the use of these overflow zones as markers in image reconstruction. This reconstruction provides a new function which exhibits a new hierarchy of extrema. This hierarchy is equivalent to the hierarchy produced by the so-called waterfall algorithm. We explain why the waterfall algorithm can be achieved by performing a watershed transform of the function reconstructed by its initial watershed lines. Finally, some examples of use of this hierarchical segmentation are described.
Spike-adding in parabolic bursters: The role of folded-saddle canards

Science.gov (United States)

Desroches, Mathieu; Krupa, Martin; Rodrigues, Serafim

2016-09-01

The present work develops a new approach to studying parabolic bursting, and also proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In addition to this new polynomial system, we also consider the conductance-based model of the Aplysia R15 neuron known as the Plant model, and a reduction of this prototypical biophysical parabolic burster to three variables, including one phase variable, namely the Baer-Rinzel-Carillo (BRC) phase model. Revisiting these models from the perspective of slow-fast dynamics reveals that the number of spikes per burst may vary upon parameter changes, however the spike-adding process occurs in an explosive fashion that involves special solutions called canards. This spike-adding canard explosion phenomenon is analysed by using tools from geometric singular perturbation theory in tandem with numerical bifurcation techniques. We find that the bifurcation structure persists across all considered systems, that is, spikes within the burst are incremented via the crossing of an excitability threshold given by a particular type of canard orbit, namely the true canard of a folded-saddle singularity. However there can be a difference in the spike-adding transitions in parameter space from one case to another, according to whether the process is continuous or discontinuous, which depends upon the geometry of the folded-saddle canard. Using these findings, we construct a new polynomial approximation of the Plant model, which retains all the key elements for parabolic bursting, including the spike-adding transitions mediated by folded-saddle canards. Finally, we briefly investigate the presence of spike-adding via canards in planar phase models of parabolic bursting, namely the theta model by Ermentrout and Kopell.
Developments of saddle field ion sources and their applications

International Nuclear Information System (INIS)

Abdelrahman, M.M.; Helal, A.G.

2009-01-01

Ion sources should have different performance parameters according to the various applications for which they are used, ranging from ion beam production to high energy ion implanters. There are many kinds of ion sources, which produce different ion beams with different characteristics. This paper deals with the developments and applications of some saddle field ion sources which were designed and constructed in our lab. Theory of operation and types of saddle field ion sources are discussed in details. Some experimental results are given. The saddle field ion sources operate at low gas pressure and require neither magnetic field nor filament. This type of ion sources is used for many different applications as ion beam machining, sputtering, cleaning and profiling for surface analysis etc
19 CFR 148.32 - Vehicles, aircraft, boats, teams and saddle horses taken abroad.

Science.gov (United States)

2010-04-01

... 19 Customs Duties 2 2010-04-01 2010-04-01 false Vehicles, aircraft, boats, teams and saddle horses... for Returning Residents § 148.32 Vehicles, aircraft, boats, teams and saddle horses taken abroad. (a) Admission free of duty. Automobiles and other vehicles, aircraft, boats, teams and saddle horses, together...
Maximal saddle solution of a nonlinear elliptic equation involving the ...

Indian Academy of Sciences (India)

College of Mathematics and Econometrics, Hunan University, Changsha 410082, China. E-mail: huahuiyan@163.com; duzr@hnu.edu.cn. MS received 3 September 2012; revised 20 December 2012. Abstract. A saddle solution is called maximal saddle solution if its absolute value is not smaller than those absolute values ...
Zero-point Energy is Needed in Molecular Dynamics Calculations to Access the Saddle Point for H+HCN→H2CN* and cis/trans-HCNH* on a New Potential Energy Surface.

Science.gov (United States)

Wang, Xiaohong; Bowman, Joel M

2013-02-12

We calculate the probabilities for the association reactions H+HCN→H2CN* and cis/trans-HCNH*, using quasiclassical trajectory (QCT) and classical trajectory (CT) calculations, on a new global ab initio potential energy surface (PES) for H2CN including the reaction channels. The surface is a linear least-squares fit of roughly 60 000 CCSD(T)-F12b/aug-cc-pVDZ electronic energies, using a permutationally invariant basis with Morse-type variables. The reaction probabilities are obtained at a variety of collision energies and impact parameters. Large differences in the threshold energies in the two types of dynamics calculations are traced to the absence of zero-point energy in the CT calculations. We argue that the QCT threshold energy is the realistic one. In addition, trajectories find a direct pathway to trans-HCNH, even though there is no obvious transition state (TS) for this pathway. Instead the saddle point (SP) for the addition to cis-HCNH is evidently also the TS for direct formation of trans-HCNH.

Evaluation of saddle and driving aptitudes in Monterufoli pony

Directory of Open Access Journals (Sweden)

Riccardo Bozzi

2010-01-01

Full Text Available The Monterufoli pony is an endangered Tuscan breed. In the 80’s began a project for the conservation of the breed and at present there are roughly 200 individuals. The equine was once utilized for saddle and driving and this study deals with the training for these two aptitudes. The mor- phologic type of the pony seems suited for saddle, in particular for children and beginners, and driving. The ponies showed developed chest, strong legs with short shanks: all these characters were useful for trot and driving. In this trial 3-4 years old never tamed Monterufoli ponies were opportunely choose and subsequently trained for saddle and driving. The ponies were submitted to the “aptitude test” for the two aptitudes and the results were good both for practical and character sides. The marks for sad- dle and driving were 8.16 and 8.06 respectively. Also the 3 ponies showed good results for the Aptitude Index: 7.60, 7.87 and 7.89. The results of the trial showed the excellent ability of the Monterufoli pony for saddle and driving. The good results of the test are important for the diffusion of the breed in the territory and in particular in horse centres and in equestrian tourism sites.
Chaotic saddles in nonlinear modulational interactions in a plasma

International Nuclear Information System (INIS)

Miranda, Rodrigo A.; Rempel, Erico L.; Chian, Abraham C.-L.

2012-01-01

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Chaotic saddles in nonlinear modulational interactions in a plasma

Energy Technology Data Exchange (ETDEWEB)

Miranda, Rodrigo A. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); University of Brasilia (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Chian, Abraham C.-L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Observatoire de Paris, LESIA, CNRS, 92195 Meudon (France)

2012-11-15

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Featured Partner: Saddle Creek Logistics Services

Science.gov (United States)

This EPA fact sheet spotlights Saddle Creek Logistics as a SmartWay partner committed to sustainability in reducing greenhouse gas emissions and air pollution caused by freight transportation, partly by growing its compressed natural gas (CNG) vehicles for
Basic kinematics of the saddle and rider in high-level dressage horses trotting on a treadmill.

Science.gov (United States)

Byström, A; Rhodin, M; von Peinen, K; Weishaupt, M A; Roepstorff, L

2009-03-01

A comprehensive kinematic description of rider and saddle movements is not yet present in the scientific literature. To describe saddle and rider movements in a group of high-level dressage horses and riders. Seven high-level dressage horses and riders were subjected to kinematic measurements while performing collected trot on a treadmill. For analysis a rigid body model for the saddle and core rider segments, projection angles of the rider's extremities and the neck and trunk of the horse, and distances between markers selected to indicate rider position were used. For a majority of the variables measured it was possible to describe a common pattern for the group. Rotations around the transverse axis (pitch) were generally biphasic for each diagonal. During the first half of stance the saddle rotated anti-clockwise and the rider's pelvis clockwise viewed from the right and the rider's lumbar back extended. During the later part of stance and the suspension phase reverse pitch rotations were observed. Rotations of the saddle and core rider segments around the longitudinal (roll) and vertical axes (yaw) changed direction only around time of contact of each diagonal. The saddles and riders of high-level dressage horses follow a common movement pattern at collected trot. The movements of the saddle and rider are clearly related to the movements of the horse and saddle movements also seem to be influenced by the rider. Knowledge about rider and saddle movements can further our understanding of, and hence possibilities to prevent, orthopaedic injuries related to the exposure of the horse to a rider and saddle.
Point-defect migration into an infinitesimal dislocation loop

International Nuclear Information System (INIS)

Woo, C.H.

1981-11-01

Point-defect migration into an infinitesimal dislocation loop in an isotropic linear elastic medium is described. Particular care has been taken to include the effects of the saddle-point shape anisotropy of the point defect. Expressions for the reaction radii and the bias are derived, both in the presence and absence of an external applied stress. These are found to depend on intrinsic parameters, such as the loop strength, the loop nature (vacancy or interstitial), the relaxation volume, the saddle-point shape, and extrinsic parameters, such as the magnitude and direction of the external stress, and the temperature. The implications of the results are discussed
Applicability of point-dipoles approximation to all-dielectric metamaterials

DEFF Research Database (Denmark)

Kuznetsova, S. M.; Andryieuski, Andrei; Lavrinenko, Andrei

2015-01-01

All-dielectric metamaterials consisting of high-dielectric inclusions in a low-dielectric matrix are considered as a low-loss alternative to resonant metal-based metamaterials. In this paper we investigate the applicability of the point electric and magnetic dipoles approximation to dielectric meta......-atoms on the example of a dielectric ring metamaterial. Despite the large electrical size of high-dielectric meta-atoms, the dipole approximation allows for accurate prediction of the metamaterials properties for the rings with diameters up to approximate to 0.8 of the lattice constant. The results provide important...... guidelines for design and optimization of all-dielectric metamaterials....
Codimension n saddle-nodes

International Nuclear Information System (INIS)

Gheiner, Jaques

2014-01-01

We consider the generic unfolding of a diffeomorphism on a compact C ∞ manifold that is Morse–Smale except for one non-hyperbolic periodic orbit being a codimension n saddle-node (one eigenvalue is 1, the other eigenvalues have norm different from 1). Local and global bifurcations are described. We characterize structural stability of the unfolding, depending on the codimension. A universal model of the unfolding is given when there is stability. Dynamical behaviour is analysed in other cases. (paper)
Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

Energy Technology Data Exchange (ETDEWEB)

Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp [Graduate School of Commerce and Management, Hitotsubashi University, Tokyo 186-8601 (Japan); Yamada, Michio [Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto 606-8502 (Japan); Chian, Abraham C.-L. [Paris Observatory, LESIA, CNRS, 92195 Meudon (France); National Institute for Space Research (INPE), P.O. Box 515, São José dos Campos, São Paulo 12227-010 (Brazil); Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil); School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005 (Australia); Department of Biomedical Engineering, George Washington University, Washington, DC 20052 (United States); Miranda, Rodrigo A. [Faculty UnB-Gama, and Plasma Physics Laboratory, Institute of Physics, University of Brasília (UnB), Brasília DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil)

2015-10-15

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.
Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C.-L.; Miranda, Rodrigo A.; Rempel, Erico L.

2015-01-01

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs
On the point-source approximation of earthquake dynamics

Directory of Open Access Journals (Sweden)

Andrea Bizzarri

2014-06-01

Full Text Available The focus on the present study is on the point-source approximation of a seismic source. First, we compare the synthetic motions on the free surface resulting from different analytical evolutions of the seismic source (the Gabor signal (G, the Bouchon ramp (B, the Cotton and Campillo ramp (CC, the Yoffe function (Y and the Liu and Archuleta function (LA. Our numerical experiments indicate that the CC and the Y functions produce synthetics with larger oscillations and correspondingly they have a higher frequency content. Moreover, the CC and the Y functions tend to produce higher peaks in the ground velocity (roughly of a factor of two. We have also found that the falloff at high frequencies is quite different: it roughly follows ω−2 in the case of G and LA functions, it decays more faster than ω−2 for the B function, while it is slow than ω−1 for both the CC and the Y solutions. Then we perform a comparison of seismic waves resulting from 3-D extended ruptures (both supershear and subshear obeying to different governing laws against those from a single point-source having the same features. It is shown that the point-source models tend to overestimate the ground motions and that they completely miss the Mach fronts emerging from the supershear transition process. When we compare the extended fault solutions against a multiple point-sources model the agreement becomes more significant, although relevant discrepancies still persist. Our results confirm that, and more importantly quantify how, the point-source approximation is unable to adequately describe the radiation emitted during a real world earthquake, even in the most idealized case of planar fault with homogeneous properties and embedded in a homogeneous, perfectly elastic medium.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

Energy Technology Data Exchange (ETDEWEB)

Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-01-22

The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
Robust surface registration using N-points approximate congruent sets

Directory of Open Access Journals (Sweden)

Yao Jian

2011-01-01

Full Text Available Abstract Scans acquired by 3D sensors are typically represented in a local coordinate system. When multiple scans, taken from different locations, represent the same scene these must be registered to a common reference frame. We propose a fast and robust registration approach to automatically align two scans by finding two sets of N-points, that are approximately congruent under rigid transformation and leading to a good estimate of the transformation between their corresponding point clouds. Given two scans, our algorithm randomly searches for the best sets of congruent groups of points using a RANSAC-based approach. To successfully and reliably align two scans when there is only a small overlap, we improve the basic RANSAC random selection step by employing a weight function that approximates the probability of each pair of points in one scan to match one pair in the other. The search time to find pairs of congruent sets of N-points is greatly reduced by employing a fast search codebook based on both binary and multi-dimensional lookup tables. Moreover, we introduce a novel indicator of the overlapping region quality which is used to verify the estimated rigid transformation and to improve the alignment robustness. Our framework is general enough to incorporate and efficiently combine different point descriptors derived from geometric and texture-based feature points or scene geometrical characteristics. We also present a method to improve the matching effectiveness of texture feature descriptors by extracting them from an atlas of rectified images recovered from the scan reflectance image. Our algorithm is robust with respect to different sampling densities and also resilient to noise and outliers. We demonstrate its robustness and efficiency on several challenging scan datasets with varying degree of noise, outliers, extent of overlap, acquired from indoor and outdoor scenarios.
Influence of girth strap placement and panel flocking material on the saddle pressure pattern during riding of horses.

Science.gov (United States)

Byström, A; Stalfelt, A; Egenvall, A; Von Peinen, K; Morgan, K; Roepstorff, L

2010-11-01

Saddle fit is well recognised as an important factor for the health and performance of riding horses. However, only few studies have addressed general effects of different saddle construction details within a group of horses. To assess the influence of girth strap placement, traditional vs. v-system, and panel flocking material, wool vs. synthetic foam, on the saddle pressure pattern during riding. Six horses were ridden by 3 riders in sitting and rising trot and sitting canter. Saddle pressure was measured with 3 different saddle variants: 1) wool flocked panels and traditional girthing (baseline); 2) wool flocked panels and v-system girthing; and 3) foam filled panels and traditional girthing. From the pressure data, a number of descriptive variables were extracted. These were analysed using ANCOVA models with horse, rider, saddle, seat (sitting/rising, trot only) and speed as independent variables. With foam filled panels stride maximum pressures under the hind part of the saddle increased by 7-12% and the area under the saddle with a stride mean pressure >11 kPa increased by 114 cm(2) in trot and 127 cm(2) in canter. With v-system girthing, the latter variable also increased, but only by 53 and 38 cm(2) in trot and canter, respectively. In addition, stride maximum pressures under the front part of the saddle tended to increase (≤ 9%). Both flocking material and girthing have a significant influence on the saddle pressure and should thus be considered in saddle fitting. Wool seems a better flocking material than foam of the type used in the current study. For girthing, traditional placement seems equally good if not better than the v-system. However, further studies are needed to show if these results are valid for a larger population of riding horses. © 2010 EVJ Ltd.
DETECTING ALIEN LIMIT CYCLES NEAR A HAMILTONIAN 2-SADDLE CYCLE

OpenAIRE

LUCA, Stijn; DUMORTIER, Freddy; Caubergh, M.; Roussarie, R.

2009-01-01

This paper aims at providing and example of a cubic Hamiltonian 2-saddle cycle that after bifurcation can give rise to an alien limit cycle; this is a limit cycle that is not controlled by a zero of the related Abelian integral. To guarantee the existence of an alien limit cycle one can verify generic conditions on the Abelian integral and on the transition map associated to the connections of the 2-saddle cycle. In this paper, a general method is developed to compute the first and second der...
Computing closest saddle node bifurcations in a radial system via conic programming

Energy Technology Data Exchange (ETDEWEB)

Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box 72, Zouk Mikhael, Zouk Mosbeh (Lebanon); Pal, B.C. [Department of Electrical and Electronic Engineering, Imperial College London, SW7 2BT (United Kingdom)

2009-07-15

This paper considers the problem of computing the loading limits in a radial system which are (i) locally closest to current operating load powers and (ii) at which saddle node bifurcation occurs. The procedure is based on a known technique which requires iterating between two computational steps until convergence. In essence, step 1 produces a vector normal to the real and/or reactive load solution space boundary, whereas step 2 computes the bifurcation point along that vector. The paper shows that each of the above computational steps can be formulated as a second-order cone program for which polynomial time interior-point methods and efficient implementations exist. The proposed conic programming approach is used to compute the closest bifurcation points and the corresponding worst case load power margins of eleven different distribution systems. The approach is validated graphically and the existence of multiple load power margins is investigated. (author)
Parametric CAD and Fea Model of a Saddle Tapping Tee

DEFF Research Database (Denmark)

A. Kristensen, Anders Schmidt; Lund Jepsen, Kristian

2007-01-01

Often it is necessary to branch of a pipe section on an oilrig. This operation is often performed by making a so-called "Hot Tapping", which involves welding a pipe and a flange on to the pipe section. A spherical valve and a gate are mounted on to the flange, i.e. weld-o-let. In order to perform...... the welding operations a so-called habitat must be constructed. This habitat encapsulates the "Hot Tapping" spot and is relatively costly. Thus, to avoid weld operations on to the pipeline, a solution with clamps has been developed, i.e. a Saddle Tapping Tee. The Saddle Tapping Tee is clamped on the pipe...... is determined from paragraph K302.3.2 in ASME B31.3. A full parametric 3D CAD model of the Saddle Tapping Tee is developed where a number of user-defined parameters are controlled from an Excel spreadsheet allowing parameter studies and technical documentation to be generated effectively. The same Excel spread...
Paleoseismic evidence for late Holocene tectonic deformation along the Saddle mountain fault zone, Southeastern Olympic Peninsula, Washington

Science.gov (United States)

Barnett, Elizabeth; Sherrod, Brian; Hughes, Jonathan F.; Kelsey, Harvey M.; Czajkowski, Jessica L.; Walsh, Timothy J.; Contreras, Trevor A.; Schermer, Elizabeth R.; Carson, Robert J.

2015-01-01

Trench and wetland coring studies show that northeast‐striking strands of the Saddle Mountain fault zone ruptured the ground about 1000 years ago, generating prominent scarps. Three conspicuous subparallel fault scarps can be traced for 15 km on Light Detection and Ranging (LiDAR) imagery, traversing the foothills of the southeast Olympic Mountains: the Saddle Mountain east fault, the Saddle Mountain west fault, and the newly identified Sund Creek fault. Uplift of the Saddle Mountain east fault scarp impounded stream flow, forming Price Lake and submerging an existing forest, thereby leaving drowned stumps still rooted in place. Stratigraphy mapped in two trenches, one across the Saddle Mountain east fault and the other across the Sund Creek fault, records one and two earthquakes, respectively, as faulting juxtaposed Miocene‐age bedrock against glacial and postglacial deposits. Although the stratigraphy demonstrates that reverse motion generated the scarps, slip indicators measured on fault surfaces suggest a component of left‐lateral slip. From trench exposures, we estimate the postglacial slip rate to be 0.2 mm/yr and between 0.7 and 3.2 mm/yr during the past 3000 years. Integrating radiocarbon data from this study with earlier Saddle Mountain fault studies into an OxCal Bayesian statistical chronology model constrains the most recent paleoearthquake age of rupture across all three Saddle Mountain faults to 1170–970 calibrated years (cal B.P.), which overlaps with the nearby Mw 7.5 1050–1020 cal B.P. Seattle fault earthquake. An earlier earthquake recorded in the Sund Creek trench exposure, dates to around 3500 cal B.P. The geometry of the Saddle Mountain faults and their near‐synchronous rupture to nearby faults 1000 years ago suggest that the Saddle Mountain fault zone forms a western boundary fault along which the fore‐arc blocks migrate northward in response to margin‐parallel shortening across the Puget Lowland.
Optimization of saddle coils for magnetic resonance imaging

International Nuclear Information System (INIS)

Salmon, Carlos Ernesto Garrido; Vidoto, Edson Luiz Gea; Martins, Mateus Jose; Tannus, Alberto

2006-01-01

In Nuclear Magnetic Resonance (NMR) experiments, besides the apparatus designed to acquire the NMR signal, it is necessary to generate a radio frequency electromagnetic field using a device capable to transduce electromagnetic power into a transverse magnetic field. We must generate this transverse homogeneous magnetic field inside the region of interest with minimum power consumption. Many configurations have been proposed for this task, from coils to resonators. For low field intensity (<0.5 T) and small sample dimensions (<30 cm), the saddle coil configuration has been widely used. In this work we present a simplified method for calculating the magnetic field distribution in these coils considering the current density profile. We propose an optimized saddle configuration as a function of the dimensions of the region of interest, taking into account the uniformity and the sensitivity. In order to evaluate the magnetic field uniformity three quantities have been analyzed: Non-uniformity, peak-to-peak homogeneity and relative uniformity. Some experimental results are presented to validate our calculation. (author)
Conjugate gradient filtering of instantaneous normal modes, saddles on the energy landscape, and diffusion in liquids.

Science.gov (United States)

Chowdhary, J; Keyes, T

2002-02-01

Instantaneous normal modes (INM's) are calculated during a conjugate-gradient (CG) descent of the potential energy landscape, starting from an equilibrium configuration of a liquid or crystal. A small number (approximately equal to 4) of CG steps removes all the Im-omega modes in the crystal and leaves the liquid with diffusive Im-omega which accurately represent the self-diffusion constant D. Conjugate gradient filtering appears to be a promising method, applicable to any system, of obtaining diffusive modes and facilitating INM theory of D. The relation of the CG-step dependent INM quantities to the landscape and its saddles is discussed.

Saddle Slow Manifolds and Canard Orbits in [Formula: see text] and Application to the Full Hodgkin-Huxley Model.

Science.gov (United States)

Hasan, Cris R; Krauskopf, Bernd; Osinga, Hinke M

2018-04-19

Many physiological phenomena have the property that some variables evolve much faster than others. For example, neuron models typically involve observable differences in time scales. The Hodgkin-Huxley model is well known for explaining the ionic mechanism that generates the action potential in the squid giant axon. Rubin and Wechselberger (Biol. Cybern. 97:5-32, 2007) nondimensionalized this model and obtained a singularly perturbed system with two fast, two slow variables, and an explicit time-scale ratio ε. The dynamics of this system are complex and feature periodic orbits with a series of action potentials separated by small-amplitude oscillations (SAOs); also referred to as mixed-mode oscillations (MMOs). The slow dynamics of this system are organized by two-dimensional locally invariant manifolds called slow manifolds which can be either attracting or of saddle type.In this paper, we introduce a general approach for computing two-dimensional saddle slow manifolds and their stable and unstable fast manifolds. We also develop a technique for detecting and continuing associated canard orbits, which arise from the interaction between attracting and saddle slow manifolds, and provide a mechanism for the organization of SAOs in [Formula: see text]. We first test our approach with an extended four-dimensional normal form of a folded node. Our results demonstrate that our computations give reliable approximations of slow manifolds and canard orbits of this model. Our computational approach is then utilized to investigate the role of saddle slow manifolds and associated canard orbits of the full Hodgkin-Huxley model in organizing MMOs and determining the firing rates of action potentials. For ε sufficiently large, canard orbits are arranged in pairs of twin canard orbits with the same number of SAOs. We illustrate how twin canard orbits partition the attracting slow manifold into a number of ribbons that play the role of sectors of rotations. The upshot is that we
Electrical design of the BUSSARD inverter system for ASDEX upgrade saddle coils

Energy Technology Data Exchange (ETDEWEB)

Teschke, Markus, E-mail: teschke@ipp.mpg.de; Arden, Nils; Eixenberger, Horst; Rott, Michael; Suttrop, Wolfgang

2015-10-15

Highlights: • A cost effective inverter topology for AUG's 16 in-vessel saddle coils has been found. • Use of commercially available power modules is possible. • A NPC-like topology of the power stage is realized in a modular way. • The high-speed controllers and PWM engines are realized on Linux-based systems. • First experimental results of AUG plasma shots are presented. - Abstract: A set of 16 in-vessel saddle coils is installed in the ASDEX Upgrade (AUG) nuclear fusion experiment for mitigation of edge localized modes (ELM) and feedback control of resistive wall modes (RWM). The coils were driven by DC current only during previous campaigns. Now, a new inverter system “BUSSARD” (German abbr. for “Bayerischer Umrichter, schnell schaltend für AUGs rasche Drehfelder”, translated: “bavarian fast switching inverter for AUG's fast rotating fields”) is built for the experiment. A four-phase system has been assembled to simultaneously operate up to 4 groups of coils consisting of up to 4 serial-connected coils each. The maximum current is 1.3 kA with a ripple in the range of 7% and the frequency is variable between DC and approx. 100 Hz. The switching frequency is variable between approximately 3 and 10 kHz. As a first application, rotating fields are generated. The system can be enhanced in two stages to 16-phase operation with a bandwidth of 500 Hz and a 24 phase system with a bandwidth of up to 3 kHz.
Bifurcations of heterodimensional cycles with two saddle points

Energy Technology Data Exchange (ETDEWEB)

Geng Fengjie [School of Information Technology, China University of Geosciences (Beijing), Beijing 100083 (China)], E-mail: gengfengjie_hbu@163.com; Zhu Deming [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: dmzhu@math.ecnu.edu.cn; Xu Yancong [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: yancongx@163.com

2009-03-15

The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
Bifurcations of heterodimensional cycles with two saddle points

International Nuclear Information System (INIS)

Geng Fengjie; Zhu Deming; Xu Yancong

2009-01-01

The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
The effectiveness of adhesives on the retention of mandibular free end saddle partial dentures: An in vitro study.

Science.gov (United States)

Quiney, Daniel; Nishio Ayre, Wayne; Milward, Paul

2017-07-01

Existing in vitro methods for testing denture adhesives do not fully replicate the complex oral geometries and environment; and in vivo methods are qualitative, prone to bias and not easily reproducible. The purpose of this study was to develop a novel, quantitative and more accurate model to test the effect of adhesives on the retentive force of mandibular free end saddle partial dentures. An in vitro model was developed based on an anatomically accurate cast of a clinical case. Experimentally, the amount of adhesive was varied (0.2g-1g) and the tensile force required for displacement was measured. Different commercially available adhesives were then tested at the optimum volume using the in vitro model. A 3D finite element model of the denture was used to assess how the forces to induce denture displacement varied according to the position of the force along the saddle length. The mass of adhesive was found to significantly alter retention forces, with 0.4-0.7g being the optimum range for this particular scenario. Use of adhesives significantly improved mandibular free end saddle partial denture retention with the worst performing adhesive increasing retention nine-fold whilst the best performing adhesive increased retention twenty three-fold. The finite element model revealed that 77% more force was required to displace the denture by positioning forces towards the mesial end of the saddle compared to the distal end. An in vitro denture adhesive model was developed, which demonstrated that mass of adhesive plays a significant role in enhancing denture retention and supported the design principle of placing as few teeth as clinically necessary on the distal end of the free end saddles. Limiting the position of teeth on free end saddles to the mesial and mid portion of the saddle will reduce displacements caused by mastication. The movement of mandibular free end saddle partial dentures can be restricted with the use of denture adhesives. Altering the mass of
Rotating saddle trap as Foucault's pendulum

Science.gov (United States)

Kirillov, Oleg N.; Levi, Mark

2016-01-01

One of the many surprising results found in the mechanics of rotating systems is the stabilization of a particle in a rapidly rotating planar saddle potential. Besides the counterintuitive stabilization, an unexpected precessional motion is observed. In this note, we show that this precession is due to a Coriolis-like force caused by the rotation of the potential. To our knowledge, this is the first example where such a force arises in an inertial reference frame. We also propose a simple mechanical demonstration of this effect.
Nonconvergence to Saddle Boundary Points under Perturbed Reinforcement Learning

Science.gov (United States)

2012-12-07

of the ODE (12). Note that for some games not all stationary points of the ODE (12) are Nash equilibria. For example, if you consider the Typewriter ...B A 4, 4 2, 2 B 2, 2 3, 3 Table 1: The Typewriter Game. On the other hand, any stationary point in the interior of the probability simplex will... Typewriter Game of Table 1. We observe that it is possible for the process to converge to a pure strategy profile which is not a Nash equilibrium when Ri(α
Flood-inundation maps for the Saddle River from Rochelle Park to Lodi, New Jersey, 2012

Science.gov (United States)

Hoppe, Heidi L.; Watson, Kara M.

2012-01-01

Digital flood-inundation maps for a 2.75-mile reach of the Saddle River from 0.2 mile upstream from the Interstate 80 bridge in Rochelle Park to 1.5 miles downstream from the U.S. Route 46 bridge in Lodi, New Jersey, were created by the U.S. Geological Survey (USGS) in cooperation with the New Jersey Department of Environmental Protection (NJDEP). The inundation maps, which can be accessed through the USGS Flood Inundation Mapping Science Web site at http://water.usgs.gov/osw/flood_inundation, depict estimates of the areal extent and depth of flooding corresponding to selected water levels (stages) at the USGS streamgage at Saddle River at Lodi, New Jersey (station 01391500). Current conditions for estimating near real-time areas of inundation using USGS streamgage information may be obtained on the Internet at http://waterdata.usgs.gov/nwis/uv?site_no=01391500. The National Weather Service (NWS) forecasts flood hydrographs at many places that are often collocated with USGS streamgages. NWS-forecasted peak-stage information may be used in conjunction with the maps developed in this study to show predicted areas of flood inundation. In this study, flood profiles were computed for the stream reach by means of a one-dimensional step-backwater model. The model was calibrated using the most current stage-discharge relations at the Saddle River at Lodi, New Jersey streamgage and documented high-water marks from recent floods. The hydraulic model was then used to determine 11 water-surface profiles for flood stages at the Saddle River streamgage at 1-ft intervals referenced to the streamgage datum, North American Vertical Datum of 1988 (NAVD 88), and ranging from bankfull, 0.5 ft below NWS Action Stage, to the extent of the stage-discharge rating, which is approximately 1 ft higher than the highest recorded water level at the streamgage. Action Stage is the stage which when reached by a rising stream the NWS or a partner needs to take some type of mitigation action in
Identification of a mutation that is associated with the saddle tan and black-and-tan phenotypes in Basset Hounds and Pembroke Welsh Corgis.

Science.gov (United States)

Dreger, Dayna L; Parker, Heidi G; Ostrander, Elaine A; Schmutz, Sheila M

2013-01-01

The causative mutation for the black-and-tan (a (t) ) phenotype in dogs was previously shown to be a SINE insertion in the 5' region of Agouti Signaling Protein (ASIP). Dogs with the black-and-tan phenotype, as well as dogs with the saddle tan phenotype, genotype as a (t) /_ at this locus. We have identified a 16-bp duplication (g.1875_1890dupCCCCAGGTCAGAGTTT) in an intron of hnRNP associated with lethal yellow (RALY), which segregates with the black-and-tan phenotype in a group of 99 saddle tan and black-and-tan Basset Hounds and Pembroke Welsh Corgis. In these breeds, all dogs with the saddle tan phenotype had RALY genotypes of +/+ or +/dup, whereas dogs with the black-and-tan phenotype were homozygous for the duplication. The presence of an a (y) /_ fawn or e/e red genotype is epistatic to the +/_ saddle tan genotype. Genotypes from 10 wolves and 1 coyote indicated that the saddle tan (+) allele is the ancestral allele, suggesting that black-and-tan is a modification of saddle tan. An additional 95 dogs from breeds that never have the saddle tan phenotype have all three of the possible RALY genotypes. We suggest that a multi-gene interaction involving ASIP, RALY, MC1R, DEFB103, and a yet-unidentified modifier gene is required for expression of saddle tan.
Surface plasma source with saddle antenna radio frequency plasma generator.

Science.gov (United States)

Dudnikov, V; Johnson, R P; Murray, S; Pennisi, T; Piller, C; Santana, M; Stockli, M; Welton, R

2012-02-01

A prototype RF H(-) surface plasma source (SPS) with saddle (SA) RF antenna is developed which will provide better power efficiency for high pulsed and average current, higher brightness with longer lifetime and higher reliability. Several versions of new plasma generators with small AlN discharge chambers and different antennas and magnetic field configurations were tested in the plasma source test stand. A prototype SA SPS was installed in the Spallation Neutron Source (SNS) ion source test stand with a larger, normal-sized SNS AlN chamber that achieved unanalyzed peak currents of up to 67 mA with an apparent efficiency up to 1.6 mA∕kW. Control experiments with H(-) beam produced by SNS SPS with internal and external antennas were conducted. A new version of the RF triggering plasma gun has been designed. A saddle antenna SPS with water cooling is fabricated for high duty factor testing.
Power inverter design for ASDEX Upgrade saddle coils

Energy Technology Data Exchange (ETDEWEB)

Teschke, M., E-mail: teschke@ipp.mpg.de [Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748 Garching (Germany); Suttrop, W.; Rott, M. [Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748 Garching (Germany)

2013-10-15

Highlights: ► A cost effective inverter topology for AUG's 16 in-vessel saddle coils has been found. ► Use of commercially available power modules is possible. ► Exchange of reactive power between multiple inverters is possible. ► Influence of electromagnetic noise to AUG's diagnostics was measured. ► Gas insulation of electric feed through significantly depends on magnetic fields. It is protected by fast turn-off circuit. -- Abstract: A set of 16 in-vessel saddle coils has been installed in the ASDEX Upgrade (AUG) experiment since the end of 2011 [1]. To achieve full performance, it is necessary to operate them with alternating current (AC) of arbitrary waveforms. To generate spatially resolved magnetic fields, it is required to allocate separate power inverters to every single coil. Therefore, different topologies are analyzed and compared. Studies of the commutation behavior of power stages, different pulse width modulation (PWM) schemes and single-phase-to-earth fault detection are executed. Experiments to evaluate the electromagnetic interference (EMI) of possible inverter topologies on the AUG diagnostics are done as well. A special focus is put on the feasibility of analyzed topologies using industrially available and fully assembled “power modules” to minimize development effort and costs.
Understanding and Modeling the Evolution of Critical Points under Gaussian Blurring

NARCIS (Netherlands)

Kuijper, A.; Florack, L.M.J.; Heyden, A.; Sparr, G.; Nielsen, M.; Johansen, P.

2002-01-01

In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of critical points under the influence of parameter-driven blurring. During this evolution two different types of special points are encountered, the so-called scale space saddles and the
On the Bonsall cone spectral radius and the approximate point spectrum

Czech Academy of Sciences Publication Activity Database

Müller, Vladimír; Peperko, A.

2017-01-01

Roč. 37, č. 10 (2017), s. 5337-5354 ISSN 1078-0947 R&D Projects: GA ČR(CZ) GA17-00941S Institutional support: RVO:67985840 Keywords : Bonsall's cone spectral radius * local spectral radii * approximate point spectrum Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.099, year: 2016 http://aimsciences.org/ journals /displayArticlesnew.jsp?paperID=14323
Properties of diffusive systems near a saddle point: application to a quartic double well

CERN Document Server

Battezzati, M

2003-01-01

This paper aims at the analysis of diffusive properties of unidimensional mechanical systems in the environment of maxima and minima of the potential. It begins with a study of the properties of the singular solutions of the Hamilton-Jacobi-Yasue equation in the above-mentioned environment, in both strong or very small frictional forces. For the quartic symmetrical double-well potential, approximate solutions are found for local validity and the diffusion operator is then calculated in the limits of deep wells and small temperature, the regime being supposed to be aperiodic, with high or moderate values of frictional coefficient. This equation is proved to be nonunique. This operator is then reduced to second order by imposing suitable boundary conditions. Thus an appropriate eigenvalue equation is obtained to describe stationary states in the environment of extremal points of the potential energy function. The main interest of this work relies upon the fact that transition times between wells mainly depend u...
Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

Science.gov (United States)

Osada, Hirofumi; Osada, Shota

2018-01-01

We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine_2 , Airy_2 , Bessel_2 , and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.
Non-linear absorption in solids

International Nuclear Information System (INIS)

Brandi, H.S.; Jalbert, G.; Malta, O.L.

1983-06-01

Multiphoton transitions in direct-gap crystals are studied considering a 'non-perturbative' approach, similar to Keldysh approximation. A simple two parabolic band model in the effective mass approximation is considered, so that exact solutions associate to the full, crystal plus field, Hamiltonian may be approximated by Volkov wavefunctions. In this manner an S matrix is constructed which incorporates the electromagnetic field to all orders in an approximated way, leading to analytical solutions for the multiphoton transition rates. The use of the saddle point method and its limitations as well as the connection between multiphoton absorption and tunneling is discussed. It is shown that the Keldysh approach is fairly accurate as long as terms arising from the saddle point integration are consistently accounted. (Author) [pt
Non-linear absorption in solids

International Nuclear Information System (INIS)

Brandi, H.S.; Jalbert, G.; Malta, O.L.

1983-01-01

Multiphoton transitions in direct-gap crystals are studied considering a 'non-perturbative' approach, similar to Keldysh approximation. A simple two parabolic band model in the effective mass approximation is considered. So that exact solutions associated to the full, crystal plus field, Hamiltonian may be approximated by Volkov wavefunctions. An S-matrix which incorporates the electromagnetic field to all orders in an approximated way is constructed leading to analytical solutions for the multiphoton transition rates. The use of the saddle-point method and its limitations as well as the connection between multiphoton absorption and tunneling is discussed. It is shown that for near threshold excitations the Keldysh approach is fairly accurate as long as terms arising from the saddle-point integration are consistently accounted. (Author) [pt
Global analysis of dynamical decision-making models through local computation around the hidden saddle.

Directory of Open Access Journals (Sweden)

Laura Trotta

Full Text Available Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity.
A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings

Directory of Open Access Journals (Sweden)

Klin-eam Chakkrid

2009-01-01

Full Text Available Abstract A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.
Correlation of zero-point energy with molecular structure and molecular forces. 1. Development of the approximation

International Nuclear Information System (INIS)

Oi, T.; Ishida, T.

1983-01-01

An approximation formula for the zero-point energy (ZPE) has been developed on the basis of Lanczos' tau method in which the ZPE has been expressed in terms of the traces of positive integral powers of the FG matrix. It requires two approximation parameters, i.e., a normalization reference point in a domain of vibration eigenvalues and a range for the purpose of expansion. These parameters have been determined for two special cases as well as for general situation at various values of a weighting function parameter. The approximation method has been tested on water, carbon dioxide, formaldehyde, and methane. The relative errors are 3% or less for the molecules examined, and the best choice of the parameters moderately depends on the frequency distribution. 25 references, 2 figures, 9 tables

Communication: Analytic continuation of the virial series through the critical point using parametric approximants

Energy Technology Data Exchange (ETDEWEB)

Barlow, Nathaniel S., E-mail: nsbsma@rit.edu [School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623 (United States); Schultz, Andrew J., E-mail: ajs42@buffalo.edu; Kofke, David A., E-mail: kofke@buffalo.edu [Department of Chemical and Biological Engineering, University at Buffalo, State University of New York, Buffalo, New York 14260 (United States); Weinstein, Steven J., E-mail: sjweme@rit.edu [Department of Chemical Engineering, Rochester Institute of Technology, Rochester, New York 14623 (United States)

2015-08-21

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.
Communication: Analytic continuation of the virial series through the critical point using parametric approximants.

Science.gov (United States)

Barlow, Nathaniel S; Schultz, Andrew J; Weinstein, Steven J; Kofke, David A

2015-08-21

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.
Tree and nontree multiparticle amplitudes

International Nuclear Information System (INIS)

Goldberg, H.; Vaughn, M.T.

1991-01-01

We examine the behavior of the connected n-point function in a zero-dimensional scalar theory (scrL=-1/2m 2 φ 2 -1/4λφ 4 ). The problematic n exclamation point(√λ ) n behavior for large n, previously found for tree graphs in scalar field theory, is again obtained in saddle-point approximation in this model. However, a similar behavior, n exclamation point[f(λ)] n , persists in the full theory, where f∼ √λ for λ→0, f∼λ -1/4 for λ much-gt 1. This behavior can be traced to the existence of zeros in the complex J plane of the generating functional Z(J), which in turn is controlled by the asymptotic behavior in |J| of Z(J) calculated in saddle-point approximation. The application of these results to field theory is discussed
A New Approach for the Approximations of Solutions to a Common Fixed Point Problem in Metric Fixed Point Theory

Directory of Open Access Journals (Sweden)

Ishak Altun

2016-01-01

Full Text Available We provide sufficient conditions for the existence of a unique common fixed point for a pair of mappings T,S:X→X, where X is a nonempty set endowed with a certain metric. Moreover, a numerical algorithm is presented in order to approximate such solution. Our approach is different to the usual used methods in the literature.
An analytical approximation scheme to two-point boundary value problems of ordinary differential equations

International Nuclear Information System (INIS)

Boisseau, Bruno; Forgacs, Peter; Giacomini, Hector

2007-01-01

A new (algebraic) approximation scheme to find global solutions of two-point boundary value problems of ordinary differential equations (ODEs) is presented. The method is applicable for both linear and nonlinear (coupled) ODEs whose solutions are analytic near one of the boundary points. It is based on replacing the original ODEs by a sequence of auxiliary first-order polynomial ODEs with constant coefficients. The coefficients in the auxiliary ODEs are uniquely determined from the local behaviour of the solution in the neighbourhood of one of the boundary points. The problem of obtaining the parameters of the global (connecting) solutions, analytic at one of the boundary points, reduces to find the appropriate zeros of algebraic equations. The power of the method is illustrated by computing the approximate values of the 'connecting parameters' for a number of nonlinear ODEs arising in various problems in field theory. We treat in particular the static and rotationally symmetric global vortex, the skyrmion, the Abrikosov-Nielsen-Olesen vortex, as well as the 't Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the monopole is also computed by the new method. We also consider some ODEs coming from the exact renormalization group. The ground-state energy level of the anharmonic oscillator is also computed for arbitrary coupling strengths with good precision. (fast track communication)
Regional anesthesia in transurethral resection of prostate (TURP surgery: A comparative study between saddle block and subarachnoid block

Directory of Open Access Journals (Sweden)

Susmita Bhattacharyya

2015-01-01

Full Text Available Background: Spinal anesthesia is the technique of choice in transurethral resection of prostate (TURP. The major complication of spinal technique is risk of hypotension. Saddle block paralyzed pelvic muscles and sacral nerve roots and hemodynamic derangement is less. Aims and objectives: To compare the hemodynamic changes and adequate surgical condition between saddle block and subarachnoid block for TURP. Material and methods: Ninety patients of aged between 50 to 70 years of ASA-PS I, II scheduled for TURP were randomly allocated into 2 groups of 45 in each group. Group A patients were received spinal (2 ml of hyperbaric bupivacaine and Group B were received saddle block (2 ml of hyperbaric bupivacaine. Baseline systolic, diastolic and mean arterial pressure, heart rate, oxygen saturation were recorded and measured subsequently. The height of block was noted in both groups. Hypotension was corrected by administration of phenylephrine 50 mcg bolus and total requirement of vasopressor was noted. Complications (volume overload, TURP syndrome etc. were noted. Results: Incidence of hypotension and vasopressor requirement was less (P < 0.01 in Gr B patients.Adequate surgical condition was achieved in both groups. There was no incidence of volume overload, TURP syndrome, and bladder perforation. Conclusion: TURP can be safely performed under saddle block without hypotension and less vasopressor requirement.
Non-invasive Investigation and Management of Aortic Saddle Embolus in a 7-Month-Old Infant

International Nuclear Information System (INIS)

O'Connell, Martin J.; Duff, Desmond F.; Hayes, Roisin M.

2002-01-01

There are few reports in the literature on the ultrasound appearance of aortic saddle embolus, and none relating to small children. This unusual condition is usually diagnosed angiographically. The purpose of this report is to show how effectively high-frequency ultrasound can identify a saddle embolus with its associated collateral circulation in a young child, and to demonstrate its usefulness in monitoring the efficacy of treatment. In this case the embolus occurred as a complication of parvovirus B19 myocarditis and was diagnosed and followed up entirely by ultrasound examination,with no invasive procedure performed. The early development of an extensive collateral circulation prevented distal tissue necrosis and allowed a conservative approach to management
Saddle-shaped reticulate Nummulites from Early Oligocene rocks of Khari area, SW Kutch, India

Science.gov (United States)

Sengupta, S.; Sarkar, Sampa; Mukhopadhyay, S.

2011-04-01

Saddle-shaped reticulate Nummulites from the Early Oligocene rocks of Khari area, SW Kutch, India is reported here for the first time. Unusual shape of this Nummulites is due to the curved nature of the coiling plane, indicating space constrained postembryonic test growth. With regular development of chambers, septa and septal filaments, the saddle-shaped Nummulites constitutes the third morphotype of N. cf. fichteli Michelotti form A. Other morphotypes of the species reported earlier include inflated lenticular and conical tests. Multiple morphotypes of N. cf. fichteli form A indicates varied test growth in response to substrate conditions. Morphological variability exhibited by N. cf. fichteli form A from Kutch and some Early Oligocene reticulate Nummulites from the Far East are comparable. This faunal suite is morphologically distinct from the contemporary reticulate Nummulites of the European localities.
Computation of saddle-type slow manifolds using iterative methods

DEFF Research Database (Denmark)

Kristiansen, Kristian Uldall

2015-01-01

with respect to , appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples, including a model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables, and the computation of homoclinic connections in the Fitz......This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, which require mesh refinements to ensure uniform convergence...
Saddle-splay screening and chiral symmetry breaking in toroidal nematics

OpenAIRE

Koning, Vinzenz; van Zuiden, Benjamin C.; Kamien, Randall D.; Vitelli, Vincenzo

2013-01-01

We present a theoretical study of director fields in toroidal geometries with degenerate planar boundary conditions. We find spontaneous chirality: despite the achiral nature of nematics the director configuration show a handedness if the toroid is thick enough. In the chiral state the director field displays a double twist, whereas in the achiral state there is only bend deformation. The critical thickness increases as the difference between the twist and saddle-splay moduli grows. A positiv...
The thumb carpometacarpal joint: curvature morphology of the articulating surfaces, mathematical description and mechanical functioning.

Science.gov (United States)

Dathe, Henning; Dumont, Clemens; Perplies, Rainer; Fanghänel, Jochen; Kubein-Meesenburg, Dietmar; Nägerl, Hans; Wachowski, Martin M

2016-01-01

The purpose is to present a mathematical model of the function of the thumb carpometacarpal joint (TCMCJ) based on measurements of human joints. In the TCMCJ both articulating surfaces are saddle-shaped. The aim was to geometrically survey the shapes of the articulating surfaces using precise replicas of 28 TCMCJs. None of these 56 articulating surfaces did mathematically extend the differential geometrical neighbourhood around the main saddle point so that each surface could be characterised by three main parameters: the two extreme radii of curvature in the main saddle point and the angle between the saddles' asymptotics (straight lines). The articulating surfaces, when contacting at the respective main saddle points, are incongruent. Hence, the TCMCJ has functionally five kinematical degrees of freedom (DOF); two DOF belong to flexion/extension, two to ab-/adduction. These four DOF are controlled by the muscular apparatus. The fifth DOF, axial rotation, cannot be adjusted but stabilized by the muscular apparatus so that physiologically under compressive load axial rotation does not exceed an angle of approximately ±3°. The TCMCJ can be stimulated by the muscular apparatus to circumduct. The mechanisms are traced back to the curvature incongruity of the saddle surfaces. Hence we mathematically proved that none of the individual saddle surfaces can be described by a quadratic saddle surface as is often assumed in literature. We derived an algebraic formula with which the articulating surfaces in the TCMCJ can be quantitatively described. This formula can be used to shape the articulating surfaces in physiologically equivalent TCMCJ-prostheses.
Microarray background correction: maximum likelihood estimation for the normal-exponential convolution

DEFF Research Database (Denmark)

Silver, Jeremy D; Ritchie, Matthew E; Smyth, Gordon K

2009-01-01

exponentially distributed, representing background noise and signal, respectively. Using a saddle-point approximation, Ritchie and others (2007) found normexp to be the best background correction method for 2-color microarray data. This article develops the normexp method further by improving the estimation...... is developed for exact maximum likelihood estimation (MLE) using high-quality optimization software and using the saddle-point estimates as starting values. "MLE" is shown to outperform heuristic estimators proposed by other authors, both in terms of estimation accuracy and in terms of performance on real data...
The low-temperature phase of the Heisenberg antiferromagnet in a fermionic representation

International Nuclear Information System (INIS)

Azakov, S.; Dilaver, M.; Oztas, A.M.

1999-09-01

Thermal properties of the ordered phase of the spin 1/2 isotropic Heisenberg Antiferromagnet on a d-dimensional hypercubical lattice are studied within the fermionic representation when the constraint of a single occupancy condition is taken into account by the method suggested by Popov and Fedotov. Using a saddle point approximation in the path integral approach we discuss not only the leading order but also the fluctuations around the saddle point at one-loop level. The influence of taking into account the single occupancy condition is discussed at all steps. (author)
Eikonal Approximation in AdS/CFT From Shock Waves to Four-Point Functions

CERN Document Server

Cornalba, L; Costa, Miguel S; Penedones, Joao; Cornalba, Lorenzo; Costa, M S; Penedones, J; Schiappa, Ricardo

2007-01-01

We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ _{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ , where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.
Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces

International Nuclear Information System (INIS)

Chidume, C.E.

1988-01-01

Let K be a subset of a real Banach space X. A mapping T:K → X is called pseudo-contractive if the inequality ||x-y|| ≤ ||(1+r)(x-y)-r(Tx-Ty)|| holds for all x,y in K and r > 0. Fixed points of Lipschitz pseudo-contractive maps are approximated under appropriate conditions, by an iteration process of the type introduced by W.R. Mann. This gives an affirmative answer to the problem stated by T.L. Hicks and J.R. Rubicek (J. Math. Anal. Appl. 59 (1977) 504). (author). 28 refs
Beyond the Point Ps Approximation

OpenAIRE

Stepanov, Sergey V.; Zvezhinskiy, Dmitry S.; Byakov, Vsevolod M.

2012-01-01

In application to positron annihilation spectroscopy, Ps atom is considered not as a point particle, but as a finite size e+ e- pair localized in a bubble-state in a medium. Variation of the internal Coulombic e+ -e- attraction vs. the bubble radius is estimated.
ADHM and D-instantons in orbifold AdS/CFT duality

International Nuclear Information System (INIS)

Hollowood, Timothy J.; Khoze, Valentin V.

2000-01-01

We consider ADHM instantons in product group gauge theories that arise from D3-branes located at points in the orbifold R 6 /Z p . At finite N we argue that the ADHM construction and collective coordinate integration measure can be deduced from the dynamics of D-instantons in the D3-brane background. For the large-N conformal field theories of this type, we compute a saddle-point approximation of the ADHM integration measure and show that it is proportional to the partition function of D-instantons in the dual AdS 5 xS 5 /Z p background, in agreement with the orbifold AdS/CFT correspondence. Matching the expected behaviour of D-instantons, we find that when S 5 /Z p is smooth a saddle-point solution only exists in the sector where the instanton charges in each gauge group factor are the same. However, when S 5 /Z p is singular, the instanton charges at large N need not be the same and the space of saddle-point solutions has a number of distinct branches which represent the possible fractionations of D-instantons at the singularity. For the theories with a type 0B dual the saddle-point solutions manifest two types of D-instantons
On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles

Energy Technology Data Exchange (ETDEWEB)

Fitzpatrick, A. Liam [Department of Physics, Boston University,Commonwealth Avenue, Boston, MA 02215 (United States); Kaplan, Jared [Department of Physics and Astronomy, Johns Hopkins University,Charles Street, Baltimore, MD 21218 (United States)

2017-04-12

Recent work has demonstrated that black hole thermodynamics and information loss/restoration in AdS{sub 3}/CFT{sub 2} can be derived almost entirely from the behavior of the Virasoro conformal blocks at large central charge, with relatively little dependence on the precise details of the CFT spectrum or OPE coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all ‘saddles’ that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit. The leading saddles, which determine the naive semiclassical behavior of the Virasoro blocks, all decay exponentially at late times, and at a rate that is independent of internal operator dimensions. Consequently, the semiclassical contribution of a finite number of high-energy states cannot resolve a well-known version of the information loss problem in AdS{sub 3}. However, we identify two infinite classes of sub-leading saddles, and one of these classes does not decay at late times.
Parameterized approximation of lacunarity functions derived from airborne laser scanning point clouds of forested areas

Science.gov (United States)

Székely, Balázs; Kania, Adam; Varga, Katalin; Heilmeier, Hermann

2017-04-01

Lacunarity, a measure of the spatial distribution of the empty space is found to be a useful descriptive quantity of the forest structure. Its calculation, based on laser-scanned point clouds, results in a four-dimensional data set. The evaluation of results needs sophisticated tools and visualization techniques. To simplify the evaluation, it is straightforward to use approximation functions fitted to the results. The lacunarity function L(r), being a measure of scale-independent structural properties, has a power-law character. Previous studies showed that log(log(L(r))) transformation is suitable for analysis of spatial patterns. Accordingly, transformed lacunarity functions can be approximated by appropriate functions either in the original or in the transformed domain. As input data we have used a number of laser-scanned point clouds of various forests. The lacunarity distribution has been calculated along a regular horizontal grid at various (relative) elevations. The lacunarity data cube then has been logarithm-transformed and the resulting values became the input of parameter estimation at each point (point of interest, POI). This way at each POI a parameter set is generated that is suitable for spatial analysis. The expectation is that the horizontal variation and vertical layering of the vegetation can be characterized by this procedure. The results show that the transformed L(r) functions can be typically approximated by exponentials individually, and the residual values remain low in most cases. However, (1) in most cases the residuals may vary considerably, and (2) neighbouring POIs often give rather differing estimates both in horizontal and in vertical directions, of them the vertical variation seems to be more characteristic. In the vertical sense, the distribution of estimates shows abrupt changes at places, presumably related to the vertical structure of the forest. In low relief areas horizontal similarity is more typical, in higher relief areas
Unstable Modes and Order Parameters of Bistable Signaling Pathways at Saddle-Node Bifurcations: A Theoretical Study Based on Synergetics

Directory of Open Access Journals (Sweden)

Till D. Frank

2016-01-01

Full Text Available Mathematical modeling has become an indispensable part of systems biology which is a discipline that has become increasingly popular in recent years. In this context, our understanding of bistable signaling pathways in terms of mathematical modeling is of particular importance because such bistable components perform crucial functions in living cells. Bistable signaling pathways can act as switches or memory functions and can determine cell fate. In the present study, properties of mathematical models of bistable signaling pathways are examined from the perspective of synergetics, a theory of self-organization and pattern formation founded by Hermann Haken. At the heart of synergetics is the concept of so-called unstable modes or order parameters that determine the behavior of systems as a whole close to bifurcation points. How to determine these order parameters for bistable signaling pathways at saddle-node bifurcation points is shown. The procedure is outlined in general and an explicit example is worked out in detail.

Binary nucleation kinetics. III. Transient behavior and time lags

International Nuclear Information System (INIS)

Wyslouzil, B.E.; Wilemski, G.

1996-01-01

Transient binary nucleation is more complex than unary because of the bidimensionality of the cluster formation kinetics. To investigate this problem qualitatively and quantitatively, we numerically solved the birth-death equations for vapor-to-liquid phase transitions. Our previous work showed that the customary saddle point and growth path approximations are almost always valid in steady state gas phase nucleation and only fail if the nucleated solution phase is significantly nonideal. Now, we demonstrate that in its early transient stages, binary nucleation rarely, if ever, occurs via the saddle point. This affects not only the number of particles forming but their composition and may be important for nucleation in glasses and other condensed mixtures for which time scales are very long. Before reaching the state of saddle point nucleation, most binary systems pass through a temporary stage in which the region of maximum flux extends over a ridge on the free energy surface. When ridge crossing nucleation is the steady state solution, it thus arises quite naturally as an arrested intermediate state that normally occurs in the development of saddle point nucleation. While the time dependent and steady state distributions of the fluxes and concentrations for each binary system are strongly influenced by the gas composition and species impingement rates, the ratio of nonequilibrium to equilibrium concentrations has a quasiuniversal behavior that is determined primarily by the thermodynamic properties of the liquid mixture. To test our quantitive results of the transient behavior, we directly calculated the time lag for the saddle point flux and compared it with the available analytical predictions. Although the analytical results overestimate the time lag by factors of 1.2-5, they should be adequate for purposes of planning experiments. We also found that the behavior of the saddle point time lag can indicate when steady state ridge crossing nucleation will occur
Risk factors for saddle-related skin lesions on elephants used in the tourism industry in Thailand.

Science.gov (United States)

Magda, Scarlett; Spohn, Olivia; Angkawanish, Taweepoke; Smith, Dale A; Pearl, David L

2015-05-19

Lesions related to working conditions and improper saddle design are a concern for a variety of working animals including elephants. The objectives of the present study were to determine the prevalence of cutaneous lesions in anatomic regions (i.e., neck, girth, back, tail) in contact with saddle-related equipment among elephants in Thailand working in the tourism industry, and to identify potential risk factors associated with these lesions. Data for this cross-sectional study were collected between May 2007 and July 2007 on 194 elephants from 18 tourism camps across Thailand. There was a high prevalence (64.4 %; 95 % CI 57.3 - 71.2) of active lesions, most often located on the back region. Using multilevel multivariable logistic regression modelling containing a random intercept for camp we identified the following risk factors: increasing elephant age, the use of rice sacks as padding material in contact with the skin, and the provision of a break for the elephants. Working hours had a quadratic relationship with the log odds of an active lesion where the probability of an active lesion initially increased with the number of working hours per day and then declined possibly reflecting a "healthy worker" bias where only animals without lesions continue to be able to work these longer hours. While we recognize that the cross-sectional nature of the study posed some inferential limitations, our results offer several potential intervention points for the prevention of these lesions. Specifically, we recommend the following until longitudinal studies can be conducted: increased monitoring of older elephants and the back region of all elephants, working less than 6 hours per day, and the avoidance of rice sacks as padding material in contact with skin.
Attractors under discretisation

CERN Document Server

Han, Xiaoying

2017-01-01

This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions

Science.gov (United States)

Hussain, N.

2008-02-01

The common fixed point theorems, similar to those of Ciric [Lj.B. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174-178; Lj.B. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145-152; Lj.B. Ciric, On a generalization of Gregus fixed point theorem, Czechoslovak Math. J. 50 (2000) 449-458], Fisher and Sessa [B. Fisher, S. Sessa, On a fixed point theorem of Gregus, Internat. J. Math. Math. Sci. 9 (1986) 23-28], Jungck [G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13 (1990) 497-500] and Mukherjee and Verma [R.N. Mukherjee, V. Verma, A note on fixed point theorem of Gregus, Math. Japon. 33 (1988) 745-749], are proved for a Banach operator pair. As applications, common fixed point and approximation results for Banach operator pair satisfying Ciric type contractive conditions are obtained without the assumption of linearity or affinity of either T or I. Our results unify and generalize various known results to a more general class of noncommuting mappings.
Gene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information.

Science.gov (United States)

Jia, Bin; Wang, Xiaodong

2013-12-17

: The extended Kalman filter (EKF) has been applied to inferring gene regulatory networks. However, it is well known that the EKF becomes less accurate when the system exhibits high nonlinearity. In addition, certain prior information about the gene regulatory network exists in practice, and no systematic approach has been developed to incorporate such prior information into the Kalman-type filter for inferring the structure of the gene regulatory network. In this paper, an inference framework based on point-based Gaussian approximation filters that can exploit the prior information is developed to solve the gene regulatory network inference problem. Different point-based Gaussian approximation filters, including the unscented Kalman filter (UKF), the third-degree cubature Kalman filter (CKF3), and the fifth-degree cubature Kalman filter (CKF5) are employed. Several types of network prior information, including the existing network structure information, sparsity assumption, and the range constraint of parameters, are considered, and the corresponding filters incorporating the prior information are developed. Experiments on a synthetic network of eight genes and the yeast protein synthesis network of five genes are carried out to demonstrate the performance of the proposed framework. The results show that the proposed methods provide more accurate inference results than existing methods, such as the EKF and the traditional UKF.
Effects of saddle height on economy and anaerobic power in well-trained cyclists.

Science.gov (United States)

Peveler, Willard W; Green, James M

2011-03-01

In cycling, saddle height adjustment is critical for optimal performance and injury prevention. A 25-35° knee angle is recommended for injury prevention, whereas 109% of inseam, measured from floor to ischium, is recommended for optimal performance. Previous research has demonstrated that these 2 methods produce significantly different saddle heights and may influence cycling performance. This study compared performance between these 2 methods for determining saddle height. Subjects consisted of 11 well-trained (VO2max = 61.55 ± 4.72 ml·kg·min) male cyclists. Subjects completed a total of 8 performance trials consisting of a graded maximal protocol, three 15-minute economy trials, and 4 anaerobic power trials. Dependent measures for economy (VO2, heart rate, and rating of perceived exertion) and anaerobic power (peak power and mean power) were compared using repeated measures analysis of variance (α = 0.05). VO2 was significantly lower (reflecting greater economy) at a 25° knee angle (44.77 ± 6.40 ml·kg·min) in comparison to a 35° knee angle (45.22 ± 6.79 ml·kg·min) and 109% of inseam (45.98 ± 5.33 ml·kg·min). Peak power at a 25° knee angle (1,041.55 ± 168.72 W) was significantly higher in relation to 109% of inseam (1,002.05 ± 147.65 W). Mean power at a 25° knee angle (672.37 ± 90.21 W) was significantly higher in relation to a 35° knee angle (654.71 ± 80.67 W). Mean power was significantly higher at 109% of inseam (662.86 ± 79.72 W) in relation to a 35° knee angle (654.71 ± 80.67 W). Use of 109% of inseam fell outside the recommended 25-35° range 73% of the time. Use of 25° knee angle appears to provide optimal performance while keeping knee angle within the recommended range for injury prevention.
On the trajectories of CRL...LR...R orbits, their period-doubling cascades and saddle-node bifurcation cascades

International Nuclear Information System (INIS)

Cerrada, Lucia; San Martin, Jesus

2011-01-01

In this Letter, it is shown that from a two region partition of the phase space of a one-dimensional dynamical system, a p-region partition can be obtained for the CRL...LR...R orbits. That is, permutations associated with symbolic sequences are obtained. As a consequence, the trajectory in phase space is directly deduced from permutation. From this permutation other permutations associated with period-doubling and saddle-node bifurcation cascades are derived, as well as other composite permutations. - Research highlights: → Symbolic sequences are the usual topological approach to dynamical systems. → Permutations bear more physical information than symbolic sequences. → Period-doubling cascade permutations associated with original sequences are obtained. → Saddle-node cascade permutations associated with original sequences are obtained. → Composite permutations are derived.
Bond selective chemistry beyond the adiabatic approximation

Energy Technology Data Exchange (ETDEWEB)

Butler, L.J. [Univ. of Chicago, IL (United States)

1993-12-01

One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.
Dissipative corrections to particle spectra and anisotropic flow from a saddle-point approximation to kinetic freeze out

International Nuclear Information System (INIS)

Lang, Christian; Borghini, Nicolas

2014-01-01

A significant fraction of the changes in momentum distributions induced by dissipative phenomena in the description of the fluid fireball created in ultrarelativistic heavy-ion collisions actually take place when the fluid turns into individual particles. We study these corrections in the limit of a low freeze-out temperature of the flowing medium, and we show that they mostly affect particles with a higher velocity than the fluid. For these, we derive relations between different flow harmonics, from which the functional form of the dissipative corrections could ultimately be reconstructed from experimental data. (orig.)
Investment decisions in the South African saddle horse industry / Johannes Hendrik Dreyer

OpenAIRE

Dreyer, Johannes Hendrik

2014-01-01

This study originated in the phenomenon that has been observed in the South African Saddle Horse Industry of substantial investments being made over time in the absence of obvious financial or economic reward. A literature study confirmed that, internationally, investment without obvious financial and economic rewards is not unknown and at the same time it was obvious that it is a rarely studied subject. From the literature study it was also evident that this phenomenon occurs ...
Point defects dynamics in a stress field

International Nuclear Information System (INIS)

Smetniansky de De Grande, Nelida.

1989-01-01

The dependence of anisotropic defect diffusion on stress is studied for a hexagonal close packed (hcp) material under irradiation and uniaxially stressed. The diffusion is described as a discrete process of thermally activated jumps. It is shown that the presence of an external stress field enhances the intrinsic anisotropic diffusion, being this variation determined by the defect dipole tensors' symmetry in the equilibrium and saddle point configurations. Also, the point defect diffusion equations to sinks, like edge dislocations and spherical cavities, are solved and the sink strengths are calculated. The conclusion is that the dynamics of the interaction between defects and sinks is controlled by the changes in diffusivity induced by stress fields. (Author) [es
A density gradient theory based method for surface tension calculations

DEFF Research Database (Denmark)

Liang, Xiaodong; Michelsen, Michael Locht; Kontogeorgis, Georgios

2016-01-01

The density gradient theory has been becoming a widely used framework for calculating surface tension, within which the same equation of state is used for the interface and bulk phases, because it is a theoretically sound, consistent and computationally affordable approach. Based on the observation...... that the optimal density path from the geometric mean density gradient theory passes the saddle point of the tangent plane distance to the bulk phases, we propose to estimate surface tension with an approximate density path profile that goes through this saddle point. The linear density gradient theory, which...... assumes linearly distributed densities between the two bulk phases, has also been investigated. Numerical problems do not occur with these density path profiles. These two approximation methods together with the full density gradient theory have been used to calculate the surface tension of various...
A point-value enhanced finite volume method based on approximate delta functions

Science.gov (United States)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.
Singlet structure function F_1 in double-logarithmic approximation

Science.gov (United States)

Ermolaev, B. I.; Troyan, S. I.

2018-03-01

The conventional ways to calculate the perturbative component of the DIS singlet structure function F_1 involve approaches based on BFKL which account for the single-logarithmic contributions accompanying the Born factor 1 / x. In contrast, we account for the double-logarithmic (DL) contributions unrelated to 1 / x and because of that they were disregarded as negligibly small. We calculate the singlet F_1 in the double-logarithmic approximation (DLA) and account at the same time for the running α _s effects. We start with a total resummation of both quark and gluon DL contributions and obtain the explicit expression for F_1 in DLA. Then, applying the saddle-point method, we calculate the small- x asymptotics of F_1, which proves to be of the Regge form with the leading singularity ω _0 = 1.066. Its large value compensates for the lack of the factor 1 / x in the DLA contributions. Therefore, this Reggeon can be identified as a new Pomeron, which can be quite important for the description of all QCD processes involving the vacuum (Pomeron) exchanges at very high energies. We prove that the expression for the small- x asymptotics of F_1 scales: it depends on a single variable Q^2/x^2 only instead of x and Q^2 separately. Finally, we show that the small- x asymptotics reliably represent F_1 at x ≤ 10^{-6}.
A vortex ring interacting with a vortex filament and its deformation near the two-dimensional stagnation point

International Nuclear Information System (INIS)

Kiya, M.; Sato, T.

1986-01-01

In this paper the interaction between vortex filaments and vortex rings and the deformation of vortex rings near the two-dimensional stagnation point are simulated by a three-dimensional vortex method. The two problems are respectively concerned with the effect of free-stream turbulence on turbulent plane mixing layers and the production of turbulence by the vortex stretching near saddles associated with large-scale coherent structures. The authors assume that the first step to understand the free-stream turbulence effect is to study the interaction between a vortex ring and a vortex filament and that the process of deformation of a vortex ring gives us a clue to understand physical processes occurring near the saddles
Decreasing Computational Time for VBBinaryLensing by Point Source Approximation

Science.gov (United States)

Tirrell, Bethany M.; Visgaitis, Tiffany A.; Bozza, Valerio

2018-01-01

The gravitational lens of a binary system produces a magnification map that is more intricate than a single object lens. This map cannot be calculated analytically and one must rely on computational methods to resolve. There are generally two methods of computing the microlensed flux of a source. One is based on ray-shooting maps (Kayser, Refsdal, & Stabell 1986), while the other method is based on an application of Green’s theorem. This second method finds the area of an image by calculating a Riemann integral along the image contour. VBBinaryLensing is a C++ contour integration code developed by Valerio Bozza, which utilizes this method. The parameters at which the source object could be treated as a point source, or in other words, when the source is far enough from the caustic, was of interest to substantially decrease the computational time. The maximum and minimum values of the caustic curves produced, were examined to determine the boundaries for which this simplification could be made. The code was then run for a number of different maps, with separation values and accuracies ranging from 10-1 to 10-3, to test the theoretical model and determine a safe buffer for which minimal error could be made for the approximation. The determined buffer was 1.5+5q, with q being the mass ratio. The theoretical model and the calculated points worked for all combinations of the separation values and different accuracies except the map with accuracy and separation equal to 10-3 for y1 max. An alternative approach has to be found in order to accommodate a wider range of parameters.
Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents

KAUST Repository

Athanassoulis, Agissilaos; Katsaounis, Theodoros; Kyza, Irene

2016-01-01

Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.
Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents

KAUST Repository

Athanassoulis, Agissilaos

2016-08-30

Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.
Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Pade approximations via the analytical inversion method

International Nuclear Information System (INIS)

Aboanber, A E; Nahla, A A

2002-01-01

A method based on the Pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity. The technique consists of treating explicitly the roots of the inhour formula. A significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation, which usually would make the Pade approximation inaccurate. Also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the Pade approximations. Results are presented for several cases of Pade approximations using various options of the method with different types of reactivity. The formalism is applicable equally well to non-linear problems, where the reactivity depends on the neutron density through temperature feedback. It was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases
Exotic Homoclinic Surface of a Saddle-Node Limit Cycle in a Leech Neuron Model

Science.gov (United States)

Yooer, Chi-Feng; Wei, Fang; Xu, Jian-Xue; Zhang, Xin-Hua

2011-03-01

We carry out numerical and theoretical investigations on the global unstable invariant set (manifold) of a saddle-node limit cycle in a leech heart interneuron model. The corresponding global bifurcation is accompanied by an explosion of secondary bifurcations of limit cycles and the emergence of loop-shaped bifurcation structures. The dynamical behaviors of the trajectories of the invariant set are very complicated and can only be partially explained by existing theories.

Quantum transitions through cosmological singularities

Energy Technology Data Exchange (ETDEWEB)

Bramberger, Sebastian F.; Lehners, Jean-Luc [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm (Germany); Hertog, Thomas; Vreys, Yannick, E-mail: sebastian.bramberger@aei.mpg.de, E-mail: thomas.hertog@kuleuven.be, E-mail: jlehners@aei.mpg.de, E-mail: yannick.vreys@kuleuven.be [Institute for Theoretical Physics, KU Leuven, 3001 Leuven (Belgium)

2017-07-01

In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Quantum transitions through cosmological singularities

International Nuclear Information System (INIS)

Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas; Vreys, Yannick

2017-01-01

In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Using a new saddle model for echinotherapy therapy.

Directory of Open Access Journals (Sweden)

Carlos Cesar Santín Alfaro

2014-09-01

Full Text Available A descriptive study with experimental design was done, having as an objective to elaborate a new riding saddle model in the Provincial Laboratory of Technical Orthopaedics in the province of Sancti Spiritus for the Echinotherapy´s treatment in disable patients that still assisting to this kind of alternative therapy having the necessity of obtaining the frame according to the adequate characteristics and adjusting to the requirements of the qualified staff that takes care of this task taking into consideration that for the rehabilitation of these children they should be closer to the horse skin. The frame was not made with the row materials of normal chair but with the one adequate in our Laboratory. Some important characteristics were developed in this kind of therapy, and was analyzed the characteristics of the frame use give to patients, offering an immediate solution to their problems in order to solve this difficulty in our province.
Saddle-splay elasticity of nematic structures confined to a cylindrical capillary

International Nuclear Information System (INIS)

Kralj, S.; Zumer, S.

1995-01-01

The stability of nematic structures within a cylindrical capillary whose wall exhibits a homeotropic boundary condition is studied. The structures are obtained numerically from Euler-Lagrange equations resulting from the minimization of the Frank free energy functional. Stability diagrams are presented showing dependence on elastic properties, surface anchoring, and external transversal field strength. Emphasis is given to the effects of the saddle-splay elastic constant (K 24 ), which plays an important role in the weak anchoring regime. A new structure---the planar polar structure with two line defects---is predicted. It is shown that it is stable in a finite interval of the external field strength in the strong anchoring regime
Hamiltonian flow over saddles for exploring molecular phase space structures

Science.gov (United States)

Farantos, Stavros C.

2018-03-01

Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue `Modern theoretical chemistry'.
Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks

KAUST Repository

Vilanova, Pedro

2015-05-04

This thesis focuses on the development and analysis of efficient simulation and inference techniques for Markovian pure jump processes with a view towards applications in dense communication networks. These techniques are especially relevant for modeling networks of smart devices —tiny, abundant microprocessors with integrated sensors and wireless communication abilities— that form highly complex and diverse communication networks. During 2010, the number of devices connected to the Internet exceeded the number of people on Earth: over 12.5 billion devices. By 2015, Cisco’s Internet Business Solutions Group predicts that this number will exceed 25 billion. The first part of this work proposes novel numerical methods to estimate, in an efficient and accurate way, observables from realizations of Markovian jump processes. In particular, hybrid Monte Carlo type methods are developed that combine the exact and approximate simulation algorithms to exploit their respective advantages. These methods are tailored to keep a global computational error below a prescribed global error tolerance and within a given statistical confidence level. Indeed, the computational work of these methods is similar to the one of an exact method, but with a smaller constant. Finally, the methods are extended to systems with a disparity of time scales. The second part develops novel inference methods to estimate the parameters of Markovian pure jump process. First, an indirect inference approach is presented, which is based on upscaled representations and does not require sampling. This method is simpler than dealing directly with the likelihood of the process, which, in general, cannot be expressed in closed form and whose maximization requires computationally intensive sampling techniques. Second, a forward-reverse Monte Carlo Expectation-Maximization algorithm is provided to approximate a local maximum or saddle point of the likelihood function of the parameters given a set of
Present status on numerical algorithms and benchmark tests for point kinetics and quasi-static approximate kinetics

International Nuclear Information System (INIS)

Ise, Takeharu

1976-12-01

Review studies have been made on algorithms of numerical analysis and benchmark tests on point kinetics and quasistatic approximate kinetics computer codes to perform efficiently benchmark tests on space-dependent neutron kinetics codes. Point kinetics methods have now been improved since they can be directly applied to the factorization procedures. Methods based on Pade rational function give numerically stable solutions and methods on matrix-splitting are interested in the fact that they are applicable to the direct integration methods. An improved quasistatic (IQ) approximation is the best and the most practical method; it is numerically shown that the IQ method has a high stability and precision and the computation time which is about one tenth of that of the direct method. IQ method is applicable to thermal reactors as well as fast reactors and especially fitted for fast reactors to which many time steps are necessary. Two-dimensional diffusion kinetics codes are most practicable though there exist also three-dimensional diffusion kinetics code as well as two-dimensional transport kinetics code. On developing a space-dependent kinetics code, in any case, it is desirable to improve the method so as to have a high computing speed for solving static diffusion and transport equations. (auth.)
An algorithm to locate optimal bond breaking points on a potential energy surface for applications in mechanochemistry and catalysis.

Science.gov (United States)

Bofill, Josep Maria; Ribas-Ariño, Jordi; García, Sergio Pablo; Quapp, Wolfgang

2017-10-21

The reaction path of a mechanically induced chemical transformation changes under stress. It is well established that the force-induced structural changes of minima and saddle points, i.e., the movement of the stationary points on the original or stress-free potential energy surface, can be described by a Newton Trajectory (NT). Given a reactive molecular system, a well-fitted pulling direction, and a sufficiently large value of the force, the minimum configuration of the reactant and the saddle point configuration of a transition state collapse at a point on the corresponding NT trajectory. This point is called barrier breakdown point or bond breaking point (BBP). The Hessian matrix at the BBP has a zero eigenvector which coincides with the gradient. It indicates which force (both in magnitude and direction) should be applied to the system to induce the reaction in a barrierless process. Within the manifold of BBPs, there exist optimal BBPs which indicate what is the optimal pulling direction and what is the minimal magnitude of the force to be applied for a given mechanochemical transformation. Since these special points are very important in the context of mechanochemistry and catalysis, it is crucial to develop efficient algorithms for their location. Here, we propose a Gauss-Newton algorithm that is based on the minimization of a positively defined function (the so-called σ-function). The behavior and efficiency of the new algorithm are shown for 2D test functions and for a real chemical example.
Topological fluid mechanics of the formation of the Kármán-vortex street

DEFF Research Database (Denmark)

Heil, Matthias; Rosso, Jordan; Hazel, Andrew L.

2017-01-01

consider to be feature points for vortices. The basic vortex creation mechanism is shown to be a topological cusp bifurcation in the vorticity field, where a saddle and an extremum of the vorticity are created simultaneously. We demonstrate that vortices are first created approximately 100 diameters...
A description of a wide beam saddle field ion source used for nuclear target applications

International Nuclear Information System (INIS)

Greene, J.P.; Schiel, S.L.; Thomas, G.E.

1997-01-01

A description is given of a new, wide beam saddle field sputter source used for the preparation of targets applied in nuclear physics experiments. The ion source characteristics are presented and compared with published results obtained with other sources. Deposition rates acquired utilizing this source are given for a variety of target materials encountered in nuclear target production. New applications involving target thinning and ion milling are discussed
On the main anhydrite scenario, illustrated by the example of the NE flank of the Stassfurt saddle

International Nuclear Information System (INIS)

Schwandt, A.; Schilder, C.; Rauche, H.; Franzke, H.J.

1991-09-01

The non-chloride successions embedded in the salt of the Zechstein with their geomechanical behaviour which is completely different from that of the salt rock play an important part in the assessment of the concrete safety situation in the salt mine destined to serve as a repository. The literature study of this report presents a safety-related assessment of the main anhydrite using the example of the NE flank of the Stassfurt saddle, on the basis of exploratory data and experience and documented data obtained by the authors of this report. The tectonic effects on the main anhydrite are studied in detail. It is found that geomechanical impacts can lead to healed or closed joints getting damaged and thus loose their tightness to water or gas. The most intensive geomechanical stress on the main anhydrite results from the flooding of mines. It is stated that, making pin-pointed investigations of the geological and hydrogeological conditions, natural or man-made hazards to the safety of a repository can be well recognized, characterized, and mastered. (orig./HP) [de
On the sighting of unicorns: A variational approach to computing invariant sets in dynamical systems

Science.gov (United States)

Junge, Oliver; Kevrekidis, Ioannis G.

2017-06-01

We propose to compute approximations to invariant sets in dynamical systems by minimizing an appropriate distance between a suitably selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments, that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topology, dimension, and stability, such as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function, which yields more evenly distributed approximating finite point sets, and illustrate the procedure through corresponding numerical experiments.
Acumulating regions of winding periodic orbits in optically driven lasers

NARCIS (Netherlands)

Krauskopf, B.; Wieczorek, S.

2002-01-01

We investigate the route to locking in class B lasers subject to optically injected light for injection strengths and detunings near a codimension-two saddle-node Hopf point. This is the parameter region where the Adler approximation is not valid and where Yeung and Strogatz recently reported a
Choosing the Optimal Number of B-spline Control Points (Part 1: Methodology and Approximation of Curves)

Science.gov (United States)

Harmening, Corinna; Neuner, Hans

2016-09-01

Due to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds. Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline's appearance; the B-spline's complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn't use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality. The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.
Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions

CERN Document Server

Cornalba, L; Penedones, J; Schiappa, R; Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo

2007-01-01

We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ . This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function _{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.
Application of the nudged elastic band method to the point-to-point radio wave ray tracing in IRI modeled ionosphere

Science.gov (United States)

Nosikov, I. A.; Klimenko, M. V.; Bessarab, P. F.; Zhbankov, G. A.

2017-07-01

Point-to-point ray tracing is an important problem in many fields of science. While direct variational methods where some trajectory is transformed to an optimal one are routinely used in calculations of pathways of seismic waves, chemical reactions, diffusion processes, etc., this approach is not widely known in ionospheric point-to-point ray tracing. We apply the Nudged Elastic Band (NEB) method to a radio wave propagation problem. In the NEB method, a chain of points which gives a discrete representation of the radio wave ray is adjusted iteratively to an optimal configuration satisfying the Fermat's principle, while the endpoints of the trajectory are kept fixed according to the boundary conditions. Transverse displacements define the radio ray trajectory, while springs between the points control their distribution along the ray. The method is applied to a study of point-to-point ionospheric ray tracing, where the propagation medium is obtained with the International Reference Ionosphere model taking into account traveling ionospheric disturbances. A 2-dimensional representation of the optical path functional is developed and used to gain insight into the fundamental difference between high and low rays. We conclude that high and low rays are minima and saddle points of the optical path functional, respectively.
Approximate entropy and point correlation dimension of heart rate variability in healthy subjects

DEFF Research Database (Denmark)

Storella, R J; Wood, H W; Mills, K M

1999-01-01

The contribution of nonlinear dynamics to heart rate variability in healthy humans was examined using surrogate data analysis. Several measures of heart rate variability were used and compared. Heart rates were recorded for three hours and original data sets of 8192 R-R intervals created. For each...... original data set (n = 34), three surrogate data sets were made by shuffling the order of the R-R intervals while retaining their linear correlations. The difference in heart rate variability between the original and surrogate data sets reflects the amount of nonlinear structure in the original data set....... Heart rate variability was analyzed by two different nonlinear methods, point correlation dimension and approximate entropy. Nonlinearity, though under 10 percent, could be detected with both types of heart rate variability measures. More importantly, not only were the correlations between...
Dynamics of Two Point Vortices in an External Compressible Shear Flow

Science.gov (United States)

Vetchanin, Evgeny V.; Mamaev, Ivan S.

2017-12-01

This paper is concerned with a system of equations that describes the motion of two point vortices in a flow possessing constant uniform vorticity and perturbed by an acoustic wave. The system is shown to have both regular and chaotic regimes of motion. In addition, simple and chaotic attractors are found in the system. Attention is given to bifurcations of fixed points of a Poincaré map which lead to the appearance of these regimes. It is shown that, in the case where the total vortex strength changes, the "reversible pitch-fork" bifurcation is a typical scenario of emergence of asymptotically stable fixed and periodic points. As a result of this bifurcation, a saddle point, a stable and an unstable point of the same period emerge from an elliptic point of some period. By constructing and analyzing charts of dynamical regimes and bifurcation diagrams we show that a cascade of period-doubling bifurcations is a typical scenario of transition to chaos in the system under consideration.
Analysis of the nine-point finite difference approximation for the heat conduction equation in a nuclear fuel element

International Nuclear Information System (INIS)

Kadri, M.

1983-01-01

The time dependent heat conduction equation in the x-y Cartesian geometry is formulated in terms of a nine-point finite difference relation using a Taylor series expansion technique. The accuracy of the nine-point formulation over the five-point formulation has been tested and evaluated for various reactor fuel-cladding plate configurations using a computer program. The results have been checked against analytical solutions for various model problems. The following cases were considered in the steady-state condition: (a) The thermal conductivity and the heat generation were uniform. (b) The thermal conductivity was constant, the heat generation variable. (c) The thermal conductivity varied linearly with the temperature, the heat generation was uniform. (d) Both thermal conductivity and heat generation vary. In case (a), approximately, for the same accuracy, 85% fewer grid points were needed for the nine-point relation which has a 14% higher convergence rate as compared to the five-point relation. In case (b), on the average, 84% fewer grid points were needed for the nine-point relation which has a 65% higher convergence rate as compared to the five-point relation. In case (c) and (d), there is significant accuracy (91% higher than the five-point relation) for the nine-point relation when a worse grid was used. The numerical solution of the nine-point formula in the time dependent case was also more accurate and converges faster than the numerical solution of the five-point formula for all comparative tests related to heat conduction problems in a nuclear fuel element
Going Beyond the Point Nucleus Approximation to Satisfy the Hellmann–Feynman Theorem: Born–Oppenheimer H2+ in the Ground State

International Nuclear Information System (INIS)

Gutlé, Claudine

2017-01-01

Incomplete spaces are investigated for solving the Schrödinger equation under the Born–Oppenheimer approximation. It is shown that the Hellmann–Feynman theorem cannot be used for computing the electronic force exerted on a nucleus, when a variational wavefunction with floating centers is used, if multicenter polynomial components are added in order to describe the polarization effects through the chemical bond. This is because the minimum of the potential energy surface is not a stationary point in the direction of the float parameter. Such a failure can be fixed by considering a molecular model with finite size nuclei, as defined herein. The classical electronic force is computed for that model, as compared with the standard point charge approximation, and it is applied to the H 2 + molecular ion. As a result, the former model is found more accurate by several orders of magnitude. (author)

Approximate Fixed Point Theorems for the Class of Almost S-KKM𝒞 Mappings in Abstract Convex Uniform Spaces

Directory of Open Access Journals (Sweden)

Tong-Huei Chang

2009-01-01

Full Text Available We use a concept of abstract convexity to define the almost S-KKM𝒞 property, al-S-KKM𝒞(X,Y family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors.
Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions

International Nuclear Information System (INIS)

Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo

2007-01-01

We introduce the impact parameter representation for conformal field theory correlators of the form A∼ 1 O 2 O 1 O 2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function 1 O 1 > shock in the presence of a shock wave in anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch cut, we find the high spin and dimension conformal partial wave decomposition of all tree-level anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high spin O 1 O 2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling
Novel spin transition between S = 5/2 and S = 3/2 in highly saddled iron(III) porphyrin complexes at extremely low temperatures.

Science.gov (United States)

Ohgo, Yoshiki; Chiba, Yuya; Hashizume, Daisuke; Uekusa, Hidehiro; Ozeki, Tomoji; Nakamura, Mikio

2006-05-14

A novel spin transition between S = 5/2 and S = 3/2 has been observed for the first time in five-coordinate, highly saddled iron(III) porphyrinates by EPR and SQUID measurements at extremely low temperatures.
Hessian eigenvalue distribution in a random Gaussian landscape

Science.gov (United States)

Yamada, Masaki; Vilenkin, Alexander

2018-03-01

The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of 1/ N expansion, where N is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.
Nested BDDC for a saddle-point problem

Czech Academy of Sciences Publication Activity Database

Sousedík, Bedřich

2013-01-01

Roč. 125, č. 4 (2013), s. 761-783 ISSN 0029-599X Institutional support: RVO:61388998 Keywords : flow * formulation * substructuring methods Subject RIV: BA - General Mathematics Impact factor: 1.551, year: 2013
Saddle point avoidance in barrier crossing problems

Energy Technology Data Exchange (ETDEWEB)

Talkner, P.; Drozdov, A.N. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

1997-06-01

The long-time behavior of the stochastic dynamics of a two-dimensional system having two metastable states is investigated by means of the low-lying part of the corresponding two-dimensional Smoluchowski operator. In particular, its dependence on three parameters describing the strength of the noise, the coupling of the degrees of freedom and a ratio of relaxation-times is considered. Further information characterizing the transition process between the metastable states is gained from the corresponding eigenfunctions. (author) 9 refs.
A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers.

Science.gov (United States)

Bhowmick, Amiya Ranjan; Bandyopadhyay, Subhadip; Rana, Sourav; Bhattacharya, Sabyasachi

2016-01-01

The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database. Copyright © 2015 Elsevier Inc. All rights reserved.
Regression with Sparse Approximations of Data

DEFF Research Database (Denmark)

Noorzad, Pardis; Sturm, Bob L.

2012-01-01

We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \$k\$-nearest neighbors regression (\$k\$-NNR), and more generally, local polynomial kernel regression. Unlike \$k\$-NNR, however, SPARROW can adapt the number of regressors to use based...
Analytical theory of noncollinear amorphous metallic magnetism

International Nuclear Information System (INIS)

Kakehashi, Y.; Uchida, T.

2001-01-01

Analytical theory of noncollinear magnetism in amorphous metals is proposed on the basis of the Gaussian model for the distribution of the interatomic distance and the saddle-point approximation. The theory removes the numerical difficulty in the previous theory based on the Monte-Carlo sampling method, and reasonably describes the magnetic properties of amorphous transition metals
Universal canonical entropy for gravitating systems

Indian Academy of Sciences (India)

Similar to this is the case of ref. [12] which also uses the saddle point approximation to express the microcanonical entropy in terms of the canonical entropy [12a]. Recalling that there is at least 'circumstantial' evidence that the microcanonical entropy has a 'universal' form [13–15], identical to that obtained in ref. [6] quoted.
Fold points and singularity induced bifurcation in inviscid transonic flow

International Nuclear Information System (INIS)

Marszalek, Wieslaw

2012-01-01

Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.
Controlling Unknown Saddle Type Steady States of Dynamical Systems with Latency in the Feedback Loop

DEFF Research Database (Denmark)

Tamasevicius, Arunas; Bumeliene, Skaidra; Tamaseviciute, Elena

2009-01-01

We suggest an adaptive control technique for stabilizing saddle type unstable steady states of dynamical systems. The controller is composed of an unstable and a stable high-pass filters operating in parallel. The mathematical model is considered analytically and numerically. The conjoint...... controller is sufficiently robust to time latencies in the feedback loop. In addition, it is not sensitive to the damping parameters of the system and is relatively fast. Experiments have been performed using a simplified version of the electronic Young-Silva circuit imitating behavior of the Duffing...
Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave Function

OpenAIRE

Carlip, Steven

1992-01-01

In most attempts to compute the Hartle-Hawking ``wave function of the universe'' in Euclidean quantum gravity, two important approximations are made: the path integral is evaluated in a saddle point approximation, and only the leading (least action) extremum is taken into account. In (2+1)-dimensional gravity with a negative cosmological constant, the second assumption is shown to lead to incorrect results: although the leading extremum gives the most important single contribution to the path...
Saddle-fin cell transistors with oxide etch rate control by using tilted ion implantation (TIS-fin) for sub-50-nm DRAMs

International Nuclear Information System (INIS)

Yoo, Min Soo; Choi, Kang Sik; Sun, Woo Kyung

2010-01-01

As DRAM cell pitch size decreases, the need for a high performance transistor is increasing. Though saddle-fin (S-fin) transistors have superior characteristics, S-fin transistors are well known to be more sensitive to process variation. To make uniform S-fin transistors, for the first time, we developed a new fin formation method using tilted ion implantation along the wordline direction after a recess gate etch. Due to the increased etch rate of the oxide film by ion implantation damage, fins are made at the bottom channel of the recess gate after wet etching. The resulting tilt implanted saddle-fin (TIS-fin) transistor has remarkably improved characteristics, such as ∼8% subthreshold swing (SS) and a 40% drain induced barrier lowering (DIBL) decrease. Especially, the TIS-fin with a neutral dopant has a reduced threshold voltage (Vth) variation within a wafer (<100 mV), which is comparable with that of a mass-produced sphere-shaped recessed channel array transistor (SRCAT).
Constrained Optimization via Stochastic approximation with a simultaneous perturbation gradient approximation

DEFF Research Database (Denmark)

Sadegh, Payman

1997-01-01

This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....
Iterative approximation of fixed points of nonexpansive mappings

International Nuclear Information System (INIS)

Chidume, C.E.; Chidume, C.O.

2007-07-01

Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gateaux differentiable norm and T : K → K be a nonexpansive mapping with F(T) := { x element of K : Tx = x} ≠ 0 . For a fixed δ element of (0, 1), define S : K → K by Sx := (1- δ)x+ δ Tx , for all x element of K. Assume that { z t } converges strongly to a fixed point z of T as t → 0, where z t is the unique element of K which satisfies z t = tu + (1 - t)Tz t for arbitrary u element of K. Let {α n } be a real sequence in (0, 1) which satisfies the following conditions: C1 : lim α n = 0; C2 : Σαn = ∞. For arbitrary x 0 element of K, let the sequence { x n } be defined iteratively by x n+1 = α n u + (1 - α n )Sx n . Then, {x n } converges strongly to a fixed point of T. (author)
Recursive B-spline approximation using the Kalman filter

Directory of Open Access Journals (Sweden)

Jens Jauch

2017-02-01

Full Text Available This paper proposes a novel recursive B-spline approximation (RBA algorithm which approximates an unbounded number of data points with a B-spline function and achieves lower computational effort compared with previous algorithms. Conventional recursive algorithms based on the Kalman filter (KF restrict the approximation to a bounded and predefined interval. Conversely RBA includes a novel shift operation that enables to shift estimated B-spline coefficients in the state vector of a KF. This allows to adapt the interval in which the B-spline function can approximate data points during run-time.
Simplest bifurcation diagrams for monotone families of vector fields on a torus

Science.gov (United States)

Baesens, C.; MacKay, R. S.

2018-06-01

In part 1, we prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in Baesens et al (1991 Physica D 49 387–475). To achieve this, we define ‘simplest’ by sequentially minimising the numbers of equilibria, Bogdanov–Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of horizontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed. In part 2, we analyse the bifurcation diagram for an explicit monotone family of vector fields on a torus and prove that it has at most two equilibria, precisely four Bogdanov–Takens points, no closed curves of centre nor closed curves of neutral saddle, at most two Reeb components, precisely four arcs of rotational homoclinic connection of ‘horizontal’ homotopy type, eight horizontal saddle-node loop points, two necklace points, four points of neutral horizontal homoclinic connection, and two half-plane fan points, and there is no simultaneous existence of centre and neutral saddle, nor contractible homoclinic connection to a neutral saddle. Furthermore, we prove that all saddle-nodes, Bogdanov–Takens points, non-neutral and neutral horizontal homoclinic bifurcations are non-degenerate and the Hopf condition is satisfied for all centres. We also find it has four points of degenerate Hopf bifurcation. It thus provides an example of a family satisfying all the assumptions of part 1 except the one of at most one contractible periodic orbit.
Anisotropy migration of self-point defects in dislocation stress fields in BCC Fe and FCC Cu

International Nuclear Information System (INIS)

Sivak, A.B.; Chernov, V.M.; Dubasova, N.A.; Romanov, V.A.

2007-01-01

Spatial dependence of the interaction energies of self-point defects (vacancies and self interstitial atoms in stable, metastable and saddle point configurations) with edge dislocations in slip systems {1 1 0} and {1 0 0} in BCC Fe and {1 1 1} in FCC Cu was calculated using the anisotropic theory of elasticity and molecular statics (hybrid method). The migration pathways of vacancies and SIA ( dumbbell in Fe and dumbbell in Cu) along which the migration of the defects with the lowest energy barriers were defined in the presence of the dislocation stress fields. These pathways are significantly different in the stress fields of dislocations
Spline approximation, Part 1: Basic methodology

Science.gov (United States)

Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

2018-04-01

In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

Environmental records from temperate glacier ice on Nevado Coropuna saddle, southern Peru

Directory of Open Access Journals (Sweden)

J. Herreros

2009-10-01

Full Text Available We investigated past climate variability and the zonal short and long-range transport of air masses in tropical South America using chemical, isotopic and palynological signals from a 42 m-long ice core recovered in 2003 from the saddle of the Nevado Coropuna, southern Peru (72°39´ W; 15°32´ S; 6080 m a.s.l.. We found that precipitation at this site depends mainly on the easterly circulation of air masses originated from the tropical Atlantic Ocean. Nevertheless, sporadic Pacific air masses arrivals, and strong cold waves coming from southern South America reach this altitude site. In spite of post-depositional effects, we were able to identify two strong ENSO (El Niño-Southern Oscillation event signatures (1982–1983 and 1992 and the eruptive activity of the nearby Sabancaya volcano (1994.
Strong approximations and sequential change-point analysis for diffusion processes

DEFF Research Database (Denmark)

Mihalache, Stefan-Radu

2012-01-01

In this paper ergodic diffusion processes depending on a parameter in the drift are considered under the assumption that the processes can be observed continuously. Strong approximations by Wiener processes for a stochastic integral and for the estimator process constructed by the one...
Correlation of zero-point energy with molecular structure and molecular forces. 3. Approximation for H/D isotope shifts and linear frequency sum rule

International Nuclear Information System (INIS)

Oi, T.; Ishida, T.

1984-01-01

The approximation methods for the zero-point energy (ZPE) previously developed using the Lanczo's tau method have been applied to the shifts in ZPE due to hydrogen isotope substitutions. Six types of approximation methods have been compared and analyzed on the basis of a weighing function Ω(lambda) varies as lambda/sup k/ and the actual eigenvalue shift spectra. The method generated by the most general optimzation treatment yields a predictable and generally satisfactory precision of the order of 1% or better. A linear frequency sum rule has been derived, which approximately holds for the sets of isotopic molecules which satisfy the second-order frequency sum rule. 19 references, 3 figures, 3 tables
Cyclic approximation to stasis

Directory of Open Access Journals (Sweden)

Stewart D. Johnson

2009-06-01

Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.
Domain decomposition method for nonconforming finite element approximations of anisotropic elliptic problems on nonmatching grids

Energy Technology Data Exchange (ETDEWEB)

Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)

1996-12-31

An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
Floating-point geometry: toward guaranteed geometric computations with approximate arithmetics

Science.gov (United States)

Bajard, Jean-Claude; Langlois, Philippe; Michelucci, Dominique; Morin, Géraldine; Revol, Nathalie

2008-08-01

Geometric computations can fail because of inconsistencies due to floating-point inaccuracy. For instance, the computed intersection point between two curves does not lie on the curves: it is unavoidable when the intersection point coordinates are non rational, and thus not representable using floating-point arithmetic. A popular heuristic approach tests equalities and nullities up to a tolerance ɛ. But transitivity of equality is lost: we can have A approx B and B approx C, but A not approx C (where A approx B means ||A - B|| < ɛ for A,B two floating-point values). Interval arithmetic is another, self-validated, alternative; the difficulty is to limit the swell of the width of intervals with computations. Unfortunately interval arithmetic cannot decide equality nor nullity, even in cases where it is decidable by other means. A new approach, developed in this paper, consists in modifying the geometric problems and algorithms, to account for the undecidability of the equality test and unavoidable inaccuracy. In particular, all curves come with a non-zero thickness, so two curves (generically) cut in a region with non-zero area, an inner and outer representation of which is computable. This last approach no more assumes that an equality or nullity test is available. The question which arises is: which geometric problems can still be solved with this last approach, and which cannot? This paper begins with the description of some cases where every known arithmetic fails in practice. Then, for each arithmetic, some properties of the problems they can solve are given. We end this work by proposing the bases of a new approach which aims to fulfill the geometric computations requirements.
THz-waves channeling in a monolithic saddle-coil for Dynamic Nuclear Polarization enhanced NMR

Science.gov (United States)

Macor, A.; de Rijk, E.; Annino, G.; Alberti, S.; Ansermet, J.-Ph.

2011-10-01

A saddle coil manufactured by electric discharge machining (EDM) from a solid piece of copper has recently been realized at EPFL for Dynamic Nuclear Polarization enhanced Nuclear Magnetic Resonance experiments (DNP-NMR) at 9.4 T. The corresponding electromagnetic behavior of radio-frequency (400 MHz) and THz (263 GHz) waves were studied by numerical simulation in various measurement configurations. Moreover, we present an experimental method by which the results of the THz-wave numerical modeling are validated. On the basis of the good agreement between numerical and experimental results, we conducted by numerical simulation a systematic analysis on the influence of the coil geometry and of the sample properties on the THz-wave field, which is crucial in view of the optimization of DNP-NMR in solids.
A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings

Directory of Open Access Journals (Sweden)

Wiyada Kumam

2016-05-01

Full Text Available In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for the solution of variational inequality problems and to find the zero points of maximal monotone operators. The theorems furnished in this work are new and well-established and generalize many well-known recent research works in this field.
Approximate Implicitization Using Linear Algebra

Directory of Open Access Journals (Sweden)

Oliver J. D. Barrowclough

2012-01-01

Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Nuclear data processing, analysis, transformation and storage with Pade-approximants

International Nuclear Information System (INIS)

Badikov, S.A.; Gay, E.V.; Guseynov, M.A.; Rabotnov, N.S.

1992-01-01

A method is described to generate rational approximants of high order with applications to neutron data handling. The problems considered are: The approximations of neutron cross-sections in resonance region producing the parameters for Adler-Adler type formulae; calculations of resulting rational approximants' errors given in analytical form allowing to compute the error at any energy point inside the interval of approximation; calculations of the correlation coefficient of error values in two arbitrary points provided that experimental errors are independent and normally distributed; a method of simultaneous generation of a few rational approximants with identical set of poles; functionals other than LSM; two-dimensional approximation. (orig.)
An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver

Energy Technology Data Exchange (ETDEWEB)

Peysson, Y. [Association Euratom-CEA, CEA Grenoble, 38 (France). Dept. de Recherches sur la Fusion Controlee; Choucri, M. [Centre Canadien de Fusion Magnetique, Varennes, PQ (Canada)

1997-09-01

A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2{sub D}) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author) 21 refs.
An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver

International Nuclear Information System (INIS)

Peysson, Y.

1997-09-01

A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2 D ) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author)
Peri-anal surgery under saddle block anaesthesia comparing three different doses of hyperbaric 0.75% bupivacaine

International Nuclear Information System (INIS)

Ali, L.; Alam, W.; Abbas, M.A.; Ali, U.

2017-01-01

To compare three doses of hyperbaric 0.75% bupivacaine and measuring time for home readiness after day care perianal surgery under saddle block anaesthesia. Study Design: Non randomized controlled trial. Place and Duration of Study: The study was conducted at the department of Anaesthesia, CMH Rawalpindi from Jun 2014 to Apr 2015. Material and Methods: In this study 90 patients who presented for perianal day care surgery, were divided in three equal groups. Group A received 7.5 mg, group B 6.0 mg and group C 4.5 mg of hyperbaric 0.75% bupivacaine. Intrathecal injection was given in L4-5 space by 25 G spinal needle in sitting position. Lithotomy position was made after five minutes. After surgery patients were monitored in recovery room. After fulfilling ambulatory and discharge criteria patients were allowed to go home with attendants. Time of intrathecal injection, assessment of above criteria and time of discharge were noted and analyzed. Results: Male patients were 85.6% and females were 14.4%. Mean time of surgery was 48 +- 10.59 min. Mean time of discharge in minutes for group A was 235.86 +- 49.38, for group B 217.7 +- 42.49 and for group C 205.76 +- 32. Time of discharge was significantly different between group A and group C (p=0.02). While it was not significantly different between group A and group B (p=0.29) and between group B and group C (p=0.819). Conclusion: Lower dose of hyperbaric bupivacaine can reduce the time for home readiness compared to higher dose. Time of discharge is mainly dependent on time to micturate after saddle block anaesthesia. (author)
Computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods

OpenAIRE

Laadhari , Aymen; Saramito , Pierre; Misbah , Chaouqi

2014-01-01

International audience; The numerical simulation of the deformation of vesicle membranes under simple shear external fluid flow is considered in this paper. A new saddle-point approach is proposed for the imposition of the fluid incompressibility and the membrane inextensibility constraints, through Lagrange multipliers defined in the fluid and on the membrane respectively. Using a level set formulation, the problem is approximated by mixed finite elements combined with an automatic adaptive ...
Approximate convex hull of affine iterated function system attractors

International Nuclear Information System (INIS)

Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry

2012-01-01

Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.
Semiclassical initial value approximation for Green's function.

Science.gov (United States)

Kay, Kenneth G

2010-06-28

A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.
Fifty per cent reduction in solution gas flaring : a report to the Saddle Hills Awareness Committee

International Nuclear Information System (INIS)

1999-01-01

Information by the Alberta Energy Company to the Saddle Hills Awareness Committee (SHAC) regarding company operations in the West Peace River Arch of the western Canadian Sedimentary Basin in northwest Alberta is presented, the purpose being to bring the Committee up-to-date, and respond to concerns about the health effects of sour gas emissions. The SHAC represents citizens who are concerned about issues relating to sour gas emissions. AEC West, a business unit of Alberta Energy Company, operates two sour gas processing plants, one sweet gas plant and three sour oil batteries in the Grande Prairie area. AEC's gas plants are connected by pipelines and process petroleum and natural gas products from approximately 200 oil and gas wells. The H 2 S content of the natural gas being processed by AEC's various plants ranges from trace amounts to 11 per cent. Activities at AEC's Hythe plant and at the Sexsmith plant, and the company's gas storage project are briefly reviewed. An analysis is included of the role that flaring plays in the petroleum and natural gas industry, emphasizing AEC West's efforts during 1997 to reduce solution gas flaring volumes from single well oil batteries by 50 per cent. Other AEC West environmental protection initiatives include the preliminary regional airshed study sponsored by the company which resulted in part from SHAC feedback and in part from the innovative approach of AEC employees. AEC West established the industry's first Ombudsman to provide a problem resolution focus on landowner complaints and introduced a policy of making available solution gas that would eventually be flared to industrial colleagues, free of charge
Analytical approximation of neutron physics data

International Nuclear Information System (INIS)

Badikov, S.A.; Vinogradov, V.A.; Gaj, E.V.; Rabotnov, N.S.

1984-01-01

The method for experimental neutron-physical data analytical approximation by rational functions based on the Pade approximation is suggested. It is shown that the existence of the Pade approximation specific properties in polar zones is an extremely favourable analytical property essentially extending the convergence range and increasing its rate as compared with polynomial approximation. The Pade approximation is the particularly natural instrument for resonance curve processing as the resonances conform to the complex poles of the approximant. But even in a general case analytical representation of the data in this form is convenient and compact. Thus representation of the data on the neutron threshold reaction cross sections (BOSPOR constant library) in the form of rational functions lead to approximately twenty fold reduction of the storaged numerical information as compared with the by-point calculation at the same accWracy
Preconditioning for Allen–Cahn variational inequalities with non-local constraints

KAUST Repository

Blank, Luise; Sarbu, Lavinia; Stoll, Martin

2012-01-01

-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate
On Convex Quadratic Approximation

NARCIS (Netherlands)

den Hertog, D.; de Klerk, E.; Roos, J.

2000-01-01

In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

Cosmological applications of Padé approximant

International Nuclear Information System (INIS)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation
Cosmological applications of Padé approximant

Science.gov (United States)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.
Local density approximations for relativistic exchange energies

International Nuclear Information System (INIS)

MacDonald, A.H.

1986-01-01

The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented
Subquadratic medial-axis approximation in $\\mathbb{R}^3$

Directory of Open Access Journals (Sweden)

Christian Scheffer

2015-09-01

Full Text Available We present an algorithm that approximates the medial axis of a smooth manifold in $\\mathbb{R}^3$ which is given by a sufficiently dense point sample. The resulting, non-discrete approximation is shown to converge to the medial axis as the sampling density approaches infinity. While all previous algorithms guaranteeing convergence have a running time quadratic in the size $n$ of the point sample, we achieve a running time of at most $\\mathcal{O}(n\\log^3 n$. While there is no subquadratic upper bound on the output complexity of previous algorithms for non-discrete medial axis approximation, the output of our algorithm is guaranteed to be of linear size.
Merging Belief Propagation and the Mean Field Approximation

DEFF Research Database (Denmark)

Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

2010-01-01

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence......) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....
Will an "island" population of voles be recolonized if eradicated? Insights from molecular genetic analyses

Science.gov (United States)

Miller, Mark P.; Haig, Susan M.; Ledig, David B.; Vander Heyden, Madeleine F.; Bennett, Gregory

2011-01-01

We performed genetic analyses of Microtus longicaudus populations within the Crook Point Unit of the Oregon Islands National Wildlife Refuge. A M. longicaudus population at Saddle Rock (located approx. 65 m off-shore from the Crook Point mainland) is suspected to be partially responsible for declines of a Leach's storm-petrel colony at this important nesting site. Using Amplified Fragment Length Polymorphism markers and mitochondrial DNA, we illustrate that Saddle Rock and Crook Point function as separate island and mainland populations despite their close proximity. In addition to genetic structure, we also observed reduced genetic diversity at Saddle Rock, suggesting that little individual movement occurs between populations. If local resource managers decide to perform an eradication at Saddle Rock, we conclude that immediate recolonization of the island by M. longicaudus would be unlikely. Because M. longicaudus is native to Oregon, we also consider the degree with which the differentiation of Saddle Rock signifies the presence of a unique entity that warrants conservation rather than eradication. ?? The Wildlife Society, 2011.
Communication: A new ab initio potential energy surface for HCl-H2O, diffusion Monte Carlo calculations of D0 and a delocalized zero-point wavefunction.

Science.gov (United States)

Mancini, John S; Bowman, Joel M

2013-03-28

We report a global, full-dimensional, ab initio potential energy surface describing the HCl-H2O dimer. The potential is constructed from a permutationally invariant fit, using Morse-like variables, to over 44,000 CCSD(T)-F12b∕aug-cc-pVTZ energies. The surface describes the complex and dissociated monomers with a total RMS fitting error of 24 cm(-1). The normal modes of the minima, low-energy saddle point and separated monomers, the double minimum isomerization pathway and electronic dissociation energy are accurately described by the surface. Rigorous quantum mechanical diffusion Monte Carlo (DMC) calculations are performed to determine the zero-point energy and wavefunction of the complex and the separated fragments. The calculated zero-point energies together with a De value calculated from CCSD(T) with a complete basis set extrapolation gives a D0 value of 1348 ± 3 cm(-1), in good agreement with the recent experimentally reported value of 1334 ± 10 cm(-1) [B. E. Casterline, A. K. Mollner, L. C. Ch'ng, and H. Reisler, J. Phys. Chem. A 114, 9774 (2010)]. Examination of the DMC wavefunction allows for confident characterization of the zero-point geometry to be dominant at the C(2v) double-well saddle point and not the C(s) global minimum. Additional support for the delocalized zero-point geometry is given by numerical solutions to the 1D Schrödinger equation along the imaginary-frequency out-of-plane bending mode, where the zero-point energy is calculated to be 52 cm(-1) above the isomerization barrier. The D0 of the fully deuterated isotopologue is calculated to be 1476 ± 3 cm(-1), which we hope will stand as a benchmark for future experimental work.
Existence of traveling waves for diffusive-dispersive conservation laws

Directory of Open Access Journals (Sweden)

Cezar I. Kondo

2013-02-01

Full Text Available In this work we show the existence existence and uniqueness of traveling waves for diffusive-dispersive conservation laws with flux function in $C^{1}(mathbb{R}$, by using phase plane analysis. Also we estimate the domain of attraction of the equilibrium point attractor corresponding to the right-hand state. The equilibrium point corresponding to the left-hand state is a saddle point. According to the phase portrait close to the saddle point, there are exactly two semi-orbits of the system. We establish that only one semi-orbit come in the domain of attraction and converges to $(u_{-},0$ as $yo -infty$. This provides the desired saddle-attractor connection.
An Approximate Approach to Automatic Kernel Selection.

Science.gov (United States)

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
Unambiguous results from variational matrix Pade approximants

International Nuclear Information System (INIS)

Pindor, Maciej.

1979-10-01

Variational Matrix Pade Approximants are studied as a nonlinear variational problem. It is shown that although a stationary value of the Schwinger functional is a stationary value of VMPA, the latter has also another stationary value. It is therefore proposed that instead of looking for a stationary point of VMPA, one minimizes some non-negative functional and then one calculates VMPA at the point where the former has the absolute minimum. This approach, which we call the Method of the Variational Gradient (MVG) gives unambiguous results and is also shown to minimize a distance between the approximate and the exact stationary values of the Schwinger functional
A Gaussian Approximation Potential for Silicon

Science.gov (United States)

Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor

We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.
Slow light effect with high group index and wideband by saddle-like mode in PC-CROW

Science.gov (United States)

Wan, Yong; Jiang, Li-Jun; Xu, Sheng; Li, Meng-Xue; Liu, Meng-Nan; Jiang, Cheng-Yi; Yuan, Feng

2018-04-01

Slow light with high group index and wideband is achieved in photonic crystal coupled-resonator optical waveguides (PC-CROWs). According to the eye-shaped scatterers and various microcavities, saddle-like curves between the normalized frequency f and wave number k can be obtained by adjusting the parameters of the scatterers, parameters of the coupling microcavities, and positions of the scatterers. Slow light with decent flat band and group index can then be achieved by optimizing the parameters. Simulations prove that the maximal value of the group index is > 104, and the normalized delay bandwidth product within a new varying range of n g > 102 or n g > 103 can be a new and effective criterion of evaluation for the slow light in PC-CROWs.
Statistical study of static gasket conductance; Etude statistique de la conductance d'un joint d'etancheite statique

Energy Technology Data Exchange (ETDEWEB)

Flukiger, F

2005-10-15

This work is motivated by tightness technological problems associated with metallic gasket. The objective is a better understanding of leakage mechanisms, through the development of new computational tools. In this study, the aperture field between two rough surfaces in contact is described by a short correlated isotropic random Gaussian process. The system is studied as a set of independent elementary surfaces. Joint conductances are evaluated from a statistical study on those elementary surfaces. A computational code is developed using a network approach based on lubrication theory estimation of local conductances. The global conductance computation becomes analogous to an electrical problem for which the resistances are distributed on a random network. The network is built from the identification of the aperture field critical points. Maxima are linked through saddle points. Bond conductances are estimated at the aperture field saddle points. First, a purely plastic model of deformations is considered. Near percolation threshold the conductances display a power behaviour. Far from percolation threshold, numerical results are favourably compared with an effective medium approximation. Secondly, we study the impact of elastic deformations. A computational code based on Boussinesq approximation is coupled to the network approach. The results indicate a significant impact of elastic deformations on conductances. Finally, the network approach is adapted to simulate quasi-static drainage thanks to a classical invasion percolation algorithm. A good comparison between previous experiments and numerical predictions is obtained. (author)
Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

DEFF Research Database (Denmark)

Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

2013-01-01

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination...... correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard...
Data approximation using a blending type spline construction

International Nuclear Information System (INIS)

Dalmo, Rune; Bratlie, Jostein

2014-01-01

Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by C k -smooth basis functions. One way of approximating discrete regular data using GERBS is by partitioning the data set into subsets and fit a local function to each subset. Partitioning and fitting strategies can be devised such that important or interesting data points are interpolated in order to preserve certain features. We present a method for fitting discrete data using a tensor product GERBS construction. The method is based on detection of feature points using differential geometry. Derivatives, which are necessary for feature point detection and used to construct local surface patches, are approximated from the discrete data using finite differences
Large N and Bethe ansatz

OpenAIRE

Jurco, B.

2003-01-01

We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brezin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal polynomials and saddle point approximation. Lagre $N$ limit of the matrix model corresponds to the thermodynamic limit of the integrable system. In this limit (functional) Bethe ansatz is the same as the generating function for correlators of the matrix models.
Bogoliubov transformations and fermion condensates in lattice field theories

International Nuclear Information System (INIS)

Caracciolo, Sergio; Palumbo, Fabrizio; Viola, Giovanni

2009-01-01

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian
Stress concentration factors at saddle and crown positions on the central brace of two-planar welded CHS DKT-connections

Science.gov (United States)

Ahmadi, Hamid; Lotfollahi-Yaghin, Mohammad Ali; Aminfar, Mohammad H.

2012-03-01

A set of parametric stress analyses was carried out for two-planar tubular DKT-joints under different axial loading conditions. The analysis results were used to present general remarks on the effects of the geometrical parameters on stress concentration factors (SCFs) at the inner saddle, outer saddle, and crown positions on the central brace. Based on results of finite element (FE) analysis and through nonlinear regression analysis, a new set of SCF parametric equations was established for fatigue design purposes. An assessment study of equations was conducted against the experimental data and original SCF database. The satisfaction of acceptance criteria proposed by the UK Department of Energy (UK DoE) was also checked. Results of parametric study showed that highly remarkable differences exist between the SCF values in a multi-planar DKT-joint and the corresponding SCFs in an equivalent uni-planar KT-joint having the same geometrical properties. It can be clearly concluded from this observation that using the equations proposed for uni-planar KT-connections to compute the SCFs in multi-planar DKT-joints will lead to either considerably under-predicting or over-predicting results. Hence, it is necessary to develop SCF formulae specially designed for multi-planar DKT-joints. Good results of equation assessment according to UK DoE acceptance criteria, high values of correlation coefficients, and the satisfactory agreement between the predictions of the proposed equations and the experimental data guarantee the accuracy of the equations. Therefore, the developed equations can be reliably used for fatigue design of offshore structures.
Prestack wavefield approximations

KAUST Repository

Alkhalifah, Tariq

2013-01-01

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, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
Prestack wavefield approximations

KAUST Repository

Alkhalifah, Tariq

2013-09-01

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, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

Tranverse beam break up in a periodic linac

International Nuclear Information System (INIS)

Decker, G.; Wang, J.M.

1987-01-01

The problem of cumulative beam break up in a periodic linac for a general impedance is discussed, with the effects of acceleration included. The transverse equations of motion for a set of identical point like bunches moving along the length of the linac are cast into a simple form using a smooth approximation. This results in a working formula that is used to analyze beam breakup. Explicit expressions for the transverse motion in the case of a single resonance impedance are found using saddle point integration. This is done first with no external focusing, and again in the strong focusing limit
Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of Kohn-Sham density functionals.

Science.gov (United States)

Li, Chen; Lu, Jianfeng; Yang, Weitao

2015-12-14

We develop the gentlest ascent dynamics for Kohn-Sham density functional theory to search for the index-1 saddle points on the energy landscape of the Kohn-Sham density functionals. These stationary solutions correspond to excited states in the ground state functionals. As shown by various examples, the first excited states of many chemical systems are given by these index-1 saddle points. Our novel approach provides an alternative, more robust way to obtain these excited states, compared with the widely used ΔSCF approach. The method can be easily generalized to target higher index saddle points. Our results also reveal the physical interest and relevance of studying the Kohn-Sham energy landscape.
A Genealogy of Convex Solids Via Local and Global Bifurcations of Gradient Vector Fields

Science.gov (United States)

Domokos, Gábor; Holmes, Philip; Lángi, Zsolt

2016-12-01

Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies, these are non-degenerate maxima, minima, and saddle points, the numbers of which provide a primary classification. Secondary and tertiary classifications use graphs to describe orbits connecting these critical points in the gradient vector field associated with each body. In previous work, it was shown that these classifications are complete in that no class is empty. Here, we construct 1- and 2-parameter families of convex bodies connecting members of adjacent primary and secondary classes and show that transitions between them can be realized by codimension 1 saddle-node and saddle-saddle (heteroclinic) bifurcations in the gradient vector fields. Our results indicate that all combinatorially possible transitions can be realized in physical shape evolution processes, e.g., by abrasion of sedimentary particles.
Approximate Noether symmetries and collineations for regular perturbative Lagrangians

Science.gov (United States)

Paliathanasis, Andronikos; Jamal, Sameerah

2018-01-01

Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.
Fission barrier heights in the A ∼ 200 mass region

Indian Academy of Sciences (India)

The know- ledge about the shell corrections at the saddle point in A ∼ 200 mass region is ambiguous. ... value of the level density parameter at the saddle-point deformation (˜af ) may be different from that of ˜an due to the ... Hence, fusion cross-sections for α-induced reactions were estimated using the Bass systematics.
A free boundary approach to the Rosensweig instability of ferrofluids

Science.gov (United States)

Parini, Enea; Stylianou, Athanasios

2018-04-01

We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid undergoing normal field instability. The starting point is the ferrohydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. These constitute the strong form for the Euler-Lagrange equations of a convex-concave functional, which we extend to include interfaces that are not necessarily graphs of functions. Saddle points are then found by iterating the direct method of the calculus of variations and applying classical results of convex analysis. For the existence part, we assume a general nonlinear magnetization law; for a linear law, we also show, via convex duality, that the saddle point is a constrained minimizer of the relevant energy functional.
evaluation of approximate design procedures for biaxially loaded

African Journals Online (AJOL)

The approximation according to the ACI is based on the work by Parme [9] who chose to approximate a as a logarithmic function 9f a parameter /3 representing an actual point on· the non-dimensional load contour, where the two moment components, . related to the respective uniaxial capacities are equal,. i.e. f3=;: my lmuy ...
Approximate furthest neighbor with application to annulus query

DEFF Research Database (Denmark)

Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen

2016-01-01

-dimensional Euclidean space. The method builds on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk׳s approximation factor and reducing the running time by a logarithmic factor. We also present......, the query-dependent approach is used for deriving a data structure for the approximate annulus query problem, which is defined as follows: given an input set S and two parameters r>0 and w≥1, construct a data structure that returns for each query point q a point p∈S such that the distance between p and q...
Lift of dilogarithm to partition identities

International Nuclear Information System (INIS)

Terhoeven, M.

1992-11-01

For the whole set of dilogarithm identities found recently using the thermodynamic Bethe-Ansatz for the ADET series of purely elastic scattering theories we give partition identities which involve characters of those conformal field theories which correspond to the UV-limits of the scattering theories. These partition identities in turn allow to derive the dilogarithm identities using modular invariance and a saddle point approximation. We conjecture on possible generalizations of this correspondance, namely, a lift from dilogarithm to partition identities. (orig.)
Approximation of fixed points of strongly pseudo-contractive mappings

International Nuclear Information System (INIS)

Chidume, C.E.

1991-10-01

Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Let T:K→K be a continuous strongly pseudocontractive mapping of K into itself. Let {c n } n=1 ∞ be a real sequence satisfying: (i) 0 n n=1 ∞ c n =∞; and (iii) Σ n=1 ∞ c n b(c n ) n } n=1 ∞ generated by x 1 is an element of K. x n+1 =(1-c n )x n +c n Tx n , n≥1, converges strongly to the unique fixed point of T. A related result deals with the Ishikawa iteration scheme when T is Lipschitzian and strongly pseudocontractive. (author). 28 refs
An Approximate Redistributed Proximal Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions

Directory of Open Access Journals (Sweden)

Jie Shen

2015-01-01

Full Text Available We describe an extension of the redistributed technique form classical proximal bundle method to the inexact situation for minimizing nonsmooth nonconvex functions. The cutting-planes model we construct is not the approximation to the whole nonconvex function, but to the local convexification of the approximate objective function, and this kind of local convexification is modified dynamically in order to always yield nonnegative linearization errors. Since we only employ the approximate function values and approximate subgradients, theoretical convergence analysis shows that an approximate stationary point or some double approximate stationary point can be obtained under some mild conditions.
Fission dynamics of the compound nucleus Fr formed in heavy-ion ...

Indian Academy of Sciences (India)

The phenomenological friction turned out to be smaller than the standard wall formula value for nuclear friction up to the saddle point, and it would sharply increase between saddle and scission points. Further ..... A556, 281 (1993). [5] J R Nix and A J Sierk, Report No. JINR-D7-87-68, 1987 (unpublished). [6] J R Nix and A J ...
Parameter Estimation for Partial Differential Equations by Collage-Based Numerical Approximation

Directory of Open Access Journals (Sweden)

Xiaoyan Deng

2009-01-01

into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov-Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.
Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions

Directory of Open Access Journals (Sweden)

Jin Liang

2008-06-01

Full Text Available This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems.
Approximate method in estimation sensitivity responses to variations in delayed neutron energy spectra

Energy Technology Data Exchange (ETDEWEB)

Yoo, J; Shin, H S; Song, T Y; Park, W S [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1998-12-31

Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)
Approximate method in estimation sensitivity responses to variations in delayed neutron energy spectra

Energy Technology Data Exchange (ETDEWEB)

Yoo, J.; Shin, H. S.; Song, T. Y.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1997-12-31

Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)
Flood-inundation maps for the Saddle River in Ho-Ho-Kus Borough, the Village of Ridgewood, and Paramus Borough, New Jersey, 2013

Science.gov (United States)

Watson, Kara M.; Niemoczynski, Michal J.

2014-01-01

Digital flood-inundation maps for a 5.4-mile reach of the Saddle River in New Jersey from Hollywood Avenue in Ho-Ho-Kus Borough downstream through the Village of Ridgewood and Paramus Borough to the confluence with Hohokus Brook in the Village of Ridgewood were created by the U.S. Geological Survey (USGS) in cooperation with the New Jersey Department of Environmental Protection (NJDEP). The inundation maps, which can be accessed through the USGS Flood Inundation Mapping Science Web site at http://water.usgs.gov/osw/flood_inundation/, depict estimates of the areal extent and depth of flooding corresponding to selected water levels (stages) at the USGS streamgage on the Saddle River at Ridgewood, New Jersey (station 01390500). Current conditions for estimating near real-time areas of inundation using USGS streamgage information may be obtained on the Internet at http://waterdata.usgs.gov/nwis/uv?site_no=01390500 or at the National Weather Services (NWS) Advanced Hydrologic Prediction Service (AHPS) at http://water.weather.gov/ahps2/hydrograph.php?wfo=okx&gage=rwdn4. In this study, flood profiles were computed for the stream reach by means of a one-dimensional step-backwater model. The model was calibrated by using the most current stage-discharge relation (March 11, 2011) at the USGS streamgage 01390500, Saddle River at Ridgewood, New Jersey. The hydraulic model was then used to compute 10 water-surface profiles for flood stages at 1-foot (ft) intervals referenced to the streamgage datum, North American Vertical Datum of 1988 (NAVD 88), and ranging from 5 ft, the NWS “action and minor flood stage”, to 14 ft, which is the maximum extent of the stage-discharge rating and 0.6 ft higher than the highest recorded water level at the streamgage. The simulated water-surface profiles were then combined with a geographic information system 3-meter (9.84-ft) digital elevation model derived from Light Detection and Ranging (lidar) data in order to delineate the area flooded
Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points

Science.gov (United States)

Jia, Bing; Gu, Huaguang

2017-06-01

Different stochastic neural firing patterns or rhythms that appeared near polarization or depolarization resting states were observed in biological experiments on three nervous systems, and closely matched those simulated near bifurcation points between stable equilibrium point and limit cycle in a theoretical model with noise. The distinct dynamics of spike trains and interspike interval histogram (ISIH) of these stochastic rhythms were identified and found to build a relationship to the coexisting behaviors or fixed firing frequency of four different types of bifurcations. Furthermore, noise evokes coherence resonances near bifurcation points and plays important roles in enhancing information. The stochastic rhythms corresponding to Hopf bifurcation points with fixed firing frequency exhibited stronger coherence degree and a sharper peak in the power spectrum of the spike trains than those corresponding to saddle-node bifurcation points without fixed firing frequency. Moreover, the stochastic firing patterns changed to a depolarization resting state as the extracellular potassium concentration increased for the injured nerve fiber related to pathological pain or static blood pressure level increased for aortic depressor nerve fiber, and firing frequency decreased, which were different from the physiological viewpoint that firing frequency increased with increasing pressure level or potassium concentration. This shows that rhythms or firing patterns can reflect pressure or ion concentration information related to pathological pain information. Our results present the dynamics of stochastic firing patterns near bifurcation points, which are helpful for the identification of both dynamics and physiological roles of complex neural firing patterns or rhythms, and the roles of noise.
A note on the nucleation with multiple steps: Parallel and series nucleation

OpenAIRE

Iwamatsu, Masao

2012-01-01

Parallel and series nucleation are the basic elements of the complex nucleation process when two saddle points exist on the free-energy landscape. It is pointed out that the nucleation rates follow formulas similar to those of parallel and series connection of resistors or conductors in an electric circuit. Necessary formulas to calculate individual nucleation rates at the saddle points and the total nucleation rate are summarized and the extension to the more complex nucleation process is su...
Diophantine approximation and Dirichlet series

CERN Document Server

Queffélec, Hervé

2013-01-01

This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

Energy Technology Data Exchange (ETDEWEB)

2017-10-24

ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.
Variational estimates of point-kinetics parameters

International Nuclear Information System (INIS)

Favorite, J.A.; Stacey, W.M. Jr.

1995-01-01

Variational estimates of the effect of flux shifts on the integral reactivity parameter of the point-kinetics equations and on regional power fractions were calculated for a variety of localized perturbations in two light water reactor (LWR) model problems representing a small, tightly coupled core and a large, loosely coupled core. For the small core, the flux shifts resulting from even relatively large localized reactivity changes (∼600 pcm) were small, and the standard point-kinetics approximation estimates of reactivity were in error by only ∼10% or less, while the variational estimates were accurate to within ∼1%. For the larger core, significant (>50%) flux shifts occurred in response to local perturbations, leading to errors of the same magnitude in the standard point-kinetics approximation of the reactivity worth. For positive reactivity, the error in the variational estimate of reactivity was only a few percent in the larger core, and the resulting transient power prediction was 1 to 2 orders of magnitude more accurate than with the standard point-kinetics approximation. For a large, local negative reactivity insertion resulting in a large flux shift, the accuracy of the variational estimate broke down. The variational estimate of the effect of flux shifts on reactivity in point-kinetics calculations of transients in LWR cores was found to generally result in greatly improved accuracy, relative to the standard point-kinetics approximation, the exception being for large negative reactivity insertions with large flux shifts in large, loosely coupled cores
A comparative study on full diagonalization of Hessian matrix and Gradient-only technique to trace out reaction path in doped noble gas clusters using stochastic optimization

International Nuclear Information System (INIS)

Biring, Shyamal Kumar; Chaudhury, Pinaki

2012-01-01

Highlights: ► Estimation of critical points in Noble-gas clusters. ► Evaluation of first order saddle point or transition states. ► Construction of reaction path for structural change in clusters. ► Use of Monte-Carlo Simulated Annealing to study structural changes. - Abstract: This paper proposes Simulated Annealing based search to locate critical points in mixed noble gas clusters where Ne and Xe are individually doped in Ar-clusters. Using Lennard–Jones (LJ) atomic interaction we try to explore the search process of transformation through Minimum Energy Path (MEP) from one minimum energy geometry to another via first order saddle point on the potential energy surface of the clusters. Here we compare the results based on diagonalization of the full Hessian all through the search and quasi-gradient only technique to search saddle points and construction of reaction path (RP) for three sizes of doped Ar-clusters, (Ar) 19 Ne/Xe,(Ar) 24 Ne/Xe and (Ar) 29 Ne/Xe.
Feature curve extraction from point clouds via developable strip intersection

Directory of Open Access Journals (Sweden)

Kai Wah Lee

2016-04-01

Full Text Available In this paper, we study the problem of computing smooth feature curves from CAD type point clouds models. The proposed method reconstructs feature curves from the intersections of developable strip pairs which approximate the regions along both sides of the features. The generation of developable surfaces is based on a linear approximation of the given point cloud through a variational shape approximation approach. A line segment sequencing algorithm is proposed for collecting feature line segments into different feature sequences as well as sequential groups of data points. A developable surface approximation procedure is employed to refine incident approximation planes of data points into developable strips. Some experimental results are included to demonstrate the performance of the proposed method.
Diophantine approximation and badly approximable sets

DEFF Research Database (Denmark)

Kristensen, S.; Thorn, R.; Velani, S.

2006-01-01

. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Point charges optimally placed to represent the multipole expansion of charge distributions.

Directory of Open Access Journals (Sweden)

Ramu Anandakrishnan

Full Text Available We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance 2x the extent of the charge distribution--the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom, is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å is half that of the point multipole expansion up to the octupole
Supersymmetric localization for BPS black hole entropy: 1-loop partition function from vector multiplets

International Nuclear Information System (INIS)

Gupta, Rajesh Kumar; Ito, Yuto; Jeon, Imtak

2015-01-01

We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2× S"2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one-loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one-loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one-loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.
Modeling and Experiments on Ballistic Impact into UHMWPE Yarns Using Flat and Saddle-Nosed Projectiles

Directory of Open Access Journals (Sweden)

Stuart Leigh Phoenix

2017-03-01

Full Text Available Yarn shooting experiments were conducted to determine the ballistically-relevant, Young’s modulus and tensile strength of ultra-high molecular weight polyethylene (UHMWPE fiber. Target specimens were Dyneema® SK76 yarns (1760 dtex, twisted to 40 turns/m, and initially tensioned to stresses ranging from 29 to 2200 MPa. Yarns were impacted, transversely, by two types of cylindrical steel projectiles at velocities ranging from 150 to 555 m/s: (i a reverse-fired, fragment simulating projectile (FSP where the flat rear face impacted the yarn rather than the beveled nose; and (ii a ‘saddle-nosed projectile’ having a specially contoured nose imparting circular curvature in the region of impact, but opposite curvature transversely to prevent yarn slippage off the nose. Experimental data consisted of sequential photographic images of the progress of the triangular transverse wave, as well as tensile wave speed measured using spaced, piezo-electric sensors. Yarn Young’s modulus, calculated from the tensile wave-speed, varied from 133 GPa at minimal initial tension to 208 GPa at the highest initial tensions. However, varying projectile impact velocity, and thus, the strain jump on impact, had negligible effect on the modulus. Contrary to predictions from the classical Cole-Smith model for 1D yarn impact, the critical velocity for yarn failure differed significantly for the two projectile types, being 18% lower for the flat-faced, reversed FSP projectile compared to the saddle-nosed projectile, which converts to an apparent 25% difference in yarn strength. To explain this difference, a wave-propagation model was developed that incorporates tension wave collision under blunt impact by a flat-faced projectile, in contrast to outward wave propagation in the classical model. Agreement between experiment and model predictions was outstanding across a wide range of initial yarn tensions. However, plots of calculated failure stress versus yarn pre
Approximating fixed points for nonself mappings in CAT(0) spaces

OpenAIRE

Razani Abdolrahman; Shabani Saeed

2011-01-01

Abstract Suppose K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T : K → X be a nonself mapping, satisfying Condition (E) with F(T): = {x ∈ K : Tx = x} ≠ ∅. Suppose {xn} is generated iteratively by x1 ∈ K, xn+1 = P ((1 - αn)xn ⊕ αnTP [(1 - βn)xn ⊕ βnTxn]),n ≥ 1, where {αn} and {βn} are real sequences in [ε, 1 - ε] for some ε W...
On some applications of diophantine approximations.

Science.gov (United States)

Chudnovsky, G V

1984-03-01

Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions at rational points have measures of diophantine approximations typical to "almost all" numbers. In particular, any such number has the "2 + epsilon" exponent of irrationality: Theta - p/q > q(-2-epsilon) for relatively prime rational integers p,q, with q >/= q(0) (Theta, epsilon). These results answer some problems posed by Lang. The methods used here are based on the introduction of graded Padé approximations to systems of functions satisfying linear differential equations with rational function coefficients. The constructions and proofs of this paper were used in the functional (nonarithmetic case) in a previous paper [Chudnovsky, D. V. & Chudnovsky, G. V. (1983) Proc. Natl. Acad. Sci. USA 80, 5158-5162].
How does the cosmic web impact assembly bias?

Science.gov (United States)

Musso, M.; Cadiou, C.; Pichon, C.; Codis, S.; Kraljic, K.; Dubois, Y.

2018-06-01

The mass, accretion rate, and formation time of dark matter haloes near protofilaments (identified as saddle points of the potential) are analytically predicted using a conditional version of the excursion set approach in its so-called upcrossing approximation. The model predicts that at fixed mass, mass accretion rate and formation time vary with orientation and distance from the saddle, demonstrating that assembly bias is indeed influenced by the tides imposed by the cosmic web. Starved, early-forming haloes of smaller mass lie preferentially along the main axis of filaments, while more massive and younger haloes are found closer to the nodes. Distinct gradients for distinct tracers such as typical mass and accretion rate occur because the saddle condition is anisotropic, and because the statistics of these observables depend on both the conditional means and their covariances. The theory is extended to other critical points of the potential field. The response of the mass function to variations of the matter density field (the so-called large-scale bias) is computed, and its trend with accretion rate is shown to invert along the filament. The signature of this model should correspond at low redshift to an excess of reddened galactic hosts at fixed mass along preferred directions, as recently reported in spectroscopic and photometric surveys and in hydrodynamical simulations. The anisotropy of the cosmic web emerges therefore as a significant ingredient to describe jointly the dynamics and physics of galaxies, e.g. in the context of intrinsic alignments or morphological diversity.
Classical geometry from the quantum Liouville theory

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Hadasz, Leszek; Jaskólski, Zbigniew; Piaţek, Marcin

2005-09-01

Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Classical geometry from the quantum Liouville theory

International Nuclear Information System (INIS)

Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin

2005-01-01

Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere
Intrinsic Diophantine approximation on general polynomial surfaces

DEFF Research Database (Denmark)

Tiljeset, Morten Hein

2017-01-01

We study the Hausdorff measure and dimension of the set of intrinsically simultaneously -approximable points on a curve, surface, etc, given as a graph of integer polynomials. We obtain complete answers to these questions for algebraically “nice” manifolds. This generalizes earlier work done...
An Approximate Method for Solving Optimal Control Problems for Discrete Systems Based on Local Approximation of an Attainability Set

Directory of Open Access Journals (Sweden)

V. A. Baturin

2017-03-01

Full Text Available An optimal control problem for discrete systems is considered. A method of successive improvements along with its modernization based on the expansion of the main structures of the core algorithm about the parameter is suggested. The idea of the method is based on local approximation of attainability set, which is described by the zeros of the Bellman function in the special problem of optimal control. The essence of the problem is as follows: from the end point of the phase is required to find a path that minimizes functional deviations of the norm from the initial state. If the initial point belongs to the attainability set of the original controlled system, the value of the Bellman function equal to zero, otherwise the value of the Bellman function is greater than zero. For this special task Bellman equation is considered. The support approximation and Bellman equation are selected. The Bellman function is approximated by quadratic terms. Along the allowable trajectory, this approximation gives nothing, because Bellman function and its expansion coefficients are zero. We used a special trick: an additional variable is introduced, which characterizes the degree of deviation of the system from the initial state, thus it is obtained expanded original chain. For the new variable initial nonzero conditions is selected, thus obtained trajectory is lying outside attainability set and relevant Bellman function is greater than zero, which allows it to hold a non-trivial approximation. As a result of these procedures algorithms of successive improvements is designed. Conditions for relaxation algorithms and conditions for the necessary conditions of optimality are also obtained.
Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

Science.gov (United States)

Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

2013-12-01

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.
Dynamical Encoding by Networks of Competing Neuron Groups: Winnerless Competition

International Nuclear Information System (INIS)

Rabinovich, M.; Volkovskii, A.; Lecanda, P.; Huerta, R.; Abarbanel, H. D. I.; Laurent, G.

2001-01-01

Following studies of olfactory processing in insects and fish, we investigate neural networks whose dynamics in phase space is represented by orbits near the heteroclinic connections between saddle regions (fixed points or limit cycles). These networks encode input information as trajectories along the heteroclinic connections. If there are N neurons in the network, the capacity is approximately e(N-1) ! , i.e., much larger than that of most traditional network structures. We show that a small winnerless competition network composed of FitzHugh-Nagumo spiking neurons efficiently transforms input information into a spatiotemporal output
Mixed boson-fermion description of correlated electrons: Fluctuation corrections in the symmetric treatment

International Nuclear Information System (INIS)

Vicente Alvarez, J.J.; Balseiro, C.A.; Ceccatto, H.A.

1995-07-01

We consider the introduction of fluctuation corrections to saddle- point results in the symmetric treatment of a mixed pseudofermion-boson representation of correlated electrons. In our calculations we avoid the complications of working in the discrete imaginary-time formulation of the functional integral, a procedure recently advocated in the literature as mandatory for this problem. For a simple two-site model our approach leads to approximate results in remarkable agreement with the exact ones, and without the spurious nonanalyticities of other similar treatments. (author). 14 refs, 2 figs
A note on the nucleation with multiple steps: parallel and series nucleation.

Science.gov (United States)

Iwamatsu, Masao

2012-01-28

Parallel and series nucleation are the basic elements of the complex nucleation process when two saddle points exist on the free-energy landscape. It is pointed out that the nucleation rates follow formulas similar to those of parallel and series connection of resistors or conductors in an electric circuit. Necessary formulas to calculate individual nucleation rates at the saddle points and the total nucleation rate are summarized, and the extension to the more complex nucleation process is suggested. © 2012 American Institute of Physics
Electron Transfer and Geometric Conversion of Co-NO Moiety in Saddled Porphyrins: Implications for Trigger Role of Tetrapyrrole Distortion.

Science.gov (United States)

Tang, Min; Yang, Yan; Zhang, Shaowei; Chen, Jiafu; Zhang, Jian; Zhou, Zaichun; Liu, Qiuhua

2018-01-02

The electrons of NO and Co are strongly delocalized in normal {Co-NO} 8 species. In this work, {Co-NO} 8 complexes are induced to convert from (Co II ) +• -NO • to Co III -NO - by a core contraction of 0.06 Å in saddled cobalt(II) porphyrins. This intramolecular electron transfer mechanism indicates that nonplanarity of porphyrin is involved in driving conversion of the NO units from electrophilic NO • as a bent geometry to nucleophilic NO - as a linear geometry. This implies that distortion acts as a trigger in enzymes containing tetrapyrrole. The electronic behaviors of the Co II ions and Co-NO moieties were confirmed by X-ray crystallography, EPR spectroscopy, theoretical calculation, UV-vis and IR spectroscopy, and electrochemistry.

Saddle-like deformation in a dielectric elastomer actuator embedded with liquid-phase gallium-indium electrodes

Science.gov (United States)

Wissman, J.; Finkenauer, L.; Deseri, L.; Majidi, C.

2014-10-01

We introduce a dielectric elastomer actuator (DEA) composed of liquid-phase Gallium-Indium (GaIn) alloy electrodes embedded between layers of poly(dimethylsiloxane) (PDMS) and examine its mechanics using a specialized elastic shell theory. Residual stresses in the dielectric and sealing layers of PDMS cause the DEA to deform into a saddle-like geometry (Gaussian curvature K <0). Applying voltage Φ to the liquid metal electrodes induces electrostatic pressure (Maxwell stress) on the dielectric and relieves some of the residual stress. This reduces the longitudinal bending curvature and corresponding angle of deflection ϑ. Treating the elastomer as an incompressible, isotropic, NeoHookean solid, we develop a theory based on the principle of minimum potential energy to predict the principal curvatures as a function of Φ. Based on this theory, we predict a dependency of ϑ on Φ that is in strong agreement with experimental measurements performed on a GaIn-PDMS composite. By accurately modeling electromechanical coupling in a soft-matter DEA, this theory can inform improvements in design and fabrication.
Saddle-like deformation in a dielectric elastomer actuator embedded with liquid-phase gallium-indium electrodes

Energy Technology Data Exchange (ETDEWEB)

Wissman, J., E-mail: jwissman@andrew.cmu.edu [Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Finkenauer, L. [Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Deseri, L. [DICAM, Department of Mechanical, Civil and Environmental Engineering, University of Trento, via Mesiano 77 38123 Trento (Italy); TMHRI-Department of Nanomedicine, The Methodist Hospital Research Institute, 6565 Fannin St., MS B-490 Houston, Texas 77030 (United States); Mechanics, Materials and Computing Center, CEE and ME-CIT, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Majidi, C. [Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Robotics Institute and Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States)

2014-10-14

We introduce a dielectric elastomer actuator (DEA) composed of liquid-phase Gallium-Indium (GaIn) alloy electrodes embedded between layers of poly(dimethylsiloxane) (PDMS) and examine its mechanics using a specialized elastic shell theory. Residual stresses in the dielectric and sealing layers of PDMS cause the DEA to deform into a saddle-like geometry (Gaussian curvature K<0). Applying voltage Φ to the liquid metal electrodes induces electrostatic pressure (Maxwell stress) on the dielectric and relieves some of the residual stress. This reduces the longitudinal bending curvature and corresponding angle of deflection ϑ. Treating the elastomer as an incompressible, isotropic, NeoHookean solid, we develop a theory based on the principle of minimum potential energy to predict the principal curvatures as a function of Φ. Based on this theory, we predict a dependency of ϑ on Φ that is in strong agreement with experimental measurements performed on a GaIn-PDMS composite. By accurately modeling electromechanical coupling in a soft-matter DEA, this theory can inform improvements in design and fabrication.
Saddle-like deformation in a dielectric elastomer actuator embedded with liquid-phase gallium-indium electrodes

International Nuclear Information System (INIS)

Wissman, J.; Finkenauer, L.; Deseri, L.; Majidi, C.

2014-01-01

We introduce a dielectric elastomer actuator (DEA) composed of liquid-phase Gallium-Indium (GaIn) alloy electrodes embedded between layers of poly(dimethylsiloxane) (PDMS) and examine its mechanics using a specialized elastic shell theory. Residual stresses in the dielectric and sealing layers of PDMS cause the DEA to deform into a saddle-like geometry (Gaussian curvature K<0). Applying voltage Φ to the liquid metal electrodes induces electrostatic pressure (Maxwell stress) on the dielectric and relieves some of the residual stress. This reduces the longitudinal bending curvature and corresponding angle of deflection ϑ. Treating the elastomer as an incompressible, isotropic, NeoHookean solid, we develop a theory based on the principle of minimum potential energy to predict the principal curvatures as a function of Φ. Based on this theory, we predict a dependency of ϑ on Φ that is in strong agreement with experimental measurements performed on a GaIn-PDMS composite. By accurately modeling electromechanical coupling in a soft-matter DEA, this theory can inform improvements in design and fabrication.
Approximative calculation of transient short-circuit currents in power-systems

Energy Technology Data Exchange (ETDEWEB)

Heuck, K; Rosenberger, R; Dettmann, K D; Kegel, R

1986-08-01

The paper shows that it is approximatively possible to calculate the transient short-circuit currents for symmetrical and asymmetrical faults in power-systems. For that purpose a simple equivalent network is found. Its error of approximation is small. For the important maximum short-circuit current limits of error are pointed out compared to VDE 0102.
Function parametrization by using 4-point transforms

International Nuclear Information System (INIS)

Dikusar, N.D.

1996-01-01

A continuous parametrization of the smooth curve f(x)=f(x;R) is suggested on a basis of four-point transformations. Coordinates of three reference points of the curve are chosen as parameters R. This approach allows to derive a number of advantages in function approximation and fitting of empiric data. The transformations have made possible to derive a new class of polynomials (monosplines) having the better approximation quality than monomials {x n }. A behaviour of an error of the approximation has a uniform character. A three-point model of the cubic spline (TPS) is proposed. The model allows to reduce a number of unknown parameters in twice and to obtain an advantage in a computing aspect. The new approach to the function approximation and fitting are shown on a number of examples. The proposed approach gives a new mathematical tool and a new possibility in both practical applications and theoretical research of numerical and computational methods. 13 refs., 13 figs., 2 tabs
Multidimensional stochastic approximation using locally contractive functions

Science.gov (United States)

Lawton, W. M.

1975-01-01

A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
APPROXIMATION OF FREE-FORM CURVE – AIRFOIL SHAPE

Directory of Open Access Journals (Sweden)

CHONG PERK LIN

2013-12-01

Full Text Available Approximation of free-form shape is essential in numerous engineering applications, particularly in automotive and aircraft industries. Commercial CAD software for the approximation of free-form shape is based almost exclusively on parametric polynomial and rational parametric polynomial. The parametric curve is defined by vector function of one independent variable R(u = (x(u, y(u, z(u, where 0≤u≤1. Bézier representation is one of the parametric functions, which is widely used in the approximating of free-form shape. Given a string of points with the assumption of sufficiently dense to characterise airfoil shape, it is desirable to approximate the shape with Bézier representation. The expectation is that the representation function is close to the shape within an acceptable working tolerance. In this paper, the aim is to explore the use of manual and automated methods for approximating section curve of airfoil with Bézier representation.
Quantum mechanical metastability: When and why?

International Nuclear Information System (INIS)

Boyanovsky, D.; Willey, R.; Holman, R.

1992-01-01

We study quantum mechanical metastability with an eye towards false vacuum decay. We point out some technical and conceptual problems with the familiar bounce treatment of this process. We illustrate with simple quantum mechanical examples that the bounce formalism fails to account for the correct boundary conditions. It is also shown, that the bounce approach overestimates the time scales for tunneling of localized packets in typical (slightly) biased double well potentials. We present a thorough WKB analysis with particular attention to semiclassical trajectories corresponding to complex saddle points. We point out that the boundary conditions determine the proper choice of saddle points and the bounce approach fails to account for semiclassical trajectories in many physically relevant cases. We recognize that these saddle points account for the matching conditions of the WKB wave functions beyond the barriers and restore unitarity and reality of eigenvalues for self-adjoint boundary conditions. We provide a novel approach to the semiclassical analysis of out of equilibrium decay in real time in quantum statistical mechanics. (orig.)
Efficient parallel implementations of approximation algorithms for guarding 1.5D terrains

Directory of Open Access Journals (Sweden)

Goran Martinović

2015-03-01

Full Text Available In the 1.5D terrain guarding problem, an x-monotone polygonal line is dened by k vertices and a G set of terrain points, i.e. guards, and a N set of terrain points which guards are to observe (guard. This involves a weighted version of the guarding problem where guards G have weights. The goal is to determine a minimum weight subset of G to cover all the points in N, including a version where points from N have demands. Furthermore, another goal is to determine the smallest subset of G, such that every point in N is observed by the required number of guards. Both problems are NP-hard and have a factor 5 approximation [3, 4]. This paper will show that if the (1+ϵ-approximate solver for the corresponding linear program is a computer, for any ϵ > 0, an extra 1+ϵ factor will appear in the final approximation factor for both problems. A comparison will be carried out the parallel implementation based on GPU and CPU threads with the Gurobi solver, leading to the conclusion that the respective algorithm outperforms the Gurobi solver on large and dense inputs typically by one order of magnitude.
Cheap contouring of costly functions: the Pilot Approximation Trajectory algorithm

International Nuclear Information System (INIS)

Huttunen, Janne M J; Stark, Philip B

2012-01-01

The Pilot Approximation Trajectory (PAT) contour algorithm can find the contour of a function accurately when it is not practical to evaluate the function on a grid dense enough to use a standard contour algorithm, for instance, when evaluating the function involves conducting a physical experiment or a computationally intensive simulation. PAT relies on an inexpensive pilot approximation to the function, such as interpolating from a sparse grid of inexact values, or solving a partial differential equation (PDE) numerically using a coarse discretization. For each level of interest, the location and ‘trajectory’ of an approximate contour of this pilot function are used to decide where to evaluate the original function to find points on its contour. Those points are joined by line segments to form the PAT approximation of the contour of the original function. Approximating a contour numerically amounts to estimating a lower level set of the function, the set of points on which the function does not exceed the contour level. The area of the symmetric difference between the true lower level set and the estimated lower level set measures the accuracy of the contour. PAT measures its own accuracy by finding an upper confidence bound for this area. In examples, PAT can estimate a contour more accurately than standard algorithms, using far fewer function evaluations than standard algorithms require. We illustrate PAT by constructing a confidence set for viscosity and thermal conductivity of a flowing gas from simulated noisy temperature measurements, a problem in which each evaluation of the function to be contoured requires solving a different set of coupled nonlinear PDEs. (paper)
Vesicle computers: Approximating a Voronoi diagram using Voronoi automata

International Nuclear Information System (INIS)

Adamatzky, Andrew; De Lacy Costello, Ben; Holley, Julian; Gorecki, Jerzy; Bull, Larry

2011-01-01

Highlights: → We model irregular arrangements of vesicles filled with chemical systems. → We examine influence of precipitation threshold on the system's computational potential. → We demonstrate computation of Voronoi diagram and skeleton. - Abstract: Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata - finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one neighbour in an excited state. The cell precipitates if the ratio of excited cells in its neighbourhood versus the number of neighbours exceeds a certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto the automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate at the points of interaction. The configuration of the precipitate represents the edges of an approximated Voronoi diagram. We discover the relationship between the quality of the Voronoi diagram approximation and the precipitation threshold, and demonstrate the feasibility of our model in approximating Voronoi diagrams of arbitrary-shaped objects and in constructing a skeleton of a planar shape.
Slab-diffusion approximation from time-constant-like calculations

International Nuclear Information System (INIS)

Johnson, R.W.

1976-12-01

Two equations were derived which describe the quantity and any fluid diffused from a slab as a function of time. One equation is applicable to the initial stage of the process; the other to the final stage. Accuracy is 0.2 percent at the one point where both approximations apply and where accuracy of either approximation is the poorest. Characterizing other rate processes might be facilitated by the use of the concept of NOLOR (normal of the logarithm of the rate) and its time dependence
Mass Spectrometry Using Nanomechanical Systems: Beyond the Point-Mass Approximation.

Science.gov (United States)

Sader, John E; Hanay, M Selim; Neumann, Adam P; Roukes, Michael L

2018-03-14

The mass measurement of single molecules, in real time, is performed routinely using resonant nanomechanical devices. This approach models the molecules as point particles. A recent development now allows the spatial extent (and, indeed, image) of the adsorbate to be characterized using multimode measurements ( Hanay , M. S. , Nature Nanotechnol. , 10 , 2015 , pp 339 - 344 ). This "inertial imaging" capability is achieved through virtual re-engineering of the resonator's vibrating modes, by linear superposition of their measured frequency shifts. Here, we present a complementary and simplified methodology for the analysis of these inertial imaging measurements that exhibits similar performance while streamlining implementation. This development, together with the software that we provide, enables the broad implementation of inertial imaging that opens the door to a range of novel characterization studies of nanoscale adsorbates.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation.

Science.gov (United States)

Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia

2005-05-13

We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.
Capped Lp approximations for the composite L0 regularization problem

OpenAIRE

Li, Qia; Zhang, Na

2017-01-01

The composite L0 function serves as a sparse regularizer in many applications. The algorithmic difficulty caused by the composite L0 regularization (the L0 norm composed with a linear mapping) is usually bypassed through approximating the L0 norm. We consider in this paper capped Lp approximations with $p>0$ for the composite L0 regularization problem. For each $p>0$, the capped Lp function converges to the L0 norm pointwisely as the approximation parameter tends to infinity. We point out tha...
Gradients estimation from random points with volumetric tensor in turbulence

Science.gov (United States)

Watanabe, Tomoaki; Nagata, Koji

2017-12-01

We present an estimation method of fully-resolved/coarse-grained gradients from randomly distributed points in turbulence. The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3 × 3 matrix determined by a geometric distribution of the points. The coarse grained gradient can be considered as a low pass filtered gradient, whose cutoff is estimated with the eigenvalues of the volumetric tensor. The present method, the volumetric tensor approximation, is tested for velocity and passive scalar gradients in incompressible planar jet and mixing layer. Comparison with a finite difference approximation on a Cartesian grid shows that the volumetric tensor approximation computes the coarse grained gradients fairly well at a moderate computational cost under various conditions of spatial distributions of points. We also show that imposing the solenoidal condition improves the accuracy of the present method for solenoidal vectors, such as a velocity vector in incompressible flows, especially when the number of the points is not large. The volumetric tensor approximation with 4 points poorly estimates the gradient because of anisotropic distribution of the points. Increasing the number of points from 4 significantly improves the accuracy. Although the coarse grained gradient changes with the cutoff length, the volumetric tensor approximation yields the coarse grained gradient whose magnitude is close to the one obtained by the finite difference. We also show that the velocity gradient estimated with the present method well captures the turbulence characteristics such as local flow topology, amplification of enstrophy and strain, and energy transfer across scales.
Dynamic effects in neutron induced fission of 230Th and 232Th

International Nuclear Information System (INIS)

Trochon, J.; Frehaut, J.; Pranal, Y.; Simon, G.; Boldeman, J.W.

1982-09-01

The fission fragment characteristics of the two thorium isotopes 230 Th and 232 Th have been measured in an attempt to study the evolution of the fissioning nucleus from saddle point to scission. The partial fission channel at the saddle point have been deduced from a fission fragment angular distribution and fission cross section analysis. Changes with energy in the average number of prompt neutron (νsub(p)) emitted per fission and the total fragment kinetic energy (TKE) have been observed in the fission threshold region. A rather good fit of νsub(p) and TKE values has been obtained on the basis of a correlation of these quantities and the partial fission channel ratios. This leads to expect for these isotopes a passage from saddle point to scission sufficiently rapid for the coupling between collective and intrinsic excitation to be very weak [fr
Strontium isotopic and trace element geochemistry of the saddle mountains and Grande Ronde Basalts of the Columbia River Basalt Group

International Nuclear Information System (INIS)

Nelson, D.O.

1980-01-01

The Columbia River Basalt (CRB) group displays significant variations in major and trace element and Sr isotopic compositions. These compositions reflect complex and variable origins for the CRB magmas. Among the most varied is the Saddle Mountains Basalt (SMB) in which Sr ratios vary from 0.7078 to 0.7147 +- 0.002. The higher ratios reflect contamination through consistent correlations with major element compositions. Modeling suggests contamination by assimilation of 4.4 to 9.4 wt % of radiogenic crustal rocks. High delta 18 O values (up to +7.68 per mil) support the model. Age and field relations suggest that the contamination flowrocks are not the result of progressive contamination of a single magma, but rather reflect the contamination of independent magmas during this ascent
Pade approximants for the ground-state energy of closed-shell quantum dots

International Nuclear Information System (INIS)

Gonzalez, A.; Partoens, B.; Peeters, F.M.

1997-08-01

Analytic approximations to the ground-state energy of closed-shell quantum dots (number of electrons from 2 to 210) are presented in the form of two-point Pade approximants. These Pade approximants are constructed from the small- and large-density limits of the energy. We estimated that the maximum error, reached for intermediate densities, is less than ≤ 3%. Within that present approximation the ground-state is found to be unpolarized. (author). 21 refs, 3 figs, 2 tabs
Magnetic X-points, edge localized modes, and stochasticity

International Nuclear Information System (INIS)

Sugiyama, L. E.; Strauss, H. R.

2010-01-01

Edge localized modes (ELMs) near the boundary of a high temperature, magnetically confined toroidal plasma represent a new type of nonlinear magnetohydrodynamic (MHD) plasma instability that grows through a coherent plasma interaction with part of a chaotic magnetic field. Under perturbation, the freely moving magnetic boundary surface with an X-point splits into two different limiting asymptotic surfaces (manifolds), similar to the behavior of a hyperbolic saddle point in Hamiltonian dynamics. Numerical simulation using the extended MHD code M3D shows that field-aligned plasma instabilities, such as ballooning modes, can couple to the ''unstable'' manifold that forms helical, field-following lobes around the original surface. Large type I ELMs proceed in stages. Initially, a rapidly growing ballooning outburst involves the entire outboard side. Large plasma fingers grow well off the midplane, while low density regions penetrate deeply into the plasma. The magnetic field becomes superficially stochastic. A secondary inboard edge instability causes inboard plasma loss. The plasma gradually relaxes back toward axisymmetry, with diminishing cycles of edge instability. Poloidal rotation of the interior and edge plasma may be driven. The magnetic tangle constrains the early nonlinear ballooning, but may encourage the later inward penetration. Equilibrium toroidal rotation and two-fluid diamagnetic drifts have relatively small effects on a strong MHD instability. Intrinsic magnetic stochasticity may help explain the wide range of experimentally observed ELMs and ELM-free behavior in fusion plasmas, as well as properties of the H-mode and plasma edge.

Classical geometry from the quantum Liouville theory

Energy Technology Data Exchange (ETDEWEB)

Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl

2005-09-26

Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Introduction to statistical field theory: from a toy model to a one-component plasma

International Nuclear Information System (INIS)

Frydel, Derek

2015-01-01

Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard–Stratonovich transformation). We then consider Gaussian-type approximations, wherein correlational contributions enter as harmonic fluctuations around the saddle-point solution. This work focuses on how to arrive at a self-consistent, non-perturbative approximation without recourse to a standard variational construction based on the Gibbs–Bogolyubov–Feynman inequality that is inapplicable to a complex action. To address this problem, we propose a construction based on selective satisfaction of a set of exact relations generated by considering a dual representation of a partition function, in its original and transformed form. (paper)
Semiclassical approximation to time-dependent Hartree--Fock theory

International Nuclear Information System (INIS)

Dworzecka, M.; Poggioli, R.

1976-01-01

Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form
Dynamical thresholds for complete fusion

International Nuclear Information System (INIS)

Davies, K.T.R.; Sierk, A.J.; Nix, J.R.

1983-01-01

It is our purpose here to study the effect of nuclear dissipation and shape parametrization on dynamical thresholds for compound-nucleus formation in symmetric heavy-ion reactions. This is done by solving numerically classical equations of motion for head-on collisions to determine whether the dynamical trajectory in a multidimensional deformation space passes inside the fission saddle point and forms a compound nucleus, or whether it passes outside the fission saddle point and reseparates in a fast-fission or deep-inelastic reaction. Specifying the nuclear shape in terms of smoothly joined portions of three quadratic surfaces of revolution, we take into account three symmetric deformation coordinates. However, in some cases we reduce the number of coordinates to two by requiring the ends of the fusing system to be spherical in shape. The nuclear potential energy of deformation is determined in terms of a Coulomb energy and a double volume energy of a Yukawa-plus-exponential folding function. The collective kinetic energy is calculated for incompressible, nearly irrotational flow by means of the Werner-Wheeler approximation. Four possibilities are studied for the transfer of collective kinetic energy into internal single-particle excitation energy: zero dissipation, ordinary two body viscosity, one-body wall-formula dissipation, and one-body wall-and-window dissipation
He{sup 3+}{sub 2} and HeH{sup 2+} molecular ions in a strong magnetic field: The Lagrange-mesh approach

Energy Technology Data Exchange (ETDEWEB)

Olivares Pilón, Horacio, E-mail: holivare@ulb.ac.be [Physique Quantique, CP 165/82, Université Libre de Bruxelles, B 1050 Brussels (Belgium)

2012-04-09

Accurate calculations for the ground state of the molecular ions He{sup 3+}{sub 2} and HeH{sup 2+} placed in a strong magnetic field B≳10{sup 2} a.u. (≈2.35×10{sup 11} G) using the Lagrange-mesh method are presented. The Born–Oppenheimer approximation of zero order (infinitely massive centers) and the parallel configuration (molecular axis parallel to the magnetic field) are considered. Total energies are found with 9–10 s.d. The obtained results show that the molecular ions He{sup 3+}{sub 2} and HeH{sup 2+} exist at B>100 a.u. and B>1000 a.u., respectively, as predicted in Turbiner and López Vieyra (2007) while a saddle point in the potential curve appears for the first time at B∼80 a.u. and B∼740 a.u., respectively. -- Highlights: ► Application of the Lagrange-mesh method to two exotic molecular systems. ► He{sup 3+}{sub 2} and HeH{sup 2+} exist at B>100 a.u. and B>1000 a.u., respectively. ► Accurate results for the total energy. ► A saddle point in the potential appears at B∼80 a.u. and B∼740 a.u., respectively.
Nonlocal electron-phonon coupling in the pentacene crystal: Beyond the Γ-point approximation

KAUST Repository

Yi, Yuanping

2012-01-01

There is currently increasing interest in understanding the impact of the nonlocal (Peierls-type) electron-phonon mechanism on charge transport in organic molecular semiconductors. Most estimates of the non-local coupling constants reported in the literature are based on the Γ-point phonon modes. Here, the influence of phonon modes spanning the entire Brillouin zone (phonon dispersion) on the nonlocal electron-phonon couplings is investigated for the pentacene crystal. The phonon modes are obtained by using a supercell approach. The results underline that the overall nonlocal couplings are substantially underestimated by calculations taking sole account of the phonons at the Γ point of the unit cell. The variance of the transfer integrals based on Γ-point normal-mode calculations at room temperature is underestimated in some cases by 40% for herringbone-type dimers and by over 80% for cofacial dimers. Our calculations show that the overall coupling is somewhat larger for holes than for electrons. The results also suggest that the interactions of charge carriers (both electrons and holes) with acoustic and optical phonons are comparable. Therefore, an adequate description of the charge-transport properties in pentacene and similar systems requires that these two electron-phonon coupling mechanisms be treated on the same footing. © 2012 American Institute of Physics.
Local and global bifurcations at infinity in models of glycolytic oscillations

DEFF Research Database (Denmark)

Sturis, Jeppe; Brøns, Morten

1997-01-01

We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node...... at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable...... sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models...
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

Energy Technology Data Exchange (ETDEWEB)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)

2017-06-15

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
Local approximation of a metapopulation's equilibrium.

Science.gov (United States)

Barbour, A D; McVinish, R; Pollett, P K

2018-04-18

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.
Background approximation in automatic qualitative X-ray-fluorescent analysis

International Nuclear Information System (INIS)

Jordanov, J.; Tsanov, T.; Stefanov, R.; Jordanov, N.; Paunov, M.

1982-01-01

An empirical method of finding the dependence of the background intensity (Isub(bg) on the wavelength is proposed, based on the approximation of the experimentally found values for the background in the course of an automatic qualitative X-ray fluorescent analysis with pre-set curve. It is assumed that the dependence I(lambda) will be well approximated by a curve of the type Isub(bg)=(lambda-lambda sub(o)sup(fsub(1)(lambda))exp[fsub(2)(lambda)] where fsub(1) (lambda) and f 2 (lambda) are linear functions with respect to the sought parameters. This assumption was checked out on a ''pure'' starch background, in which it is not known beforehand which points belong to the background. It was assumed that the dependence I(lambda) can be found from all minima in the spectrum. Three types of minima has been distinguished: 1. the lowest point between two well-solved X-ray lines; 2. a minimum obtained as a result of statistical fluctuations of the measured signal; 3. the lowest point between two overlapped lines. The minima strongly deviating from the background are removed from the obtained set. The sum-total of the remaining minima serves as a base for the approximation of the dependence I(lambda). The unknown parameters are determined by means of the LSM. The approximated curve obtained by this method is closer to the real background than the background determined by the method described by Kigaki Denki, as the effect of all recorded minima is taken into account. As an example the PbTe spectrum recorded with crystal LiF 220 is shown graphically. The curve well describes the background of the spectrum even in the regions in which there are no minima belonging to the background. (authors)
Adaptive Dynamic Programming for Discrete-Time Zero-Sum Games.

Science.gov (United States)

Wei, Qinglai; Liu, Derong; Lin, Qiao; Song, Ruizhuo

2018-04-01

In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.
Modelling of the Woods-Saxon eikonal function for nuclear elastic scattering; Modelirovanie ehjkonal`noj funktsii uprugogo rasseyaniya v pole potentsiala Vudsa-Saksona

Energy Technology Data Exchange (ETDEWEB)

Luk` yanov, V K; Permyakov, V P; Chubov, Yu V

1999-12-31

The eikonal phase is needed for the analytical calculations for the nuclear scattering in the high energy approximation (E>>U, kR>>1). In this paper we obtain its model expression for scattering on Woods-Saxon potential which with a good accuracy reproduces its behaviour in complex plane which is found numerically. In the case one evaluates explicitly the scattering amplitude using saddle-point method makes the physics more understandable. The numerical amplitudes and cross sections of nucleus-nucleus scattering are compared with exact calculations. (author) 9 refs., 7 figs. Submitted to Izvestiya Akademii Nauk. Rossijskaya Akademiya Nauk. Seriya Fizicheskaya
Computing gap free Pareto front approximations with stochastic search algorithms.

Science.gov (United States)

Schütze, Oliver; Laumanns, Marco; Tantar, Emilia; Coello, Carlos A Coello; Talbi, El-Ghazali

2010-01-01

Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of epsilon-dominance. Though bounds on the quality of the limit approximation-which are entirely determined by the archiving strategy and the value of epsilon-have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a epsilon A, is "large." Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy-multi-objective continuation methods-by showing that the concept of epsilon-dominance can be integrated into this approach in a suitable way.
Distributed approximation of Pareto surfaces in multicriteria radiation therapy treatment planning

International Nuclear Information System (INIS)

Bokrantz, Rasmus

2013-01-01

We consider multicriteria radiation therapy treatment planning by navigation over the Pareto surface, implemented by interpolation between discrete treatment plans. Current state of the art for calculation of a discrete representation of the Pareto surface is to sandwich this set between inner and outer approximations that are updated one point at a time. In this paper, we generalize this sequential method to an algorithm that permits parallelization. The principle of the generalization is to apply the sequential method to an approximation of an inexpensive model of the Pareto surface. The information gathered from the model is sub-sequently used for the calculation of points from the exact Pareto surface, which are processed in parallel. The model is constructed according to the current inner and outer approximations, and given a shape that is difficult to approximate, in order to avoid that parts of the Pareto surface are incorrectly disregarded. Approximations of comparable quality to those generated by the sequential method are demonstrated when the degree of parallelization is up to twice the number of dimensions of the objective space. For practical applications, the number of dimensions is typically at least five, so that a speed-up of one order of magnitude is obtained. (paper)
Distributed approximation of Pareto surfaces in multicriteria radiation therapy treatment planning.

Science.gov (United States)

Bokrantz, Rasmus

2013-06-07

We consider multicriteria radiation therapy treatment planning by navigation over the Pareto surface, implemented by interpolation between discrete treatment plans. Current state of the art for calculation of a discrete representation of the Pareto surface is to sandwich this set between inner and outer approximations that are updated one point at a time. In this paper, we generalize this sequential method to an algorithm that permits parallelization. The principle of the generalization is to apply the sequential method to an approximation of an inexpensive model of the Pareto surface. The information gathered from the model is sub-sequently used for the calculation of points from the exact Pareto surface, which are processed in parallel. The model is constructed according to the current inner and outer approximations, and given a shape that is difficult to approximate, in order to avoid that parts of the Pareto surface are incorrectly disregarded. Approximations of comparable quality to those generated by the sequential method are demonstrated when the degree of parallelization is up to twice the number of dimensions of the objective space. For practical applications, the number of dimensions is typically at least five, so that a speed-up of one order of magnitude is obtained.
The binary collision approximation: Background and introduction

International Nuclear Information System (INIS)

Robinson, M.T.

1992-08-01

The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented
Hierarchical low-rank approximation for high dimensional approximation

KAUST Repository

Nouy, Anthony

2016-01-07

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Hierarchical low-rank approximation for high dimensional approximation

KAUST Repository

Nouy, Anthony

2016-01-01

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
An improved JWKB approximation for multiple-humped fission barriers

International Nuclear Information System (INIS)

Martinelli, T.; Menapace, E.; Ventura, A.

1977-01-01

Penetrabilities of two- and three-humped fission barriers are calculated in semiclassical (JWKB) approximation, valid also in the case where classical turning points are close, or coincident (excitation energy near the top of some hump). Numerical results are shown for Th 234 . (author)
Experimental Investigation of Triplet Correlation Approximations for Fluid Water.

Science.gov (United States)

Pallewela, Gayani N; Ploetz, Elizabeth A; Smith, Paul E

2018-08-25

Triplet correlations play a central role in our understanding of fluids and their properties. Of particular interest is the relationship between the pair and triplet correlations. Here we use a combination of Fluctuation Solution Theory and experimental pair radial distribution functions to investigate the accuracy of the Kirkwood Superposition Approximation (KSA), as given by integrals over the relevant pair and triplet correlation functions, at a series of state points for pure water using only experimental quantities. The KSA performs poorly, in agreement with a variety of other studies. Several additional approximate relationships between the pair and triplet correlations in fluids are also investigated and generally provide good agreement for the fluid thermodynamics for regions of the phase diagram where the compressibility is small. A simple power law relationship between the pair and triplet fluctuations is particularly successful for state points displaying low to moderately high compressibilities.

Magnetic properties of point defect interaction with impurity atoms in Fe-Cr alloys

Science.gov (United States)

Nguyen-Manh, D.; Lavrentiev, M. Yu.; Dudarev, S. L.

2009-04-01

An integrated ab initio and statistical Monte Carlo investigation has been recently carried out to model the thermodynamic and kinetic properties of Fe-Cr alloys. We found that the conventional Fe-Cr phase diagram is not adequate at low temperature region where the magnetic contribution to the free energy plays an important role in the prediction of an ordered Fe 15Cr phase and its negative enthalpy of formation. The origin of the anomalous thermodynamic and magnetic properties of Fe-Cr alloys can be understood using a tight-binding Stoner model combined with the charge neutrality condition. We investigate the environmental dependence of magnetic moment distributions for various self-interstitial atom dumbbells configurations using spin density maps found using density functional theory calculations. The mixed dumbbell Fe-Cr and Fe-Mn binding energies are found to be positive due to magnetic interactions. Finally, we discuss the relationship between the migration energy of vacancy in Fe-Cr alloys and magnetism at the saddle point configuration.
Phase-plane analysis to an “anisotropic” higher-order traffic flow model

Science.gov (United States)

Wu, Chun-Xiu

2018-04-01

The qualitative theory of differential equations is applied to investigate the traveling wave solution to an “anisotropic” higher-order viscous traffic flow model under the Lagrange coordinate system. The types and stabilities of the equilibrium points are discussed in the phase plane. Through the numerical simulation, the overall distribution structures of trajectories are drawn to analyze the relation between the phase diagram and the selected conservative solution variables, and the influences of the parameters on the system are studied. The limit-circle, limit circle-spiral point, saddle-spiral point and saddle-nodal point solutions are obtained. These steady-state solutions provide good explanation for the phenomena of the oscillatory and homogeneous congestions in real-world traffic.
A new way of obtaining analytic approximations of Chandrasekhar's H function

International Nuclear Information System (INIS)

Vukanic, J.; Arsenovic, D.; Davidovic, D.

2007-01-01

Applying the mean value theorem for definite integrals in the non-linear integral equation for Chandrasekhar's H function describing conservative isotropic scattering, we have derived a new, simple analytic approximation for it, with a maximal relative error below 2.5%. With this new function as a starting-point, after a single iteration in the corresponding integral equation, we have obtained a new, highly accurate analytic approximation for the H function. As its maximal relative error is below 0.07%, it significantly surpasses the accuracy of other analytic approximations
An extension of Brosowski-Meinardus theorem on invariant approximation

International Nuclear Information System (INIS)

Liaqat Ali Khan; Abdul Rahim Khan.

1991-07-01

We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs
Animating Nested Taylor Polynomials to Approximate a Function

Science.gov (United States)

Mazzone, Eric F.; Piper, Bruce R.

2010-01-01

The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…
Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation

Directory of Open Access Journals (Sweden)

Berenguer MI

2010-01-01

Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .
Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Application

KAUST Repository

Chambolle, Antonin; Ehrhardt, Matthias J.; Richtarik, Peter; Schö nlieb, Carola-Bibiane

2017-01-01

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.
A Blue Lagoon Function

DEFF Research Database (Denmark)

Markvorsen, Steen

2007-01-01

We consider a specific function of two variables whose graph surface resembles a blue lagoon. The function has a saddle point $p$, but when the function is restricted to any given straight line through $p$ it has a {\\em{strict local minimum}} along that line at $p$.......We consider a specific function of two variables whose graph surface resembles a blue lagoon. The function has a saddle point $p$, but when the function is restricted to any given straight line through $p$ it has a {\\em{strict local minimum}} along that line at $p$....
Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Application

KAUST Repository

Chambolle, Antonin

2017-06-15

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.
Tunneling and reflection in unimolecular reaction kinetic energy release distributions

Science.gov (United States)

Hansen, K.

2018-02-01

The kinetic energy release distributions in unimolecular reactions is calculated with detailed balance theory, taking into account the tunneling and the reflection coefficient in three different types of transition states; (i) a saddle point corresponding to a standard RRKM-type theory, (ii) an attachment Langevin cross section, and (iii) an absorbing sphere potential at short range, without long range interactions. Corrections are significant in the one dimensional saddle point states. Very light and lightly bound absorbing systems will show measurable effects in decays from the absorbing sphere, whereas the Langevin cross section is essentially unchanged.
Preconditioning for Allen–Cahn variational inequalities with non-local constraints

KAUST Repository

Blank, Luise

2012-06-01

The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach. © 2012 Elsevier Inc.
Multibreather solitons in the diffraction managed NLS equation

International Nuclear Information System (INIS)

Panayotaros, Panayotis

2006-01-01

We study analytically and numerically localized breather solutions in the averaged discrete nonlinear Schroedinger equation (NLS) with diffraction management, a system that models coupled waveguide arrays with periodic diffraction management geometries. Localized breathers can be characterized as constrained critical points of the Hamiltonian of the averaged diffraction managed NLS. In addition to local extrema, we find numerically more general solutions that are saddle points of the constrained Hamiltonian. An interesting class of saddle points are 'multi-bump' solutions that are close to superpositions of translates of simpler breathers. In the case of zero residual diffraction and small diffraction management, the existence of multibumps can be shown rigorously by a continuation argument
Approximations for transport parameters and self-averaging properties for point-like injections in heterogeneous media

International Nuclear Information System (INIS)

Eberhard, Jens

2004-01-01

We focus on transport parameters in heterogeneous media with a flow modelled by an ensemble of periodic and Gaussian random fields. The parameters are determined by ensemble averages. We study to what extent these averages represent the behaviour in a single realization. We calculate the centre-of-mass velocity and the dispersion coefficient using approximations based on a perturbative expansion for the transport equation, and on the iterative solution of the Langevin equation. Compared with simulations, the perturbation theory reproduces the numerical results only poorly, whereas the iterative solution yields good results. Using these approximations, we investigate the self-averaging properties. The ensemble average of the velocity characterizes the behaviour of a realization for large times in both ensembles. The dispersion coefficient is not self-averaging in the ensemble of periodic fields. For the Gaussian ensemble the asymptotic dispersion coefficient is self-averaging. For finite times, however, the fluctuations are so large that the average does not represent the behaviour in a single realization
An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics.

Science.gov (United States)

Fu, Chunjiang; Suzuki, Yasuyuki; Kiyono, Ken; Morasso, Pietro; Nomura, Taishin

2014-12-06

Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather
Topological fixed point theory of multivalued mappings

CERN Document Server

Górniewicz, Lech

1999-01-01

This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework. Topics covered include the basic theory of set-valued mappings with both convex and nonconvex values, approximation and homological methods in the fixed point theory together with a thorough discussion of various index theories for mappings with a topologically complex structure of values, applications to many fields of mathematics, mathematical economics and related subjects, and the fixed point approach to the theory of ordinary differential inclusions. The work emphasises the topological aspect of the theory, and gives special attention to the Lefschetz and Nielsen fixed point theory for acyclic valued mappings with diverse compactness assumptions via graph approximation and the homological approach. Audience: This work will be of interest to researchers an...
Integral approximants for functions of higher monodromic dimension

Energy Technology Data Exchange (ETDEWEB)

Baker, G.A. Jr.

1987-01-01

In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.
On the mathematical treatment of the Born-Oppenheimer approximation

International Nuclear Information System (INIS)

Jecko, Thierry

2014-01-01

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics
On the mathematical treatment of the Born-Oppenheimer approximation

Energy Technology Data Exchange (ETDEWEB)

Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr [AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Département de mathématiques, site de Saint Martin, 2 avenue Adolphe Chauvin, F-95000 Pontoise (France)

2014-05-15

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.
Point kinetics modeling

International Nuclear Information System (INIS)

Kimpland, R.H.

1996-01-01

A normalized form of the point kinetics equations, a prompt jump approximation, and the Nordheim-Fuchs model are used to model nuclear systems. Reactivity feedback mechanisms considered include volumetric expansion, thermal neutron temperature effect, Doppler effect and void formation. A sample problem of an excursion occurring in a plutonium solution accidentally formed in a glovebox is presented
Random-phase approximation and broken symmetry

International Nuclear Information System (INIS)

Davis, E.D.; Heiss, W.D.

1986-01-01

The validity of the random-phase approximation (RPA) in broken-symmetry bases is tested in an appropriate many-body system for which exact solutions are available. Initially the regions of stability of the self-consistent quasiparticle bases in this system are established and depicted in a 'phase' diagram. It is found that only stable bases can be used in an RPA calculation. This is particularly true for those RPA modes which are not associated with the onset of instability of the basis; it is seen that these modes do not describe any excited state when the basis is unstable, although from a formal point of view they remain acceptable. The RPA does well in a stable broken-symmetry basis provided one is not too close to a point where a phase transition occurs. This is true for both energies and matrix elements. (author)

The strong running coupling from an approximate gluon Dyson-Schwinger equation

International Nuclear Information System (INIS)

Alkofer, R.; Hauck, A.

1996-01-01

Using Mandelstam's approximation to the gluon Dyson-Schwinger equation we calculate the gluon self-energy in a renormalisation group invariant fashion. We obtain a non-perturbative Β function. The scaling behavior near the ultraviolet stable fixed point is in good agreement with perturbative QCD. No further fixed point for positive values of the coupling is found: α S increases without bound in the infrared
On the initial conditions of time-dependent mean-field equations of evolution. Pt. 2

International Nuclear Information System (INIS)

Troudet, T.; Paris-11 Univ., 91 - Orsay

1986-01-01

We analyze the problem so far untouched of determining the initial mean-field wavefunction in the context of zero-temperature mean-field descriptions of time-dependent expectation values and quantum fluctuations of nuclear observables. The nucleus, at zero temperature, is taken to be in a low-lying excited many-body eigenstate and is approximated by the corresponding RPA wavefunction as a continuous superposition of coherent states (i.e. Slater determinants). A generating function Gsub(A)(lambda) for time-dependent expectation values and quantum fluctuations is constructed within the formalism of functional integration. By applying the saddle-point method to the functional action of Gsub(A)(lambda) and then taking its lambda-derivatives, we recover the well-known TDHF theory and propose a simple determination of the initial Slater determinant for an appropriate mean-field description of time-dependent expectation values. The analog mean-field description of quadratic-quantum fluctuations proceeds similarly and in addition includes the contribution of the uncorrelated TDHF-RPA phonons coupled to collective excitations of the initial (static) mean-field configuration. When the collective TDHF-RPA excitations are solely taken into account, we obtain an improved version of the Balian-Veneroni dispersion formula by showing how to determine the initial mean-field wavefunction. By first taking the lambda-derivatives of Gsub(A)(lambda) before applying the saddle-point method, the initial mean-field wavefunction is found to be non-linearly coupled to the mean-field dynamics themselves. In return, and in contrast to the first quantization scheme, these both depend non-trivially upon the observable A being measured so that approximations must be proposed to simplify the resulting mean-field equations. (orig.)
Control Point Generated PLS - lines

Data.gov (United States)

Minnesota Department of Natural Resources — The Control Point Generated PLS layer contains line and polygon features to the 1/4 of 1/4 PLS section (approximately 40 acres) and government lot level. The layer...
Control Point Generated PLS - polygons

Data.gov (United States)

Minnesota Department of Natural Resources — The Control Point Generated PLS layer contains line and polygon features to the 1/4 of 1/4 PLS section (approximately 40 acres) and government lot level. The layer...
The quasilocalized charge approximation

International Nuclear Information System (INIS)

Kalman, G J; Golden, K I; Donko, Z; Hartmann, P

2005-01-01

The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two
Effects of scattering anisotropy approximation in multigroup radiation shielding calculations

International Nuclear Information System (INIS)

Altiparmakov, D.

1983-01-01

Expansion of the scattering cross sections into Legendre series is the usual way of solving neutron transport problems. Because of the large space gradients of the neutron flux, the effects of that approximation become especially remarkable in the radiation shielding calculations. In this paper, a method taking into account the scattering anisotropy is presented. From the point od view of the accuracy and computing rate, the optimal approximation of the scattering anisotropy is established for the basic protective materials on the basis of simple problem calculations. (author)
A Monte Carlo Application to Approximate the Integral from a to b of e Raised to the x Squared.

Science.gov (United States)

Easterday, Kenneth; Smith, Tommy

1992-01-01

Proposes an alternative means of approximating the value of complex integrals, the Monte Carlo procedure. Incorporating a discrete approach and probability, an approximation is obtained from the ratio of computer-generated points falling under the curve to the number of points generated in a predetermined rectangle. (MDH)
A mean field theory of study of lattice gauge theory with finite temperature and with finite fermion density

International Nuclear Information System (INIS)

Naik, S.

1990-01-01

We have developed a mean field theory technique to study the confinement-deconfinement phase transition and chiral symmetry restoring phase transition with dynamical fermions and with finite chemical potential and finite temperature. The approximation scheme concerns the saddle point scenario and large space dimension. The static quark-antiquark potentials are identified from the Wilson loop correlation functions in both the fundamental and the adjoint representation of the gauge group with different temperatures. The difference between the responses of the chemical potential to the fermion number with singlet and non-singlet isospin configuration is found. We compare our results with recent Monte Carlo data. (orig.)
Iterative choice of the optimal regularization parameter in TV image deconvolution

International Nuclear Information System (INIS)

Sixou, B; Toma, A; Peyrin, F; Denis, L

2013-01-01

We present an iterative method for choosing the optimal regularization parameter for the linear inverse problem of Total Variation image deconvolution. This approach is based on the Morozov discrepancy principle and on an exponential model function for the data term. The Total Variation image deconvolution is performed with the Alternating Direction Method of Multipliers (ADMM). With a smoothed l 2 norm, the differentiability of the value of the Lagrangian at the saddle point can be shown and an approximate model function obtained. The choice of the optimal parameter can be refined with a Newton method. The efficiency of the method is demonstrated on a blurred and noisy bone CT cross section
Delta function excitation of waves in the earth's ionosphere

Science.gov (United States)

Vidmar, R. J.; Crawford, F. W.; Harker, K. J.

1983-01-01

Excitation of the earth's ionosphere by delta function current sheets is considered, and the temporal and spatial evolution of wave packets is analyzed for a two-component collisional F2 layer. Approximations of an inverse Fourier-Laplace transform via saddle point methods provide plots of typical wave packets. These illustrate cold plasma wave theory and may be used as a diagnostic tool since it is possible to relate specific features, e.g., the frequency of a modulation envelope, to plasma parameters such as the electron cyclotron frequency. It is also possible to deduce the propagation path length and orientation of a remote radio beacon.
A new approach to calculate charge carrier transport mobility in organic molecular crystals from imaginary time path integral simulations

International Nuclear Information System (INIS)

Song, Linze; Shi, Qiang

2015-01-01

We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated
Probing N=2 superconformal field theories with localization

Energy Technology Data Exchange (ETDEWEB)

Fiol, Bartomeu [Departament de Física Fonamental i Institut de Ciències del Cosmos,Universitat de Barcelona,Martí i Franquès 1, 08028 Barcelona, Catalonia (Spain); Garolera, Blai [Escuela de Física, Universidad de Costa Rica,11501-2060 San José (Costa Rica); Torrents, Genís [Departament de Física Fonamental i Institut de Ciències del Cosmos,Universitat de Barcelona,Martí i Franquès 1, 08028 Barcelona, Catalonia (Spain)

2016-01-27

We use supersymmetric localization to study probes of four dimensional Lagrangian N=2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a Wigner eigenvalue density precisely when they satisfy a necessary condition for having a holographic dual with a sensible higher-derivative expansion. We then compute in the saddle-point approximation the vacuum expectation value of 1/2-BPS circular Wilson loops, and the two-point functions of these Wilson loops with the Lagrangian density and with the stress-energy tensor. This last computation also provides the corresponding Bremsstrahlung functions and entanglement entropies. As expected, whenever a finite fraction of the matter is in the fundamental representation, the results are drastically different from those of N=4 supersymmetric Yang-Mills theory.
Multi-scaling in the critical phenomena in the quenched disordered systems

Science.gov (United States)

Wu, X. T.

2018-04-01

The Landau-Ginzburg-Wilson Hamiltonian with random temperature for the phase transition in disordered systems from the Griffiths phase to ordered phase is reexamined. From the saddle point solutions, especially the excited state solutions, it is shown that the system self-organizes into blocks coupled with their neighbors like superspins, which are emergent variables. Taking the fluctuation around these saddle point solutions into account, we get an effective Hamiltonian, including the emergent superspins of the blocks, the fluctuation around the saddle point solutions, and their couplings. Applying Stratonovich-Hubbard transformation to the part of superspins, we get a Landau-Ginzburg-Wilson Hamiltonian for the blocks. From the saddle point equations for the blocks, we can get the second generation blocks, of which sizes are much larger than the first generation blocks. Repeating this procedure again and again, we get many generations of blocks to describe the asymptotic behavior. If a field is applied, the effective field on the superspins is multiplied greatly and proportional to the block size. For a very small field, the effective field on the higher generation superspins can be so strong to cause the superspins polarized radically. This can explain the extra large critical isotherm exponent discovered in the experiments. The phase space of reduced temperature vs. field is divided into many layers , in which different generation blocks dominate the critical behavior. The sizes of the different generation emergent blocks are new relevant length scales. This can explain a lot of puzzles in the experiments and the Monte Carlo simulation.
Saddle-nose and bilateral cauliflower ear deformities with pyoderma gangrenosum-like ulcers, cavitary pulmonary lesions, digital gangrene and pulselessness in a young female.

Science.gov (United States)

Subhadarshani, Sweta; Gupta, Vishal; Chahal, Anurag; Verma, Kaushal K

2017-06-15

We report a young female who presented with saddle-nose and bilateral cauliflower ear deformities along with pyoderma gangrenosum-like ulcers, digital gangrene and pulselessness. Subsequently, she was found to have bilateral conductive hearing loss, a corneal opacity, mild aortic regurgitation and radiological evidence of cavitary changes in lungs and aortoarteritis. Our patient had a constellation of symptoms which posed a diagnostic challenge. Finally, a diagnosis of relapsing polychondritis with several unusual features was made. Overlap with Takayasu's arteritis and granulomatosis with polyangitis, which has been reported rarely in the literature, cannot be excluded. © BMJ Publishing Group Ltd (unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.
On the approximation of crack shapes found during inservice inspection

International Nuclear Information System (INIS)

Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S.

1997-01-01

This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component
On the approximation of crack shapes found during inservice inspection

Energy Technology Data Exchange (ETDEWEB)

Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S. [Bhabha Atomic Research Centre, Bombay (India)] [and others

1997-04-01

This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component.
Analysis of the stability and accuracy of the discrete least-squares approximation on multivariate polynomial spaces

KAUST Repository

Migliorati, Giovanni

2016-01-05

We review the main results achieved in the analysis of the stability and accuracy of the discrete leastsquares approximation on multivariate polynomial spaces, with noiseless evaluations at random points, noiseless evaluations at low-discrepancy point sets, and noisy evaluations at random points.
Evidence of pair correlations in actinide neutron-induced fission cross sections

International Nuclear Information System (INIS)

Maslov, V.M.

2000-01-01

It is shown that irregularities in fission cross sections in MeV incident neutron energy region could be attributed to the interplay of few-quasiparticle excitations in the level density of the fissioning and residual nuclei. It is suggested the intrinsic quasiparticle state density modelling approach both at stable and saddle-point deformations. The experimental manifestation of few-quasiparticle irregularities in the level density depends on the fission barrier structure and internal excitation energy at the saddle point, corresponding to the higher barrier hump. The explicit evidence is observed in case of fissile and non-fissile target nuclides [ru
A unified kinetic approach to binary nucleation

Energy Technology Data Exchange (ETDEWEB)

Kevrekidis, P.G. [Department of Physics, Rutgers University, 136 Frelinghuysen Road]|[E.O.H.S.I., Rutgers University]|[UMDNJ, 170 Frelinghuysen Road, Piscataway, New Jersey 08854-8019 (United States); Lazaridis, M. [Norwegian Institute for Air Research (NILU), Instittutvein 18, P. O. Box 100, N-2007 Kjeller (Norway); Drossinos, Y. [European Commission, Joint Research Centre, I-21020 Ispra (Vatican City State, Holy See) (Italy); Georgopoulos, P.G. [E.O.H.S.I., Rutgers University]|[UMDNJ, 170 Frelinghuysen Road, Piscataway, New Jersey 08854 (United States)

1999-11-01

Two different methods to calculate the steady-state nucleation rate in heteromolecular systems proposed by Stauffer (1976) and Langer (1969) are analyzed. Their mathematical equivalence is explicitly demonstrated, thereby obtaining a generic expression for the rate of binary nucleation. Its numerical evaluation does not entail rotation of the coordinate system at the saddle point, but it only requires data in the natural coordinate system of number fluctuations, namely molecular impingement rates, the droplet free energy and its second order derivatives at the saddle point, and the total density of condensible vapors. {copyright} {ital 1999 American Institute of Physics.}
Multi-phase induced inflation in theories with non-minimal coupling to gravity

Energy Technology Data Exchange (ETDEWEB)

Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Lalak, Zygmunt; Lewicki, Marek, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Zygmunt.Lalak@fuw.edu.pl, E-mail: Marek.Lewicki@fuw.edu.pl [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw ul. Hoża 69, 00-681 Warszawa (Poland)

2017-01-01

In this paper we investigate the induced inflation with two flat regions: one Starobinsky-like plateau in strong coupling regime and one shorter plateau around the saddle point of the Einstein frame potential. This multi-phase inflationary scenario can be used to solve problems of classical cosmology as well as the problem of initial conditions for inflation. The inflation at the saddle-point plateau is consistent with the data and can have arbitrarily low scale. The results can be useful in the context of the Higgs-Axion relaxation and in a certain limit they are equivalent to the α-attractors.

Big geo data surface approximation using radial basis functions: A comparative study

Science.gov (United States)

Majdisova, Zuzana; Skala, Vaclav

2017-12-01

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n-dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.
On the Approximate Controllability of Some Semilinear Parabolic Boundary-Value Problems

International Nuclear Information System (INIS)

Diaz, J. I.; Henry, J.; Ramos, A. M.

1998-01-01

We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem
S-AMP: Approximate Message Passing for General Matrix Ensembles

DEFF Research Database (Denmark)

Cakmak, Burak; Winther, Ole; Fleury, Bernard H.

2014-01-01

the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its......We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends...
Systematic approximation of multi-scale Feynman integrals arXiv

CERN Document Server

Borowka, Sophia; Hulme, Daniel

An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman integrals, allowing for fast numerical evaluation. The results are valid in all kinematical regions, both above and below thresholds, up to in principle arbitrary orders in the dimensional regulator. The scope of the algorithm is demonstrated by presenting results for selected two-loop three-point and four-point integrals with an internal mass scale that appear in the two-loop amplitudes for Higgs+jet production.
An alternative technique for the implementation of an analytical approximation for transients with temperature feedback

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [Instituto Federal do Rio de Janeiro, Nilopolis, RJ (Brazil)], e-mail: dpalmaster@gmail.com; Silva, Adilson C. da; Goncalves, Alessandro C.; Martinez, Aquilino S. [Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear], e-mail: asilva@con.ufrj.br, e-mail: agoncalves@con.ufrj.br, e-mail: aquilino@lmp.ufrj.br

2009-07-01

The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting neutron density variation during the operation of a nuclear reactor. Although different approximate solutions for the system of point kinetics equations with temperature feedback may be found in literature, some of them do not present an explicit dependence in time, which makes the computing implementation difficult and, as a result, its applicability in practical cases. The present paper uses the polynomial adjustment technique to overcome this problem in the analytical approximation as proposed by Nahla. In a systematic comparison with other existing approximations it is concluded that the method is adequate, presenting small deviations in relation to the reference values obtained from the reference numerical method. (author)
An alternative technique for the implementation of an analytical approximation for transients with temperature feedback

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Silva, Adilson C. da; Goncalves, Alessandro C.; Martinez, Aquilino S.

2009-01-01

The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting neutron density variation during the operation of a nuclear reactor. Although different approximate solutions for the system of point kinetics equations with temperature feedback may be found in literature, some of them do not present an explicit dependence in time, which makes the computing implementation difficult and, as a result, its applicability in practical cases. The present paper uses the polynomial adjustment technique to overcome this problem in the analytical approximation as proposed by Nahla. In a systematic comparison with other existing approximations it is concluded that the method is adequate, presenting small deviations in relation to the reference values obtained from the reference numerical method. (author)
Traveling-cluster approximation for uncorrelated amorphous systems

International Nuclear Information System (INIS)

Sen, A.K.; Mills, R.; Kaplan, T.; Gray, L.J.

1984-01-01

We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performed some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results
The Poisson equation in axisymmetric domains with conical points

International Nuclear Information System (INIS)

Nkemzi, B.

2003-01-01

This paper analyzes the application of the Fourier-finite-element method (FFEM) for the resolution of the Derichlet problem for the Poisson equation -Δu-circumflex = f-circumflex in axisymmetric domains Ω-circumflex subset of R 3 with conical points on the rotation axis. The FFEM combines the approximate Fourier method with respect to one space direction with the finite element method for the approximate calculation of the Fourier coefficients of the solution. Here, the influence of the conical points on the regularity of the Fourier coefficients of the solution is analyzed and the asymptotic behaviour of the coefficients near the conical points is described by some singularity functions and treated numerically by mesh grading in the two-dimensional meridian of Ω-circumflex. It is proved that for f-circumflex in L 2 (Ω-circumflex), the rate of convergence of the combined approximations in the Sobolev space W 2 1 (Ω-circumflex) is of the order O(h + N -1 ), where h and N represent, respectively, the parameters of the finite-element- and the Fourier-approximation, with h → 0 and n → ∞. (author)
Comment on "Current fluctuations in non-equilibrium diffusive systems: an additivity principle"

OpenAIRE

Sukhorukov, Eugene V.; Jordan, Andrew N.

2004-01-01

We point out that the "additivity principle" and "scaling hypothesis" postulated by Bodineau and Derrida in Phys. Rev. Lett 92, 180601 (2004), follow naturally from the saddle point evaluation of a diffusive field theory.
On an elastic dissipation model as continuous approximation for discrete media

Directory of Open Access Journals (Sweden)

I. V. Andrianov

2006-01-01

Full Text Available Construction of an accurate continuous model for discrete media is an important topic in various fields of science. We deal with a 1D differential-difference equation governing the behavior of an n-mass oscillator with linear relaxation. It is known that a string-type approximation is justified for low part of frequency spectra of a continuous model, but for free and forced vibrations a solution of discrete and continuous models can be quite different. A difference operator makes analysis difficult due to its nonlocal form. Approximate equations can be obtained by replacing the difference operators via a local derivative operator. Although application of a model with derivative of more than second order improves the continuous model, a higher order of approximated differential equation seriously complicates a solution of continuous problem. It is known that accuracy of the approximation can dramatically increase using Padé approximations. In this paper, one- and two-point Padé approximations suitable for justify choice of structural damping models are used.
Geology and geologic history of the Moscow-Pullman basin, Idaho and Washington, from late Grande Ronde to late Saddle Mountains time

Science.gov (United States)

Bush, John H; Garwood, Dean L; Dunlap, Pamela

2016-01-01

The Moscow-Pullman basin, located on the eastern margin of the Columbia River flood basalt province, consists of a subsurface mosaic of interlayered Miocene sediments and lava flows of the Imnaha, Grande Ronde, Wanapum, and Saddle Mountains Basalts of the Columbia River Basalt Group. This sequence is ~1800 ft (550 m) thick in the east around Moscow, Idaho, and exceeds 2300 ft (700 m) in the west at Pullman, Washington. Most flows entered from the west into a topographic low, partially surrounded by steep mountainous terrain. These flows caused a rapid rise in base level and deposition of immature sediments. This field guide focuses on the upper Grande Ronde Basalt, Wanapum Basalt, and sediments of the Latah Formation.Late Grande Ronde flows terminated midway into the basin to begin the formation of a topographic high that now separates a thick sediment wedge of the Vantage Member to the east of the high from a thin layer to the west. Disrupted by lava flows, streams were pushed from a west-flowing direction to a north-northwest orientation and drained the basin through a gap between steptoes toward Palouse, Washington. Emplacement of the Roza flow of the Wanapum Basalt against the western side of the topographic high was instrumental in this process, plugging west-flowing drainages and increasing deposition of Vantage sediments east of the high. The overlying basalt of Lolo covered both the Roza flow and Vantage sediments, blocking all drainages, and was in turn covered by sediments interlayered with local Saddle Mountains Basalt flows. Reestablishment of west-flowing drainages has been slow.The uppermost Grande Ronde, the Vantage, and the Wanapum contain what is known as the upper aquifer. The water supply is controlled, in part, by thickness, composition, and distribution of the Vantage sediments. A buried channel of the Vantage likely connects the upper aquifer to Palouse, Washington, outside the basin. This field guide locates outcrops; relates them to
An approximation method for nonlinear integral equations of Hammerstein type

International Nuclear Information System (INIS)

Chidume, C.E.; Moore, C.

1989-05-01

The solution of a nonlinear integral equation of Hammerstein type in Hilbert spaces is approximated by means of a fixed point iteration method. Explicit error estimates are given and, in some cases, convergence is shown to be at least as fast as a geometric progression. (author). 25 refs
The Wigner transform and the semi-classical approximations

International Nuclear Information System (INIS)

Shlomo, S.

1985-01-01

The Wigner transform provides a reformulation of quantum mechanics in terms of classical concepts. Some properties of the Wigner transform of the density matrix which justify its interpretation as the quantum-mechanical analog of the classical phase-space distribution function are presented. Considering some applications, it is demonstrated that the Wigner distribution function serves as a good starting point for semi-classical approximations to properties of the (nuclear) many-body system
Tracking coherent structures in massively-separated and turbulent flows

Science.gov (United States)

Rockwood, Matthew; Huang, Yangzi; Green, Melissa

2018-01-01

Coherent vortex structures are tracked in simulations of massively-separated and turbulent flows. Topological Lagrangian saddle points are found using intersections of the positive and negative finite-time Lyapunov exponent ridges, and these points are then followed in order to track individual coherent structure motion both in a complex interacting three-dimensional flow (turbulent channel) and during vortex formation (two-dimensional bluff body shedding). For a simulation of wall-bounded turbulence in a channel flow, tracking Lagrangian saddles shows that the average structure convection speed exhibits a similar trend as a previously published result based on velocity and pressure correlations, giving validity to the method. When this tracking method is applied in a study of a circular cylinder in cross-flow it shows that Lagrangian saddles rapidly accelerate away from the cylinder surface as the vortex sheds. This saddle behavior is compared with the time-resolved static pressure distribution on the circular cylinder, yielding locations on a cylinder surface where common sensors could detect this phenomenon, which is not available from force measurements or vortex circulation calculations. The current method of tracking coherent structures yields insight into the behavior of the coherent structures in both of the diverse flows presented, highlighting the breadth of its potential application.
Angular distributions of evaporated particles, fission and intermediate-mass fragments: on the search for consistent models

International Nuclear Information System (INIS)

Alexander, J.M.

1987-01-01

During the last two years there has been a true cacophony concerning the meaning of experimental angular distributions for fission and fission-like fragments. The heavily used, saddle-point, transition-state model has been shown to be of limited value for high-spin systems, and a wide variety of proposals has appeared often with mutual inconsistencies and conflicting views. Even though equilibrium statistical models for fragment emission and particle evaporation must have a very close kinship, this relationship, often left as murky, has now come onto center stage for understanding reactions at ≥ 100 MeV. Basic questions concern the nature of the decision-point configurations, their degrees of freedom, the role of deformation and the relevant moments of inertia. This paper points out serious inconsistencies in several recent scission-point models and discusses conditions for applicability of saddle-point and scission-point approaches
Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states.

Science.gov (United States)

Vlasov, Sergei; Bessarab, Pavel F; Uzdin, Valery M; Jónsson, Hannes

2016-12-22

Transitions between states of a magnetic system can occur by jumps over an energy barrier or by quantum mechanical tunneling through the energy barrier. The rate of such transitions is an important consideration when the stability of magnetic states is assessed for example for nanoscale candidates for data storage devices. The shift in transition mechanism from jumps to tunneling as the temperature is lowered is analyzed and a general expression derived for the crossover temperature. The jump rate is evaluated using a harmonic approximation to transition state theory. First, the minimum energy path for the transition is found with the geodesic nudged elastic band method. The activation energy for the jumps is obtained from the maximum along the path, a saddle point on the energy surface, and the eigenvalues of the Hessian matrix at that point as well as at the initial state minimum used to estimate the entropic pre-exponential factor. The crossover temperature for quantum mechanical tunneling is evaluated from the second derivatives of the energy with respect to orientation of the spin vector at the saddle point. The resulting expression is applied to test problems where analytical results have previously been derived, namely uniaxial and biaxial spin systems with two-fold anisotropy. The effect of adding four-fold anisotropy on the crossover temperature is demonstrated. Calculations of the jump rate and crossover temperature for tunneling are also made for a molecular magnet containing an Mn 4 group. The results are in excellent agreement with previously reported experimental measurements on this system.
Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis

CERN Document Server

Layton, William J

2012-01-01

This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting Approximate Deconvolution Models or ADMs have some advantages over more commonly used turbulence models – as well as some disadvantages. Our goal in this book is to provide a clear and complete mathematical development of ADMs, while pointing out the difficulties that remain. In order to do so, we present the analytical theory of ADMs, along with its connections, motivations and complements in the phenomenology of and algorithms for ADMs.
Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation.

Science.gov (United States)

Madain, Alia; Abu Dalhoum, Abdel Latif; Sleit, Azzam

2018-06-01

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic-hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H-H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H's at even positions and the other side ignores H's at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H-H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation

OpenAIRE

Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia

2005-01-01

We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-depend...
Relationship between relative humidity and the dew point ...

African Journals Online (AJOL)

This research was aimed at determining the relationship between relative humidity and the dew point temperature in Benin City, Edo State, Nigeria. The dew point temperature was approximated from the measured air temperature and relative humidity with the aid of a currently self-designed weather monitoring system.

Characterization of the best polynomial approximation with a sign-sensitive weight to a continuous function

International Nuclear Information System (INIS)

Ramazanov, A.-R K

2005-01-01

Necessary and sufficient conditions for the best polynomial approximation with an arbitrary and, generally speaking, unbounded sign-sensitive weight to a continuous function are obtained; the components of the weight can also take infinite values, therefore the conditions obtained cover, in particular, approximation with interpolation at fixed points and one-sided approximation; in the case of the weight with components equal to 1 one arrives at Chebyshev's classical alternation theorem.
Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network

Energy Technology Data Exchange (ETDEWEB)

Keplinger, Keegan, E-mail: keegankeplinger@gmail.com; Wackerbauer, Renate, E-mail: rawackerbauer@alaska.edu [Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920 (United States)

2014-03-15

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.
Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network.

Science.gov (United States)

Keplinger, Keegan; Wackerbauer, Renate

2014-03-01

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.
Approximate critical surface of the bond-mixed square-lattice Ising model

International Nuclear Information System (INIS)

Levy, S.V.F.; Tsallis, C.; Curado, E.M.F.

1979-09-01

The critical surface of the quenched bond-mixed square-lattice spin-1/2 first-neighbour-interaction ferromagnetic Ising model (with exchange interactions J 1 and J 2 ) has been investigated. Through renormalization group and heuristical procedures, a very accurate (error inferior to 3x10 -4 in the variables t sub(i) = th (J sub(i)/k sub(b)T)) approximate numerical proposal for all points of this surface is presented. This proposal simultaneously satisfies all the available exact results concerning the surface, namely P sub(c) = 1/2, t sub(c) = √2 - 1, both limiting slopes in these points, and t 2 = (1-t 1 )/(1+t 1 ) for p = 1/2. Furthemore an analytic approximation (namely (1 - p) 1n(1 + t 1 ) + p 1n(1 + t 2 ) =(1/2)1n 2) is also proposed. In what concerns the available exact results, it only fails in reproducing one of the two limiting slopes, where there is an error of 1% in the derivative: these facts result in an estimated error less than 10 -3 (in the t-variables) for any points in the surface. (Author) [pt
Quasi-particle excitations in low energy fission

International Nuclear Information System (INIS)

Ashgar, M.; Djebara, M.; Bocquet, J.P.; Brissot, R.; Maurel, M.; Nifenecker, H.; Ristori, C.

1985-05-01

Proton odd-even effect for 229 Th(nsub(th),f) and 232 U(nsub(th),f) has been determined with a ΔE-Esub(R) gas telescope. These data indicate that the qp-particle excitation probability at the saddle point is small and most of its results, when the nucleus moves from saddle to scission and the neck ruptures into final fragments. These results are discussed in terms of the different ideas and models
A nine-dimensional ab initio global potential energy surface for the H2O+ + H2 → H3O+ + H reaction

Science.gov (United States)

Li, Anyang; Guo, Hua

2014-06-01

An accurate full-dimensional global potential energy surface (PES) is developed for the title reaction. While the long-range interactions in the reactant asymptote are represented by an analytical expression, the interaction region of the PES is fit to more than 81 000 of ab initio points at the UCCSD(T)-F12b/AVTZ level using the permutation invariant polynomial neural network approach. Fully symmetric with respect to permutation of all four hydrogen atoms, the PES provides a faithful representation of the ab initio points, with a root mean square error of 1.8 meV or 15 cm-1. The reaction path for this exoergic reaction features an attractive and barrierless entrance channel, a submerged saddle point, a shallow H4O+ well, and a barrierless exit channel. The rate coefficients for the title reaction and kinetic isotope effect have been determined on this PES using quasi-classical trajectories, and they are in good agreement with available experimental data. It is further shown that the H2O+ rotational enhancement of reactivity observed experimentally can be traced to the submerged saddle point. Using our recently proposed Sudden Vector Projection model, we demonstrate that a rotational degree of freedom of the H2O+ reactant is strongly coupled with the reaction coordinate at this saddle point, thus unraveling the origin of the pronounced mode specificity in this reaction.
A nine-dimensional ab initio global potential energy surface for the H2O+ + H2 → H3O+ + H reaction

International Nuclear Information System (INIS)

Li, Anyang; Guo, Hua

2014-01-01

An accurate full-dimensional global potential energy surface (PES) is developed for the title reaction. While the long-range interactions in the reactant asymptote are represented by an analytical expression, the interaction region of the PES is fit to more than 81 000 of ab initio points at the UCCSD(T)-F12b/AVTZ level using the permutation invariant polynomial neural network approach. Fully symmetric with respect to permutation of all four hydrogen atoms, the PES provides a faithful representation of the ab initio points, with a root mean square error of 1.8 meV or 15 cm −1 . The reaction path for this exoergic reaction features an attractive and barrierless entrance channel, a submerged saddle point, a shallow H 4 O + well, and a barrierless exit channel. The rate coefficients for the title reaction and kinetic isotope effect have been determined on this PES using quasi-classical trajectories, and they are in good agreement with available experimental data. It is further shown that the H 2 O + rotational enhancement of reactivity observed experimentally can be traced to the submerged saddle point. Using our recently proposed Sudden Vector Projection model, we demonstrate that a rotational degree of freedom of the H 2 O + reactant is strongly coupled with the reaction coordinate at this saddle point, thus unraveling the origin of the pronounced mode specificity in this reaction
The electrostatic interaction of two point charges in equilibrium plasmas within the Debye approximation

International Nuclear Information System (INIS)

Filippov, A V

2015-01-01

This paper is devoted to a careful study of two charge interaction in an equilibrium plasma within the Debye approximation. The effect of external boundary conditions for the electric field strength and potential on the electrostatic force is studied. The problem is solved by the method of potential decomposition into Legendre polynomials up to the fifth multipole term included. It is shown that the effect of attraction of identically charged macroparticles is explained by the influence of the external boundary. When the size of a calculation cell is increased the attraction effect disappears and the electrostatic force is well described by the screened Debye-Hückel potential. (paper)
Basin stability measure of different steady states in coupled oscillators

Science.gov (United States)

Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar

2017-04-01

In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.
APPROXIMATION OF VOLUME AND BRANCH SIZE DISTRIBUTION OF TREES FROM LASER SCANNER DATA

Directory of Open Access Journals (Sweden)

P. Raumonen

2012-09-01

Full Text Available This paper presents an approach for automatically approximating the above-ground volume and branch size distribution of trees from dense terrestrial laser scanner produced point clouds. The approach is based on the assumption that the point cloud is a sample of a surface in 3D space and the surface is locally like a cylinder. The point cloud is covered with small neighborhoods which conform to the surface. Then the neighborhoods are characterized geometrically and these characterizations are used to classify the points into trunk, branch, and other points. Finally, proper subsets are determined for cylinder ﬁtting using geometric characterizations of the subsets.
Calculating Resonance Positions and Widths Using the Siegert Approximation Method

Science.gov (United States)

Rapedius, Kevin

2011-01-01

Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…
Modified mean generation time parameter in the neutron point kinetics equations

Energy Technology Data Exchange (ETDEWEB)

Diniz, Rodrigo C.; Gonçalves, Alessandro C.; Rosa, Felipe S.S., E-mail: alessandro@nuclear.ufrj.br, E-mail: frosa@if.ufrj.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil)

2017-07-01

This paper proposes an approximation for the modified point kinetics equations proposed by NUNES et. al, 2015, through the adjustment of a kinetic parameter. This approximation consists of analyzing the terms of the modified point kinetics equations in order to identify the least important ones for the solution, resulting in a modification of the mean generation time parameter that incorporates all influences of the additional terms of the modified kinetics. This approximation is applied on the inverse kinetics, to compare the results with the inverse kinetics from the modified kinetics in order to validate the proposed model. (author)
Modified mean generation time parameter in the neutron point kinetics equations

International Nuclear Information System (INIS)

Diniz, Rodrigo C.; Gonçalves, Alessandro C.; Rosa, Felipe S.S.

2017-01-01

This paper proposes an approximation for the modified point kinetics equations proposed by NUNES et. al, 2015, through the adjustment of a kinetic parameter. This approximation consists of analyzing the terms of the modified point kinetics equations in order to identify the least important ones for the solution, resulting in a modification of the mean generation time parameter that incorporates all influences of the additional terms of the modified kinetics. This approximation is applied on the inverse kinetics, to compare the results with the inverse kinetics from the modified kinetics in order to validate the proposed model. (author)
Extreme Simplification and Rendering of Point Sets using Algebraic Multigrid

NARCIS (Netherlands)

Reniers, Dennie; Telea, Alexandru

2005-01-01

We present a novel approach for extreme simplification of point set models in the context of real-time rendering. Point sets are often rendered using simple point primitives, such as oriented discs. However efficient, simple primitives are less effective in approximating large surface areas. A large
Effects of the scattering anisotropy approximation in multigroup radiation shielding calculations

International Nuclear Information System (INIS)

Altiparmarkov, D.

1983-01-01

Expansion of the scattering cross-sections into Legendre series is the usual way of solving the neutron transport problem. Because of the large space gradients of the neutron flux, the effects of that approximations become especially remarkable in the radiation shielding calculations. In this paper, a method taking into account scattering anisotropy is presented. From the point of view of the accuracy and computing speed, the optimal approximation of the scattering anisotropy is established for the basic protective materials on the basis of simple problem calculations (author) [sr
Flow topology of rare back flow events and critical points in turbulent channels and toroidal pipes

Science.gov (United States)

Chin, C.; Vinuesa, R.; Örlü, R.; Cardesa, J. I.; Noorani, A.; Schlatter, P.; Chong, M. S.

2018-04-01

A study of the back flow events and critical points in the flow through a toroidal pipe at friction Reynolds number Re τ ≈ 650 is performed and compared with the results in a turbulent channel flow at Re τ ≈ 934. The statistics and topological properties of the back flow events are analysed and discussed. Conditionally-averaged flow fields in the vicinity of the back flow event are obtained, and the results for the torus show a similar streamwise wall-shear stress topology which varies considerably for the spanwise wall-shear stress when compared to the channel flow. The comparison between the toroidal pipe and channel flows also shows fewer back flow events and critical points in the torus. This cannot be solely attributed to differences in Reynolds number, but is a clear effect of the secondary flow present in the toroidal pipe. A possible mechanism is the effect of the secondary flow present in the torus, which convects momentum from the inner to the outer bend through the core of the pipe, and back from the outer to the inner bend through the pipe walls. In the region around the critical points, the skin-friction streamlines and vorticity lines exhibit similar flow characteristics with a node and saddle pair for both flows. These results indicate that back flow events and critical points are genuine features of wall-bounded turbulence, and are not artifacts of specific boundary or inflow conditions in simulations and/or measurement uncertainties in experiments.
The Zeldovich approximation and wide-angle redshift-space distortions

Science.gov (United States)

Castorina, Emanuele; White, Martin

2018-06-01

The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum . In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multi-frequency angular power spectrum. We compare different definitions of the line-of-sight direction and discuss how to translate between them. We show that wide angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide angle effects is to slightly shift the Baryon Acoustic Oscillation scale.
Parameters of the center of pressure displacement on the saddle during hippotherapy on different surfaces

Directory of Open Access Journals (Sweden)

Fabiana M. Flores

2015-06-01

Full Text Available Background: Hippotherapy uses horseback riding movements for therapeutic purposes. In addition to the horse's movement, the choice of equipment and types of floor are also useful in the intervention. The quantification of dynamic parameters that define the interaction of the surface of contact between horse and rider provides insight into how the type of floor surface variations act upon the subject's postural control. Objective: To test whether different types of surfaces promote changes in the amplitude (ACOP and velocity (VCOP of the center of pressure (COP displacement during the rider's contact with the saddle on the horse's back. Method: Twenty two healthy adult male subjects with experience in riding were evaluated. The penetration resistances of asphalt, sand and grass surfaces were measured. The COP data were collected on the three surfaces using a pressure measurement mat. Results: ACOP values were higher in sand, followed by grass and asphalt, with significant differences between sand and asphalt (anteroposterior, p=0.042; mediolateral, p=0.019. The ACOP and VCOP values were higher in the anteroposterior than in the mediolateral direction on all surfaces (ACOP, p=0.001; VCOP, p=0.006. The VCOP did not differ between the surfaces. Conclusion: Postural control, measured by the COP displacement, undergoes variations in its amplitude as a result of the type of floor surface. Therefore, these results reinforce the importance of the choice of floor surface when defining the strategy to be used during hippotherapy intervention.
Parameters of the center of pressure displacement on the saddle during hippotherapy on different surfaces.

Science.gov (United States)

Flores, Fabiana M; Dagnese, Frederico; Mota, Carlos B; Copetti, Fernando

2015-01-01

Hippotherapy uses horseback riding movements for therapeutic purposes. In addition to the horse's movement, the choice of equipment and types of floor are also useful in the intervention. The quantification of dynamic parameters that define the interaction of the surface of contact between horse and rider provides insight into how the type of floor surface variations act upon the subject's postural control. To test whether different types of surfaces promote changes in the amplitude (ACOP) and velocity (VCOP) of the center of pressure (COP) displacement during the rider's contact with the saddle on the horse's back. Twenty two healthy adult male subjects with experience in riding were evaluated. The penetration resistances of asphalt, sand and grass surfaces were measured. The COP data were collected on the three surfaces using a pressure measurement mat. ACOP values were higher in sand, followed by grass and asphalt, with significant differences between sand and asphalt (anteroposterior, p=0.042; mediolateral, p=0.019). The ACOP and VCOP values were higher in the anteroposterior than in the mediolateral direction on all surfaces (ACOP, p=0.001; VCOP, p=0.006). The VCOP did not differ between the surfaces. Postural control, measured by the COP displacement, undergoes variations in its amplitude as a result of the type of floor surface. Therefore, these results reinforce the importance of the choice of floor surface when defining the strategy to be used during hippotherapy intervention.
Fixed-point image orthorectification algorithms for reduced computational cost

Science.gov (United States)

French, Joseph Clinton

Imaging systems have been applied to many new applications in recent years. With the advent of low-cost, low-power focal planes and more powerful, lower cost computers, remote sensing applications have become more wide spread. Many of these applications require some form of geolocation, especially when relative distances are desired. However, when greater global positional accuracy is needed, orthorectification becomes necessary. Orthorectification is the process of projecting an image onto a Digital Elevation Map (DEM), which removes terrain distortions and corrects the perspective distortion by changing the viewing angle to be perpendicular to the projection plane. Orthorectification is used in disaster tracking, landscape management, wildlife monitoring and many other applications. However, orthorectification is a computationally expensive process due to floating point operations and divisions in the algorithm. To reduce the computational cost of on-board processing, two novel algorithm modifications are proposed. One modification is projection utilizing fixed-point arithmetic. Fixed point arithmetic removes the floating point operations and reduces the processing time by operating only on integers. The second modification is replacement of the division inherent in projection with a multiplication of the inverse. The inverse must operate iteratively. Therefore, the inverse is replaced with a linear approximation. As a result of these modifications, the processing time of projection is reduced by a factor of 1.3x with an average pixel position error of 0.2% of a pixel size for 128-bit integer processing and over 4x with an average pixel position error of less than 13% of a pixel size for a 64-bit integer processing. A secondary inverse function approximation is also developed that replaces the linear approximation with a quadratic. The quadratic approximation produces a more accurate approximation of the inverse, allowing for an integer multiplication calculation

Comparison of Clenshaw–Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

KAUST Repository

Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2015-01-01

In this work we compare different families of nested quadrature points, i.e. the classic Clenshaw–Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence
Self-similar factor approximants

International Nuclear Information System (INIS)

Gluzman, S.; Yukalov, V.I.; Sornette, D.

2003-01-01

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties
Obtaining Approximate Values of Exterior Orientation Elements of Multi-Intersection Images Using Particle Swarm Optimization

Science.gov (United States)

Li, X.; Li, S. W.

2012-07-01

In this paper, an efficient global optimization algorithm in the field of artificial intelligence, named Particle Swarm Optimization (PSO), is introduced into close range photogrammetric data processing. PSO can be applied to obtain the approximate values of exterior orientation elements under the condition that multi-intersection photography and a small portable plane control frame are used. PSO, put forward by an American social psychologist J. Kennedy and an electrical engineer R.C. Eberhart, is a stochastic global optimization method based on swarm intelligence, which was inspired by social behavior of bird flocking or fish schooling. The strategy of obtaining the approximate values of exterior orientation elements using PSO is as follows: in terms of image coordinate observed values and space coordinates of few control points, the equations of calculating the image coordinate residual errors can be given. The sum of absolute value of each image coordinate is minimized to be the objective function. The difference between image coordinate observed value and the image coordinate computed through collinear condition equation is defined as the image coordinate residual error. Firstly a gross area of exterior orientation elements is given, and then the adjustment of other parameters is made to get the particles fly in the gross area. After iterative computation for certain times, the satisfied approximate values of exterior orientation elements are obtained. By doing so, the procedures like positioning and measuring space control points in close range photogrammetry can be avoided. Obviously, this method can improve the surveying efficiency greatly and at the same time can decrease the surveying cost. And during such a process, only one small portable control frame with a couple of control points is employed, and there are no strict requirements for the space distribution of control points. In order to verify the effectiveness of this algorithm, two experiments are
OBTAINING APPROXIMATE VALUES OF EXTERIOR ORIENTATION ELEMENTS OF MULTI-INTERSECTION IMAGES USING PARTICLE SWARM OPTIMIZATION

Directory of Open Access Journals (Sweden)

X. Li

2012-07-01

Full Text Available In this paper, an efficient global optimization algorithm in the field of artificial intelligence, named Particle Swarm Optimization (PSO, is introduced into close range photogrammetric data processing. PSO can be applied to obtain the approximate values of exterior orientation elements under the condition that multi-intersection photography and a small portable plane control frame are used. PSO, put forward by an American social psychologist J. Kennedy and an electrical engineer R.C. Eberhart, is a stochastic global optimization method based on swarm intelligence, which was inspired by social behavior of bird flocking or fish schooling. The strategy of obtaining the approximate values of exterior orientation elements using PSO is as follows: in terms of image coordinate observed values and space coordinates of few control points, the equations of calculating the image coordinate residual errors can be given. The sum of absolute value of each image coordinate is minimized to be the objective function. The difference between image coordinate observed value and the image coordinate computed through collinear condition equation is defined as the image coordinate residual error. Firstly a gross area of exterior orientation elements is given, and then the adjustment of other parameters is made to get the particles fly in the gross area. After iterative computation for certain times, the satisfied approximate values of exterior orientation elements are obtained. By doing so, the procedures like positioning and measuring space control points in close range photogrammetry can be avoided. Obviously, this method can improve the surveying efficiency greatly and at the same time can decrease the surveying cost. And during such a process, only one small portable control frame with a couple of control points is employed, and there are no strict requirements for the space distribution of control points. In order to verify the effectiveness of this algorithm
Modulated Pade approximant

International Nuclear Information System (INIS)

Ginsburg, C.A.

1980-01-01

In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)
Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

Science.gov (United States)

Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

2018-06-01

An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.
A naturally large four-point function in single field inflation

International Nuclear Information System (INIS)

Senatore, Leonardo; Zaldarriaga, Matias

2011-01-01

Non-Gaussianities of the primordial density perturbations have emerged as a very powerful possible signal to test the dynamics that drove the period of inflation. While in general the most sensitive observable is the three-point function in this paper we show that there are technically natural inflationary models where the leading source of non-Gaussianity is the four-point function. Using the recently developed Effective Field Theory of Inflation, we are able to show that it is possible to impose an approximate parity symmetry and an approximate continuos shift symmetry on the inflaton fluctuations that allow, when the dispersion relation if of the form ω ∼ c s k, for a unique quartic operator, while approximately forbidding all the cubic ones. The resulting shape for the four-point function is unique. In the models where the dispersion relation is of the form ω ∼ k 2 /M a similar construction can be carried out and additional shapes are possible
Conjugation of cascades

International Nuclear Information System (INIS)

San Martin, Jesus; Rodriguez-Perez, Daniel

2009-01-01

Presented in this work are some results relative to sequences found in the logistic equation bifurcation diagram, which is the unimodal quadratic map prototype. All of the different saddle-node bifurcation cascades, associated with every last appearance p-periodic orbit (p=3,4,5,...), can also be generated from the very Feigenbaum cascade. In this way it is evidenced the relationship between both cascades. The orbits of every saddle-node bifurcation cascade, mentioned above, are located in different chaotic bands, and this determines a sequence of orbits converging to every band-merging Misiurewicz point. In turn, these accumulation points form a sequence whose accumulation point is the Myrberg-Feigenbaum point. It is also proven that the first appearance orbits in the n-chaotic band converge to the same point as the last appearance orbits of the (n + 1)-chaotic band. The symbolic sequences of band-merging Misiurewicz points are computed for any window.
A harmonic expansion for the magnetic field of the helical solenoid

International Nuclear Information System (INIS)

Dewar, R.L.; Gardner, H.J.

1987-03-01

We discuss the boundary value problem for calculating the scalar magnetic potentials inside and outside of a helically symmetric solenoid. Under some circumstances the potentials can be expanded in infinite series of cylindrical harmonics. For a circular cross-section solenoid, we derive a Green's function integral representation of the series coefficients and calculate the radii of convergence of the series by a saddle point method. In some cases the cylinders of convergence can intersect the coil, so that there are physically accessible regions where the series fail to converge. Numerical evidence is presented to show that, even in some of these cases, the potentials can be accurately approximated by finite sums of cylindrical harmonics using boundary collocation
Designing quantum information processing via structural physical approximation.

Science.gov (United States)

Bae, Joonwoo

2017-10-01

In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.
Semi-classical approximation to path integrals - phases and catastrophes

International Nuclear Information System (INIS)

Levit, S.

1977-01-01

Problems of phases and catastrophes were encountered when trying to apply the classical S-matrix theory to the scattering phenomena in nuclear physics. The path integral formulation provided a suitable basis for the treatment of these and related problems. Within conventional mathematical language it was possible to give practical prescriptions and discuss their limitations. Since the semi-classical (stationary phase) approximation is commonly used in any application of the path integral method, the results are not restricted to the scattering problems and may be of general interest. The derivation of the uniform approximations in the energy representation should use the exact path integral expression as the starting point, rather than performing Fourier transforms on the expressions derived in the present lecture. (B.G.)
First-principles study of point defects in CePO{sub 4} monazite

Energy Technology Data Exchange (ETDEWEB)

Yi, Yong; Zhao, Xiaofeng [State Key Laboratory Cultivation Base for Nonmetal Composites and Functional Materials, Southwest University of Science and Technology, Mianyang 621010 (China); Teng, Yuancheng, E-mail: tyc239@163.com [State Key Laboratory Cultivation Base for Nonmetal Composites and Functional Materials, Southwest University of Science and Technology, Mianyang 621010 (China); Bi, Beng [Joint Laboratory for Extreme Conditions Matter Properties, Southwest University of Science and Technology, Mianyang 621010 (China); Wang, Lili [Institute of Computer Application, China Academy of Engineering Physics, Mianyang 621900 (China); Wu, Lang; Zhang, Kuibao [State Key Laboratory Cultivation Base for Nonmetal Composites and Functional Materials, Southwest University of Science and Technology, Mianyang 621010 (China)

2016-12-15

CePO{sub 4} monazite is an important radiation-resistant material that may act as a potential minor actinides waste form. Here, we present the results of the calculations for the basic radiation defect modellings in CePO{sub 4} crystals, along with the examination of their defect formation energies and effect of the defect concentrations. This study focused on building a fully-relaxed CePO{sub 4} model with the step iterative optimization from the DFT-GGA calculations using the VASP and CASTEP databases. The results show that the Frenkel defect configuration resulting from the center interstitials has a lower energy when compared to two adjacent orthophosphate centers (the saddle point position). High formation energies were found for all the types of intrinsic Frenkel and vacancy defects. The formation energies conform to the following trend (given in the decreasing order of energy): Ce Frenkel (12.41 eV) > O Frenkel (11.02 eV) > Ce vacancy (9.09 eV) > O vacancy (6.69 eV). We observed almost no effect from the defect concentrations on the defect formation energies.
About Applications of the Fixed Point Theory

Directory of Open Access Journals (Sweden)

Bucur Amelia

2017-06-01

Full Text Available The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.
Implementation of Steiner point of fuzzy set.

Science.gov (United States)

Liang, Jiuzhen; Wang, Dejiang

2014-01-01

This paper deals with the implementation of Steiner point of fuzzy set. Some definitions and properties of Steiner point are investigated and extended to fuzzy set. This paper focuses on establishing efficient methods to compute Steiner point of fuzzy set. Two strategies of computing Steiner point of fuzzy set are proposed. One is called linear combination of Steiner points computed by a series of crisp α-cut sets of the fuzzy set. The other is an approximate method, which is trying to find the optimal α-cut set approaching the fuzzy set. Stability analysis of Steiner point of fuzzy set is also studied. Some experiments on image processing are given, in which the two methods are applied for implementing Steiner point of fuzzy image, and both strategies show their own advantages in computing Steiner point of fuzzy set.
Induced fission of nuclei: dynamical chaos and lifetime of compound nucleus

Energy Technology Data Exchange (ETDEWEB)

Krivoshej, I V

1987-01-01

A semi-phenomenological theory is proposed to describe the induced fission of heavy nuclei at low and intermediate excitation energies. The theory is based on the concept of the dynamical chaos, arising because of a negative curvature of the n-dimensional potential energy surface (PES). The nuclear fission is treated as a diffusion of the representing point across a vicinity of the saddle point in PES. The diffusion coefficient is calculated for various metrics in PES as an explicit function of the two-dimensional curvatures at the saddle point of PES. The present theory suggests an estimate for the fission time, tau/sub f/approx.10/sup -14/ s. Coefficients of nuclear friction and viscosity are also calculated in general, and the resulting numerical estimates are in agreement with the experimental data.
Approximate thermodynamic state relations in partially ionized gas mixtures

International Nuclear Information System (INIS)

Ramshaw, John D.

2004-01-01

Thermodynamic state relations for mixtures of partially ionized nonideal gases are often approximated by artificially partitioning the mixture into compartments or subvolumes occupied by the pure partially ionized constituent gases, and requiring these subvolumes to be in temperature and pressure equilibrium. This intuitively reasonable procedure is easily shown to reproduce the correct thermal and caloric state equations for a mixture of neutral (nonionized) ideal gases. The purpose of this paper is to point out that (a) this procedure leads to incorrect state equations for a mixture of partially ionized ideal gases, whereas (b) the alternative procedure of requiring that the subvolumes all have the same temperature and free electron density reproduces the correct thermal and caloric state equations for such a mixture. These results readily generalize to the case of partially degenerate and/or relativistic electrons, to a common approximation used to represent pressure ionization effects, and to two-temperature plasmas. This suggests that equating the subvolume electron number densities or chemical potentials instead of pressures is likely to provide a more accurate approximation in nonideal plasma mixtures
Classical dynamics and localization of resonances in the high-energy region of the hydrogen atom in crossed fields.

Science.gov (United States)

Schweiner, Frank; Main, Jörg; Cartarius, Holger; Wunner, Günter

2015-01-01

When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom, a saddle point (called the Stark saddle point) appears. For energies slightly above the saddle point energy, one can find classical orbits that are located in the vicinity of this point. We follow those so-called quasi-Penning orbits to high energies and field strengths, observing structural changes and uncovering their bifurcation behavior. By plotting the stability behavior of those orbits against energy and field strength, the appearance of a stability apex is reported. A cusp bifurcation, located in the vicinity of the apex, will be investigated in detail. In this cusp bifurcation, another orbit of similar shape is found. This orbit becomes completely stable in the observed region of positive energy, i.e., in a region of parameter space, where the Kepler-like orbits located around the nucleus are already unstable. By quantum mechanically exact calculations, we prove the existence of signatures in quantum spectra belonging to those orbits. Husimi distributions are used to compare quantum-Poincaré sections with the extension of the classical torus structure around the orbits. Since periodic orbit theory predicts that each classical periodic orbit contributes an oscillating term to photoabsorption spectra, we finally give an estimation for future experiments, which could verify the existence of the stable orbits.
The average number of critical rank-one approximations to a tensor

NARCIS (Netherlands)

Draisma, J.; Horobet, E.

2014-01-01

Motivated by the many potential applications of low-rank multi-way tensor approximations, we set out to count the rank-one tensors that are critical points of the distance function to a general tensor v. As this count depends on v, we average over v drawn from a Gaussian distribution, and find
Photogrammetric Processing of Planetary Linear Pushbroom Images Based on Approximate Orthophotos

Science.gov (United States)

Geng, X.; Xu, Q.; Xing, S.; Hou, Y. F.; Lan, C. Z.; Zhang, J. J.

2018-04-01

It is still a great challenging task to efficiently produce planetary mapping products from orbital remote sensing images. There are many disadvantages in photogrammetric processing of planetary stereo images, such as lacking ground control information and informative features. Among which, image matching is the most difficult job in planetary photogrammetry. This paper designs a photogrammetric processing framework for planetary remote sensing images based on approximate orthophotos. Both tie points extraction for bundle adjustment and dense image matching for generating digital terrain model (DTM) are performed on approximate orthophotos. Since most of planetary remote sensing images are acquired by linear scanner cameras, we mainly deal with linear pushbroom images. In order to improve the computational efficiency of orthophotos generation and coordinates transformation, a fast back-projection algorithm of linear pushbroom images is introduced. Moreover, an iteratively refined DTM and orthophotos scheme was adopted in the DTM generation process, which is helpful to reduce search space of image matching and improve matching accuracy of conjugate points. With the advantages of approximate orthophotos, the matching results of planetary remote sensing images can be greatly improved. We tested the proposed approach with Mars Express (MEX) High Resolution Stereo Camera (HRSC) and Lunar Reconnaissance Orbiter (LRO) Narrow Angle Camera (NAC) images. The preliminary experimental results demonstrate the feasibility of the proposed approach.
R Implementation of a Polyhedral Approximation to a 3D Set of Points Using the ?-Shape

Directory of Open Access Journals (Sweden)

Thomas Lafarge

2014-01-01

Full Text Available This work presents the implementation in R of the ?-shape of a finite set of points in the three-dimensional space R3. This geometric structure generalizes the convex hull and allows to recover the shape of non-convex and even non-connected sets in 3D, given a ran- dom sample of points taken into it. Besides the computation of the ?-shape, the R package alphashape3d provides users with tools to facilitate the three-dimensional graphical visu- alization of the estimated set as well as the computation of important characteristics such as the connected components or the volume, among others.

One-dimensional unstable eigenfunction and manifold computations in delay differential equations

International Nuclear Information System (INIS)

Green, Kirk; Krauskopf, Bernd; Engelborghs, Koen

2004-01-01

In this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation. This is used to obtain the necessary starting data for an established algorithm for computing one-dimensional (1D) unstable manifolds of an associated saddle fixed point of a suitable Poincare map. To illustrate our method, we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase-conjugate feedback
Approximated solutions to the Schroedinger equation

International Nuclear Information System (INIS)

Rico, J.F.; Fernandez-Alonso, J.I.

1977-01-01

The authors are currently working on a couple of the well-known deficiencies of the variation method and present here some of the results that have been obtained so far. The variation method does not give information a priori on the trial functions best suited for a particular problem nor does it give information a posteriori on the degree of precision attained. In order to clarify the origin of both difficulties, a geometric interpretation of the variation method is presented. This geometric interpretation is the starting point for the exact formal solution to the fundamental state and for the step-by-step approximations to the exact solution which are also given. Some comments on these results are included. (Auth.)
A nine-dimensional ab initio global potential energy surface for the H{sub 2}O{sup +} + H{sub 2} → H{sub 3}O{sup +} + H reaction

Energy Technology Data Exchange (ETDEWEB)

Li, Anyang; Guo, Hua, E-mail: hguo@unm.edu [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States)

2014-06-14

An accurate full-dimensional global potential energy surface (PES) is developed for the title reaction. While the long-range interactions in the reactant asymptote are represented by an analytical expression, the interaction region of the PES is fit to more than 81 000 of ab initio points at the UCCSD(T)-F12b/AVTZ level using the permutation invariant polynomial neural network approach. Fully symmetric with respect to permutation of all four hydrogen atoms, the PES provides a faithful representation of the ab initio points, with a root mean square error of 1.8 meV or 15 cm{sup −1}. The reaction path for this exoergic reaction features an attractive and barrierless entrance channel, a submerged saddle point, a shallow H{sub 4}O{sup +} well, and a barrierless exit channel. The rate coefficients for the title reaction and kinetic isotope effect have been determined on this PES using quasi-classical trajectories, and they are in good agreement with available experimental data. It is further shown that the H{sub 2}O{sup +} rotational enhancement of reactivity observed experimentally can be traced to the submerged saddle point. Using our recently proposed Sudden Vector Projection model, we demonstrate that a rotational degree of freedom of the H{sub 2}O{sup +} reactant is strongly coupled with the reaction coordinate at this saddle point, thus unraveling the origin of the pronounced mode specificity in this reaction.
Zero-Point Corrections for Isotropic Coupling Constants for Cyclohexadienyl Radical, C6H7 and C6H6Mu: Beyond the Bond Length Change Approximation

Directory of Open Access Journals (Sweden)

Bruce S. Hudson

2013-04-01

Full Text Available Zero-point vibrational level averaging for electron spin resonance (ESR and muon spin resonance (µSR hyperfine coupling constants (HFCCs are computed for H and Mu isotopomers of the cyclohexadienyl radical. A local mode approximation previously developed for computation of the effect of replacement of H by D on 13C-NMR chemical shifts is used. DFT methods are used to compute the change in energy and HFCCs when the geometry is changed from the equilibrium values for the stretch and both bend degrees of freedom. This variation is then averaged over the probability distribution for each degree of freedom. The method is tested using data for the methylene group of C6H7, cyclohexadienyl radical and its Mu analog. Good agreement is found for the difference between the HFCCs for Mu and H of CHMu and that for H of CHMu and CH2 of the parent radical methylene group. All three of these HFCCs are the same in the absence of the zero point average, a one-parameter fit of the static HFCC, a(0, can be computed. That value, 45.2 Gauss, is compared to the results of several fixed geometry electronic structure computations. The HFCC values for the ortho, meta and para H atoms are then discussed.
Constraints from conformal symmetry on the three point scalar correlator in inflation

International Nuclear Information System (INIS)

Kundu, Nilay; Shukla, Ashish; Trivedi, Sandip P.

2015-01-01

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.
Comparison of Clenshaw–Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

KAUST Repository

Nobile, Fabio

2015-11-26

In this work we compare different families of nested quadrature points, i.e. the classic Clenshaw–Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence suggests that both families perform comparably within such framework.
Origin of chaos near critical points of quantum flow.

Science.gov (United States)

Efthymiopoulos, C; Kalapotharakos, C; Contopoulos, G

2009-03-01

The general theory of motion in the vicinity of a moving quantum nodal point (vortex) is studied in the framework of the de Broglie-Bohm trajectory method of quantum mechanics. Using an adiabatic approximation, we find that near any nodal point of an arbitrary wave function psi there is an unstable point (called the X point) in a frame of reference moving with the nodal point. The local phase portrait forms always a characteristic pattern called the "nodal-point- X -point complex." We find general formulas for this complex as well as necessary and sufficient conditions of validity of the adiabatic approximation. We demonstrate that chaos emerges from the consecutive scattering events of the orbits with nodal-point- X -point complexes. The scattering events are of two types (called type I and type II). A theoretical model is constructed yielding the local value of the Lyapunov characteristic numbers in scattering events of both types. The local Lyapunov characteristic number scales as an inverse power of the speed of the nodal point in the rest frame, implying that it scales proportionally to the size of the nodal-point- X -point complex. It is also an inverse power of the distance of a trajectory from the X point's stable manifold far from the complex. This distance plays the role of an effective "impact parameter." The results of detailed numerical experiments with different wave functions, possessing one, two, or three moving nodal points, are reported. Examples are given of regular and chaotic trajectories, and the statistics of the Lyapunov characteristic numbers of the orbits are found and compared to the number of encounter events of each orbit with the nodal-point- X -point complexes. The numerical results are in agreement with the theory, and various phenomena appearing at first as counterintuitive find a straightforward explanation.
Accurate gradient approximation for complex interface problems in 3D by an improved coupling interface method

Energy Technology Data Exchange (ETDEWEB)

Shu, Yu-Chen, E-mail: ycshu@mail.ncku.edu.tw [Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan (China); Mathematics Division, National Center for Theoretical Sciences (South), Tainan 701, Taiwan (China); Chern, I-Liang, E-mail: chern@math.ntu.edu.tw [Department of Applied Mathematics, National Chiao Tung University, Hsin Chu 300, Taiwan (China); Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (China); Mathematics Division, National Center for Theoretical Sciences (Taipei Office), Taipei 106, Taiwan (China); Chang, Chien C., E-mail: mechang@iam.ntu.edu.tw [Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan (China); Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (China)

2014-10-15

Most elliptic interface solvers become complicated for complex interface problems at those “exceptional points” where there are not enough neighboring interior points for high order interpolation. Such complication increases especially in three dimensions. Usually, the solvers are thus reduced to low order accuracy. In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26]. Yet the idea is also applicable to other interface solvers. The main idea is to have at least first order approximations for second order derivatives at those exceptional points. Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible. Recipe 2 is to flip domain signatures and introduce a ghost state so that a second-order method can be applied. This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface. The original state is recovered by a post-processing using nearby states and jump conditions. The choice of recipes is determined by a classification scheme of the exceptional points. The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain. Numerical examples are provided to illustrate the second order accuracy of the presently proposed method in approximating the gradients of the original states for some complex interfaces which we had tested previous in two and three dimensions, and a real molecule ( (1D63)) which is double-helix shape and composed of hundreds of atoms.
The self-consistent effective medium approximation (SEMA): New tricks from an old dog

International Nuclear Information System (INIS)

Bergman, David J.

2007-01-01

The fact that the self-consistent effective medium approximation (SEMA) leads to incorrect values for the percolation threshold, as well as for the critical exponents which characterize that threshold, has led to a decline in using that approximation. In this article I argue that SEMA has the unique capability, which is lacking in other approximation schemes for macroscopic response of composite media, of leading to the discovery or prediction of new critical points. This is due to the fact that SEMA can often lead to explicit equations for the macroscopic response of a composite medium, even when that medium has a rather complicated character. In such cases, the SEMA equations are usually coupled and nonlinear, often even transcendental in character. Thus there is no question of finding exact solutions. Nevertheless, a useful ansatz, leading to a closed form asymptotic solution, can often be made. In this way, singularities in the macroscopic response can be identified from a theoretical or mathematical treatment of the physical problem. This is demonstrated for two problems of magneto-transport in a composite medium, where the SEMA equations are solved using asymptotic analysis, leading to new types of critical points and critical behavior
Approximate symmetries of Hamiltonians

Science.gov (United States)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Wolf Point Substation, Roosevelt County, Montana

International Nuclear Information System (INIS)

1991-05-01

The Western Area Power Administration (Western), an agency of the United States Department of Energy, is proposing to construct the 115-kV Wolf Point Substation near Wolf Point in Roosevelt County, Montana (Figure 1). As part of the construction project, Western's existing Wolf Point Substation would be taken out of service. The existing 115-kV Wolf Point Substation is located approximately 3 miles west of Wolf Point, Montana (Figure 2). The substation was constructed in 1949. The existing Wolf Point Substation serves as a ''Switching Station'' for the 115-kV transmission in the region. The need for substation improvements is based on operational and reliability issues. For this environmental assessment (EA), the environmental review of the proposed project took into account the removal of the old Wolf Point Substation, rerouting of the five Western lines and four lines from the Cooperatives and Montana-Dakota Utilities Company, and the new road into the proposed substation. Reference to the new proposed Wolf Point Substation in the EA includes these facilities as well as the old substation site. The environmental review looked at the impacts to all resource areas in the Wolf Point area. 7 refs., 6 figs
The Post-Newtonian Approximation for Relativistic Compact Binaries

Directory of Open Access Journals (Sweden)

Futamase Toshifumi

2007-03-01

Full Text Available We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.
Data-Driven Model Reduction and Transfer Operator Approximation

Science.gov (United States)

Klus, Stefan; Nüske, Feliks; Koltai, Péter; Wu, Hao; Kevrekidis, Ioannis; Schütte, Christof; Noé, Frank

2018-06-01

In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.
Geometric approximation algorithms

CERN Document Server

Har-Peled, Sariel

2011-01-01

Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Identification of discrete chaotic maps with singular points

Directory of Open Access Journals (Sweden)

P. G. Akishin

2001-01-01

Full Text Available We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.
Accuracy of the Approximation Function Deduced from the Fixed 3-Points Calibration Delivered with the Cernox™ Sensor

CERN Document Server

Balle, C; Fortescue-Beck, E; Vauthier, N

2013-01-01

The cernox™ sensor is delivered with a 3-point resistance versus temperature cal-ibration that permits the construction of an individual interpolation table by using the data in the CERN thermometer database. For instance at the 4.2 K point, the individual calibration and the manufacturer data are within +/-0.1 K for 99.39% of a sample population of about 5700 sensors. Preliminary results also indicate that accuracies of 0.1 K and 1 K can be obtained below respectively 5 K and 77 K.
Cosmological viability conditions for f(T) dark energy models

Energy Technology Data Exchange (ETDEWEB)

Setare, M.R.; Mohammadipour, N., E-mail: rezakord@ipm.ir, E-mail: N.Mohammadipour@uok.ac.ir [Department of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

2012-11-01

Recently f(T) modified teleparallel gravity where T is the torsion scalar has been proposed as the natural gravitational alternative for dark energy. We perform a detailed dynamical analysis of these models and find conditions for the cosmological viability of f(T) dark energy models as geometrical constraints on the derivatives of these models. We show that in the phase space exists two cosmologically viable trajectory which (i) The universe would start from an unstable radiation point, then pass a saddle standard matter point which is followed by accelerated expansion de sitter point. (ii) The universe starts from a saddle radiation epoch, then falls onto the stable matter era and the system can not evolve to the dark energy dominated epoch. Finally, for a number of f(T) dark energy models were proposed in the more literature, the viability conditions are investigated.
Bessel collocation approach for approximate solutions of Hantavirus infection model

Directory of Open Access Journals (Sweden)

Suayip Yuzbasi

2017-11-01

Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.
Approximating the Ising model on fractal lattices of dimension less than two

DEFF Research Database (Denmark)

Codello, Alessandro; Drach, Vincent; Hietanen, Ari

2015-01-01

We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of a zero external magnetic field, based on the combinatorial method of Feynman and Vdovichenko. We show that the procedure is applicable to any fractal obtained...... with, possibly, arbitrary accuracy and paves the way for determination Tc of any fractal of dimension less than two. Critical exponents are more diffcult to determine since the free energy of any periodic approximation still has a logarithmic singularity at the critical point implying α = 0. We also...
Sparse approximation with bases

CERN Document Server

2015-01-01

This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

The adiabatic versus the diabatic approximation in the decoupling of electron and nuclear motion

International Nuclear Information System (INIS)

Every, A.G.

1975-01-01

There are two limiting approximations that are used as starting points for the analysis of a system of interacting electrons and nuclei. The more widely used is the adiabatic approximation in which one assumes that the electrons adjust adiabatically to the instantaneous configuration of the nuclei. This yields an effective internuclear potential. In treating the nuclear motion, this potential can legitimately be expanded to fourth order in nuclear displacements from equilibrium. The difficulties of extending this expansion further are discussed. In situations where two adiabatic potentials approach each other the so-called diabatic approximation has to be used. A novel application to non-radioactive processes in solids is discussed. (author)
ASPHERICAL SURFACES APPROXIMATION IN AUTOMATED DESIGN OF OPTICAL SYSTEMS

Directory of Open Access Journals (Sweden)

T. V. Ivanova

2015-07-01

Full Text Available Subject of Research. The paper deals with the problems of higher order aspherical surfaces approximation using different equation types. The objects of research are two types of equations for higher order aspherical surfaces description used in different software for optical systems design (SАRО, OPAL, ZEMAX, CODE-V, etc. and dependent on z-coordinate or on a radial coordinate on the surface. Conversion from one type of equations to another is considered in view of application in different software for optical systems design. Methods. The subject matter of the method lies in usage of mean square method approximation for recalculation of high-order aspherical surface. Iterative algorithm for recalculation is presented giving the possibility to recalculate coefficients for different types of equations with required accuracy. Recommendations are given for choosing recalculation parameters such as the number of result equation coefficients, the number of points for recalculation and point allocation on a surface. Main Results. Example of recalculation for aspherical surface and accuracy estimation, including result aberration comparison between initial surface and recalculated surface are presented. The example has shown that required accuracy of surface representation was obtained. Practical Relevance. This technique is usable for recalculation of higher order aspherical surfaces in various types of software for optical systems design and also for research of optimal higher order aspherical surfaces description.
Maximum error-bounded Piecewise Linear Representation for online stream approximation

KAUST Repository

Xie, Qing; Pang, Chaoyi; Zhou, Xiaofang; Zhang, Xiangliang; Deng, Ke

2014-01-01

Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.
Maximum error-bounded Piecewise Linear Representation for online stream approximation

KAUST Repository

Xie, Qing

2014-04-04

Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.
Fitting Social Network Models Using Varying Truncation Stochastic Approximation MCMC Algorithm

KAUST Repository

Jin, Ick Hoon

2013-10-01

The exponential random graph model (ERGM) plays a major role in social network analysis. However, parameter estimation for the ERGM is a hard problem due to the intractability of its normalizing constant and the model degeneracy. The existing algorithms, such as Monte Carlo maximum likelihood estimation (MCMLE) and stochastic approximation, often fail for this problem in the presence of model degeneracy. In this article, we introduce the varying truncation stochastic approximation Markov chain Monte Carlo (SAMCMC) algorithm to tackle this problem. The varying truncation mechanism enables the algorithm to choose an appropriate starting point and an appropriate gain factor sequence, and thus to produce a reasonable parameter estimate for the ERGM even in the presence of model degeneracy. The numerical results indicate that the varying truncation SAMCMC algorithm can significantly outperform the MCMLE and stochastic approximation algorithms: for degenerate ERGMs, MCMLE and stochastic approximation often fail to produce any reasonable parameter estimates, while SAMCMC can do; for nondegenerate ERGMs, SAMCMC can work as well as or better than MCMLE and stochastic approximation. The data and source codes used for this article are available online as supplementary materials. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
Aspects of statistical model for multifragmentation

International Nuclear Information System (INIS)

Bhattacharyya, P.; Das Gupta, S.; Mekjian, A. Z.

1999-01-01

We deal with two different aspects of an exactly soluble statistical model of fragmentation. First we show, using zero range force and finite temperature Thomas-Fermi theory, that a common link can be found between finite temperature mean field theory and the statistical fragmentation model. We show the latter naturally arises in the spinodal region. Next we show that although the exact statistical model is a canonical model and uses temperature, microcanonical results which use constant energy rather than constant temperature can also be obtained from the canonical model using saddle-point approximation. The methodology is extremely simple to implement and at least in all the examples studied in this work is very accurate. (c) 1999 The American Physical Society
Indirect determination of the thermodynamic temperature of the copper point by a multi-fixed-point technique

Science.gov (United States)

Battuello, M.; Florio, M.; Girard, F.

2010-06-01

An indirect determination of the thermodynamic temperature of the fixed point of copper was made at INRIM by measuring four cells with a Si-based and an InGaAs-based precision radiation thermometer carrying approximated thermodynamic scales realized up to the Ag point. An average value TCu = 1357.840 K was found with a standard uncertainty of 0.047 K. A consequent (T - T90)Cu value of 70 mK can be derived which is 18 mK higher than, but consistent with, the presently available (T - T90)Cu as elaborated by the CCT-WG4.
Model-Free Adaptive Control for Unknown Nonlinear Zero-Sum Differential Game.

Science.gov (United States)

Zhong, Xiangnan; He, Haibo; Wang, Ding; Ni, Zhen

2018-05-01

In this paper, we present a new model-free globalized dual heuristic dynamic programming (GDHP) approach for the discrete-time nonlinear zero-sum game problems. First, the online learning algorithm is proposed based on the GDHP method to solve the Hamilton-Jacobi-Isaacs equation associated with optimal regulation control problem. By setting backward one step of the definition of performance index, the requirement of system dynamics, or an identifier is relaxed in the proposed method. Then, three neural networks are established to approximate the optimal saddle point feedback control law, the disturbance law, and the performance index, respectively. The explicit updating rules for these three neural networks are provided based on the data generated during the online learning along the system trajectories. The stability analysis in terms of the neural network approximation errors is discussed based on the Lyapunov approach. Finally, two simulation examples are provided to show the effectiveness of the proposed method.
Efficient algorithms for multiscale modeling in porous media

KAUST Repository

Wheeler, Mary F.; Wildey, Tim; Xue, Guangri

2010-01-01

We describe multiscale mortar mixed finite element discretizations for second-order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mortar basis and extend this concept to nonlinear interface operators. We present a multiscale preconditioning strategy to minimize the computational cost associated with construction of the multiscale mortar basis. We also discuss the use of appropriate quadrature rules and approximation spaces to reduce the saddle point system to a cell-centered pressure scheme. In particular, we focus on multiscale mortar multipoint flux approximation method for general hexahedral grids and full tensor permeabilities. Numerical results are presented to verify the accuracy and efficiency of these approaches. © 2010 John Wiley & Sons, Ltd.
Weak-noise limit of a piecewise-smooth stochastic differential equation.

Science.gov (United States)

Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram

2013-11-01

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.
Efficient algorithms for multiscale modeling in porous media

KAUST Repository

Wheeler, Mary F.

2010-09-26

We describe multiscale mortar mixed finite element discretizations for second-order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mortar basis and extend this concept to nonlinear interface operators. We present a multiscale preconditioning strategy to minimize the computational cost associated with construction of the multiscale mortar basis. We also discuss the use of appropriate quadrature rules and approximation spaces to reduce the saddle point system to a cell-centered pressure scheme. In particular, we focus on multiscale mortar multipoint flux approximation method for general hexahedral grids and full tensor permeabilities. Numerical results are presented to verify the accuracy and efficiency of these approaches. © 2010 John Wiley & Sons, Ltd.
Coherent combs in ionization by intense and short laser pulses

Energy Technology Data Exchange (ETDEWEB)

Krajewska, K., E-mail: Katarzyna.Krajewska@fuw.edu.pl [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa (Poland); Department of Physics and Astronomy, University of Nebraska, Lincoln, NE 68588-0299 (United States); Kamiński, J.Z., E-mail: Jerzy.Kaminski@fuw.edu.pl [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa (Poland)

2016-03-22

Photoionization of positive ions by a train of intense, short laser pulses is investigated within the relativistic strong field approximation, using the velocity gauge. The formation of broad peak structures in the high-energy domain of photoelectrons is observed and interpreted. The emergence of coherent photoelectron energy combs within these structures is demonstrated, and it is interpreted as the consequence of the Fraunhofer-type interference/diffraction of probability amplitudes of ionization from individual pulses comprising the train. Extensions to the coherent angular combs are also studied, and effects related to the radiation pressure are presented. - Highlights: • We develop relativistic Strong-Field Approximation for ionization by intense and short laser pulses of arbitrary spectral compositions. • We show that the consistent interpretation of results is provided by the Keldysh-type saddle point analysis of probability amplitudes. • We derive a general Fraunhofer-type interference/diffraction formula for finite train of pulses. • We study the coherent combs in photoelectron probability distributions.
Collective mass and zero-point energy in the generator-coordinate method

International Nuclear Information System (INIS)

Fiolhais, C.

1982-01-01

The aim of the present thesis if the study of the collective mass parameters and the zero-point energies in the GCM framework with special regards to the fission process. After the derivation of the collective Schroedinger equation in the framework of the Gaussian overlap approximation the inertia parameters are compared with those of the adiabatic time-dependent Hartree-Fock method. Then the kinetic and the potential zero-point energy occurring in this formulation are studied. Thereafter the practical application of the described formalism is discussed. Then a numerical calculation of the GCM mass parameter and the zero-point energy for the fission process on the base of a two-center shell model with a pairing force in the BCS approximation is presented. (HSI) [de
Boiling point measurement of a small amount of brake fluid by thermocouple and its application.

Science.gov (United States)

Mogami, Kazunari

2002-09-01

This study describes a new method for measuring the boiling point of a small amount of brake fluid using a thermocouple and a pear shaped flask. The boiling point of brake fluid was directly measured with an accuracy that was within approximately 3 C of that determined by the Japanese Industrial Standards method, even though the sample volume was only a few milliliters. The method was applied to measure the boiling points of brake fluid samples from automobiles. It was clear that the boiling points of brake fluid from some automobiles dropped to approximately 140 C from about 230 C, and that one of the samples from the wheel cylinder was approximately 45 C lower than brake fluid from the reserve tank. It is essential to take samples from the wheel cylinder, as this is most easily subjected to heating.
Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in non-smooth axisymmetric domains

International Nuclear Information System (INIS)

Nkemzi, B.

2005-10-01

Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains Ω-circumflex with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N (N → ∞), with the finite element approximation of the Fourier coefficients on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with mesh size h (h → 0). The singular behaviors of the Fourier coefficients near angular points of the domain Ω a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H 1 (Ω-circumflex) 3 is of the order O (h+N -1 ) as known for the classical Fourier-finite-element approximation of problems with regular solutions. (author)
Data analysis and approximate models model choice, location-scale, analysis of variance, nonparametric regression and image analysis

CERN Document Server

Davies, Patrick Laurie

2014-01-01

Introduction IntroductionApproximate Models Notation Two Modes of Statistical AnalysisTowards One Mode of Analysis Approximation, Randomness, Chaos, Determinism ApproximationA Concept of Approximation Approximation Approximating a Data Set by a Model Approximation Regions Functionals and EquivarianceRegularization and Optimality Metrics and DiscrepanciesStrong and Weak Topologies On Being (almost) Honest Simulations and Tables Degree of Approximation and p-values ScalesStability of Analysis The Choice of En(α, P) Independence Procedures, Approximation and VaguenessDiscrete Models The Empirical Density Metrics and Discrepancies The Total Variation Metric The Kullback-Leibler and Chi-Squared Discrepancies The Po(λ) ModelThe b(k, p) and nb(k, p) Models The Flying Bomb Data The Student Study Times Data OutliersOutliers, Data Analysis and Models Breakdown Points and Equivariance Identifying Outliers and Breakdown Outliers in Multivariate Data Outliers in Linear Regression Outliers in Structured Data The Location...
Approximation of High-Dimensional Rank One Tensors

KAUST Repository

Bachmayr, Markus

2013-11-12

Many real world problems are high-dimensional in that their solution is a function which depends on many variables or parameters. This presents a computational challenge since traditional numerical techniques are built on model classes for functions based solely on smoothness. It is known that the approximation of smoothness classes of functions suffers from the so-called \\'curse of dimensionality\\'. Avoiding this curse requires new model classes for real world functions that match applications. This has led to the introduction of notions such as sparsity, variable reduction, and reduced modeling. One theme that is particularly common is to assume a tensor structure for the target function. This paper investigates how well a rank one function f(x 1,...,x d)=f 1(x 1)⋯f d(x d), defined on Ω=[0,1]d can be captured through point queries. It is shown that such a rank one function with component functions f j in W∞ r([0,1]) can be captured (in L ∞) to accuracy O(C(d,r)N -r) from N well-chosen point evaluations. The constant C(d,r) scales like d dr. The queries in our algorithms have two ingredients, a set of points built on the results from discrepancy theory and a second adaptive set of queries dependent on the information drawn from the first set. Under the assumption that a point z∈Ω with nonvanishing f(z) is known, the accuracy improves to O(dN -r). © 2013 Springer Science+Business Media New York.
Approximation of High-Dimensional Rank One Tensors

KAUST Repository

Bachmayr, Markus; Dahmen, Wolfgang; DeVore, Ronald; Grasedyck, Lars

2013-01-01

Many real world problems are high-dimensional in that their solution is a function which depends on many variables or parameters. This presents a computational challenge since traditional numerical techniques are built on model classes for functions based solely on smoothness. It is known that the approximation of smoothness classes of functions suffers from the so-called 'curse of dimensionality'. Avoiding this curse requires new model classes for real world functions that match applications. This has led to the introduction of notions such as sparsity, variable reduction, and reduced modeling. One theme that is particularly common is to assume a tensor structure for the target function. This paper investigates how well a rank one function f(x 1,...,x d)=f 1(x 1)⋯f d(x d), defined on Ω=[0,1]d can be captured through point queries. It is shown that such a rank one function with component functions f j in W∞ r([0,1]) can be captured (in L ∞) to accuracy O(C(d,r)N -r) from N well-chosen point evaluations. The constant C(d,r) scales like d dr. The queries in our algorithms have two ingredients, a set of points built on the results from discrepancy theory and a second adaptive set of queries dependent on the information drawn from the first set. Under the assumption that a point z∈Ω with nonvanishing f(z) is known, the accuracy improves to O(dN -r). © 2013 Springer Science+Business Media New York.
Approximating distributions from moments

Science.gov (United States)

Pawula, R. F.

1987-11-01

A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.
A predicted directional bias of the mass asymmetry in 230Th(n,f)

International Nuclear Information System (INIS)

Lang, D.W.

1983-01-01

Heavy and light fragments in fission usually share a common angular distribution, associated with a defined parity for an isolated saddle-point state. In 230 Th(n,f) at 708 keV, the triple-humped fission barrier model suggests an overlap of two saddle-point states of opposite parity based on the same asymmetric configuration. The model then predicts fore-and-aft asymmetry for, say, the distribution of heavy fragments at a given neutron energy. For neutrons polarized perpendicular to the beam there is asymmetry in the third perpendicular direction. Experimental verification may depend critically on energy resolution. At lower energies the effect may be more general in fissionable nuclei and there is a possibility of detecting and identifying p-wave resonances at much lower energies. (Auth.)

Transport properties of clean and disordered superconductors in matrix field theory

International Nuclear Information System (INIS)

Zhou Lubo; Kirkpatrick, T.R.

2004-01-01

A comprehensive field theory is developed for superconductors with quenched disorder. We first show that the matrix field theory, used previously to describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also has a saddle-point solution that describes a disordered superconductor. A general gap equation is obtained. We then expand about the saddle point to Gaussian order to explicitly obtain the physical correlation functions. The ultrasonic attenuation, number density susceptibility, spin-density susceptibility, and the electrical conductivity are used as examples. Results in the clean limit and in the disordered case are discussed, respectively. This formalism is expected to be a powerful tool to study the quantum phase transitions between the normal-metal state and the superconductor state
Adaptive jump barrier height in Monte Carlo configuration kinetics.

Energy Technology Data Exchange (ETDEWEB)

Leitner, Martin; Pfeiler, Wolfgang; Pueschl, Wolfgang [Dynamics of Condensed Systems, Faculty of Physics, University of Vienna, Strudlhofgasse 4, A-1090 Wien (Austria); Vogtenhuber, Doris [Computational Materials Science, Faculty of Physics, University of Vienna, Sensengasse 8, A-1090 Wien (Austria)

2008-07-01

In usual MC simulations of configuration kinetics atom jump probabilities are calculated from energies of the initial and/or final bound states of the moving atom, leaving aside the exact energy of the intermediate saddle point state. This energy may however be critically influenced by the local atomic environment. We propose a strategy to explicitly take account of this influence. The basis is ab initio calculation of representative jump paths in the framework of the nudged elastic band method. From these results, an influence function is derived which modifies the energy of the saddle point and therefore the effective jump barrier height as calculated from the initial and final states according to a cluster expansion scheme. The overall effect is demonstrated on the NiAl system.
Ternary fission induced by polarized neutrons

Directory of Open Access Journals (Sweden)

Gönnenwein Friedrich

2013-12-01

Full Text Available Ternary fission of (e,e U- and Pu- isotopes induced by cold polarized neutrons discloses some new facets of the process. In the so-called ROT effect shifts in the angular distributions of ternary particles relative to the fission fragments show up. In the so-called TRI effect an asymmetry in the emission of ternary particles relative to a plane formed by the fragment momentum and the spin of the neutron appear. The two effects are shown to be linked to the components of angular momentum perpendicular and parallel to the fission axis at the saddle point of fission. Based on theoretical models the spectroscopic properties of the collective transitional states at the saddle point are inferred from experiment.
Stokes line width

International Nuclear Information System (INIS)

Nikiskov, A.I.; Ritus, V.I.

1993-01-01

The concept of Stokes line width is introduced for the asymptotic expansions of functions near an essential singularity. Explicit expressions are found for functions (switching functions) that switch on the exponentially small terms for the Dawson integral, Airy function, and the gamma function. A different, more natural representation of a function, not associated with expansion in an asymptotic series, in the form of dominant and recessive terms is obtained by a special division of the contour integral which represents the function into contributions of higher and lower saddle points. This division leads to a narrower, natural Stokes line width and a switching function of an argument that depends on the topology of the lines of steepest descent from the saddle point
General Rytov approximation.

Science.gov (United States)

Potvin, Guy

2015-10-01

We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.
Landmark-based elastic registration using approximating thin-plate splines.

Science.gov (United States)

Rohr, K; Stiehl, H S; Sprengel, R; Buzug, T M; Weese, J; Kuhn, M H

2001-06-01

We consider elastic image registration based on a set of corresponding anatomical point landmarks and approximating thin-plate splines. This approach is an extension of the original interpolating thin-plate spline approach and allows to take into account landmark localization errors. The extension is important for clinical applications since landmark extraction is always prone to error. Our approach is based on a minimizing functional and can cope with isotropic as well as anisotropic landmark errors. In particular, in the latter case it is possible to include different types of landmarks, e.g., unique point landmarks as well as arbitrary edge points. Also, the scheme is general with respect to the image dimension and the order of smoothness of the underlying functional. Optimal affine transformations as well as interpolating thin-plate splines are special cases of this scheme. To localize landmarks we use a semi-automatic approach which is based on three-dimensional (3-D) differential operators. Experimental results are presented for two-dimensional as well as 3-D tomographic images of the human brain.
A Closed-Form Approximation Solution for an Inventory Model with Supply Disruptions and Non-ZIO Reorder Policy

Directory of Open Access Journals (Sweden)

David Heimann

2007-08-01

Full Text Available In supply chains, domestic and global, a producer must decide on an optimal quantity of items to order from suppliers and at what inventory level to place this order (the EOQ problem. We discuss how to modify the EOQ in the face of failures and recoveries by the supplier. This is the EOQ with disruption problem (EOQD. The supplier makes transitions between being capable and not being capable of filling an order in a Markov failure and recovery process. The producer adjusts the reorder point and the inventories to provide a margin of safety. Numerical solutions to the EOQD problem have been developed. In addition, a closed-form approximate solution has been developed for the zero inventory option (ZIO, where the inventory level on reordering is set to be zero. This paper develops a closed-form approximate solution for the EOQD problem when the reorder point can be non-zero, obtaining for that situation an optimal reorder quantity and optimal reorder point that represents an improvement on the optimal ZIO solution. The paper also supplies numerical examples demonstrating the cost savings against the ZIO situation, as well as the accuracy of the approximation technique.
Efficient approximation of the Struve functions Hn occurring in the calculation of sound radiation quantities.

Science.gov (United States)

Aarts, Ronald M; Janssen, Augustus J E M

2016-12-01

The Struve functions H n (z), n=0, 1, ... are approximated in a simple, accurate form that is valid for all z≥0. The authors previously treated the case n = 1 that arises in impedance calculations for the rigid-piston circular radiator mounted in an infinite planar baffle [Aarts and Janssen, J. Acoust. Soc. Am. 113, 2635-2637 (2003)]. The more general Struve functions occur when other acoustical quantities and/or non-rigid pistons are considered. The key step in the paper just cited is to express H 1 (z) as (2/π)-J 0 (z)+(2/π) I(z), where J 0 is the Bessel function of order zero and the first kind and I(z) is the Fourier cosine transform of [(1-t)/(1+t)] 1/2 , 0≤t≤1. The square-root function is optimally approximated by a linear function ĉt+d̂, 0≤t≤1, and the resulting approximated Fourier integral is readily computed explicitly in terms of sin z/z and (1-cos z)/z 2 . The same approach has been used by Maurel, Pagneux, Barra, and Lund [Phys. Rev. B 75, 224112 (2007)] to approximate H 0 (z) for all z≥0. In the present paper, the square-root function is optimally approximated by a piecewise linear function consisting of two linear functions supported by [0,t̂ 0 ] and [t̂ 0 ,1] with t̂ 0 the optimal take-over point. It is shown that the optimal two-piece linear function is actually continuous at the take-over point, causing a reduction of the additional complexity in the resulting approximations of H 0 and H 1 . Furthermore, this allows analytic computation of the optimal two-piece linear function. By using the two-piece instead of the one-piece linear approximation, the root mean square approximation error is reduced by roughly a factor of 3 while the maximum approximation error is reduced by a factor of 4.5 for H 0 and of 2.6 for H 1 . Recursion relations satisfied by Struve functions, initialized with the approximations of H 0 and H 1 , yield approximations for higher order Struve functions.
Autonomous vehicle motion control, approximate maps, and fuzzy logic

Science.gov (United States)

Ruspini, Enrique H.

1993-01-01

Progress on research on the control of actions of autonomous mobile agents using fuzzy logic is presented. The innovations described encompass theoretical and applied developments. At the theoretical level, results of research leading to the combined utilization of conventional artificial planning techniques with fuzzy logic approaches for the control of local motion and perception actions are presented. Also formulations of dynamic programming approaches to optimal control in the context of the analysis of approximate models of the real world are examined. Also a new approach to goal conflict resolution that does not require specification of numerical values representing relative goal importance is reviewed. Applied developments include the introduction of the notion of approximate map. A fuzzy relational database structure for the representation of vague and imprecise information about the robot's environment is proposed. Also the central notions of control point and control structure are discussed.
First observation of the fourth neutral polarization point in the atmosphere

Science.gov (United States)

Horvath, Gabor; Bernath, Balazs; Suhai, Bence; Barta, Andras; Wehner, Rudiger

2002-10-01

In the clear sky there are three commonly known loci, the Arago, Babinet, and Brewster neutral points, where the skylight is unpolarized. These peculiar celestial points, bearing the names of their discoverers, have been the subject of many ground-based investigations, because their positions are sensitive indicators of the amount and type of atmospheric turbidity. According to theoretical considerations and computer simulations, there should exist an additional neutral point approximately opposite to the Babinet point, which can be observed only at higher altitudes in the air or space. Until now, this anonymous fourth neutral point has not been observed during air- or space-borne polarimetric experiments and has been forgotten, in spite of the fact that the neutral points were a basic tool in atmospheric research for a century. Here, we report on the first observation of this fourth neutral point from a hot air balloon. Using 180-field-of-view imaging polarimetry, we could observe the fourth neutral point at 450, 550, and 650 nm from different altitudes between 900 and 3500 m during and after sunrise at approximately 2240 below the anti-solar point along the anti-solar meridian, depending on the wavelength and solar elevation. We show that the fourth neutral point exists at the expected location and has characteristics similar to those of the Arago, Babinet, and Brewster points. We discuss why the fourth neutral point has not been observed in previous air- or space-borne polarimetric experiments. 2002 Optical Society of America
The Dynamical Mechanisms of the Cell Cycle Size Checkpoint

International Nuclear Information System (INIS)

Feng Shi-Fu; Yang Ling; Yan Jie; Liu Zeng-Rong

2012-01-01

Cell division must be tightly coupled to cell growth in order to maintain cell size, whereas the mechanisms of how initialization of mitosis is regulated by cell size remain to be elucidated. We develop a mathematical model of the cell cycle, which incorporates cell growth to investigate the dynamical properties of the size checkpoint in embryos of Xenopus laevis. We show that the size checkpoint is naturally raised from a saddle-node bifurcation, and in a mutant case, the cell loses its size control ability due to the loss of this saddle-node point
Chaotic advection and heat transfer in two similar 2-D periodic flows and in their corresponding 3-D periodic flows

Science.gov (United States)

Vinsard, G.; Dufour, S.; Saatdjian, E.; Mota, J. P. B.

2016-03-01

Chaotic advection can effectively enhance the heat transfer rate between a boundary and fluids with high Prandtl number. These fluids are usually highly viscous and thus turbulent agitation is not a viable solution since the energy required to mix the fluid would be prohibitive. Here, we analyze previously obtained results on chaotic advection and heat transfer in two similar 2-D periodic flows and on their corresponding 3-D periodic flows when an axial velocity component is superposed. The two flows studied are the flow between eccentric rotating cylinders and the flow between confocal ellipses. For both of these flows the analysis is simplified because the Stokes equations can be solved analytically to obtain a closed form solution. For both 2-D periodic flows, we show that chaotic heat transfer is enhanced by the displacement of the saddle point location during one period. Furthermore, the enhancement by chaotic advection in the elliptical geometry is approximately double that obtained in the cylindrical geometry because there are two saddle points instead of one. We also explain why, for high eccentricity ratios, there is no heat transfer enhancement in the cylindrical geometry. When an axial velocity component is added to both of these flows so that they become 3-D, previous work has shown that there is an optimum modulation frequency for which chaotic advection and heat transfer enhancement is a maximum. Here we show that the optimum modulation frequency can be derived from results without an axial flow. We also explain by physical arguments other previously unanswered questions in the published data.
33 CFR 80.135 - Hull, MA to Race Point, MA.

Science.gov (United States)

2010-07-01

... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Hull, MA to Race Point, MA. 80... INTERNATIONAL NAVIGATION RULES COLREGS DEMARCATION LINES Atlantic Coast § 80.135 Hull, MA to Race Point, MA. (a... the east coast of Massachusetts from the easternmost radio tower at Hull, charted in approximate...
Three points of view in transport theory

International Nuclear Information System (INIS)

Ruben, Panta Pazos; Tilio de Vilhena, M.

2001-01-01

A lot of efforts in Transport Theory is used to develop numerical methods or hybrid numerical-analytical techniques. We present in this work three points of view about transport problems. First the C0 semigroup approach, in which the free transport operator ψ → μ ∇ generates an strongly continuous semigroup. The operators operator ψ → σt and operator ψ → ∫ ∇ k(x,μ,μ' ψ(x,μ') dμ' are bounded operators, and by perturbation the transport operator ψ → μ ∇ ψ + σt ψ - K ψ also generates an strongly continuous semigroup. To prove the convergence of the approximations of a numerical methods to the exact solution we use the approximation theorem of C0 semi-groups in canonical form. In other way, the discrete schemes theory is employed in searching the rate of convergence of numerical techniques in transport theory. For 1D dependent of time transport problem and two-dimensional steady state problem we summarize some estimates, incorporating different boundary conditions. Finally we give a survey about the dynamical behavior of the SN approximations. In order to give a unified approach, some results illustrates the equivalence of the three points of views for the case of the steady-state transport problem for slab geometry. (author)
Application of an analytical method for the field calculation in superconducting magnets

International Nuclear Information System (INIS)

Martinelli, G.; Morini, A.

1983-01-01

Superconducting magnets are taking on ever-growing importance due to their increasing prospects of utilization in electrical machines, nuclear fusion, MHD conversion and high-energy physics. These magnets are generally composed of cylindrical or saddle coils, while a ferromagnetic shield is generally situated outside them. This paper uses an analytical method for calculating the magnetic field at every point in a superconducting magnet composed of cylindrical or saddle coils. The method takes into account the real lengths and finite thickness of the coils as well as their radial and axial ferromagnetic shields, if present. The values and distribution of the flux density for some superconducting magnets of high dimensions and high magnetic field, composed of cylindrical or saddle coils, are also given. The results obtained with analytical method are compared with those obtained using numerical methods
Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: Analysis of local bifurcations via the hybrid Poincaré map

International Nuclear Information System (INIS)

Gritli, Hassène; Belghith, Safya

2017-01-01

Highlights: • We study the passive walking dynamics of the compass-gait model under OGY-based state-feedback control. • We analyze local bifurcations via a hybrid Poincaré map. • We show exhibition of the super(sub)-critical flip bifurcation, the saddle-node(saddle) bifurcation and a saddle-flip bifurcation. • An analysis via a two-parameter bifurcation diagram is presented. • Some new hidden attractors in the controlled passive walking dynamics are displayed. - Abstract: In our previous work, we have analyzed the passive dynamic walking of the compass-gait biped model under the OGY-based state-feedback control using the impulsive hybrid nonlinear dynamics. Such study was carried out through bifurcation diagrams. It was shown that the controlled bipedal gait exhibits attractive nonlinear phenomena such as the cyclic-fold (saddle-node) bifurcation, the period-doubling (flip) bifurcation and chaos. Moreover, we revealed that, using the controlled continuous-time dynamics, we encountered a problem in finding, identifying and hence following branches of (un)stable solutions in order to characterize local bifurcations. The present paper solves such problem and then provides a further investigation of the controlled bipedal walking dynamics using the developed analytical expression of the controlled hybrid Poincaré map. Thus, we show that analysis via such Poincaré map allows to follow branches of both stable and unstable fixed points in bifurcation diagrams and hence to explore the complete dynamics of the controlled compass-gait biped model. We demonstrate the generation, other than the conventional local bifurcations in bipedal walking, i.e. the flip bifurcation and the saddle-node bifurcation, of a saddle-saddle bifurcation, a subcritical flip bifurcation and a new type of a local bifurcation, the saddle-flip bifurcation. In addition, to further understand the occurrence of the local bifurcations, we present an analysis with a two-parameter bifurcation
Algorithms for solving common fixed point problems

CERN Document Server

Zaslavski, Alexander J

2018-01-01

This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems, the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning. Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter ...
Super-Relaxed ( -Proximal Point Algorithms, Relaxed ( -Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions

Directory of Open Access Journals (Sweden)

Agarwal RaviP

2009-01-01

Full Text Available We glance at recent advances to the general theory of maximal (set-valued monotone mappings and their role demonstrated to examine the convex programming and closely related field of nonlinear variational inequalities. We focus mostly on applications of the super-relaxed ( -proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems, based on the notion of maximal ( -monotonicity. Investigations highlighted in this communication are greatly influenced by the celebrated work of Rockafellar (1976, while others have played a significant part as well in generalizing the proximal point algorithm considered by Rockafellar (1976 to the case of the relaxed proximal point algorithm by Eckstein and Bertsekas (1992. Even for the linear convergence analysis for the overrelaxed (or super-relaxed ( -proximal point algorithm, the fundamental model for Rockafellar's case does the job. Furthermore, we attempt to explore possibilities of generalizing the Yosida regularization/approximation in light of maximal ( -monotonicity, and then applying to first-order evolution equations/inclusions.
Soft dipole mode of 11Li in approximation of asymptotic potential

International Nuclear Information System (INIS)

Filippov, G.F.; Lashko, Yu.A.

2001-01-01

The soft dipole mode of 11 Li is studied in the frame of microscopic tri-cluster model and in the asymptotic potential approximation. The theory reproduces well the ground state energy, matter radius and the behaviour of the effective photodisintegration cross section in the range of low energies above the decay threshold of 11 Li. Our calculations point two resonant states in this range [ru
Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

Directory of Open Access Journals (Sweden)

Mourad Kerboua

2014-12-01

Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.

Fixed point iterations for quasi-contractive maps in uniformly smooth Banach spaces

International Nuclear Information System (INIS)

Chidume, C.E.; Osilike, M.O.

1992-05-01

Two well-known fixed point iteration methods are applied to approximate fixed points of quasi-contractive maps in real uniformly smooth Banach spaces. While our theorems generalize important known results, our method is of independent interest. (author). 25 refs
Approximation techniques for engineers

CERN Document Server

Komzsik, Louis

2006-01-01

Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
International Conference Approximation Theory XV

CERN Document Server

Schumaker, Larry

2017-01-01

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Defect production in nonlinear quench across a quantum critical point.

Science.gov (United States)

Sen, Diptiman; Sengupta, K; Mondal, Shreyoshi

2008-07-04

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.
Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point

International Nuclear Information System (INIS)

Giribet, Gaston; Goya, Andres; Leston, Mauricio

2011-01-01

Chiral gravity admits asymptotically AdS 3 solutions that are not locally equivalent to AdS 3 ; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally AdS 3 solutions to chiral gravity is relevant to understanding the quantum theory. Here, we discuss a special family of nonlocally AdS 3 solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally AdS 3 solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote AdS 3 space without being locally equivalent to it appear. Defining the boundary stress tensor for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.
Application of the QSPR approach to the boiling points of azeotropes.

Science.gov (United States)

Katritzky, Alan R; Stoyanova-Slavova, Iva B; Tämm, Kaido; Tamm, Tarmo; Karelson, Mati

2011-04-21

CODESSA Pro derivative descriptors were calculated for a data set of 426 azeotropic mixtures by the centroid approximation and the weighted-contribution-factor approximation. The two approximations produced almost identical four-descriptor QSPR models relating the structural characteristic of the individual components of azeotropes to the azeotropic boiling points. These models were supported by internal and external validations. The descriptors contributing to the QSPR models are directly related to the three components of the enthalpy (heat) of vaporization.
Development of the point-depletion code DEPTH

International Nuclear Information System (INIS)

She, Ding; Wang, Kan; Yu, Ganglin

2013-01-01

Highlights: ► The DEPTH code has been developed for the large-scale depletion system. ► DEPTH uses the data library which is convenient to couple with MC codes. ► TTA and matrix exponential methods are implemented and compared. ► DEPTH is able to calculate integral quantities based on the matrix inverse. ► Code-to-code comparisons prove the accuracy and efficiency of DEPTH. -- Abstract: The burnup analysis is an important aspect in reactor physics, which is generally done by coupling of transport calculations and point-depletion calculations. DEPTH is a newly-developed point-depletion code of handling large burnup depletion systems and detailed depletion chains. For better coupling with Monte Carlo transport codes, DEPTH uses data libraries based on the combination of ORIGEN-2 and ORIGEN-S and allows users to assign problem-dependent libraries for each depletion step. DEPTH implements various algorithms of treating the stiff depletion systems, including the Transmutation trajectory analysis (TTA), the Chebyshev Rational Approximation Method (CRAM), the Quadrature-based Rational Approximation Method (QRAM) and the Laguerre Polynomial Approximation Method (LPAM). Three different modes are supported by DEPTH to execute the decay, constant flux and constant power calculations. In addition to obtaining the instantaneous quantities of the radioactivity, decay heats and reaction rates, DEPTH is able to calculate the integral quantities by a time-integrated solver. Through calculations compared with ORIGEN-2, the validity of DEPTH in point-depletion calculations is proved. The accuracy and efficiency of depletion algorithms are also discussed. In addition, an actual pin-cell burnup case is calculated to illustrate the DEPTH code performance in coupling with the RMC Monte Carlo code
Criteria governing electron plasma waves in a two-temperature plasma

International Nuclear Information System (INIS)

Dell, M.P.; Gledhill, I.M.A.; Hellberg, M.A.

1987-01-01

Using a technique based on the saddle-points of the dielectric function, criteria are found which govern the behaviour of electron plasma waves in plasmas with two electron populations having different temperatures. (orig.)
Simultaneous misalignment correction for approximate circular cone-beam computed tomography

International Nuclear Information System (INIS)

Kyriakou, Y; Hillebrand, L; Ertel, D; Kalender, W A; Lapp, R M

2008-01-01

Currently, CT scanning is often performed using flat detectors which are mounted on C-arm units or dedicated gantries as in radiation therapy or micro CT. For perspective cone-beam backprojection of the Feldkamp type (FDK) the geometry of an approximately circular scan trajectory has to be available for reconstruction. If the system or the scan geometry is afflicted with geometrical instabilities, referred to as misalignment, a non-perfect approximate circular scan is the case. Reconstructing a misaligned scan without knowledge of the true trajectory results in severe artefacts in the CT images. Unlike current methods which use a pre-scan calibration of the geometry for defined scan protocols and calibration phantoms, we propose a real-time iterative restoration of reconstruction geometry by means of entropy minimization. Entropy minimization is performed combining a simplex algorithm for multi-parameter optimization and iterative graphics card (GPU)-based FDK-reconstructions. Images reconstructed with the misaligned geometry were used as an input for the entropy minimization algorithm. A simplex algorithm changes the geometrical parameters of the source and detector with respect to the reduction of entropy. In order to reduce the size of the high-dimensional space required for minimization, the trajectory was described by only eight fix points. A virtual trajectory is generated for each iteration using a least-mean-squares algorithm to calculate an approximately circular path including these points. Entropy was minimal for the ideal dataset, whereas strong misalignment resulted in a higher entropy value. For the datasets used in this study, the simplex algorithm required 64-200 iterations to achieve an entropy value equivalent to the ideal dataset, depending on the grade of misalignment using random initialization conditions. The use of the GPU reduced the time per iteration as compared to a quad core CPU-based backprojection by a factor of 10 resulting in a total
Green's Kernels and meso-scale approximations in perforated domains

CERN Document Server

Maz'ya, Vladimir; Nieves, Michael

2013-01-01

There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions. The main focus of the present text is on two topics: (a) asymptotics of Green’s kernels in domai...
Inflation with a graceful exit in a random landscape

International Nuclear Information System (INIS)

Pedro, F.G.; Westphal, A.

2016-11-01

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N<<10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Inflation with a graceful exit in a random landscape

Energy Technology Data Exchange (ETDEWEB)

Pedro, F.G. [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica y Inst. de Fisica Teorica UAM/CSIC; Westphal, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group

2016-11-15

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N<<10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Inflation with a graceful exit in a random landscape

Energy Technology Data Exchange (ETDEWEB)

Pedro, F.G. [Departamento de Física Teórica and Instituto de Física Teórica UAM/CSIC,Universidad Autónoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Westphal, A. [Deutsches Elektronen-Synchrotron DESY, Theory Group,D-22603 Hamburg (Germany)

2017-03-30

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N≪10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Electron-phonon interactions and intrinsic nonadiabatic state of superconductors

International Nuclear Information System (INIS)

Banacky, Pavol

2007-01-01

Study of band structure of YBa 2 Cu 3 O 7 has shown that electron coupling to A g , B 2g and B 3g modes results in fluctuation of saddle point of one of the CuO plane d-pσ band in Y point of 1st BZ across Fermi level. It represents breakdown of adiabatic Born-Oppenheimer approximation and transition of the system into intrinsic nonadiabatic state, ω > E F . Results show that system is stabilized in this state at distorted nuclear geometry. Stabilization effect is mainly due to strong dependence of the electronic motion on instantaneous nuclear momenta. On the lattice scale, the intrinsic nonadiabatic state is geometrically degenerate at broken translation symmetry - system has fluxional nuclear configuration of O2, O3 atoms in CuO planes. It enables formation of mobile bipolarons that can move in the lattice without dissipation. Described effects are absent in non-superconducting YBa 2 Cu 3 O 6
Electron phonon interactions and intrinsic nonadiabatic state of superconductors

Science.gov (United States)

Baňacký, Pavol

2007-09-01

Study of band structure of YBa 2Cu 3O 7 has shown that electron coupling to A g, B 2g and B 3g modes results in fluctuation of saddle point of one of the CuO plane d-pσ band in Y point of 1st BZ across Fermi level. It represents breakdown of adiabatic Born-Oppenheimer approximation and transition of the system into intrinsic nonadiabatic state, ω > EF. Results show that system is stabilized in this state at distorted nuclear geometry. Stabilization effect is mainly due to strong dependence of the electronic motion on instantaneous nuclear momenta. On the lattice scale, the intrinsic nonadiabatic state is geometrically degenerate at broken translation symmetry - system has fluxional nuclear configuration of O2, O3 atoms in CuO planes. It enables formation of mobile bipolarons that can move in the lattice without dissipation. Described effects are absent in non-superconducting YBa 2Cu 3O 6.
Ordered cones and approximation

CERN Document Server

Keimel, Klaus

1992-01-01

This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Space-Efficient Approximation Scheme for Circular Earth Mover Distance

DEFF Research Database (Denmark)

Brody, Joshua Eric; Liang, Hongyu; Sun, Xiaoming

2012-01-01

The Earth Mover Distance (EMD) between point sets A and B is the minimum cost of a bipartite matching between A and B. EMD is an important measure for estimating similarities between objects with quantifiable features and has important applications in several areas including computer vision...... to computer vision [13] and can be seen as a special case of computing EMD on a discretized grid. We achieve a (1 ±ε) approximation for EMD in $\\tilde O(\\varepsilon^{-3})$ space, for every 0 ... that matches the space bound asked in [9]....
Black hole equations of motion in the quasistationary approximation

International Nuclear Information System (INIS)

Zhdanov, V.I.; Shtelen', V.M.

1980-01-01

Black hole motion is considered under the effect of external actions from the point of view of a remoted observer. The shift of the black hole and the metrix structure are found at the presence of other gravitational bodies using the Zerilli equation. It is shown that in the region, where the space curvature is small, the contribution of the field of the black hole, moving with acceleration, coincides in configuration with the field of usual body, black hole motion in quasistationary approximation occuring according to laws of Newtonian dynamics
Minimizing the effect of automotive pollution in urban geometry using mathematical optimization

Energy Technology Data Exchange (ETDEWEB)

Craig, K.J.; De Kock, D.J.; Snyman, J.A. [Pretoria Univ. (South Africa). Dept. of Mechanical and Aeronautical Engineering

2001-07-01

One of the factors that needs to be considered during the layout of new urban geometry (e.g. street direction, spacing and width, building height restrictions) is the effect of the air pollution associated with the automotive transport that would use routes in this urban area. Although the pollution is generated at street level, its effect can be widespread due to interaction of the pollutant dispersion and diffusion with the wind speed and direction. In order to study the effect of a new urban geometry on the pollutant levels and dispersion, a very time-consuming experimental or parametric numerical study would have to be performed. This paper proposes an alternative approach, that of combining mathematical optimization with the techniques of computational fluid dynamics (CFD). In essence, the meteorological information as represented by a wind rose (wind speed and direction), is used to calculate pollutant levels as a function of urban geometry variables: street canyon depth and street canyon width. The pollutant source specified in conjunction with a traffic scenario with CO is used as pollutant. The main aim of the study is to be able to suggest the most beneficial configuration of an idealized urban geometry that minimizes the peak pollutant levels due to assumed traffic distributions. This study uses two mathematical optimization methods. The first method is implemented through a successive maximization-minimization approach, while the second method determines the location of saddle points of the pollutant level, considered as a function of urban geometry and wind rose. Locally, a saddle point gives the best urban geometry for the worst meteorological scenario. The commercial CFD code, STAR-CD, is coupled with a version of the DYNAMIC-Q optimization algorithm of Snyman, first to successively locate maxima and minima in a min-max approach; and then to locate saddle points. It is shown that the saddle-point method is more cost-effective. The methodology
Multi-lane detection based on multiple vanishing points detection

Science.gov (United States)

Li, Chuanxiang; Nie, Yiming; Dai, Bin; Wu, Tao

2015-03-01

Lane detection plays a significant role in Advanced Driver Assistance Systems (ADAS) for intelligent vehicles. In this paper we present a multi-lane detection method based on multiple vanishing points detection. A new multi-lane model assumes that a single lane, which has two approximately parallel boundaries, may not parallel to others on road plane. Non-parallel lanes associate with different vanishing points. A biological plausibility model is used to detect multiple vanishing points and fit lane model. Experimental results show that the proposed method can detect both parallel lanes and non-parallel lanes.

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