Kinematical Correlations for Higgs Boson Plus High P_{T} Jet Production at Hadron Colliders.

PubMed

Sun, Peng; Yuan, C-P; Yuan, Feng

2015-05-22

We investigate the effect of QCD resummation to kinematical correlations in the Higgs boson plus high transverse momentum (P(T)) jet events produced at hadron colliders. We show that at the complete one-loop order, the Collins-Soper-Sterman resummation formalism can be applied to derive the Sudakov form factor. We compare the singular behavior of resummation calculation to fixed order prediction in the case that a Higgs boson and high P(T) jet are produced nearly back to back in their transverse momenta, and find perfect agreement. The phenomenological importance of the resummation effect at the LHC is also demonstrated.

Kinematical Correlations for Higgs Boson Plus High PT Jet Production at Hadron Colliders

NASA Astrophysics Data System (ADS)

Sun, Peng; Yuan, C.-P.; Yuan, Feng

2015-05-01

We investigate the effect of QCD resummation to kinematical correlations in the Higgs boson plus high transverse momentum (PT) jet events produced at hadron colliders. We show that at the complete one-loop order, the Collins-Soper-Sterman resummation formalism can be applied to derive the Sudakov form factor. We compare the singular behavior of resummation calculation to fixed order prediction in the case that a Higgs boson and high PT jet are produced nearly back to back in their transverse momenta, and find perfect agreement. The phenomenological importance of the resummation effect at the LHC is also demonstrated.

Third-order dissipative hydrodynamics from the entropy principle

NASA Astrophysics Data System (ADS)

El, Andrej; Xu, Zhe; Greiner, Carsten

2010-06-01

We review the entropy based derivation of third-order hydrodynamic equations and compare their solutions in one-dimensional boost-invariant geometry with calculations by the partonic cascade BAMPS. We demonstrate that Grad's approximation, which underlies the derivation of both Israel-Stewart and third-order equations, describes the transverse spectra from BAMPS with high accuracy. At the same time solutions of third-order equations are much closer to BAMPS results than solutions of Israel-Stewart equations. Introducing a resummation scheme for all higher-oder corrections to one-dimensional hydrodynamic equation we demonstrate the importance of higher-order terms if the Knudsen number is large.

Signal inference with unknown response: calibration-uncertainty renormalized estimator.

PubMed

Dorn, Sebastian; Enßlin, Torsten A; Greiner, Maksim; Selig, Marco; Boehm, Vanessa

2015-01-01

The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.

Associated t t ¯ production at the LHC: Theoretical predictions at NLO +NNLL accuracy

NASA Astrophysics Data System (ADS)

Kulesza, Anna; Motyka, Leszek; Stebel, Tomasz; Theeuwes, Vincent

2018-06-01

We perform threshold resummation of soft gluon corrections to the total cross section and the invariant mass distribution for the process p p →t t ¯H . The resummation is carried out at next-to-next-to-leading-logarithmic (NNLL) accuracy using the direct QCD Mellin space technique in the three-particle invariant mass kinematics. After presenting analytical expressions we discuss the impact of resummation on the numerical predictions for the associated Higgs boson production with top quarks at the LHC. We find that next-to-leading-order (NLO)+NNLL resummation leads to predictions for which the central values are remarkably stable with respect to scale variation and for which theoretical uncertainties are reduced in comparison to NLO predictions.

Resummation of jet veto logarithms at N 3 LL a + NNLO for W + W ? production at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dawson, S.; Jaiswal, P.; Li, Ye

We compute the resummed on-shell W+W- production cross section under a jet veto at the LHC to partial N3LL order matched to the fixed-order NNLO result. Differential NNLO cross sections are obtained from an implementation of qT subtraction in Sherpa. The two-loop virtual corrections to the qq¯→W+W- amplitude, used in both fixed-order and resummation predictions, are extracted from the public code qqvvamp. We perform resummation using soft collinear effective theory, with approximate beam functions where only the logarithmic terms are included at two-loop. In addition to scale uncertainties from the hard matching scale and the factorization scale, rapidity scale variationsmore » are obtained within the analytic regulator approach. Our resummation results show a decrease in the jet veto cross section compared to NNLO fixed-order predictions, with reduced scale uncertainties compared to NNLL+NLO resummed predictions. We include the loop-induced gg contribution with jet veto resummation to NLL+LO. The prediction shows good agreement with recent LHC measurements.« less

Resummation of jet veto logarithms at N 3 LL a + NNLO for W + W ? production at the LHC

DOE PAGES

Dawson, S.; Jaiswal, P.; Li, Ye; ...

2016-12-01

We compute the resummed on-shell W+W- production cross section under a jet veto at the LHC to partial N3LL order matched to the fixed-order NNLO result. Differential NNLO cross sections are obtained from an implementation of qT subtraction in Sherpa. The two-loop virtual corrections to the qq¯→W+W- amplitude, used in both fixed-order and resummation predictions, are extracted from the public code qqvvamp. We perform resummation using soft collinear effective theory, with approximate beam functions where only the logarithmic terms are included at two-loop. In addition to scale uncertainties from the hard matching scale and the factorization scale, rapidity scale variationsmore » are obtained within the analytic regulator approach. Our resummation results show a decrease in the jet veto cross section compared to NNLO fixed-order predictions, with reduced scale uncertainties compared to NNLL+NLO resummed predictions. We include the loop-induced gg contribution with jet veto resummation to NLL+LO. The prediction shows good agreement with recent LHC measurements.« less

On the IR-resummation in the EFTofLSS

NASA Astrophysics Data System (ADS)

Senatore, Leonardo; Trevisan, Gabriele

2018-05-01

We propose a simplification for the IR-resummation scheme of [1] and also include its next-to-leading order corrections coming from the tree-level three-point function of the long displacement field. First we show that the new simplified formula shares the same properties of the resummation of [2]. In Fourier space, the IR-resummed power spectrum has no residual wiggles and the two-loop calculation matches the non-linear power spectrum of the Dark Sky simulation at z=0 up to ksimeq0.34 h Mpc‑1 within cosmic variance. Then, we find that the additional subleading terms (although parametrically infrared-enhanced) modify the leading-order IR-resummed correlation function only in a marginal way, implying that the IR-resummation scheme can robustly predict the shape of the BAO peak.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Höche, Stefan; Reichelt, Daniel; Siegert, Frank

We present a systematic study of differences between NLL resummation and parton showers. We first construct a Markovian Monte-Carlo algorithm for resummation of additive observables in electron-positron annihilation. Approximations intrinsic to the pure NLL result are then removed, in order to obtain a traditional, momentum and probability conserving parton shower based on the coherent branching formalism. The impact of each approximation is studied, and an overall comparison is made between the parton shower and pure NLL resummation. Differences compared to modern parton-shower algorithms formulated in terms of color dipoles are analyzed.

Top-pair production at hadron colliders with next-to-next-to-leading logarithmic soft-gluon resummation

NASA Astrophysics Data System (ADS)

Cacciari, Matteo; Czakon, Michał; Mangano, Michelangelo; Mitov, Alexander; Nason, Paolo

2012-04-01

Incorporating all recent theoretical advances, we resum soft-gluon corrections to the total ttbar cross-section at hadron colliders at the next-to-next-to-leading logarithmic (NNLL) order. We perform the resummation in the well established framework of Mellin N-space resummation. We exhaustively study the sources of systematic uncertainty like renormalization and factorization scale variation, power suppressed effects and missing two- and higher-loop corrections. The inclusion of soft-gluon resummation at NNLL brings only a minor decrease in the perturbative uncertainty with respect to the NLL approximation, and a small shift in the central value, consistent with the quoted uncertainties. These numerical predictions agree with the currently available measurements from the Tevatron and LHC and have uncertainty of similar size. We conclude that significant improvements in the ttbar cross-sections can potentially be expected only upon inclusion of the complete NNLO corrections.

Resummation of high order corrections in Higgs boson plus jet production at the LHC

DOE PAGES

Sun, Peng; Isaacson, Joshua; Yuan, C. -P.; ...

2017-02-22

We study the effect of multiple parton radiation to Higgs boson plus jet production at the LHC. The large logarithms arising from the small imbalance in the transverse momentum of the Higgs boson plus jet final state system are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of Next-to-Leading Logarithm (NLL), by applying the transverse momentum dependent (TMD) factorization formalism. We show that the appropriate resummation scale should be the jet transverse momentum, rather than the partonic center of mass energy which has been normally used in the TMD resummation formalism. Furthermore, themore » transverse momentum distribution of the Higgs boson, particularly near the lower cut-off applied on the jet transverse momentum, can only be reliably predicted by the resummation calculation which is free of the so-called Sudakov-shoulder singularity problem, present in fixed-order calculations.« less

Resummation of high order corrections in Higgs boson plus jet production at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Peng; Isaacson, Joshua; Yuan, C. -P.

We study the effect of multiple parton radiation to Higgs boson plus jet production at the LHC. The large logarithms arising from the small imbalance in the transverse momentum of the Higgs boson plus jet final state system are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of Next-to-Leading Logarithm (NLL), by applying the transverse momentum dependent (TMD) factorization formalism. We show that the appropriate resummation scale should be the jet transverse momentum, rather than the partonic center of mass energy which has been normally used in the TMD resummation formalism. Furthermore, themore » transverse momentum distribution of the Higgs boson, particularly near the lower cut-off applied on the jet transverse momentum, can only be reliably predicted by the resummation calculation which is free of the so-called Sudakov-shoulder singularity problem, present in fixed-order calculations.« less

Infrared dynamics of cold atoms on hot graphene membranes

NASA Astrophysics Data System (ADS)

Sengupta, Sanghita; Kotov, Valeri N.; Clougherty, Dennis P.

2016-06-01

We study the infrared dynamics of low-energy atoms interacting with a sample of suspended graphene at finite temperature. The dynamics exhibits severe infrared divergences order by order in perturbation theory as a result of the singular nature of low-energy flexural phonon emission. Our model can be viewed as a two-channel generalization of the independent boson model with asymmetric atom-phonon coupling. This allows us to take advantage of the exact nonperturbative solution of the independent boson model in the stronger channel while treating the weaker one perturbatively. In the low-energy limit, the exact solution can be viewed as a resummation (exponentiation) of the most divergent diagrams in the perturbative expansion. As a result of this procedure, we obtain the atom's Green function which we use to calculate the atom damping rate, a quantity equal to the quantum sticking rate. A characteristic feature of our results is that the Green's function retains a weak, infrared cutoff dependence that reflects the reduced dimensionality of the problem. As a consequence, we predict a measurable dependence of the sticking rate on graphene sample size. We provide detailed predictions for the sticking rate of atomic hydrogen as a function of temperature and sample size. The resummation yields an enhanced sticking rate relative to the conventional Fermi golden rule result (equivalent to the one-loop atom self-energy), as higher-order processes increase damping at finite temperature.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Next-to-leading order Balitsky-Kovchegov equation with resummation

DOE PAGES

Lappi, T.; Mantysaari, H.

2016-05-03

Here, we solve the Balitsky-Kovchegov evolution equation at next-to-leading order accuracy including a resummation of large single and double transverse momentum logarithms to all orders. We numerically determine an optimal value for the constant under the large transverse momentum logarithm that enables including a maximal amount of the full NLO result in the resummation. When this value is used, the contribution from the α 2 s terms without large logarithms is found to be small at large saturation scales and at small dipoles. Close to initial conditions relevant for phenomenological applications, these fixed-order corrections are shown to be numerically important.

Transverse momentum resummation for dijet correlation in hadronic collisions

NASA Astrophysics Data System (ADS)

Sun, Peng; Yuan, C.-P.; Yuan, Feng

2015-11-01

We study transverse momentum resummation for the azimuthal angular correlation in dijet production in hadron collisions based on the Collins-Soper-Sterman formalism. The complete one-loop calculations are carried out in the collinear framework for the differential cross sections at low imbalance transverse momentum between the two jets. Important cross-checks are performed to demonstrate that the soft divergences are canceled out between different diagrams and, in particular, for those associated with the final state jets. The leading and subleading logarithms are identified. All order resummation is derived following the transverse momentum dependent factorization at this order. Its phenomenological applications are also presented.

Momentum-space resummation for transverse observables and the Higgs p ⊥ at N3LL+NNLO

NASA Astrophysics Data System (ADS)

Bizoń, Wojciech; Monni, Pier Francesco; Re, Emanuele; Rottoli, Luca; Torrielli, Paolo

2018-02-01

We present an approach to the momentum-space resummation of global, recursively infrared and collinear safe observables that can vanish away from the Sudakov region. We focus on the hadro-production of a generic colour singlet, and we consider the class of observables that depend only upon the total transverse momentum of the radiation, prime examples being the transverse momentum of the singlet, and ϕ ∗ in Drell-Yan pair production. We derive a resummation formula valid up to next-to-next-to-next-to-leading-logarithmic accuracy for the considered class of observables. We use this result to compute state-of-the-art predictions for the Higgs-boson transverse-momentum spectrum at the LHC at next-to-next-to-next-to-leading-logarithmic accuracy matched to fixed next-to-next-to-leading order. Our resummation formula reduces exactly to the customary resummation performed in impact-parameter space in the known cases, and it also predicts the correct power-behaved scaling of the cross section in the limit of small value of the observable. We show how this formalism is efficiently implemented by means of Monte Carlo techniques in a fully exclusive generator that allows one to apply arbitrary cuts on the Born variables for any colour singlet, as well as to automatically match the resummed results to fixed-order calculations.

Threshold resummation S factor in QCD: The case of unequal masses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Solovtsova, O. P., E-mail: olsol@theor.jinr.r; Chernichenko, Yu. D., E-mail: chern@gstu.gomel.b

A new relativistic Coulomb-like threshold resummation S factor in quantum chromodynamics is obtained. The analysis in question is performed within the quantum-field-theory quasipotential approach formulated in the relativistic configuration representation for the case of interaction between two relativistic particles that have unequal masses.

Fast summation of divergent series and resurgent transseries from Meijer-G approximants

NASA Astrophysics Data System (ADS)

Mera, Héctor; Pedersen, Thomas G.; Nikolić, Branislav K.

2018-05-01

We develop a resummation approach based on Meijer-G functions and apply it to approximate the Borel sum of divergent series and the Borel-Écalle sum of resurgent transseries in quantum mechanics and quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parametrized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-hypergeometric method [Mera et al., Phys. Rev. Lett. 115, 143001 (2015), 10.1103/PhysRevLett.115.143001]. Here we demonstrate the accuracy of this technique in various examples from quantum mechanics and QFT, traditionally employed as benchmark models for resummation, such as zero-dimensional ϕ4 theory; the quartic anharmonic oscillator; the calculation of critical exponents for the N -vector model; ϕ4 with degenerate minima; self-interacting QFT in zero dimensions; and the summation of one- and two-instanton contributions in the quantum-mechanical double-well problem.

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

NASA Astrophysics Data System (ADS)

Casalderrey-Solana, Jorge; Gushterov, Nikola I.; Meiring, Ben

2018-04-01

We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter λGB. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of N=4 Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of λGB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.

Early-Time Solution of the Horizontal Unconfined Aquifer in the Buildup Phase

NASA Astrophysics Data System (ADS)

Gravanis, Elias; Akylas, Evangelos

2017-10-01

We derive the early-time solution of the Boussinesq equation for the horizontal unconfined aquifer in the buildup phase under constant recharge and zero inflow. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turns out to be asymptotic and it is regularized by resummation techniques that are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.

ResBos2: Precision Resummation for the LHC ERA

NASA Astrophysics Data System (ADS)

Isaacson, Joshua Paul

With the precision of data at the LHC, it is important to advance theoretical calculations to match it. Previously, the ResBos code was insufficient to adequately describe the data at the LHC. This requires an advancement in the ResBos code, and led to the development of the ResBos2 package. This thesis discusses some of the major improvements that were implemented into the code to advance it and prepare it for the precision of the LHC. The resummation for color singlet particles is improved from approximate NNLL+NLO accuracy to an accuracy of N3LL+NNLO accuracy. The ResBos2 code is validated against the calculation of the total cross-section for Drell-Yan processes against fixed order calculations, to ensure that the calculations are performed correctly. This allows for a prediction of the transverse momentum and φ*eta distributions for the Z boson to be consistent with the data from ATLAS at a collider energy of √s = 8 TeV. Also, the effects of choice of resummation scheme are investigated for the Collins-Soper-Sterman and Catani-deFlorian-Grazzini formalisms. It is shown that as long as the calculation of each of these is performed such that the order of the B coefficient is exactly 1 order higher than that of the C and H coefficients, then the two formalisms are consistent. Additionally, using the improved theoretical prediction will help to reduce the theoretical uncertainty on the mass of the W boson, by reducing the uncertainty in extrapolating the dsigma/dpTW distribution from the data for the dsigma/dpT Z distribution by taking the ratio of the theory predictions for the Z and W transverse momentum. In addition to improving the accuracy of the color singlet final state resummation calculations, the ResBos2 code introduces the resummation of non-color singlet states in the final state. Here the details for the Higgs plus jet calculation are illustrated as an example of one such process. It is shown that it is possible to perform this resummation, but the resummation formalism needs to be modified in order to do so. The major modification that is made is the inclusion of the jet cone-size dependence in the Sudakov form factor. This result resolves, analytically, the Sudakov shoulder singularity. The results of the ResBos2 prediction are compared to both the fixed order and parton shower calculations. The calculations are shown to be consistent for all of the distributions considered up to the theoretical uncertainty. As the LHC continues to increase their data, and their precision on these observables, the ability to have analytic resummation calculations for non-color singlet final states will provide a strong check of perturbative QCD. Finally, the calculation of the terms needed to match to N3LO are done in this work. Once the results become sufficiently publicly available for the perturbative calculation, the ResBos2 code can easily be extended to include these corrections, and be used as a means to predict the total cross-section at N3LO as well.

Anisotropic nonequilibrium hydrodynamic attractor

NASA Astrophysics Data System (ADS)

Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.

2018-02-01

We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a 0 +1 d conformal system using kinetic theory in the relaxation time approximation. We compare our results to the nonequilibrium attractor obtained from the exact solution of the 0 +1 d conformal Boltzmann equation, the Navier-Stokes theory, and the second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal-to-transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that an optimized hydrodynamic treatment of kinetic theory involves a resummation not only in gradients (Knudsen number) but also in the inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation of the exact kinetic theory attractor than the Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in the inverse Reynolds number. We then carry this expansion out to the third order, and compare these third-order results to the exact kinetic theory solution.

Resummation of divergent perturbation series: Application to the vibrational states of H2CO molecule

NASA Astrophysics Data System (ADS)

Duchko, A. N.; Bykov, A. D.

2015-10-01

Large-order Rayleigh-Schrödinger perturbation theory (RSPT) is applied to the calculation of anharmonic vibrational energy levels of H2CO molecule. We use the model of harmonic oscillators perturbed by anharmonic terms of potential energy. Since the perturbation series typically diverge due to strong couplings, we apply the algebraic approximation technique because of its effectiveness shown earlier by Goodson and Sergeev [J. Chem. Phys. 110, 8205 (1999); ibid. 124, 094111 (2006)] and in our previous articles [A. D. Bykov et al. Opt. Spectrosc. 114, 396 (2013); ibid. 116, 598 (2014)]. To facilitate the resummation of terms contributing to perturbed states, when resonance mixing between states is especially strong and perturbation series diverge very quick, we used repartition of the Hamiltonian by shifting the normal mode frequencies. Energy levels obtained by algebraic approximants were compared with the results of variational calculation. It was found that for low energy states (up to ˜5000 cm-1), algebraic approximants gave accurate values of energy levels, which were in excellent agreement with the variational method. For highly excited states, strong and multiple resonances complicate series resummation, but a suitable change of normal mode frequencies allows one to reduce the resonance mixing and to get accurate energy levels. The theoretical background of the problem of RSPT series divergence is discussed along with its numerical analysis. For these purposes, the vibrational energy is considered as a function of a complex perturbation parameter. Layout and classification of its singularities allow us to model the asymptotic behavior of the perturbation series and prove the robustness of the algorithm.

Resummation of divergent perturbation series: Application to the vibrational states of H2CO molecule.

PubMed

Duchko, A N; Bykov, A D

2015-10-21

Large-order Rayleigh-Schrödinger perturbation theory (RSPT) is applied to the calculation of anharmonic vibrational energy levels of H2CO molecule. We use the model of harmonic oscillators perturbed by anharmonic terms of potential energy. Since the perturbation series typically diverge due to strong couplings, we apply the algebraic approximation technique because of its effectiveness shown earlier by Goodson and Sergeev [J. Chem. Phys. 110, 8205 (1999); ibid. 124, 094111 (2006)] and in our previous articles [A. D. Bykov et al. Opt. Spectrosc. 114, 396 (2013); ibid. 116, 598 (2014)]. To facilitate the resummation of terms contributing to perturbed states, when resonance mixing between states is especially strong and perturbation series diverge very quick, we used repartition of the Hamiltonian by shifting the normal mode frequencies. Energy levels obtained by algebraic approximants were compared with the results of variational calculation. It was found that for low energy states (up to ∼5000 cm(-1)), algebraic approximants gave accurate values of energy levels, which were in excellent agreement with the variational method. For highly excited states, strong and multiple resonances complicate series resummation, but a suitable change of normal mode frequencies allows one to reduce the resonance mixing and to get accurate energy levels. The theoretical background of the problem of RSPT series divergence is discussed along with its numerical analysis. For these purposes, the vibrational energy is considered as a function of a complex perturbation parameter. Layout and classification of its singularities allow us to model the asymptotic behavior of the perturbation series and prove the robustness of the algorithm.

A continued fraction resummation form of bath relaxation effect in the spin-boson model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gong, Zhihao; Tang, Zhoufei; Wu, Jianlan, E-mail: jianlanwu@zju.edu.cn

2015-02-28

In the spin-boson model, a continued fraction form is proposed to systematically resum high-order quantum kinetic expansion (QKE) rate kernels, accounting for the bath relaxation effect beyond the second-order perturbation. In particular, the analytical expression of the sixth-order QKE rate kernel is derived for resummation. With higher-order correction terms systematically extracted from higher-order rate kernels, the resummed quantum kinetic expansion approach in the continued fraction form extends the Pade approximation and can fully recover the exact quantum dynamics as the expansion order increases.

A modification of \\mathsf {WKB} method for fractional differential operators of Schrödinger's type

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2017-09-01

In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called WKB method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the WKB to the scope of fractional derivative, we proposed a relatively new derivative called the local fractional derivative. By use of properties of local fractional derivative, we extend the WKB method in the scope of the fractional differential equation. By means of this extension, the WKB analysis based on the Borel resummation, for fractional differential operators of WKB type are investigated. The convergence and the Mittag-Leffler stability of the proposed approach is proven. The obtained results are in excellent agreement with the existing ones in open literature and it is shown that the present approach is very effective and accurate. Furthermore, we are mainly interested to construct the solution of fractional Schrödinger equation in the Mittag-Leffler form and how it leads naturally to this semi-classical approximation namely modified WKB.

Z -boson decays to a vector quarkonium plus a photon

NASA Astrophysics Data System (ADS)

Bodwin, Geoffrey T.; Chung, Hee Sok; Ee, June-Haak; Lee, Jungil

2018-01-01

We compute the decay rates for the processes Z →V +γ , where Z is the Z -boson, γ is the photon, and V is one of the vector quarkonia J /ψ or ϒ (n S ), with n =1 , 2, or 3. Our computations include corrections through relative orders αs and v2 and resummations of logarithms of mZ2/mQ2, to all orders in αs, at next-to-leading-logarithmic accuracy. (v is the velocity of the heavy quark Q or the heavy antiquark Q ¯ in the quarkonium rest frame, and mZ and mQ are the masses of Z and Q , respectively.) Our calculations are the first to include both the order-αs correction to the light-cone distributions amplitude and the resummation of logarithms of mZ2/mQ2 and are the first calculations for the ϒ (2 S ) and ϒ (3 S ) final states. The resummations of logarithms of mZ2/mQ2 that are associated with the order-αs and order-v2 corrections are carried out by making use of the Abel-Padé method. We confirm the analytic result for the order-v2 correction that was presented in a previous publication, and we correct the relative sign of the direct and indirect amplitudes and some choices of scales in that publication. Our branching fractions for Z →J /ψ +γ and Z →ϒ (1 S )+γ differ by 2.0 σ and -4.0 σ , respectively, from the branching fractions that are given in the most recent publication on this topic (in units of the uncertainties that are given in that publication). However, we argue that the uncertainties in the rates are underestimated in that publication.

Resummation of divergent perturbation series: Application to the vibrational states of H{sub 2}CO molecule

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duchko, A. N.; V.E. Zuev Institute of Atmospheric Optics, Tomsk; Bykov, A. D., E-mail: adbykov@rambler.ru

2015-10-21

Large-order Rayleigh–Schrödinger perturbation theory (RSPT) is applied to the calculation of anharmonic vibrational energy levels of H{sub 2}CO molecule. We use the model of harmonic oscillators perturbed by anharmonic terms of potential energy. Since the perturbation series typically diverge due to strong couplings, we apply the algebraic approximation technique because of its effectiveness shown earlier by Goodson and Sergeev [J. Chem. Phys. 110, 8205 (1999); ibid. 124, 094111 (2006)] and in our previous articles [A. D. Bykov et al. Opt. Spectrosc. 114, 396 (2013); ibid. 116, 598 (2014)]. To facilitate the resummation of terms contributing to perturbed states, when resonancemore » mixing between states is especially strong and perturbation series diverge very quick, we used repartition of the Hamiltonian by shifting the normal mode frequencies. Energy levels obtained by algebraic approximants were compared with the results of variational calculation. It was found that for low energy states (up to ∼5000 cm{sup −1}), algebraic approximants gave accurate values of energy levels, which were in excellent agreement with the variational method. For highly excited states, strong and multiple resonances complicate series resummation, but a suitable change of normal mode frequencies allows one to reduce the resonance mixing and to get accurate energy levels. The theoretical background of the problem of RSPT series divergence is discussed along with its numerical analysis. For these purposes, the vibrational energy is considered as a function of a complex perturbation parameter. Layout and classification of its singularities allow us to model the asymptotic behavior of the perturbation series and prove the robustness of the algorithm.« less

HTL resummation in the light cone gauge

NASA Astrophysics Data System (ADS)

Chen, Qi; Hou, De-fu

2018-04-01

The light cone gauge with light cone variables is often used in pQCD calculations in relativistic heavy-ion collision physics. The Hard Thermal Loops (HTL) resummation is an indispensable technique for hot QCD calculation. It was developed in covariant gauges with conventional Minkowski varaiables; we shall extend this method to the light cone gauge. In the real time formalism, using the Mandelstam-Leibbrant prescription of (n·K)‑1, we calculate the transverse and longitudinal components of the gluon HTL self energy, and prove that there are no infrared divergences. With this HTL self energy, we derive the HTL resummed gluon propagator in the light cone gauge. We also calculate the quark HTL self energy and the resummed quark propagator in the light cone gauge and find it is gauge independent. As application examples, we analytically calculate the damping rates of hard quarks and gluons with the HTL resummed gluon propagator in the light cone gauge and showed that they are gauge independent. The final physical results are identical to those computed in covariant gauge, as they should be. Supported by National Natural Science Foundation of China (11375070, 11735007, 11521064)

Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks

DOE PAGES

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared; ...

2017-03-30

Here, one can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS 3/CFT 2. In this paper we use the technique to perform calculations in the small 1/c ∝ GN expansion: (1) we prove the all-orders resummation of logarithmic factors ∝1/clog z in the Lorentzian regime, demonstrating that 1/c corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large c withmore » fixed cz, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order 1/c 2 and 1/c 3 with external dimensions fixed, corresponding to 2 and 3 loop calculations in AdS 3, and (4) we derive the heavy-light vacuum blocks in theories with N = 1, 2 superconformal symmetry.« less

Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared

Here, one can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS 3/CFT 2. In this paper we use the technique to perform calculations in the small 1/c ∝ GN expansion: (1) we prove the all-orders resummation of logarithmic factors ∝1/clog z in the Lorentzian regime, demonstrating that 1/c corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large c withmore » fixed cz, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order 1/c 2 and 1/c 3 with external dimensions fixed, corresponding to 2 and 3 loop calculations in AdS 3, and (4) we derive the heavy-light vacuum blocks in theories with N = 1, 2 superconformal symmetry.« less

Interplay of threshold resummation and hadron mass corrections in deep inelastic processes

DOE PAGES

Accardi, Alberto; Anderle, Daniele P.; Ringer, Felix

2015-02-01

We discuss hadron mass corrections and threshold resummation for deep-inelastic scattering lN-->l'X and semi-inclusive annihilation e +e - → hX processes, and provide a prescription how to consistently combine these two corrections respecting all kinematic thresholds. We find an interesting interplay between threshold resummation and target mass corrections for deep-inelastic scattering at large values of Bjorken x B. In semi-inclusive annihilation, on the contrary, the two considered corrections are relevant in different kinematic regions and do not affect each other. A detailed analysis is nonetheless of interest in the light of recent high precision data from BaBar and Belle onmore » pion and kaon production, with which we compare our calculations. For both deep inelastic scattering and single inclusive annihilation, the size of the combined corrections compared to the precision of world data is shown to be large. Therefore, we conclude that these theoretical corrections are relevant for global QCD fits in order to extract precise parton distributions at large Bjorken x B, and fragmentation functions over the whole kinematic range.« less

Threshold and Jet Radius Joint Resummation for Single-Inclusive Jet Production

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xiaohui; Moch, Sven -Olaf; Ringer, Felix

Here, we present the first threshold and jet radius jointly resummed cross section for single-inclusive hadronic jet production. We work at next-to-leading logarithmic accuracy and our framework allows for a systematic extension beyond the currently achieved precision. Long-standing numerical issues are overcome by performing the resummation directly in momentum space within soft collinear effective theory. We present the first numerical results for the LHC and observe an improved description of the available data. Our results are of immediate relevance for LHC precision phenomenology including the extraction of parton distribution functions and the QCD strong coupling constant.

Threshold and Jet Radius Joint Resummation for Single-Inclusive Jet Production

DOE PAGES

Liu, Xiaohui; Moch, Sven -Olaf; Ringer, Felix

2017-11-20

Here, we present the first threshold and jet radius jointly resummed cross section for single-inclusive hadronic jet production. We work at next-to-leading logarithmic accuracy and our framework allows for a systematic extension beyond the currently achieved precision. Long-standing numerical issues are overcome by performing the resummation directly in momentum space within soft collinear effective theory. We present the first numerical results for the LHC and observe an improved description of the available data. Our results are of immediate relevance for LHC precision phenomenology including the extraction of parton distribution functions and the QCD strong coupling constant.

Two-Jet Rate in e+e- at Next-to-Next-to-Leading-Logarithmic Order

NASA Astrophysics Data System (ADS)

Banfi, Andrea; McAslan, Heather; Monni, Pier Francesco; Zanderighi, Giulia

2016-10-01

We present the first next-to-next-to-leading-logarithmic resummation for the two-jet rate in e+e- annihilation in the Durham and Cambridge algorithms. The results are obtained by extending the ares method to observables involving any global, recursively infrared and collinear safe jet algorithm in e+e- collisions. As opposed to other methods, this approach does not require a factorization theorem for the observables. We present predictions matched to next-to-next-to-leading order and a comparison to LEP data.

Threshold resummation for top-pair hadroproduction to next-to-next-to-leading log

NASA Astrophysics Data System (ADS)

Czakon, Michal; Mitov, Alexander; Sterman, George

2009-10-01

We derive the threshold-resummed total cross section for heavy quark production in hadronic collisions accurate to next-to-next-to-leading logarithm, employing recent advances on soft anomalous dimension matrices for massive pair production in the relevant kinematic limit. We also derive the relation between heavy quark threshold resummations for fixed pair kinematics and the inclusive cross section. As a check of our results, we have verified that they reproduce all poles of the color-averaged qq¯→tt¯ amplitudes at two loops, noting that the latter are insensitive to the color-antisymmetric terms of the soft anomalous dimension.

Z-Boson Decays To A Vector Quarkonium Plus A Photon

DOE PAGES

Bodwin, Geoffrey T.; Chung, Hee Sok; Ee, June-Haak; ...

2018-01-18

We compute the decay rates for the processes Z → V + γ , where Z is the Z -boson, γ is the photon, and V is one of the vector quarkonia J / ψ or Υ ( n S ) , with n = 1 , 2, or 3. Our computations include corrections through relative orders α s and v 2 and resummations of logarithms of mmore » $$2\\atop{Z}$$/$$2\\atop{Q}$$, to all orders in α s , at next-to-leading-logarithmic accuracy. ( v is the velocity of the heavy quark Q or the heavy antiquark $$\\bar{Q}$$ in the quarkonium rest frame, and m Z and m Q are the masses of Z and Q , respectively.) Our calculations are the first to include both the order- α s correction to the light-cone distributions amplitude and the resummation of logarithms of m$$2\\atop{Z}$$/$$2\\atop{Q}$$ and are the first calculations for the Υ (2S) and Υ (3S) final states. The resummations of logarithms of m$$2\\atop{Z}$$/$$2\\atop{Q}$$ that are associated with the order- α s and order- v 2 corrections are carried out by making use of the Abel-Padé method. We confirm the analytic result for the order- v 2 correction that was presented in a previous publication, and we correct the relative sign of the direct and indirect amplitudes and some choices of scales in that publication. In conclusion, our branching fractions for Z → J / ψ + γ and Z → Υ (1 S) + γ differ by 2.0σ and -4.0 σ, respectively, from the branching fractions that are given in the most recent publication on this topic (in units of the uncertainties that are given in that publication). However, we argue that the uncertainties in the rates are underestimated in that publication.« less

Z-Boson Decays To A Vector Quarkonium Plus A Photon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bodwin, Geoffrey T.; Chung, Hee Sok; Ee, June-Haak

We compute the decay rates for the processes Z → V + γ , where Z is the Z -boson, γ is the photon, and V is one of the vector quarkonia J / ψ or Υ ( n S ) , with n = 1 , 2, or 3. Our computations include corrections through relative orders α s and v 2 and resummations of logarithms of mmore » $$2\\atop{Z}$$/$$2\\atop{Q}$$, to all orders in α s , at next-to-leading-logarithmic accuracy. ( v is the velocity of the heavy quark Q or the heavy antiquark $$\\bar{Q}$$ in the quarkonium rest frame, and m Z and m Q are the masses of Z and Q , respectively.) Our calculations are the first to include both the order- α s correction to the light-cone distributions amplitude and the resummation of logarithms of m$$2\\atop{Z}$$/$$2\\atop{Q}$$ and are the first calculations for the Υ (2S) and Υ (3S) final states. The resummations of logarithms of m$$2\\atop{Z}$$/$$2\\atop{Q}$$ that are associated with the order- α s and order- v 2 corrections are carried out by making use of the Abel-Padé method. We confirm the analytic result for the order- v 2 correction that was presented in a previous publication, and we correct the relative sign of the direct and indirect amplitudes and some choices of scales in that publication. In conclusion, our branching fractions for Z → J / ψ + γ and Z → Υ (1 S) + γ differ by 2.0σ and -4.0 σ, respectively, from the branching fractions that are given in the most recent publication on this topic (in units of the uncertainties that are given in that publication). However, we argue that the uncertainties in the rates are underestimated in that publication.« less

Precision direct photon spectra at high energy and comparison to the 8 TeV ATLAS data

DOE PAGES

Schwartz, Matthew D.

2016-09-01

The direct photon spectrum is computed to the highest currently available precision and compared to ATLAS data from 8 TeV collisions at the LHC. The prediction includes threshold resummation at next-to-next-to-next-to-leading logarithmic order through the program PeTeR, matched to next-to-leading fixed order with fragmentation effects using JetPhox and includes the resummation of leading-logarithmic electroweak Sudakov effects. Remarkably, improved agreement with data can be seen when each component of the calculation is added successively. This comparison demonstrates the importance of both threshold logs and electroweak Sudakov effects. Numerical values for the predictions are included.

Nonperturbative contributions to a resummed leptonic angular distribution in inclusive neutral vector boson production

NASA Astrophysics Data System (ADS)

Guzzi, Marco; Nadolsky, Pavel M.; Wang, Bowen

2014-07-01

We present an analysis of nonperturbative contributions to the transverse momentum distribution of Z/γ* bosons produced at hadron colliders. The new data on the angular distribution ϕη* of Drell-Yan pairs measured at the Tevatron are shown to be in excellent agreement with a perturbative QCD prediction based on the Collins-Soper-Sterman (CSS) resummation formalism at next-to-next-to-leading logarithmic (NNLL) accuracy. Using these data, we determine the nonperturbative component of the CSS resummed cross section and estimate its dependence on arbitrary resummation scales and other factors. With the scale dependence included at the NNLL level, a significant nonperturbative component is needed to describe the angular data.

A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Chiu, Jui-Yu; Jain, Ambar; Neill, Duff; Rothstein, Ira Z.

2012-05-01

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the relevant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. Such observables include: transverse momentum distributions at p T much less then the high energy scattering scale, jet broadening, exclusive hadroproduction and decay, as well as the Sudakov form factor. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any sce- nario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form fac- tor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are universal. We present details of the factorization and re- summation of the jet broadening cross section including a renormalization in p ⊥ space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

Delayed coherent quantum feedback from a scattering theory and a matrix product state perspective

NASA Astrophysics Data System (ADS)

Guimond, P.-O.; Pletyukhov, M.; Pichler, H.; Zoller, P.

2017-12-01

We study the scattering of photons propagating in a semi-infinite waveguide terminated by a mirror and interacting with a quantum emitter. This paradigm constitutes an example of coherent quantum feedback, where light emitted towards the mirror gets redirected back to the emitter. We derive an analytical solution for the scattering of two-photon states, which is based on an exact resummation of the perturbative expansion of the scattering matrix, in a regime where the time delay of the coherent feedback is comparable to the timescale of the quantum emitter’s dynamics. We compare the results with numerical simulations based on matrix product state techniques simulating the full dynamics of the system, and extend the study to the scattering of coherent states beyond the low-power limit.

Polarization and Resummation in Slepton Production at Hadron Colliders

NASA Astrophysics Data System (ADS)

Klasen, M.

2006-10-01

In R-parity conserving supersymmetric (SUSY) models, sleptons are produced in pairs at hadron colliders through neutral and charged electroweak currents. We demonstrate that the polarization of the initial hadron beams allows for a direct extraction of the slepton mixing angle and thus for a determination of the underlying SUSY-breaking mechanism. We also perform a first precision calculation of the transverse-momentum ( q T) spectrum of the slepton pairs by resumming soft multiple-gluon emission at next-to-leading logarithmic order. The results show a relevant contribution of resummation both in the small and intermediate q T-regions, which strongly influences the extraction of the missing transverse-momentum signal and the subsequent slepton mass-determination, and little dependence on unphysical scales and non-perturbative contributions.

Scheme dependence and transverse momentum distribution interpretation of Collins-Soper-Sterman resummation

DOE PAGES

Prokudin, Alexei; Sun, Peng; Yuan, Feng

2015-10-01

Following an earlier derivation by Catani-de Florian-Grazzini (2000) on the scheme dependence in the Collins-Soper- Sterman (CSS) resummation formalism in hard scattering processes, we investigate the scheme dependence of the Transverse Momentum Distributions (TMDs) and their applications. By adopting a universal C-coefficient function associated with the integrated parton distributions, the difference between various TMD schemes can be attributed to a perturbative calculable function depending on the hard momentum scale. Thus, we further apply several TMD schemes to the Drell-Yan process of lepton pair production in hadronic collisions, and find that the constrained non-perturbative form factors in different schemes are remarkablymore » consistent with each other and with that of the standard CSS formalism.« less

Scheme dependence and transverse momentum distribution interpretation of Collins-Soper-Sterman resummation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prokudin, Alexei; Sun, Peng; Yuan, Feng

Following an earlier derivation by Catani-de Florian-Grazzini (2000) on the scheme dependence in the Collins-Soper- Sterman (CSS) resummation formalism in hard scattering processes, we investigate the scheme dependence of the Transverse Momentum Distributions (TMDs) and their applications. By adopting a universal C-coefficient function associated with the integrated parton distributions, the difference between various TMD schemes can be attributed to a perturbative calculable function depending on the hard momentum scale. Thus, we further apply several TMD schemes to the Drell-Yan process of lepton pair production in hadronic collisions, and find that the constrained non-perturbative form factors in different schemes are remarkablymore » consistent with each other and with that of the standard CSS formalism.« less

Scheme dependence and transverse momentum distribution interpretation of Collins-Soper-Sterman resummation

NASA Astrophysics Data System (ADS)

Prokudin, Alexei; Sun, Peng; Yuan, Feng

2015-11-01

Following an earlier derivation by Catani, de Florian and Grazzini (2000) on the scheme dependence in the Collins-Soper-Sterman (CSS) resummation formalism in hard scattering processes, we investigate the scheme dependence of the Transverse Momentum Distributions (TMDs) and their applications. By adopting a universal C-coefficient function associated with the integrated parton distributions, the difference between various TMD schemes can be attributed to a perturbative calculable function depending on the hard momentum scale. We further apply several TMD schemes to the Drell-Yan process of lepton pair production in hadronic collisions, and find that the constrained non-perturbative form factors in different schemes are consistent with each other and with that of the standard CSS formalism.

New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon

NASA Astrophysics Data System (ADS)

Bodwin, Geoffrey T.; Chung, Hee Sok; Ee, June-Haak; Lee, Jungil

2017-03-01

We present a calculation of the rates for Higgs-boson decays to a vector heavy-quarkonium state plus a photon, where the heavy-quarkonium states are the J /ψ and the ϒ (n S ) states, with n =1 , 2, or 3. The calculation is carried out in the light-cone formalism, combined with nonrelativistic QCD factorization, and is accurate at leading order in mQ2/mH2, where mQ is the heavy-quark mass and mH is the Higgs-boson mass. The calculation contains corrections through next-to-leading order in the strong-coupling constant αs and the square of the heavy-quark velocity v , and includes a resummation of logarithms of mH2/mQ2 at next-to-leading logarithmic accuracy. We have developed a new method, which makes use of Abel summation, accelerated through the use of Padé approximants, to deal with divergences in the resummed expressions for the quarkonium light-cone distribution amplitudes. This approach allows us to make definitive calculations of the resummation effects. Contributions from the order-αs and order-v2 corrections to the light-cone distribution amplitudes that we obtain with this new method differ substantially from the corresponding contributions that one obtains from a model light-cone distribution amplitude [M. König and M. Neubert, J. High Energy Phys. 08 (2015) 012, 10.1007/JHEP08(2015)012]. Our results for the real parts of the direct-process amplitudes are considerably smaller than those from one earlier calculation [G. T. Bodwin, H. S. Chung, J.-H. Ee, J. Lee, and F. Petriello, Phys. Rev. D 90, 113010 (2014), 10.1103/PhysRevD.90.113010], reducing the sensitivity to the Higgs-boson-heavy-quark couplings, and are somewhat smaller than those from another earlier calculation [M. König and M. Neubert, J. High Energy Phys. 08 (2015) 012, 10.1007/JHEP08(2015)012]. However, our results for the standard-model Higgs-boson branching fractions are in good agreement with those in M. König and M. Neubert, J. High Energy Phys. 08 (2015) 012, 10.1007/JHEP08(2015)012.

Theories of time-dependent and time-independent nearside-farside reactive scattering dynamics

NASA Astrophysics Data System (ADS)

Monks, Phillip David Durrant

The first application of nearside-farside (NF) theory is made to the time-dependent partial wave series (PWS) representation of the scattering amplitude for the reaction H + D[2](v = 0,j = 0, m = 0) → HD(v' = 3,j' = 0, m'= 0) + D. Time-dependent NF angular distributions and time-dependent NF local angular momenta (LAMs) are defined and used to analyse the dynamics in terms of time- direct and time-delayed reaction mechanisms. The concept of a cumulative time-evolving differential cross section (DCS) is introduced and used to provide a new method for visualising the time evolution of a chemical reaction. Time-independent NF DCS and LAM analyses of the H + D[2] reaction are presented, highlighting a distinctive "trench-ridge" feature present in the full and N LAMs. It is used to define a cut line which separates the energy-analogs of the two time- distinct reaction mechanisms. This trench-ridge feature is shown to be an interference between the time-direct (backward-scattered) and time-delayed (forward-scattered) reaction mechanisms. Resummation PWS theory is used to "clean" plots of the NF DCSs and LAMs of unphysical effects. A limitation of the resummation theory is described, whereby unphysical behaviour is sometimes introduced into the N and F subamplitudes. A technique for predicting and avoiding these undesired effects is used to further improve the usefulness of the resummation technique. The fundamental identity for NF local angular momenta is stated and derived by two methods. This identity gives rise to a CLAM plot (where CLAM denotes Cross section x LAM), which provides insight into the empirical obsei'vation that DCS and LAM analyses give consistent, yet complementary, information on the reaction dynamics. Applications are reported for the H + D[2] reaction, as well as for F + H[2](v = 0,j=0, m = 0)→ FH(v' = 3,j' = 3, m' = 0) + H. The angular time-delay for a state-to-state reactive collision often displays complicated behaviour. It is shown for the H + D[2] and F + H[2] reactions that this behaviour is caused by NF interference. The fundamental identity for NF angular time-delays is stated, and CATD (Cross section x Angular Time-Delay) results are reported, which provide further insight into the properties of the angular time-delay.

Novel Infrared Dynamics of Cold Atoms on Hot Graphene

NASA Astrophysics Data System (ADS)

Sengupta, Sanghita; Kotov, Valeri; Clougherty, Dennis

The low-energy dynamics of cold atoms interacting with macroscopic graphene membranes exhibits severe infrared divergences when treated perturbatively. These infrared problems are even more pronounced at finite temperature due to the (infinitely) many flexural phonons excited in graphene. We have devised a technique to take account (resummation) of such processes in the spirit of the well-known exact solution of the independent boson model. Remarkably, there is also similarity to the infrared problems and their treatment (via the Bloch-Nordsieck scheme) in finite temperature ``hot'' quantum electrodynamics and chromodynamics due to the long-range, unscreened nature of gauge interactions. The method takes into account correctly the strong damping provided by the many emitted phonons at finite temperature. In our case, the inverse membrane size plays the role of an effective low-energy scale, and, unlike the above mentioned field theories, there remains an unusual, highly nontrivial dependence on that scale due to the 2D nature of the problem. We present detailed results for the sticking (atomic damping rate) rate of cold atomic hydrogen as a function of the membrane temperature and size. We find that the rate is very strongly dependent on both quantities.

An Exponential Regulator for Rapidity Divergences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Ye; Neill, Duff; Zhu, Hua Xing

2016-04-01

Finding an efficient and compelling regularization of soft and collinear degrees of freedom at the same invariant mass scale, but separated in rapidity is a persistent problem in high-energy factorization. In the course of a calculation, one encounters divergences unregulated by dimensional regularization, often called rapidity divergences. Once regulated, a general framework exists for their renormalization, the rapidity renormalization group (RRG), leading to fully resummed calculations of transverse momentum (to the jet axis) sensitive quantities. We examine how this regularization can be implemented via a multi-differential factorization of the soft-collinear phase-space, leading to an (in principle) alternative non-perturbative regularization ofmore » rapidity divergences. As an example, we examine the fully-differential factorization of a color singlet's momentum spectrum in a hadron-hadron collision at threshold. We show how this factorization acts as a mother theory to both traditional threshold and transverse momentum resummation, recovering the classical results for both resummations. Examining the refactorization of the transverse momentum beam functions in the threshold region, we show that one can directly calculate the rapidity renormalized function, while shedding light on the structure of joint resummation. Finally, we show how using modern bootstrap techniques, the transverse momentum spectrum is determined by an expansion about the threshold factorization, leading to a viable higher loop scheme for calculating the relevant anomalous dimensions for the transverse momentum spectrum.« less

Threshold resummation of the rapidity distribution for Higgs production at NNLO +NNLL

NASA Astrophysics Data System (ADS)

Banerjee, Pulak; Das, Goutam; Dhani, Prasanna K.; Ravindran, V.

2018-03-01

We present a formalism that resums threshold-enhanced logarithms to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We achieve this by exploiting the factorization properties and K +G equations satisfied by the soft and virtual parts of the cross section. We compute for the first time compact and most general expressions in two-dimensional Mellin space for the resummed coefficients. Using various state-of-the-art multiloop and multileg results, we demonstrate the numerical impact of our resummed results up to next-to-next-to-leading order for the rapidity distribution of the Higgs boson at the LHC. We find that inclusion of these threshold logs through resummation improves the reliability of perturbative predictions.

Theory of the classical electron gas

NASA Technical Reports Server (NTRS)

Guernsey, R. L.

1978-01-01

In a previous paper Cohen and Murphy (1969) used the Meeron resummation (1958) of the Mayer diagrams (1950) to calculate the pair correlation for the classical electron gas in thermal equilibrium. They found that successive terms in the expression for the pair correlation were more and more singular for small interparticle spacing, actually dominating the Debye-Hueckel result for sufficiently small distances. This led to apparent divergence in the higher order contributions to the internal energy. The present paper shows that the apparent anomalies in the Cohen-Murphy results can be removed without further resummation by a more careful treatment of the region of small interparticle spacing. It is shown that there is really no anomalous behavior at short range in any order and all integrals in the expression for the internal energy converge.

Nonperturbative Contributions to a Resummed Leptonic Angular Distribution in Inclusive Z/γ* Boson Production

NASA Astrophysics Data System (ADS)

Guzzi, Marco; Nadolsky, Pavel M.

We summarize a new analysis of the distribution φ η * of charged leptons produced in decays of Z and γ* bosons in the Collins-Soper-Sterman (CSS) formalism for transverse momentum resummation. By comparing the φ η * distribution measured at the Tevatron with the resummed CSS cross section with approximate {O}(α s2) Wilson coefficients, we constrain the magnitude of the nonperturbative Gaussian smearing factor and analyze its uncertainty caused by variations in scale parameters. We find excellent agreement between the φ η * data and our theoretical prediction, provided by the RESBOS resummation program. The nonperturbative factor that we obtained can be used to update resummed QCD predictions for precision measurements in inclusive W and Z production and for comparisons to various models of nonperturbative dynamics.

Borel Summability of Perturbative Series in 4D N=2 and 5D N=1 Supersymmetric Theories.

PubMed

Honda, Masazumi

2016-05-27

We study weak coupling perturbative series in 4D N=2 and 5D N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in the zero-instanton sector are Borel summable for various observables. Our result for the 4D N=2 case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely, Borel summable. We also prove that the perturbative series in an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.

Factorization and resummation: A new paradigm to improve gravitational wave amplitudes. II. The higher multipolar modes

NASA Astrophysics Data System (ADS)

Messina, Francesco; Maldarella, Alberto; Nagar, Alessandro

2018-04-01

The factorization and resummation approach of Nagar and Shah [Phys. Rev. D 94, 104017 (2016), 10.1103/PhysRevD.94.104017], designed to improve the strong-field behavior of the post-Newtonian (PN) residual waveform amplitudes fℓm's entering the effective-one-body, circularized, gravitational waveform for spinning coalescing binaries, is improved and generalized here to all multipoles up to ℓ=6 . For a test particle orbiting a Kerr black hole, each multipolar amplitude is truncated at relative 6 PN order, both for the orbital (nonspinning) and spin factors. By taking a certain Padé approximant (typically the P24 one) of the orbital factor in conjunction with the inverse Taylor (iResum) representation of the spin factor, it is possible to push the analytical/numerical agreement of the energy flux at the level of 5% at the last-stable orbit for a quasimaximally spinning black hole with dimensionless spin parameter +0.99 . When the procedure is generalized to comparable-mass binaries, each orbital factor is kept at relative 3+3 PN order; i.e., the globally 3 PN-accurate comparable-mass terms are hybridized with higher-PN test-particle terms up to 6 PN relative order in each mode. The same Padé resummation is used for continuity. By contrast, the spin factor is only kept at the highest comparable-mass PN order currently available. We illustrate that the consistency between different truncations in the spin content of the waveform amplitudes is more marked in the resummed case than when using the standard Taylor-expanded form of Pan et al. [Phys. Rev. D 83, 064003 (2011), 10.1103/PhysRevD.83.064003]. We finally introduce a method to consistently hybridize comparable-mass and test-particle information also in the presence of spin (including the spin of the particle), discussing it explicitly for the ℓ=m =2 spin-orbit and spin-square terms. The improved, factorized and resummed, multipolar waveform amplitudes presented here are expected to set a new standard for effective one body-based gravitational waveform models.

Generalized quantum kinetic expansion: Higher-order corrections to multichromophoric Förster theory

NASA Astrophysics Data System (ADS)

Wu, Jianlan; Gong, Zhihao; Tang, Zhoufei

2015-08-01

For a general two-cluster energy transfer network, a new methodology of the generalized quantum kinetic expansion (GQKE) method is developed, which predicts an exact time-convolution equation for the cluster population evolution under the initial condition of the local cluster equilibrium state. The cluster-to-cluster rate kernel is expanded over the inter-cluster couplings. The lowest second-order GQKE rate recovers the multichromophoric Förster theory (MCFT) rate. The higher-order corrections to the MCFT rate are systematically included using the continued fraction resummation form, resulting in the resummed GQKE method. The reliability of the GQKE methodology is verified in two model systems, revealing the relevance of higher-order corrections.

On the accuracy of the Padé-resummed master equation approach to dissipative quantum dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Hsing-Ta; Reichman, David R.; Berkelbach, Timothy C.

2016-04-21

Well-defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Padé resummation of the first two moments in the electronic coupling. These criteria partition the parameter space into distinct levels of expected accuracy, ranging from quantitatively accurate regimes to regions of parameter space where the approach is not expected to be applicable. Extensive comparison of Padé-resummed master equations with numerically exact results in the context of the spin–boson model demonstrates that the proposed criteria correctly demarcate the regions of parameter space where the Padé approximation is reliable. The applicability analysis we presentmore » is not confined to the specifics of the Hamiltonian under consideration and should provide guidelines for other classes of resummation techniques.« less

Double Resummation for Higgs Production

NASA Astrophysics Data System (ADS)

Bonvini, Marco; Marzani, Simone

2018-05-01

We present the first double-resummed prediction of the inclusive cross section for the main Higgs production channel in proton-proton collisions, namely, gluon fusion. Our calculation incorporates to all orders in perturbation theory two distinct towers of logarithmic corrections which are enhanced, respectively, at threshold, i.e., large x , and in the high-energy limit, i.e., small x . Large-x logarithms are resummed to next-to-next-to-next-to-leading logarithmic accuracy, while small-x ones to leading logarithmic accuracy. The double-resummed cross section is furthermore matched to the state-of-the-art fixed-order prediction at next-to-next-to-next-to-leading accuracy. We find that double resummation corrects the Higgs production rate by 2% at the currently explored center-of-mass energy of 13 TeV and its impact reaches 10% at future circular colliders at 100 TeV.

Light-cone singularities and transverse-momentum-dependent factorization at twist-3

NASA Astrophysics Data System (ADS)

Chen, A. P.; Ma, J. P.

2017-05-01

We study transverse-momentum-dependent factorization at twist-3 for Drell-Yan processes. The factorization can be derived straightforwardly at leading order of αs. But at this order we find that light-cone singularities already exist and effects of soft gluons are not correctly factorized. We regularize the singularities with gauge links off the light-cone and introduce a soft factor to factorize the effects of soft gluons. Interestingly, the soft factor must be included in the definition of subtracted TMD parton distributions to correctly factorize the effects of soft gluons. We derive the Collins-Soper equation for one of twist-3 TMD parton distributions. The equation can be useful for resummation of large logarithms terms appearing in the corresponding structure function in collinear factorization. However, the derived equation is nonhomogeneous. This will make the resummation complicated.

A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

NASA Astrophysics Data System (ADS)

Kang, Daekyoung; Lee, Christopher; Vaidya, Varun

2018-04-01

We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons ( γ ∗, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.

A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kang, Daekyoung; Lee, Christopher; Vaidya, Varun

Here, we propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons (γ*, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impactmore » parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.« less

A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

DOE PAGES

Kang, Daekyoung; Lee, Christopher; Vaidya, Varun

2018-04-27

Here, we propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons (γ*, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impactmore » parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.« less

Semi-inclusive Deep Inelastic Scattering at Small-x

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marquet, C.; Xiao, B.-W.; Yuan, Feng

We study the semi-inclusive hadron production in deep inelastic scattering at small-x.A transverse momentum dependent factorization is found consistent with the resultscalculated in the color-dipole framework in the appropriate kinematic region. The transverse momentum dependent quark distribution can be studied in this processas a probe for the small-x saturation physics. Especially, the ratio of the quark distributions as functions of transverse momentum at different x demonstrates strong dependence on the saturation scale. The Q2 dependence of the same ratio is also studied by applying the Collins-Soper-Sterman resummation method.

Exact semiclassical expansions for one-dimensional quantum oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delabaere, E.; Dillinger, H.; Pham, F.

1997-12-01

A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borelmore » resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}« less

Particle–hole ring diagrams for fermions in two dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaiser, N., E-mail: nkaiser@ph.tum.de

2014-11-15

The set of particle–hole ring diagrams for a many-fermion system in two dimensions is studied. The complex-valued polarization function is derived in detail and shown to be expressible in terms of square-root functions. For a contact-interaction the perturbative contributions to the energy per particle Ē(k{sub f}) are calculated in a closed analytical form from third up to twelfth order. The resummation of the particle–hole ring diagrams to all orders is studied and a pronounced dependence on the dimensionless coupling parameter α is found. There is a substantial difference between the complete ring-sum with all exchange-type diagrams included and the standardmore » resummation of the leading n-ring diagrams only. The spin factor S{sub n}(g) associated to the nth order ring diagrams is derived for arbitrary spin-degeneracy g.« less

Replica Resummation of the Baker-Campbell-Hausdorff Series

NASA Astrophysics Data System (ADS)

Vajna, Szabolcs; Klobas, Katja; Prosen, Tomaž; Polkovnikov, Anatoli

2018-05-01

We developed a novel perturbative expansion based on the replica trick for the Floquet Hamiltonian governing the dynamics of periodically kicked systems where the kick strength is the small parameter. The expansion is formally equivalent to an infinite resummation of the Baker-Campbell-Hausdorff series in the undriven (nonperturbed) Hamiltonian, while considering terms up to a finite order in the kick strength. As an application of the replica expansion, we analyze an Ising spin 1 /2 chain periodically kicked with a magnetic field with a strength h , which has both longitudinal and transverse components. We demonstrate that even away from the regime of high frequency driving, if there is heating, its rate is nonperturbative in the kick strength, bounded from above by a stretched exponential: e-const h-1 /2 . This guarantees the existence of a very long prethermal regime, where the dynamics is governed by the Floquet Hamiltonian obtained from the replica expansion.

The Higgs transverse momentum distribution at NNLL and its theoretical errors

DOE PAGES

Neill, Duff; Rothstein, Ira Z.; Vaidya, Varun

2015-12-15

In this letter, we present the NNLL-NNLO transverse momentum Higgs distribution arising from gluon fusion. In the regime p ⊥ << m h we include the resummation of the large logs at next to next-to leading order and then match on to the α 2 s fixed order result near p ⊥~m h. By utilizing the rapidity renormalization group (RRG) we are able to smoothly match between the resummed, small p ⊥ regime and the fixed order regime. We give a detailed discussion of the scale dependence of the result including an analysis of the rapidity scale dependence. Our centralmore » value differs from previous results, in the transition region as well as the tail, by an amount which is outside the error band. Lastly, this difference is due to the fact that the RRG profile allows us to smoothly turn off the resummation.« less

Transverse momentum in double parton scattering: factorisation, evolution and matching

NASA Astrophysics Data System (ADS)

Buffing, Maarten G. A.; Diehl, Markus; Kasemets, Tomas

2018-01-01

We give a description of double parton scattering with measured transverse momenta in the final state, extending the formalism for factorisation and resummation developed by Collins, Soper and Sterman for the production of colourless particles. After a detailed analysis of their colour structure, we derive and solve evolution equations in rapidity and renormalisation scale for the relevant soft factors and double parton distributions. We show how in the perturbative regime, transverse momentum dependent double parton distributions can be expressed in terms of simpler nonperturbative quantities and compute several of the corresponding perturbative kernels at one-loop accuracy. We then show how the coherent sum of single and double parton scattering can be simplified for perturbatively large transverse momenta, and we discuss to which order resummation can be performed with presently available results. As an auxiliary result, we derive a simple form for the square root factor in the Collins construction of transverse momentum dependent parton distributions.

Holographic reconstruction of AdS exchanges from crossing symmetry

DOE PAGES

Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric

2017-08-31

Motivated by AdS/CFT, we address the following outstanding question in large N conformal field theory: given the appearance of a single-trace operator in the O x O OPE of a scalar primary O, what is its total contribution to the vacuum four-point function (OOOO) as dictated by crossing symmetry? We solve this problem in 4d conformal field theories at leading order in 1/N. Viewed holographically, this provides a field theory reconstruction of crossing-symmetric, four-point exchange amplitudes in AdS 5. Our solution takes the form of a resummation of the large spin solution to the crossing equations, supplemented by corrections atmore » finite spin, required by crossing. The method can be applied to the exchange of operators of arbitrary twist τ and spin s, although it vastly simplifies for even-integer twist, where we give explicit results. The output is the set of OPE data for the exchange of all double-trace operators [OO] n,ℓ. We find that the double-trace anomalous dimensions γ n,ℓ are negative, monotonic and convex functions of ℓ, for all n and all ℓ > s. This constitutes a holographic signature of bulk causality and classical dynamics of even-spin fields. We also find that the “derivative relation” between double-trace anomalous dimensions and OPE coefficients does not hold in general, and derive the explicit form of the deviation in several cases. Finally, we study large n limits of γ n,ℓ, relevant for the Regge and bulk-point regimes.« less

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

NASA Astrophysics Data System (ADS)

Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.

2018-02-01

The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

Post-Newtonian factorized multipolar waveforms for spinning, nonprecessing black-hole binaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Yi; Buonanno, Alessandra; Racine, Etienne

2011-03-15

We generalize the factorized resummation of multipolar waveforms introduced by Damour, Iyer, and Nagar to spinning black holes. For a nonspinning test particle spiraling a Kerr black hole in the equatorial plane, we find that factorized multipolar amplitudes which replace the residual relativistic amplitude f{sub lm} with its lth root, {rho}{sub lm}=f{sub lm}{sup 1/l}, agree quite well with the numerical amplitudes up to the Kerr-spin value q{<=}0.95 for orbital velocities v{<=}0.4. The numerical amplitudes are computed solving the Teukolsky equation with a spectral code. The agreement for prograde orbits and large spin values of the Kerr black-hole can be furthermore » improved at high velocities by properly factoring out the lower-order post-Newtonian contributions in {rho}{sub lm}. The resummation procedure results in a better and systematic agreement between numerical and analytical amplitudes (and energy fluxes) than standard Taylor-expanded post-Newtonian approximants. This is particularly true for higher-order modes, such as (2,1), (3,3), (3,2), and (4,4), for which less spin post-Newtonian terms are known. We also extend the factorized resummation of multipolar amplitudes to generic mass-ratio, nonprecessing, spinning black holes. Lastly, in our study we employ new, recently computed, higher-order post-Newtonian terms in several subdominant modes and compute explicit expressions for the half and one-and-half post-Newtonian contributions to the odd-parity (current) and even-parity (odd) multipoles, respectively. Those results can be used to build more accurate templates for ground-based and space-based gravitational-wave detectors.« less

Convergence from divergence

NASA Astrophysics Data System (ADS)

Costin, Ovidiu; Dunne, Gerald V.

2018-01-01

We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series. This can be interpreted physically as a novel resummation of perturbative series. Being convergent, these new series allow rigorous extrapolation from an asymptotic region with a large parameter, to the opposite region where the parameter is small. We illustrate the method with various physical examples, and discuss how these convergent series relate to standard methods such as Borel summation, and also how they incorporate the physical Stokes phenomenon. We comment on the relation of these results to Dyson’s physical argument for the divergence of perturbation theory. This approach also leads naturally to a wide class of relations between bosonic and fermionic partition functions, and Klein-Gordon and Dirac determinants.

Dressed tunneling approximation for electronic transport through molecular transistors

NASA Astrophysics Data System (ADS)

Seoane Souto, R.; Yeyati, A. Levy; Martín-Rodero, A.; Monreal, R. C.

2014-02-01

A theoretical approach for the nonequilibrium transport properties of nanoscale systems coupled to metallic electrodes with strong electron-phonon interactions is presented. It consists of a resummation of the dominant Feynman diagrams from the perturbative expansion in the coupling to the leads. We show that this scheme eliminates the main pathologies found in previous simple analytical approaches for the polaronic regime. The results for the spectral and transport properties are compared with those from several other approaches for a wide range of parameters. The method can be formulated in a simple way to obtain the full counting statistics. Results for the shot and thermal noise are presented.

Resumming double logarithms in the QCD evolution of color dipoles

DOE PAGES

Iancu, E.; Madrigal, J. D.; Mueller, A. H.; ...

2015-05-01

The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. This equation can be equivalently rewritten inmore » local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. We extend this resummation to the next-to-leading order BFKL and BK equations. The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.« less

Renormalization of dijet operators at order 1 /Q 2 in soft-collinear effective theory

NASA Astrophysics Data System (ADS)

Goerke, Raymond; Inglis-Whalen, Matthew

2018-05-01

We make progress towards resummation of power-suppressed logarithms in dijet event shapes such as thrust, which have the potential to improve high-precision fits for the value of the strong coupling constant. Using a newly developed formalism for Soft-Collinear Effective Theory (SCET), we identify and compute the anomalous dimensions of all the operators that contribute to event shapes at order 1 /Q 2. These anomalous dimensions are necessary to resum power-suppressed logarithms in dijet event shape distributions, although an additional matching step and running of observable-dependent soft functions will be necessary to complete the resummation. In contrast to standard SCET, the new formalism does not make reference to modes or λ-scaling. Since the formalism does not distinguish between collinear and ultrasoft degrees of freedom at the matching scale, fewer subleading operators are required when compared to recent similar work. We demonstrate how the overlap subtraction prescription extends to these subleading operators.

Effective field theory approach to heavy quark fragmentation

DOE PAGES

Fickinger, Michael; Fleming, Sean; Kim, Chul; ...

2016-11-17

Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the b-quark fragmentation function from electron-positron annihilation data at the Z-boson peak at next-to-next-to leading order with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to-next-to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the b-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Usingmore » an approach based on effective field theory allows us to systematically control theoretical errors. Furthermore, while the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the b-quark fragmentation function at smaller values of momentum fraction.« less

Spin polarized photons from an axially charged plasma at weak coupling: Complete leading order

DOE PAGES

Mamo, Kiminad A.; Yee, Ho-Ung

2016-03-24

In the presence of (approximately conserved) axial charge in the QCD plasma at finite temperature, the emitted photons are spin aligned, which is a unique P- and CP-odd signature of axial charge in the photon emission observables. We compute this “P-odd photon emission rate” in a weak coupling regime at a high temperature limit to complete leading order in the QCD coupling constant: the leading log as well as the constant under the log. As in the P-even total emission rate in the literature, the computation of the P-odd emission rate at leading order consists of three parts: (1) Comptonmore » and pair annihilation processes with hard momentum exchange, (2) soft t- and u-channel contributions with hard thermal loop resummation, (3) Landau-Pomeranchuk-Migdal resummation of collinear bremsstrahlung and pair annihilation. In conclusion, we present analytical and numerical evaluations of these contributions to our P-odd photon emission rate observable.« less

High precision predictions for exclusive VH production at the LHC

DOE PAGES

Li, Ye; Liu, Xiaohui

2014-06-04

We present a resummation-improved prediction for pp → VH + 0 jets at the Large Hadron Collider. We focus on highly-boosted final states in the presence of jet veto to suppress the tt¯ background. In this case, conventional fixed-order calculations are plagued by the existence of large Sudakov logarithms α n slog m(p veto T/Q) for Q ~ m V + m H which lead to unreliable predictions as well as large theoretical uncertainties, and thus limit the accuracy when comparing experimental measurements to the Standard Model. In this work, we show that the resummation of Sudakov logarithms beyond themore » next-to-next-to-leading-log accuracy, combined with the next-to-next-to-leading order calculation, reduces the scale uncertainty and stabilizes the perturbative expansion in the region where the vector bosons carry large transverse momentum. Thus, our result improves the precision with which Higgs properties can be determined from LHC measurements using boosted Higgs techniques.« less

Heavy quarkonium production at low P⊥ in nonrelativistic QCD with soft gluon resummation

NASA Astrophysics Data System (ADS)

Sun, Peng; Yuan, C.-P.; Yuan, Feng

2013-09-01

We extend the nonrelativistic QCD (NRQCD) prediction for the production of heavy quarkonium with low transverse momentum in hadronic collisions by taking into account effects from all-order soft gluon resummation. Following the Collins-Soper-Sterman formalism, we resum the most singular terms in the partonic subprocesses. The theoretical predictions of J/ψ and Υ productions are compared to the experimental data from the fixed target experiments (E866) and the collider experiments (RHIC, Tevatron, LHC). The associated nonperturbative Sudakov form factor for the gluon distributions is found to be different from the previous assumption of rescaling the quark form factor by the ratio of color factors. This conclusion should be further checked by future experiments on Higgs boson and/or diphoton production in pp collisions. We also comment on the implication of our results on determining the color-octet matrix elements associated with the J/ψ and Υ productions in the NRQCD factorization formalism.

Long range correlation in Higgs boson plus two jets production at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Peng; Yuan, C. -P.; Yuan, Feng

Here, we study Higgs boson plus two high energy jets production at the LHC in the kinematics where the two jets are well separated in rapidity. The partonic processes are dominated by the t-channel weak boson fusion (WBF) and gluon fusion (GF) contributions. We derive the associated QCD resummation formalism for the correlation analysis where the total transverse momentum q⊥ of the Higgs boson and two jets is small. Because of different color structures, the resummation results lead to distinguished behaviors: the WBF contribution peaks at relative low q⊥ while all GF channel contributions are strongly de-correlated and spread tomore » a much wider q⊥ range. Furthermore, by applying a kinematic cut on q⊥, one can effectively increase the WBF signal to the GF background by a significant factor. This, then strengthens the ability to investigate the WBF channel in Higgs boson production and study the couplings of Higgs to electroweak bosons.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolodrubetz, Daniel W.; Pietrulewicz, Piotr; Stewart, Iain W.

To predict the jet mass spectrum at a hadron collider it is crucial to account for the resummation of logarithms between the transverse momentum of the jet and its invariant mass m J . For small jet areas there are additional large logarithms of the jet radius R, which affect the convergence of the perturbative series. We present an analytic framework for exclusive jet production at the LHC which gives a complete description of the jet mass spectrum including realistic jet algorithms and jet vetoes. It factorizes the scales associated with m J , R, and the jet veto, enablingmore » in addition the systematic resummation of jet radius logarithms in the jet mass spectrum beyond leading logarithmic order. We discuss the factorization formulae for the peak and tail region of the jet mass spectrum and for small and large R, and the relations between the different regimes and how to combine them. Regions of experimental interest are classified which do not involve large nonglobal logarithms. We also present universal results for nonperturbative effects and discuss various jet vetoes.« less

Linearized self-consistent quasiparticle GW method: Application to semiconductors and simple metals

NASA Astrophysics Data System (ADS)

Kutepov, A. L.; Oudovenko, V. S.; Kotliar, G.

2017-10-01

We present a code implementing the linearized quasiparticle self-consistent GW method (LQSGW) in the LAPW basis. Our approach is based on the linearization of the self-energy around zero frequency which differs it from the existing implementations of the QSGW method. The linearization allows us to use Matsubara frequencies instead of working on the real axis. This results in efficiency gains by switching to the imaginary time representation in the same way as in the space time method. The all electron LAPW basis set eliminates the need for pseudopotentials. We discuss the advantages of our approach, such as its N3 scaling with the system size N, as well as its shortcomings. We apply our approach to study the electronic properties of selected semiconductors, insulators, and simple metals and show that our code produces the results very close to the previously published QSGW data. Our implementation is a good platform for further many body diagrammatic resummations such as the vertex-corrected GW approach and the GW+DMFT method. Program Files doi:http://dx.doi.org/10.17632/cpchkfty4w.1 Licensing provisions: GNU General Public License Programming language: Fortran 90 External routines/libraries: BLAS, LAPACK, MPI (optional) Nature of problem: Direct implementation of the GW method scales as N4 with the system size, which quickly becomes prohibitively time consuming even in the modern computers. Solution method: We implemented the GW approach using a method that switches between real space and momentum space representations. Some operations are faster in real space, whereas others are more computationally efficient in the reciprocal space. This makes our approach scale as N3. Restrictions: The limiting factor is usually the memory available in a computer. Using 10 GB/core of memory allows us to study the systems up to 15 atoms per unit cell.

Semi-inclusive deep inelastic scattering at small- x

NASA Astrophysics Data System (ADS)

Marquet, Cyrille; Xiao, Bo-Wen; Yuan, Feng

2009-11-01

We study the semi-inclusive hadron production in deep inelastic scattering at small-x. A transverse-momentum-dependent factorization is found consistent with the results calculated in the small-x approaches, such as the color-dipole framework and the color glass condensate, in the appropriate kinematic region at the lowest order. The transverse-momentum-dependent quark distribution can be studied in this process as a probe for the small-x saturation physics. Especially, the ratio of quark distributions as a function of transverse momentum at different x demonstrates strong dependence on the saturation scale. The Q2 dependence of the same ratio is also studied by applying the Collins-Soper-Sterman resummation method.

Underlying-event sensitive observables in Drell–Yan production using GENEVA

DOE PAGES

Alioli, Simone; Bauer, Christian W.; Guns, Sam; ...

2016-11-09

We present an extension of the Geneva Monte Carlo framework to include multiple parton interactions (MPI) provided by Pythia8. This allows us to obtain predictions for underlying-event sensitive measurements in Drell–Yan production, in conjunction with Geneva ’s fully differential NNLO calculation, NNLL' resummation for the 0-jet resolution variable (beam thrust), and NLL resummation for the 1-jet resolution variable. We describe the interface with the parton-shower algorithm and MPI model of Pythia8, which preserves both the precision of the partonic N-jet cross sections in Geneva as well as the shower accuracy and good description of soft hadronic physics of Pythia8. Wemore » present results for several underlying-event sensitive observables and compare to data from ATLAS and CMS as well as to standalone Pythia8 predictions. This includes a comparison with the recent ATLAS measurement of the beam thrust spectrum, which provides a potential avenue to fully disentangle the physical effects from the primary hard interaction, primary soft radiation, multiple parton interactions, and nonperturbative hadronization.« less

Two-loop beam and soft functions for rapidity-dependent jet vetoes

NASA Astrophysics Data System (ADS)

Gangal, Shireen; Gaunt, Jonathan R.; Stahlhofen, Maximilian; Tackmann, Frank J.

2017-02-01

Jet vetoes play an important role in many analyses at the LHC. Traditionally, jet vetoes have been imposed using a restriction on the transverse momentum p Tj of jets. Alternatively, one can also consider jet observables for which p Tj is weighted by a smooth function of the jet rapidity y j that vanishes as | y j | → ∞. Such observables are useful as they provide a natural way to impose a tight veto on central jets but a looser one at forward rapidities. We consider two such rapidity-dependent jet veto observables, T_{Bj} and {T_{Cj} , and compute the required beam and dijet soft functions for the jet-vetoed color-singlet production cross section at two loops. At this order, clustering effects from the jet algorithm become important. The dominant contributions are computed fully analytically while corrections that are subleading in the limit of small jet radii are expressed in terms of finite numerical integrals. Our results enable the full NNLL' resummation and are an important step towards N3LL resummation for cross sections with a T_{Bj} or T_{Cj} jet veto.

Underlying-event sensitive observables in Drell–Yan production using GENEVA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alioli, Simone; Bauer, Christian W.; Guns, Sam

We present an extension of the Geneva Monte Carlo framework to include multiple parton interactions (MPI) provided by Pythia8. This allows us to obtain predictions for underlying-event sensitive measurements in Drell–Yan production, in conjunction with Geneva ’s fully differential NNLO calculation, NNLL' resummation for the 0-jet resolution variable (beam thrust), and NLL resummation for the 1-jet resolution variable. We describe the interface with the parton-shower algorithm and MPI model of Pythia8, which preserves both the precision of the partonic N-jet cross sections in Geneva as well as the shower accuracy and good description of soft hadronic physics of Pythia8. Wemore » present results for several underlying-event sensitive observables and compare to data from ATLAS and CMS as well as to standalone Pythia8 predictions. This includes a comparison with the recent ATLAS measurement of the beam thrust spectrum, which provides a potential avenue to fully disentangle the physical effects from the primary hard interaction, primary soft radiation, multiple parton interactions, and nonperturbative hadronization.« less

Measurements of the electron and muon inclusive cross-sections in proton–proton collisions at s = 7   TeV with the ATLAS detector

DOE PAGES

Aad, G.; Abbott, B.; Abdallah, J.; ...

2011-12-27

Here, this Letter presents measurements of the differential cross-sections for inclusive electron and muon production in proton–proton collisions at a centre-of-mass energy of √s = 7 TeV, using data collected by the ATLAS detector at the LHC. The muon cross-section is measured as a function of p T in the range 4 < p T < 100 GeV and within pseudorapidity |η| < 2.5. In addition the electron and muon cross-sections are measured in the range 7 < p T < 26 GeV and within |η| < 2.0, excluding 1.37 < |η| < 1.52. Integrated luminosities of 1.3 pb –1more » and 1.4 pb –1 are used for the electron and muon measurements, respectively. After subtraction of the W/Z/γ* contribution, the differential cross-sections are found to be in good agreement with theoretical predictions for heavy-flavour production obtained from Fixed Order NLO calculations with NLL high-p T resummation, and to be sensitive to the effects of NLL resummation.« less

Factorization for jet radius logarithms in jet mass spectra at the LHC

DOE PAGES

Kolodrubetz, Daniel W.; Pietrulewicz, Piotr; Stewart, Iain W.; ...

2016-12-14

To predict the jet mass spectrum at a hadron collider it is crucial to account for the resummation of logarithms between the transverse momentum of the jet and its invariant mass m J . For small jet areas there are additional large logarithms of the jet radius R, which affect the convergence of the perturbative series. We present an analytic framework for exclusive jet production at the LHC which gives a complete description of the jet mass spectrum including realistic jet algorithms and jet vetoes. It factorizes the scales associated with m J , R, and the jet veto, enablingmore » in addition the systematic resummation of jet radius logarithms in the jet mass spectrum beyond leading logarithmic order. We discuss the factorization formulae for the peak and tail region of the jet mass spectrum and for small and large R, and the relations between the different regimes and how to combine them. Regions of experimental interest are classified which do not involve large nonglobal logarithms. We also present universal results for nonperturbative effects and discuss various jet vetoes.« less

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boglione, M.; Gonzalez Hernandez, J. O.; Melis, S.

We study the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, qT. In order to describe it over a wide region of qT, soft gluon resummation has to be performed. Here we will use the original Collins-Soper-Sterman (CSS) formalism; however, the same procedure would hold within the improved Transverse Momentum Dependent (TMD) framework. We study the matching between the region where fixed order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be appliedmore » in the SIDIS kinematical configurations we examine. In particular, the non-perturbative component of the resummed cross section turns out to play a crucial role and should not be overlooked even at relatively high energies. As a result, the perturbative expansion of the resummed cross section in the matching region is not as reliable as it is usually believed and its treatment requires special attention.« less

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes

NASA Astrophysics Data System (ADS)

Boglione, M.; Gonzalez Hernandez, J. O.; Melis, S.; Prokudin, A.

2015-02-01

We study the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, q T . In order to describe it over a wide region of q T , soft gluon resummation has to be performed. Here we will use the original Collins-Soper-Sterman (CSS) formalism; however, the same procedure would hold within the improved Transverse Momentum Dependent (TMD) framework. We study the matching between the region where fixed order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be applied in the SIDIS kinematical configurations we examine. In particular, the non-perturbative component of the resummed cross section turns out to play a crucial role and should not be overlooked even at relatively high energies. Moreover, the perturbative expansion of the resummed cross section in the matching region is not as reliable as it is usually believed and its treatment requires special attention.

Asymptotic behaviour of two-point functions in multi-species models

NASA Astrophysics Data System (ADS)

Kozlowski, Karol K.; Ragoucy, Eric

2016-05-01

We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the SU (3)-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.

Factorization and resummation: A new paradigm to improve gravitational wave amplitudes

NASA Astrophysics Data System (ADS)

Nagar, Alessandro; Shah, Abhay

2016-11-01

We introduce a new resummed analytical form of the post-Newtonian (PN), factorized, multipolar amplitude corrections fℓm of the effective-one-body (EOB) gravitational waveform of spinning, nonprecessing, circularized, coalescing black hole binaries (BBHs). This stems from the following two-step paradigm: (i) the factorization of the orbital (spin-independent) terms in fℓm; (ii) the resummation of the residual spin (or orbital) factors. We find that resumming the residual spin factor by taking its inverse resummed (iResum) is an efficient way to obtain amplitudes that are more accurate in the strong-field, fast-velocity regime. The performance of the method is illustrated on the ℓ=2 and m =(1 ,2 ) waveform multipoles, both for a test mass orbiting around a Kerr black hole and for comparable-mass BBHs. In the first case, the iResum fℓm's are much closer to the corresponding "exact" functions (obtained by numerically solving the Teukolsky equation) up to the light ring than the nonresummed ones, especially when the black-hole spin is nearly extremal. The iResum paradigm is also more efficient than including higher post-Newtonian terms (up to 20PN order): the resummed 5PN information yields per se a rather good numerical or analytical agreement at the last stable orbit and a well-controlled behavior up to the light ring. For comparable mass binaries (including the highest PN-order information available, 3.5PN), comparing EOB with numerical relativity (NR) data shows that the EOB/NR fractional disagreement at merger, without NR calibration of the EOB waveform, is generically reduced by iResum, from 40% of the usual approach to just a few percent. This suggests that EOBNR waveform models for coalescing BBHs may be improved by using iResum amplitudes.

Computing singularities of perturbation series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kvaal, Simen; Jarlebring, Elias; Michiels, Wim

2011-03-15

Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schroedinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be usefulmore » for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with {delta}-function interactions for which Moeller-Plesset perturbation theory is considered and the radius of convergence found.« less

Collins-Soper equation for the energy evolution of transverse-momentum and spin dependent parton distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Idilbi, Ahmad; Ji Xiangdong; Yuan Feng

The hadron-energy evolution (Collins and Soper) equation for all the leading-twist transverse-momentum and spin dependent parton distributions is derived in the impact parameter space. Based on this equation, we present a resummation formulas for the spin dependent structure functions of the semi-inclusive deep-inelastic scattering.

Linearized self-consistent quasiparticle GW method: Application to semiconductors and simple metals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kutepov, A. L.; Oudovenko, V. S.; Kotliar, G.

We present a code implementing the linearized self-consistent quasiparticle GW method (QSGW) in the LAPW basis. Our approach is based on the linearization of the self-energy around zero frequency which differs it from the existing implementations of the QSGW method. The linearization allows us to use Matsubara frequencies instead of working on the real axis. This results in efficiency gains by switching to the imaginary time representation in the same way as in the space time method. The all electron LAPW basis set eliminates the need for pseudopotentials. We discuss the advantages of our approach, such as its N 3more » scaling with the system size N, as well as its shortcomings. We apply our approach to study the electronic properties of selected semiconductors, insulators, and simple metals and show that our code produces the results very close to the previously published QSGW data. Our implementation is a good platform for further many body diagrammatic resummations such as the vertex-corrected GW approach and the GW+DMFT method.« less

Linearized self-consistent quasiparticle GW method: Application to semiconductors and simple metals

DOE PAGES

Kutepov, A. L.; Oudovenko, V. S.; Kotliar, G.

2017-06-23

We present a code implementing the linearized self-consistent quasiparticle GW method (QSGW) in the LAPW basis. Our approach is based on the linearization of the self-energy around zero frequency which differs it from the existing implementations of the QSGW method. The linearization allows us to use Matsubara frequencies instead of working on the real axis. This results in efficiency gains by switching to the imaginary time representation in the same way as in the space time method. The all electron LAPW basis set eliminates the need for pseudopotentials. We discuss the advantages of our approach, such as its N 3more » scaling with the system size N, as well as its shortcomings. We apply our approach to study the electronic properties of selected semiconductors, insulators, and simple metals and show that our code produces the results very close to the previously published QSGW data. Our implementation is a good platform for further many body diagrammatic resummations such as the vertex-corrected GW approach and the GW+DMFT method.« less

Anomalous dimension of subleading-power N-jet operators

NASA Astrophysics Data System (ADS)

Beneke, Martin; Garny, Mathias; Szafron, Robert; Wang, Jian

2018-03-01

We begin a systematic investigation of the anomalous dimension of subleading power N-jet operators in view of resummation of logarithmically enhanced terms in partonic cross sections beyond leading power. We provide an explicit result at the one-loop order for fermion-number two N-jet operators at the second order in the power expansion parameter of soft-collinear effective theory.

A factorization approach to next-to-leading-power threshold logarithms

NASA Astrophysics Data System (ADS)

Bonocore, D.; Laenen, E.; Magnea, L.; Melville, S.; Vernazza, L.; White, C. D.

2015-06-01

Threshold logarithms become dominant in partonic cross sections when the selected final state forces gluon radiation to be soft or collinear. Such radiation factorizes at the level of scattering amplitudes, and this leads to the resummation of threshold logarithms which appear at leading power in the threshold variable. In this paper, we consider the extension of this factorization to include effects suppressed by a single power of the threshold variable. Building upon the Low-Burnett-Kroll-Del Duca (LBKD) theorem, we propose a decomposition of radiative amplitudes into universal building blocks, which contain all effects ultimately responsible for next-to-leading-power (NLP) threshold logarithms in hadronic cross sections for electroweak annihilation processes. In particular, we provide a NLO evaluation of the radiative jet function, responsible for the interference of next-to-soft and collinear effects in these cross sections. As a test, using our expression for the amplitude, we reproduce all abelian-like NLP threshold logarithms in the NNLO Drell-Yan cross section, including the interplay of real and virtual emissions. Our results are a significant step towards developing a generally applicable resummation formalism for NLP threshold effects, and illustrate the breakdown of next-to-soft theorems for gauge theory amplitudes at loop level.

Beam Thrust Cross Section for Drell-Yan Production at Next-to-Next-to-Leading-Logarithmic Order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stewart, Iain W.; Tackmann, Frank J.; Waalewijn, Wouter J.

2011-01-21

At the LHC and Tevatron strong initial-state radiation (ISR) plays an important role. It can significantly affect the partonic luminosity available to the hard interaction or contaminate a signal with additional jets and soft radiation. An ideal process to study ISR is isolated Drell-Yan production, pp{yields}Xl{sup +}l{sup -} without central jets, where the jet veto is provided by the hadronic event shape beam thrust {tau}{sub B}. Most hadron collider event shapes are designed to study central jets. In contrast, requiring {tau}{sub B}<<1 provides an inclusive veto of central jets and measures the spectrum of ISR. For {tau}{sub B}<<1 we carrymore » out a resummation of {alpha}{sub s}{sup n}ln{sup m{tau}}{sub B} corrections at next-to-next-to-leading-logarithmic order. This is the first resummation at this order for a hadron-hadron collider event shape. Measurements of {tau}{sub B} at the Tevatron and LHC can provide crucial tests of our understanding of ISR and of {tau}{sub B}'s utility as a central jet veto.« less

Integrated and differential accuracy in resummed cross sections

DOE PAGES

Bertolini, Daniele; Solon, Mikhail P.; Walsh, Jonathan R.

2017-03-30

Standard QCD resummation techniques provide precise predictions for the spectrum and the cumulant of a given observable. The integrated spectrum and the cumulant differ by higher-order terms which, however, can be numerically significant. Here in this paper we propose a method, which we call the σ-improved scheme, to resolve this issue. It consists of two steps: (i) include higher-order terms in the spectrum to improve the agreement with the cumulant central value, and (ii) employ profile scales that encode correlations between different points to give robust uncertainty estimates for the integrated spectrum. We provide a generic algorithm for determining suchmore » profile scales, and show the application to the thrust distribution in e +e - collisions at NLL'+NLO and NNLL'+NNLO.« less

Asymptotically free theory with scale invariant thermodynamics

NASA Astrophysics Data System (ADS)

Ferrari, Gabriel N.; Kneur, Jean-Loïc; Pinto, Marcus Benghi; Ramos, Rudnei O.

2017-12-01

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasiparticle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

Multichannel conformal blocks for scattering amplitudes

NASA Astrophysics Data System (ADS)

Belitsky, A. V.

2018-05-01

By performing resummation of small fermion-antifermion pairs within the pentagon form factor program to scattering amplitudes in planar N = 4 superYang-Mills theory, we construct multichannel conformal blocks within the flux-tube picture for N-sided NMHV polygons. This procedure is equivalent to summation of descendants of conformal primaries in the OPE framework. The resulting conformal partial waves are determined by multivariable hypergeometric series of Lauricella-Saran type.

Towards precision constraints on gravity with the Effective Field Theory of Large-Scale Structure

NASA Astrophysics Data System (ADS)

Bose, Benjamin; Koyama, Kazuya; Lewandowski, Matthew; Vernizzi, Filippo; Winther, Hans A.

2018-04-01

We compare analytical computations with numerical simulations for dark-matter clustering, in general relativity and in the normal branch of DGP gravity (nDGP). Our analytical frameword is the Effective Field Theory of Large-Scale Structure (EFTofLSS), which we use to compute the one-loop dark-matter power spectrum, including the resummation of infrared bulk displacement effects. We compare this to a set of 20 COLA simulations at redshifts z = 0, z = 0.5, and z = 1, and fit the free parameter of the EFTofLSS, called the speed of sound, in both ΛCDM and nDGP at each redshift. At one-loop at z = 0, the reach of the EFTofLSS is kreach ≈ 0.14 Mpc‑1 for both ΛCDM and nDGP. Along the way, we compare two different infrared resummation schemes and two different treatments of the time dependence of the perturbative expansion, concluding that they agree to approximately 1% over the scales of interest. Finally, we use the ratio of the COLA power spectra to make a precision measurement of the difference between the speeds of sound in ΛCDM and nDGP, and verify that this is proportional to the modification of the linear coupling constant of the Poisson equation.

C -parameter distribution at N 3 LL ' including power corrections

DOE PAGES

Hoang, André H.; Kolodrubetz, Daniel W.; Mateu, Vicent; ...

2015-05-15

We compute the e⁺e⁻ C-parameter distribution using the soft-collinear effective theory with a resummation to next-to-next-to-next-to-leading-log prime accuracy of the most singular partonic terms. This includes the known fixed-order QCD results up to O(α 3 s), a numerical determination of the two-loop nonlogarithmic term of the soft function, and all logarithmic terms in the jet and soft functions up to three loops. Our result holds for C in the peak, tail, and far tail regions. Additionally, we treat hadronization effects using a field theoretic nonperturbative soft function, with moments Ω n. To eliminate an O(Λ QCD) renormalon ambiguity in themore » soft function, we switch from the MS¯ to a short distance “Rgap” scheme to define the leading power correction parameter Ω 1. We show how to simultaneously account for running effects in Ω 1 due to renormalon subtractions and hadron-mass effects, enabling power correction universality between C-parameter and thrust to be tested in our setup. We discuss in detail the impact of resummation and renormalon subtractions on the convergence. In the relevant fit region for αs(m Z) and Ω 1, the perturbative uncertainty in our cross section is ≅ 2.5% at Q=m Z.« less

Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory

NASA Astrophysics Data System (ADS)

Mantry, Sonny; Petriello, Frank

2010-05-01

We derive a factorization theorem for the Higgs boson transverse momentum (pT) and rapidity (Y) distributions at hadron colliders, using the soft-collinear effective theory (SCET), for mh≫pT≫ΛQCD, where mh denotes the Higgs mass. In addition to the factorization of the various scales involved, the perturbative physics at the pT scale is further factorized into two collinear impact-parameter beam functions (IBFs) and an inverse soft function (ISF). These newly defined functions are of a universal nature for the study of differential distributions at hadron colliders. The additional factorization of the pT-scale physics simplifies the implementation of higher order radiative corrections in αs(pT). We derive formulas for factorization in both momentum and impact parameter space and discuss the relationship between them. Large logarithms of the relevant scales in the problem are summed using the renormalization group equations of the effective theories. Power corrections to the factorization theorem in pT/mh and ΛQCD/pT can be systematically derived. We perform multiple consistency checks on our factorization theorem including a comparison with known fixed-order QCD results. We compare the SCET factorization theorem with the Collins-Soper-Sterman approach to low-pT resummation.

Resummed tree heptagon

NASA Astrophysics Data System (ADS)

Belitsky, A. V.

2018-04-01

The form factor program for the regularized space-time S-matrix in planar maximally supersymmetric gauge theory, known as the pentagon operator product expansion, is formulated in terms of flux-tube excitations propagating on a dual two-dimensional world-sheet, whose dynamics is known exactly as a function of 't Hooft coupling. Both MHV and non-MHV amplitudes are described in a uniform, systematic fashion within this framework, with the difference between the two encoded in coupling-dependent helicity form factors expressed via Zhukowski variables. The nontrivial SU(4) tensor structure of flux-tube transitions is coupling independent and is known for any number of charged excitations from solutions of a system of Watson and Mirror equations. This description allows one to resum the infinite series of form factors and recover the space-time S-matrix exactly in kinematical variables at a given order of perturbation series. Recently, this was done for the hexagon. Presently, we successfully perform resummation for the seven-leg tree NMHV amplitude. To this end, we construct the flux-tube integrands of the fifteen independent Grassmann component of the heptagon with an infinite number of small fermion-antifermion pairs accounted for in NMHV two-channel conformal blocks.

Small parameters in infrared quantum chromodynamics

NASA Astrophysics Data System (ADS)

Peláez, Marcela; Reinosa, Urko; Serreau, Julien; Tissier, Matthieu; Wschebor, Nicolás

2017-12-01

We study the long-distance properties of quantum chromodynamics in the Landau gauge in an expansion in powers of the three-gluon, four-gluon, and ghost-gluon couplings, but without expanding in the quark-gluon coupling. This is motivated by two observations. First, the gauge sector is well described by perturbation theory in the context of a phenomenological model with a massive gluon. Second, the quark-gluon coupling is significantly larger than those in the gauge sector at large distances. In order to resum the contributions of the remaining infinite set of QED-like diagrams, we further expand the theory in 1 /Nc, where Nc is the number of colors. At leading order, this double expansion leads to the well-known rainbow approximation for the quark propagator. We take advantage of the systematic expansion to get a renormalization-group improvement of the rainbow resummation. A simple numerical solution of the resulting coupled set of equations reproduces the phenomenology of the spontaneous chiral symmetry breaking: for sufficiently large quark-gluon coupling constant, the constituent quark mass saturates when its valence mass approaches zero. We find very good agreement with lattice data for the scalar part of the propagator and explain why the vectorial part is poorly reproduced.

Universality of qT resummation for electroweak boson production

DOE Office of Scientific and Technical Information (OSTI.GOV)

Konychev, Anton V.; Nadolsky, Pavel M.

We perform a global analysis of transverse momentum distributions in Drell-Yan pair and Z boson production in order to investigate universality of nonperturbative contributions to the Collins-Soper-Sterman resummed form factor. Our fit made in an improved nonperturbative model suggests that the nonperturbative contributions follow universal nearly-linear dependence on the logarithm of the heavy boson invariant mass Q, which closely agrees with an estimate from the infrared renormalon analysis.

Universality of q{sub T} resummation for electroweak boson production.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Konychev, A. V.; Nadolsky, P. M.; High Energy Physics

We perform a global analysis of transverse momentum distributions in Drell-Yan pair and Z boson production in order to investigate universality of nonperturbative contributions to the Collins-Soper-Sterman resummed form factor. Our fit made in an improved nonperturbative model suggests that the nonperturbative contributions follow universal nearly-linear dependence on the logarithm of the heavy boson invariant mass Q, which closely agrees with an estimate from the infrared renormalon analysis.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aslangul, C.; Bouchaud, J.; Georges, A.

The authors present new exact results for a one-dimensional asymmetric disordered hopping model. The lattice is taken infinite from the start and they do not resort to the periodization scheme used by Derrida. An explicit resummation allows for the calculation of the velocity V and the diffusion constant D (which are found to coincide with those given by Derrida) and for demonstrating that V is indeed a self-averaging quantity; the same property is established for D in the limiting case of a directed walk.

EFT of large scale structures in redshift space

NASA Astrophysics Data System (ADS)

Lewandowski, Matthew; Senatore, Leonardo; Prada, Francisco; Zhao, Cheng; Chuang, Chia-Hsun

2018-03-01

We further develop the description of redshift-space distortions within the effective field theory of large scale structures. First, we generalize the counterterms to include the effect of baryonic physics and primordial non-Gaussianity. Second, we evaluate the IR resummation of the dark matter power spectrum in redshift space. This requires us to identify a controlled approximation that makes the numerical evaluation straightforward and efficient. Third, we compare the predictions of the theory at one loop with the power spectrum from numerical simulations up to ℓ=6 . We find that the IR resummation allows us to correctly reproduce the baryon acoustic oscillation peak. The k reach—or, equivalently, the precision for a given k —depends on additional counterterms that need to be matched to simulations. Since the nonlinear scale for the velocity is expected to be longer than the one for the overdensity, we consider a minimal and a nonminimal set of counterterms. The quality of our numerical data makes it hard to firmly establish the performance of the theory at high wave numbers. Within this limitation, we find that the theory at redshift z =0.56 and up to ℓ=2 matches the data at the percent level approximately up to k ˜0.13 h Mpc-1 or k ˜0.18 h Mpc-1 , depending on the number of counterterms used, with a potentially large improvement over former analytical techniques.

Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mantry, Sonny; Petriello, Frank

We derive a factorization theorem for the Higgs boson transverse momentum (p{sub T}) and rapidity (Y) distributions at hadron colliders, using the soft-collinear effective theory (SCET), for m{sub h}>>p{sub T}>>{Lambda}{sub QCD}, where m{sub h} denotes the Higgs mass. In addition to the factorization of the various scales involved, the perturbative physics at the p{sub T} scale is further factorized into two collinear impact-parameter beam functions (IBFs) and an inverse soft function (ISF). These newly defined functions are of a universal nature for the study of differential distributions at hadron colliders. The additional factorization of the p{sub T}-scale physics simplifies themore » implementation of higher order radiative corrections in {alpha}{sub s}(p{sub T}). We derive formulas for factorization in both momentum and impact parameter space and discuss the relationship between them. Large logarithms of the relevant scales in the problem are summed using the renormalization group equations of the effective theories. Power corrections to the factorization theorem in p{sub T}/m{sub h} and {Lambda}{sub QCD}/p{sub T} can be systematically derived. We perform multiple consistency checks on our factorization theorem including a comparison with known fixed-order QCD results. We compare the SCET factorization theorem with the Collins-Soper-Sterman approach to low-p{sub T} resummation.« less

Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case.

PubMed

Gehrmann, Thomas; Lübbert, Thomas; Yang, Li Lin

2012-12-14

We present a calculation of the perturbative quark-to-quark transverse parton distribution function at next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate for the first time that such a definition works beyond the first nontrivial order. We extract from our calculation the coefficient functions relevant for a next-to-next-to-next-to-leading logarithmic Q(T) resummation in a large class of processes at hadron colliders.

Forward J /ψ and very backward jet inclusive production at the LHC

NASA Astrophysics Data System (ADS)

Boussarie, R.; Ducloué, B.; Szymanowski, L.; Wallon, S.

2018-01-01

In the spirit of Mueller-Navelet dijet production, we propose and study the inclusive production of a forward J /ψ and a very backward jet at the LHC as an observable to reveal high-energy resummation effects à la Balitsky, Fadin, Kuraev, Lipatov. We obtain several predictions, which are based on the various mechanisms discussed in the literature to describe the production of the J /ψ , namely, nonrelativistic QCD singlet and octet contributions, and the color evaporation model.

High energy behavior of gravity at large N

DOE Office of Scientific and Technical Information (OSTI.GOV)

Canfora, F.

2006-09-15

A first step in the analysis of the renormalizability of gravity at large N is carried out. Suitable resummations of planar diagrams give rise to a theory in which there is only a finite number of primitive, superficially divergent, Feynman diagrams. The mechanism is similar to the one which makes the 3D Gross-Neveu model renormalizable at large N. The connections with gravitational confinement and Kawai-Lewellen-Tye relations are briefly analyzed. Some potential problems in fulfilling the Zinn-Justin equations are pointed out.

Beauty and charm production in fixed target experiments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kidonakis, Nikolaos; Vogt, Ramona

We present calculations of NNLO threshold corrections for beauty and charm production in {pi}{sup -} p and pp interactions at fixed-target experiments. Recent calculations for heavy quark hadroproduction have included next-to-next-to-leading-order (NNLO) soft-gluon corrections [1] to the double differential cross section from threshold resummation techniques [2]. These corrections are important for near-threshold beauty and charm production at fixed-target experiments, including HERA-B and some of the current and future heavy ion experiments.

Matching the Nagy-Soper parton shower at next-to-leading order

NASA Astrophysics Data System (ADS)

Czakon, M.; Hartanto, H. B.; Kraus, M.; Worek, M.

2015-06-01

We present an Mc@Nlo-like matching of next-to-leading order QCD calculations with the Nagy-Soper parton shower. An implementation of the algorithm within the Helac-Dipoles Monte Carlo generator is used to address the uncertainties and ambiguities of the matching scheme. First results obtained using the Nagy-Soper parton shower implementation in Deductor in conjunction with the Helac-Nlo framework are given for the process at the LHC with TeV. Effects of resummation are discussed for various observables.

Radiative corrections to quantum sticking on graphene

NASA Astrophysics Data System (ADS)

Sengupta, Sanghita; Clougherty, Dennis P.

2017-07-01

We study the sticking rate of atomic hydrogen to suspended graphene using four different methods that include contributions from processes with multiphonon emission. We compare the numerical results of the sticking rate obtained by: (i) the loop expansion of the atom self-energy; (ii) the noncrossing approximation (NCA); (iii) the independent boson model approximation (IBMA); and (iv) a leading-order soft-phonon resummation method (SPR). The loop expansion reveals an infrared problem, analogous to the infamous infrared problem in QED. The two-loop contribution to the sticking rate gives a result that tends to diverge for large membranes. The latter three methods remedy this infrared problem and give results that are finite in the limit of an infinite membrane. We find that for micromembranes (sizes ranging 100 nm to 10 μ m ), the latter three methods give results that are in good agreement with each other and yield sticking rates that are mildly suppressed relative to the lowest-order golden rule rate. Lastly, we find that the SPR sticking rate decreases slowly to zero with increasing membrane size, while both the NCA and IBMA rates tend to a nonzero constant in this limit. Thus, approximations to the sticking rate can be sensitive to the effects of soft-phonon emission for large membranes.

Collinearly-improved BK evolution meets the HERA data

DOE PAGES

Iancu, E.; Madrigal, J. D.; Mueller, A. H.; ...

2015-10-03

In a previous publication, we have established a collinearly-improved version of the Balitsky–Kovchegov (BK) equation, which resums to all orders the radiative corrections enhanced by large double transverse logarithms. Here, we study the relevance of this equation as a tool for phenomenology, by confronting it to the HERA data. To that aim, we first improve the perturbative accuracy of our resummation, by including two classes of single-logarithmic corrections: those generated by the first non-singular terms in the DGLAP splitting functions and those expressing the one-loop running of the QCD coupling. The equation thus obtained includes all the next-to-leading order correctionsmore » to the BK equation which are enhanced by (single or double) collinear logarithms. Furthermore, we then use numerical solutions to this equation to fit the HERA data for the electron–proton reduced cross-section at small Bjorken x. We obtain good quality fits for physically acceptable initial conditions. Our best fit, which shows a good stability up to virtualities as large as Q 2 = 400 GeV 2 for the exchanged photon, uses as an initial condition the running-coupling version of the McLerran–Venugopalan model, with the QCD coupling running according to the smallest dipole prescription.« less

EFT of large scale structures in redshift space [On the EFT of large scale structures in redshift space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewandowski, Matthew; Senatore, Leonardo; Prada, Francisco

Here, we further develop the description of redshift-space distortions within the effective field theory of large scale structures. First, we generalize the counterterms to include the effect of baryonic physics and primordial non-Gaussianity. Second, we evaluate the IR resummation of the dark matter power spectrum in redshift space. This requires us to identify a controlled approximation that makes the numerical evaluation straightforward and efficient. Third, we compare the predictions of the theory at one loop with the power spectrum from numerical simulations up to ℓ = 6. We find that the IR resummation allows us to correctly reproduce the baryonmore » acoustic oscillation peak. The k reach—or, equivalently, the precision for a given k—depends on additional counterterms that need to be matched to simulations. Since the nonlinear scale for the velocity is expected to be longer than the one for the overdensity, we consider a minimal and a nonminimal set of counterterms. The quality of our numerical data makes it hard to firmly establish the performance of the theory at high wave numbers. Within this limitation, we find that the theory at redshift z = 0.56 and up to ℓ = 2 matches the data at the percent level approximately up to k~0.13 hMpc –1 or k~0.18 hMpc –1, depending on the number of counterterms used, with a potentially large improvement over former analytical techniques.« less

Effective potential of the three-dimensional Ising model: The pseudo-ɛ expansion study

NASA Astrophysics Data System (ADS)

Sokolov, A. I.; Kudlis, A.; Nikitina, M. A.

2017-08-01

The ratios R2k of renormalized coupling constants g2k that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λϕ4 field theory (3D Ising model) within the pseudo-ɛ expansion approach. Pseudo-ɛ expansions for the critical values of g6, g8, g10, R6 =g6 / g42, R8 =g8 / g43 and R10 =g10 / g44 originating from the five-loop renormalization group (RG) series are derived. Pseudo-ɛ expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé-Borel-Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R6* = 1.6488 and R6* = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-ɛ expansions is less favorable. Nevertheless, the conform-Borel resummation gives R8* = 0.868, the number being close to the lattice estimate R8* = 0.871 and compatible with the result of 3D RG analysis R8* = 0.857. Pseudo-ɛ expansions for R10* and g10* are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.

EFT of large scale structures in redshift space [On the EFT of large scale structures in redshift space

DOE PAGES

Lewandowski, Matthew; Senatore, Leonardo; Prada, Francisco; ...

2018-03-15

Here, we further develop the description of redshift-space distortions within the effective field theory of large scale structures. First, we generalize the counterterms to include the effect of baryonic physics and primordial non-Gaussianity. Second, we evaluate the IR resummation of the dark matter power spectrum in redshift space. This requires us to identify a controlled approximation that makes the numerical evaluation straightforward and efficient. Third, we compare the predictions of the theory at one loop with the power spectrum from numerical simulations up to ℓ = 6. We find that the IR resummation allows us to correctly reproduce the baryonmore » acoustic oscillation peak. The k reach—or, equivalently, the precision for a given k—depends on additional counterterms that need to be matched to simulations. Since the nonlinear scale for the velocity is expected to be longer than the one for the overdensity, we consider a minimal and a nonminimal set of counterterms. The quality of our numerical data makes it hard to firmly establish the performance of the theory at high wave numbers. Within this limitation, we find that the theory at redshift z = 0.56 and up to ℓ = 2 matches the data at the percent level approximately up to k~0.13 hMpc –1 or k~0.18 hMpc –1, depending on the number of counterterms used, with a potentially large improvement over former analytical techniques.« less

Soft collinear effective theory for heavy WIMP annihilation

DOE PAGES

Bauer, Martin; Cohen, Timothy; Hill, Richard J.; ...

2015-01-19

In a large class of models for Weakly Interacting Massive Particles (WIMPs), the WIMP mass M lies far above the weak scale m W . This work identifies universal Sudakov-type logarithms ~ α log 2(2 M/m W) that spoil the naive convergence of perturbation theory for annihilation processes. An effective field theory (EFT) framework is presented, allowing the systematic resummation of these logarithms. Another impact of the large separation of scales is that a long-distance wavefunction distortion from electroweak boson exchange leads to observable modifications of the cross section. Careful accounting of momentum regions in the EFT allows the rigorousmore » disentanglement of this so-called Sommerfeld enhancement from the short-distance hard annihilation process. In addition, the WIMP is described as a heavy-particle field, while the electroweak gauge bosons are treated as soft and collinear fields. Hard matching coefficients are computed at renormalization scale μ ~ 2 M , then evolved down to μ ~ m W , where electroweak symmetry breaking is incorporated and the matching onto the relevant quantum mechanical Hamiltonian is performed. The example of an SU(2) W triplet scalar dark matter candidate annihilating to line photons is used for concreteness, allowing the numerical exploration of the impact of next-to-leading order corrections and log resummation. As a result, for M ≃ 3 TeV, the resummed Sommerfeld enhanced cross section is reduced by a factor of ~ 3 with respect to the treelevel fixed order result.« less

The complete two-loop integrated jet thrust distribution in soft-collinear effective theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

von Manteuffel, Andreas; Schabinger, Robert M.; Zhu, Hua Xing

2014-03-01

In this work, we complete the calculation of the soft part of the two-loop integrated jet thrust distribution in e+e- annihilation. This jet mass observable is based on the thrust cone jet algorithm, which involves a veto scale for out-of-jet radiation. The previously uncomputed part of our result depends in a complicated way on the jet cone size, r, and at intermediate stages of the calculation we actually encounter a new class of multiple polylogarithms. We employ an extension of the coproduct calculus to systematically exploit functional relations and represent our results concisely. In contrast to the individual contributions, themore » sum of all global terms can be expressed in terms of classical polylogarithms. Our explicit two-loop calculation enables us to clarify the small r picture discussed in earlier work. In particular, we show that the resummation of the logarithms of r that appear in the previously uncomputed part of the two-loop integrated jet thrust distribution is inextricably linked to the resummation of the non-global logarithms. Furthermore, we find that the logarithms of r which cannot be absorbed into the non-global logarithms in the way advocated in earlier work have coefficients fixed by the two-loop cusp anomalous dimension. We also show that in many cases one can straightforwardly predict potentially large logarithmic contributions to the integrated jet thrust distribution at L loops by making use of analogous contributions to the simpler integrated hemisphere soft function.« less

Merging weak and QCD showers with matrix elements

DOE PAGES

Christiansen, Jesper Roy; Prestel, Stefan

2016-01-22

In this study, we present a consistent way of combining associated weak boson radiation in hard dijet events with hard QCD radiation in Drell–Yan-like scatterings. This integrates multiple tree-level calculations with vastly different cross sections, QCD- and electroweak parton-shower resummation into a single framework. The new merging strategy is implemented in the P ythia event generator and predictions are confronted with LHC data. Improvements over the previous strategy are observed. Results of the new electroweak-improved merging at a future 100 TeV proton collider are also investigated.

Finite coupling corrections to holographic predictions for hot QCD

DOE PAGES

Waeber, Sebastian; Schafer, Andreas; Vuorinen, Aleksi; ...

2015-11-13

Finite ’t Hooft coupling corrections to multiple physical observables in strongly coupled N=4 supersymmetric Yang-Mills plasma are examined, in an attempt to assess the stability of the expansion in inverse powers of the ’t Hooft coupling λ. Observables considered include thermodynamic quantities, transport coefficients, and quasinormal mode frequencies. Furthermore large λ expansions for quasinormal mode frequencies are notably less well behaved than the expansions of other quantities, we find that a partial resummation of higher order corrections can significantly reduce the sensitivity of the results to the value of λ.

Threshold Resummation for Squark-Antisquark and Gluino-Pair Production at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulesza, A.; Motyka, L.; II Institute for Theoretical Physics, University of Hamburg, Luruper Chaussee 149, D-22761, Germany and Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Krakow

2009-03-20

We study the effect of soft gluon emission in the hadroproduction of squark-antisquark and gluino-gluino pairs at the next-to-leading logarithmic (NLL) accuracy within the framework of the minimal supersymmetric model. The one-loop soft anomalous dimension matrices controlling the color evolution of the underlying hard-scattering processes are calculated. We present the resummed total cross sections and show numerical results for proton-proton collisions at 14 TeV. For the gluino-pair production, the theoretical uncertainty due to scale variation is reduced to the few-percent level.

Heavy dark matter annihilation from effective field theory.

PubMed

Ovanesyan, Grigory; Slatyer, Tracy R; Stewart, Iain W

2015-05-29

We formulate an effective field theory description for SU(2)_{L} triplet fermionic dark matter by combining nonrelativistic dark matter with gauge bosons in the soft-collinear effective theory. For a given dark matter mass, the annihilation cross section to line photons is obtained with 5% precision by simultaneously including Sommerfeld enhancement and the resummation of electroweak Sudakov logarithms at next-to-leading logarithmic order. Using these results, we present more accurate and precise predictions for the gamma-ray line signal from annihilation, updating both existing constraints and the reach of future experiments.

Merging weak and QCD showers with matrix elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christiansen, Jesper Roy; Prestel, Stefan

In this study, we present a consistent way of combining associated weak boson radiation in hard dijet events with hard QCD radiation in Drell–Yan-like scatterings. This integrates multiple tree-level calculations with vastly different cross sections, QCD- and electroweak parton-shower resummation into a single framework. The new merging strategy is implemented in the P ythia event generator and predictions are confronted with LHC data. Improvements over the previous strategy are observed. Results of the new electroweak-improved merging at a future 100 TeV proton collider are also investigated.

Early-time solution of the horizontal unconfined aquifer in the build-up phase

NASA Astrophysics Data System (ADS)

Gravanis, Elias; Akylas, Evangelos

2017-04-01

The Boussinesq equation is a dynamical equation for the free surface of saturated subsurface flows over an impervious bed. Boussinesq equation is non-linear. The non-linearity comes from the reduction of the dimensionality of the problem: The flow is assumed to be vertically homogeneous, therefore the flow rate through a cross section of the flow is proportional to the free surface height times the hydraulic gradient, which is assumed to be equal to the slope of the free surface (Dupuit approximation). In general, 'vertically' means normally on the bed; combining the Dupuit approximation with the continuity equation leads to the Boussinesq equation. There are very few transient exact solutions. Self- similar solutions have been constructed in the past by various authors. A power series type of solution was derived for a self-similar Boussinesq equation by Barenblatt in 1990. That type of solution has generated a certain amount of literature. For the unconfined flow case for zero recharge rate Boussinesq derived for the horizontal aquifer an exact solution assuming separation of variables. This is actually an exact asymptotic solution of the horizontal aquifer recession phase for late times. The kinematic wave is an interesting solution obtained by dropping the non-linear term in the Boussinesq equation. Although it is an approximate solution, and holds well only for small values of the Henderson and Wooding λ parameter (that is, for steep slopes, high conductivity or small recharge rate), it becomes less and less approximate for smaller values of the parameter, that is, it is asymptotically exact with respect to that parameter. In the present work we consider the case of the unconfined subsurface flow over horizontal bed in the build-up phase under constant recharge rate. This is a case with an infinite Henderson and Wooding parameter, that is, it is the limiting case where the non-linear term is present in the Boussinesq while the linear spatial derivative term goes away. Nonetheless, no analogue of the kinematic wave or the Boussinesq separable solution exists in this case. The late time state of the build-up phase under constant recharge rate is very simply the steady state solution. Our aim is to construct the early time asymptotic solution of this problem. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turn out to be asymptotic and it is regularized by re-summation techniques which are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.

On the soft-gluon resummation in top quark pair production at hadron colliders

NASA Astrophysics Data System (ADS)

Czakon, M.; Mitov, A.

2009-09-01

We uncover a contribution to the NLO/NLL threshold resummed total cross section for top quark pair production at hadron colliders, which has not been taken into account in earlier literature. We derive this contribution - the difference between the singlet and octet hard (matching) coefficients - in exact analytic form. The numerical impact of our findings on the Sudakov resummed cross section turns out to be large, and comparable in size to the current estimates for the theoretical uncertainty of the total cross section. A rough estimate points toward a few percent decrease of the latter at the LHC.

Calculation of the transverse parton distribution functions at next-to-next-to-leading order

NASA Astrophysics Data System (ADS)

Gehrmann, Thomas; Lübbert, Thomas; Yang, Li Lin

2014-06-01

We describe the perturbative calculation of the transverse parton distribution functions in all partonic channels up to next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate the cancellation of light-cone divergences and show that universal process-independent transverse parton distribution functions can be obtained through a refactorization. Our results serve as the first explicit higher-order calculation of these functions starting from first principles, and can be used to perform next-to-next-to-next-to-leading logarithmic q T resummation for a large class of processes at hadron colliders.

Quark matter in the perturbation QCD model with a rapidly convergent matching-invariant running coupling

NASA Astrophysics Data System (ADS)

Xu, Jian-Feng; Luo, Yan-An; Li, Lei; Peng, Guang-Xiong

The properties of dense quark matter are investigated in the perturbation theory with a rapidly convergent matching-invariant running coupling. The fast convergence is mainly due to the resummation of an infinite number of known logarithmic terms in a compact form. The only parameter in this model, the ratio of the renormalization subtraction point to the chemical potential, is restricted to be about 2.64 according to the Witten-Bodmer conjecture, which gives the maximum mass and the biggest radius of quark stars to be, respectively, two times the solar mass and 11.7km.

Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD

NASA Astrophysics Data System (ADS)

Dixon, Lance J.; Luo, Ming-xing; Shtabovenko, Vladyslav; Yang, Tong-Zhi; Zhu, Hua Xing

2018-03-01

The energy-energy correlation (EEC) between two detectors in e+e- annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.

Factorization and resummation for groomed multi-prong jet shapes

NASA Astrophysics Data System (ADS)

Larkoski, Andrew J.; Moult, Ian; Neill, Duff

2018-02-01

Observables which distinguish boosted topologies from QCD jets are playing an increasingly important role at the Large Hadron Collider (LHC). These observables are often used in conjunction with jet grooming algorithms, which reduce contamination from both theoretical and experimental sources. In this paper we derive factorization formulae for groomed multi-prong substructure observables, focusing in particular on the groomed D 2 observable, which is used to identify boosted hadronic decays of electroweak bosons at the LHC. Our factorization formulae allow systematically improvable calculations of the perturbative D 2 distribution and the resummation of logarithmically enhanced terms in all regions of phase space using renormalization group evolution. They include a novel factorization for the production of a soft subjet in the presence of a grooming algorithm, in which clustering effects enter directly into the hard matching. We use these factorization formulae to draw robust conclusions of experimental relevance regarding the universality of the D 2 distribution in both e + e - and pp collisions. In particular, we show that the only process dependence is carried by the relative quark vs. gluon jet fraction in the sample, no non-global logarithms from event-wide correlations are present in the distribution, hadronization corrections are controlled by the perturbative mass of the jet, and all global color correlations are completely removed by grooming, making groomed D 2 a theoretically clean QCD observable even in the LHC environment. We compute all ingredients to one-loop accuracy, and present numerical results at next-to-leading logarithmic accuracy for e + e - collisions, comparing with parton shower Monte Carlo simulations. Results for pp collisions, as relevant for phenomenology at the LHC, are presented in a companion paper [1].

Measurement of dijet production with a veto on additional central jet activity in pp collisions at $$ \\sqrt {s} = 7 $$ TeV using the ATLAS detector

DOE PAGES

Aad, G.; Abbott, B.; Abdallah, J.; ...

2011-09-12

A measurement of jet activity in the rapidity interval bounded by a dijet system is presented. Events are vetoed if a jet with transverse momentum greater than 20 GeV is found between the two boundary jets. The fraction of dijet events that survive the jet veto is presented for boundary jets that are separated by up to six units of rapidity and with mean transverse momentum 50 < p¯ T < 500 GeV. The mean multiplicity of jets above the veto scale in the rapidity interval bounded by the dijet system is also presented as an alternative method for quantifyingmore » perturbative QCD emission. The data are compared to a next-to-leading order plus parton shower prediction from the powheg-box, an all-order resummation using the hej calculation and the pythia, herwig++ and alpgen event generators. In conclusion, the measurement was performed using pp collisions at √s = 7 TeV using data recorded by the ATLAS detector in 2010.« less

Exclusive QCD processes, quark-hadron duality, and the transition to perturbative QCD

NASA Astrophysics Data System (ADS)

Corianò, Claudio; Li, Hsiang-nan; Savkli, Cetin

1998-07-01

Experiments at CEBAF will scan the intermediate-energy region of the QCD dynamics for the nucleon form factors and for Compton Scattering. These experiments will definitely clarify the role of resummed perturbation theory and of quark-hadron duality (QCD sum rules) in this regime. With this perspective in mind, we review the factorization theorem of perturbative QCD for exclusive processes at intermediate energy scales, which embodies the transverse degrees of freedom of a parton and the Sudakov resummation of the corresponding large logarithms. We concentrate on the pion and proton electromagnetic form factors and on pion Compton scattering. New ingredients, such as the evolution of the pion wave function and the complete two-loop expression of the Sudakov factor, are included. The sensitivity of our predictions to the infrared cutoff for the Sudakov evolution is discussed. We also elaborate on QCD sum rule methods for Compton Scattering, which provide an alternative description of this process. We show that, by comparing the local duality analysis to resummed perturbation theory, it is possible to describe the transition of exclusive processes to perturbative QCD.

Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD [The Energy-Energy Correlation at Next-to-Leading Order in QCD, Analytically

DOE PAGES

Dixon, Lance J.; Luo, Ming-xing; Shtabovenko, Vladyslav; ...

2018-03-09

Here, the energy-energy correlation (EEC) between two detectors in e +e – annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.

The massive soft anomalous dimension matrix at two loops

NASA Astrophysics Data System (ADS)

Mitov, Alexander; Sterman, George; Sung, Ilmo

2009-05-01

We study two-loop anomalous dimension matrices in QCD and related gauge theories for products of Wilson lines coupled at a point. We verify by an analysis in Euclidean space that the contributions to these matrices from diagrams that link three massive Wilson lines do not vanish in general. We show, however, that for two-to-two processes the two-loop anomalous dimension matrix is diagonal in the same color-exchange basis as the one-loop matrix for arbitrary masses at absolute threshold and for scattering at 90 degrees in the center of mass. This result is important for applications of threshold resummation in heavy quark production.

Transverse momentum dependent (TMD) parton distribution functions: Status and prospects*

DOE PAGES

Angeles-Martinez, R.; Bacchetta, A.; Balitsky, Ian I.; ...

2015-01-01

In this study, we review transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q T spectra of Higgs and vector bosons for low q T, and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present the application of a new tool, TMD LIB, to parton density fits andmore » parameterizations.« less

Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD [The Energy-Energy Correlation at Next-to-Leading Order in QCD, Analytically

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dixon, Lance J.; Luo, Ming-xing; Shtabovenko, Vladyslav

Here, the energy-energy correlation (EEC) between two detectors in e +e – annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.

Interpolation of hard and soft dilepton rates

NASA Astrophysics Data System (ADS)

Ghisoiu, I.; Laine, M.

2014-10-01

Strict next-to-leading order (NLO) results for the dilepton production rate from a QCD plasma at temperatures above a few hundred MeV suffer from a breakdown of the loop expansion in the regime of soft invariant masses M 2 ≪ ( πT)2. In this regime an LPM resummation is needed for obtaining the correct leading-order result. We show how to construct an interpolation between the hard NLO and the leading-order LPM expression, which is theoretically consistent in both regimes and free from double counting. The final numerical results are presented in a tabulated form, suitable for insertion into hydrodynamical codes.

Threshold region for Higgs boson production in gluon fusion.

PubMed

Bonvini, Marco; Forte, Stefano; Ridolfi, Giovanni

2012-09-07

We provide a quantitative determination of the effective partonic kinematics for Higgs boson production in gluon fusion in terms of the collider energy at the LHC. We use the result to assess, as a function of the Higgs boson mass, whether the large m(t) approximation is adequate and Sudakov resummation advantageous. We argue that our results hold to all perturbative orders. Based on our results, we conclude that the full inclusion of finite top mass corrections is likely to be important for accurate phenomenology for a light Higgs boson with m(H)~125 GeV at the LHC with √s=14 TeV.

U(1) current from the AdS/CFT: diffusion, conductivity and causality

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2016-04-01

For a holographically defined finite temperature theory, we derive an off-shell constitutive relation for a global U(1) current driven by a weak external non-dynamical electromagnetic field. The constitutive relation involves an all order gradient expansion resummed into three momenta-dependent transport coefficient functions: diffusion, electric conductivity, and "magnetic" conductivity. These transport functions are first computed analytically in the hydrodynamic limit, up to third order in the derivative expansion, and then numerically for generic values of momenta. We also compute a diffusion memory function, which, as a result of all order gradient resummation, is found to be causal.

Challenges in the extraction of TMDs from SIDIS data: perturbative vs non-perturbative aspects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boglione, Mariaelena; Gonzalez Hernandez, Jose O.; Melis, Stefano

We present our recent results on the study of the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, q T. Using the Collins-Soper-Sterman (CSS) formalism, we study the matching between the region where fixed-order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be applied in the SIDIS kinematical configurations we examine. We comment on the impact that the nonperturbative component has even at relatively high energies.

Nonperturbative functions for SIDIS and Drell-Yan processes

NASA Astrophysics Data System (ADS)

Sun, Peng; Isaacson, Joshua; Yuan, C.-P.; Yuan, Feng

2018-04-01

We update the well-known BLNY fit to the low transverse momentum Drell-Yan lepton pair productions in hadronic collisions, by considering the constraints from the semi-inclusive hadron production in deep inelastic scattering (SIDIS) from HERMES and COMPASS experiments. We follow the Collins-Soper-Sterman (CSS) formalism with the b∗-prescription. A nonperturbative form factor associated with the transverse momentum dependent quark distributions is found in the analysis with a new functional form different from that of BLNY. This releases the tension between the BLNY fit to the Drell-Yan data with the SIDIS data from HERMES/COMPASS in the CSS resummation formalism.

Analytic calculation of 1-jettiness in DIS at O (α s)

DOE PAGES

Kang, Daekyoung; Lee, Christopher; Stewart, Iain W.

2014-11-01

We present an analytic O(α s) calculation of cross sections in deep inelastic scattering (DIS) dependent on an event shape, 1-jettiness, that probes final states with one jet plus initial state radiation. This is the first entirely analytic calculation for a DIS event shape cross section at this order. We present results for the differential and cumulative 1-jettiness cross sections, and express both in terms of structure functions dependent not only on the usual DIS variables x, Q 2 but also on the 1-jettiness τ. Combined with previous results for log resummation, predictions are obtained over the entire range ofmore » the 1-jettiness distribution.« less

Higgs boson couplings to bottom quarks: two-loop supersymmetry-QCD corrections.

PubMed

Noth, David; Spira, Michael

2008-10-31

We present two-loop supersymmetry (SUSY) QCD corrections to the effective bottom Yukawa couplings within the minimal supersymmetric extension of the standard model (MSSM). The effective Yukawa couplings include the resummation of the nondecoupling corrections Deltam_{b} for large values of tanbeta. We have derived the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-quark-induced SUSY-electroweak contributions to Deltam_{b}. The scale dependence of the resummed Yukawa couplings is reduced from O(10%) to the percent level. These results reduce the theoretical uncertainties of the MSSM Higgs branching ratios to the accuracy which can be achieved at a future linear e;{+}e;{-} collider.

Time-sliced perturbation theory for large scale structure I: general formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution ofmore » the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.« less

Nonlocal quantum effective actions in Weyl-Flat spacetimes

NASA Astrophysics Data System (ADS)

Bautista, Teresa; Benevides, André; Dabholkar, Atish

2018-06-01

Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite N corrections in holography. We describe how the quantum effective actions summarizing these effects can be computed efficiently for Weyl-flat metrics by integrating the Weyl anomaly or, equivalently, the local renormalization group equation. This method relies only on the local Schwinger-DeWitt expansion of the heat kernel and allows for a re-summation of the anomalous leading large logarithms of the scale factor, log a( x), in situations where the Weyl factor changes by several e-foldings. As an illustration, we obtain the quantum effective action for the Yang-Mills field coupled to massless matter, and the self-interacting massless scalar field. Our action reduces to the nonlocal action obtained using the Barvinsky-Vilkovisky covariant perturbation theory in the regime R 2 ≪ ∇2 R for a typical curvature scale R, but has a greater range of validity effectively re-summing the covariant perturbation theory to all orders in curvatures. In particular, it is applicable also in the opposite regime R 2 ≫ ∇2 R, which is often of interest in cosmology.

Doubly magic nuclei from lattice QCD forces at MPS=469 MeV /c2

NASA Astrophysics Data System (ADS)

McIlroy, C.; Barbieri, C.; Inoue, T.; Doi, T.; Hatsuda, T.

2018-02-01

We perform ab initio self-consistent Green's function calculations of the closed shell nuclei 4He, 16O, and 40Ca, based on two-nucleon potentials derived from lattice QCD simulations, in the flavor SU(3) limit and at the pseudoscalar meson mass of 469 MeV/c2. The nucleon-nucleon interaction is obtained using the hadrons-to-atomic-nuclei-from-lattice (HAL) QCD method, and its short-distance repulsion is treated by means of ladder resummations outside the model space. Our results show that this approach diagonalizes ultraviolet degrees of freedom correctly. Therefore, ground-state energies can be obtained from infrared extrapolations even for the relatively hard potentials of HAL QCD. Comparing to previous Brueckner Hartree-Fock calculations, the total binding energies are sensibly improved by the full account of many-body correlations. The results suggest an interesting possible behavior in which nuclei are unbound at very large pion masses and islands of stability appear at first around the traditional doubly magic numbers when the pion mass is lowered toward its physical value. The calculated one-nucleon spectral distributions are qualitatively close to those of real nuclei even for the pseudoscalar meson mass considered here.

Drell-Yan production at small q T , transverse parton distributions and the collinear anomaly

NASA Astrophysics Data System (ADS)

Becher, Thomas; Neubert, Matthias

2011-06-01

Using methods from effective field theory, an exact all-order expression for the Drell-Yan cross section at small transverse momentum is derived directly in q T space, in which all large logarithms are resummed. The anomalous dimensions and matching coefficients necessary for resummation at NNLL order are given explicitly. The precise relation between our result and the Collins-Soper-Sterman formula is discussed, and as a by-product the previously unknown three-loop coefficient A (3) is obtained. The naive factorization of the cross section at small transverse momentum is broken by a collinear anomaly, which prevents a process-independent definition of x T -dependent parton distribution functions. A factorization theorem is derived for the product of two such functions, in which the dependence on the hard momentum transfer is separated out. The remainder factors into a product of two functions of longitudinal momentum variables and xT2, whose renormalization-group evolution is derived and solved in closed form. The matching of these functions at small x T onto standard parton distributions is calculated at O(αs), while their anomalous dimensions are known to three loops.

Applications of QCD factorization in multiscale Hadronic scattering

NASA Astrophysics Data System (ADS)

Wang, Bowen

In this thesis I apply QCD factorization theorems to two important hadronic processes. In the first study, I treat the inclusive cross section of the production of massive quarks through neutral current deep inelasitc scattering (DIS): (n/a). In this study I work out a method to consistently organize the QCD radiative contributions up to O(alphas 3) (N3LO), with a proper inclusion of the heavy quark mass dependence at different momentum scales. The generic implementation of the mass dependence developed in this thesis can be used by calculations in both an intermediate-mass factorization scheme and a general-mass factorization scheme. The mass effect is relevant to the predictions for Higgs, and W and Z cross sections measured at the LHC. The second study examines the transverse-momentum distribution of the lepton-pair production in Drell-yan process. The theory predictions based on the Collins-Soper-Sterman (CSS) resummation formalism at NNLL accuracy are compared with the new data on the angular distribution *eta of Drell-Yan pairs measured at the Tevatron and the LHC. The main finding is that the nonperturbative component of the CSS resummed cross section plays a crucial part in explaining the data in the small transverse momentum region.

Nonlinear response from transport theory and quantum field theory at finite temperature

NASA Astrophysics Data System (ADS)

Carrington, M. E.; Defu, Hou; Kobes, R.

2001-07-01

We study the nonlinear response in weakly coupled hot φ4 theory. We obtain an expression for a quadratic shear viscous response coefficient using two different formalisms: transport theory and response theory. The transport theory calculation is done by assuming a local equilibrium form for the distribution function and expanding in the gradient of the local four dimensional velocity field. By performing a Chapman-Enskog expansion on the Boltzmann equation we obtain a hierarchy of equations for the coefficients of the expanded distribution function. To do the response theory calculation we use Zubarev's techniques in nonequilibrium statistical mechanics to derive a generalized Kubo formula. Using this formula allows us to obtain the quadratic shear viscous response from the three-point retarded Green function of the viscous shear stress tensor. We use the closed time path formalism of real time finite temperature field theory to show that this three-point function can be calculated by writing it as an integral equation involving a four-point vertex. This four-point vertex can in turn be obtained from an integral equation which represents the resummation of an infinite series of ladder and extended-ladder diagrams. The connection between transport theory and response theory is made when we show that the integral equation for this four-point vertex has exactly the same form as the equation obtained from the Boltzmann equation for the coefficient of the quadratic term of the gradient expansion of the distribution function. We conclude that calculating the quadratic shear viscous response using transport theory and keeping terms that are quadratic in the gradient of the velocity field in the Chapman-Enskog expansion of the Boltzmann equation is equivalent to calculating the quadratic shear viscous response from response theory using the next-to-linear response Kubo formula, with a vertex given by an infinite resummation of ladder and extended-ladder diagrams.

How to resum perturbative series in 3d N =2 Chern-Simons matter theories

NASA Astrophysics Data System (ADS)

Honda, Masazumi

2016-07-01

Continuing the work of Honda [Phys. Rev. Lett. 116, 211601 (2016)], we study the perturbative series in general 3d N =2 supersymmetric Chern-Simons matter theory with U (1 )R symmetry, which is given by a power series expansion of inverse Chern-Simons levels. We find that the perturbative series is usually non-Borel summable along a positive real axis for various observables. Alternatively, we prove that the perturbative series is always Borel summable along a negative (positive) imaginary axis for positive (negative) Chern-Simons levels. It turns out that the Borel resummations along this direction are the same as the exact results and, therefore, are correct ways of resumming the perturbative series.

Top++: A program for the calculation of the top-pair cross-section at hadron colliders

NASA Astrophysics Data System (ADS)

Czakon, Michał; Mitov, Alexander

2014-11-01

We present the program Top++ for the numerical evaluation of the total inclusive cross-section for producing top quark pairs at hadron colliders. The program calculates the cross-section in (a) fixed order approach with exact next-to-next-to leading order (NNLO) accuracy and (b) by including soft-gluon resummation for the hadronic cross-section in Mellin space with full next-to-next-to-leading logarithmic (NNLL) accuracy. The program offers the user significant flexibility through the large number (29) of available options. Top++ is written in C++. It has a very simple to use interface that is intuitive and directly reflects the physics. The running of the program requires no programming experience from the user.

Improved perturbative QCD formalism for Bc meson decays

NASA Astrophysics Data System (ADS)

Liu, Xin; Li, Hsiang-nan; Xiao, Zhen-Jun

2018-06-01

We derive the kT resummation for doubly heavy-flavored Bc meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the "golden channel" Bc+→J /ψ π+. With a reasonable model for the Bc meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the Bc→J /ψ transition form factor appears to be power suppressed, and the Bc+→J /ψ π+ branching ratio is not lower than 10-3. The above improved perturbative QCD formalism is applicable to Bc meson decays to other charmonia and charmed mesons.

Addendum: New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon [Phys. Rev. D 95, 054018 (2017)

DOE PAGES

Bodwin, Geoffrey T.; Chung, Hee Sok; Ee, June-Haak; ...

2017-12-20

In this addendum to Phys. Rev. D 95, 054018 (2017) we recompute the rates for the decays of the Higgs boson to a vector quarkonium plus a photon, where the vector quarkonium is J/psi, Upsilon(1S) Upsilon(2S). We correct an error in the Abel-Pad'e summation formula that was used to carry out the evolution of the quarkonium light-cone distribution amplitude in Phys. Rev. D 95, 054018 (2017). We also correct an error in the scale of quarkonium wave function at the origin in Phys. Rev. D 95, 054018 (2017) and introduce several additional refinements in the calculation.

Addendum: New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon [Phys. Rev. D 95, 054018 (2017)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bodwin, Geoffrey T.; Chung, Hee Sok; Ee, June-Haak

In this addendum to Phys. Rev. D 95, 054018 (2017) we recompute the rates for the decays of the Higgs boson to a vector quarkonium plus a photon, where the vector quarkonium is J/psi, Upsilon(1S) Upsilon(2S). We correct an error in the Abel-Pad'e summation formula that was used to carry out the evolution of the quarkonium light-cone distribution amplitude in Phys. Rev. D 95, 054018 (2017). We also correct an error in the scale of quarkonium wave function at the origin in Phys. Rev. D 95, 054018 (2017) and introduce several additional refinements in the calculation.

Bilocal expansion of the Borel amplitude and the hadronic tau decay width

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cvetic, Gorazd; Lee, Taekoon

2001-07-01

The singular part of the Borel transform of a QCD amplitude near the infrared renormalon can be expanded in terms of higher order Wilson coefficients of the operators associated with the renormalon. In this paper we observe that this expansion gives nontrivial constraints on the Borel amplitude that can be used to improve the accuracy of the ordinary perturbative expansion of the Borel amplitude. In particular, we consider the Borel transform of the Adler function and its expansion around the first infrared renormalon due to the gluon condensate. Using the next-to-leading order (NLO) Wilson coefficient of the gluon condensate operator,more » we obtain an exact constraint on the Borel amplitude at the first IR renormalon. We then extrapolate, using judiciously chosen conformal transformations and Pade{prime} approximants, the ordinary perturbative expansion of the Borel amplitude in such a way that this constraint is satisfied. This procedure allows us to predict the O({alpha}{sub s}{sup 4}) coefficient of the Adler function, which gives a result consistent with the estimate by Kataev and Starshenko using a completely different method. We then apply this improved Borel amplitude to the tau decay width and obtain the strong coupling constant {alpha}{sub s}(M{sub z}{sup 2})=0.1193{+-}0.0007{sub exp.}{+-}0.0010{sub EW+CKM}{+-}0.0009{sub meth.}{+-}0.0003{sub evol.}. We then compare this result with those of other resummation methods.« less

Phenomenological study of the interplay between IR-improved DGLAP-CS theory and the precision of an NLO ME matched parton shower MC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Majhi, S.K., E-mail: tpskm@iacs.res.in; Mukhopadhyay, A., E-mail: aditi_mukhopadhyay@baylor.edu; Ward, B.F.L., E-mail: bfl_ward@baylor.edu

2014-11-15

We present a phenomenological study of the current status of the application of our approach of exact amplitude-based resummation in quantum field theory to precision QCD calculations, by realistic MC event generator methods, as needed for precision LHC physics. We discuss recent results as they relate to the interplay of the attendant IR-improved DGLAP-CS theory of one of us and the precision of exact NLO matrix-element matched parton shower MC’s in the Herwig6.5 environment as determined by comparison to recent LHC experimental observations on single heavy gauge boson production and decay. The level of agreement between the new theory andmore » the data continues to be a reason for optimism. In the spirit of completeness, we discuss as well other approaches to the same theoretical predictions that we make here from the standpoint of physical precision with an eye toward the (sub-)1% QCD⊗EW total theoretical precision regime for LHC physics. - Highlights: • Using LHC data, we show that IR-improved DGLAP-CS kernels with exact NLO Shower/ME matching improves MC precision. • We discuss other possible approaches in comparison with ours. • We propose experimental tests to discriminate between competing approaches.« less

A dispersive treatment of decays

NASA Astrophysics Data System (ADS)

Stoffer, Peter; Colangelo, Gilberto; Passemar, Emilie

2017-01-01

decays have several features of interest: they allow an accurate measurement of ππ-scattering lengths; the decay is the best source for the determination of some low-energy constants of chiral perturbation theory (χPT) one form factor of the decay is connected to the chiral anomaly. We present the results of our dispersive analysis of decays, which provides a resummation of ππ- and Kπ-rescattering effects. The free parameters of the dispersion relation are fitted to the data of the high-statistics experiments E865 and NA48/2. By matching to χPT at NLO and NNLO, we determine the low-energy constants and . In contrast to a pure chiral treatment, the dispersion relation describes the observed curvature of one of the form factors, which we understand as an effect of rescattering beyond NNLO.

Transverse momentum cross section of e⁺e⁻ pairs in the Z-boson region from pp̄ collisions at √s=1.96 TeV

DOE PAGES

Aaltonen, T.; Álvarez González, B.; Amerio, S.; ...

2012-09-26

The transverse momentum cross section of e⁺e⁻ pairs in the Z-boson mass region of 66–116 GeV/c² is precisely measured using Run II data corresponding to 2.1 fb⁻¹ of integrated luminosity recorded by the Collider Detector at Fermilab. The cross section is compared with two quantum chromodynamic calculations. One is a fixed-order perturbative calculation at O(α 2s), and the other combines perturbative predictions at high transverse momentum with the gluon resummation formalism at low transverse momentum. Comparisons of the measurement with calculations show reasonable agreement. The measurement is of sufficient precision to allow refinements in the understanding of the transverse momentummore » distribution.« less

Hard diffraction in the QCD dipole picture

NASA Astrophysics Data System (ADS)

Bialas, A.; Peschanski, R.

1996-02-01

Using the QCD dipole picture of the BFKL pomeron, the gluon contribution to the cross-section for single diffractive dissociation in deep-inelastic high-energy scattering is calculated. The resulting contribution to the proton diffractive structure function integrated over t is given in terms of relevant variables, xP, Q2, and β = {x Bj}/{x P}. It factorizes into an explicit x P-dependent Hard Pomeron flux factor and structure function. The lux factor is found to have substantial logarithmic corrections which may account for the recent measurements of the Pomeron intercept in this process. The triple Pomeron coupling is shown to be strongly enhanced by the resummation of leading logs. The obtained pattern of scaling violation at small β is similar to that for F2 at small xBj.

Tunneling probe of fluctuating superconductivity in disordered thin films

NASA Astrophysics Data System (ADS)

Dentelski, David; Frydman, Aviad; Shimshoni, Efrat; Dalla Torre, Emanuele G.

2018-03-01

Disordered thin films close to the superconductor-insulator phase transition (SIT) hold the key to understanding quantum phase transition in strongly correlated materials. The SIT is governed by superconducting quantum fluctuations, which can be revealed, for example, by tunneling measurements. These experiments detect a spectral gap, accompanied by suppressed coherence peaks, on both sides of the transition. Here we describe the insulating side in terms of a fluctuating superconducting field with finite-range correlations. We perform a controlled diagrammatic resummation and derive analytic expressions for the tunneling differential conductance. We find that short-range superconducting fluctuations suppress the coherence peaks even in the presence of long-range correlations. Our approach offers a quantitative description of existing measurements on disordered thin films and accounts for tunneling spectra with suppressed coherence peaks.

Massive neutral gauge boson production as a probe of nuclear modifications of parton distributions at the LHC

NASA Astrophysics Data System (ADS)

Guzey, Vadim; Guzzi, Marco; Nadolsky, Pavel M.; Strikman, Mark; Wang, Bowen

2013-03-01

We analyze the role of nuclear modifications of parton distributions, notably, the nuclear shadowing and antishadowing corrections, in the production of lepton pairs from decays of neutral Z and γ∗ gauge bosons in proton-lead and lead-lead collisions at the LHC. Using the Collins-Soper-Sterman resummation formalism that we extended to the case of nuclear parton distributions, we observed a direct correlation between the predicted behavior of the transverse momentum and rapidity distributions of the produced vector bosons and the pattern of quark and gluon nuclear modifications. This makes the production of Z/γ∗ in pA and AA collisions at the LHC a useful tool for constraining nuclear PDFs in the small- x shadowing and moderate- x antishadowing regions.

The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Larkoski, Andrew J.; Moult, Ian; Neill, Duff Austin

Non-global logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon ex-pansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an all-orders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and large-N c master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluonmore » expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of α slog. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also use the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. Furthermore, this allows us to calculate the NGL distribution for all values of α slog from the coefficients of the fixed order expansion.« less

The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion

DOE PAGES

Larkoski, Andrew J.; Moult, Ian; Neill, Duff Austin

2016-11-15

Non-global logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon ex-pansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an all-orders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and large-N c master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluonmore » expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of α slog. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also use the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. Furthermore, this allows us to calculate the NGL distribution for all values of α slog from the coefficients of the fixed order expansion.« less

New template family for the detection of gravitational waves from comparable-mass black hole binaries

NASA Astrophysics Data System (ADS)

Porter, Edward K.

2007-11-01

In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various resummation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on reexpressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical methods as they display the fastest convergence of any of the orthogonal polynomials. In this case they are also particularly useful as they eliminate one of the features that plagues the post-Newtonian expansion. The Chebyshev binding energy now has information at all post-Newtonian orders, compared to the post-Newtonian templates which only have information at full integer orders. In this work, we compare both the post-Newtonian and Chebyshev templates against a fiducially exact waveform. This waveform is constructed from a hybrid method of using the test-mass results combined with the mass dependent parts of the post-Newtonian expansions for the binding energy and flux functions. Our results show that the Chebyshev templates achieve extremely high fitting factors at all post-Newtonian orders and provide excellent parameter extraction. We also show that this new template family has a faster Cauchy convergence, gives a better prediction of the position of the last stable orbit and in general recovers higher Signal-to-Noise ratios than the post-Newtonian templates.

Parton shower and NLO-matching uncertainties in Higgs boson pair production

NASA Astrophysics Data System (ADS)

Jones, Stephen; Kuttimalai, Silvan

2018-02-01

We perform a detailed study of NLO parton shower matching uncertainties in Higgs boson pair production through gluon fusion at the LHC based on a generic and process independent implementation of NLO subtraction and parton shower matching schemes for loop-induced processes in the Sherpa event generator. We take into account the full top-quark mass dependence in the two-loop virtual corrections and compare the results to an effective theory approximation. In the full calculation, our findings suggest large parton shower matching uncertainties that are absent in the effective theory approximation. We observe large uncertainties even in regions of phase space where fixed-order calculations are theoretically well motivated and parton shower effects expected to be small. We compare our results to NLO matched parton shower simulations and analytic resummation results that are available in the literature.

Jet angularity measurements for single inclusive jet production

NASA Astrophysics Data System (ADS)

Kang, Zhong-Bo; Lee, Kyle; Ringer, Felix

2018-04-01

We study jet angularity measurements for single-inclusive jet production at the LHC. Jet angularities depend on a continuous parameter a allowing for a smooth interpolation between different traditional jet shape observables. We establish a factorization theorem within Soft Collinear Effective Theory (SCET) where we consistently take into account in- and out-of-jet radiation by making use of semi-inclusive jet functions. For comparison, we elaborate on the differences to jet angularities measured on an exclusive jet sample. All the necessary ingredients for the resummation at next-to-leading logarithmic (NLL) accuracy are presented within the effective field theory framework. We expect semiinclusive jet angularity measurements to be feasible at the LHC and we present theoretical predictions for the relevant kinematic range. In addition, we investigate the potential impact of jet angularities for quark-gluon discrimination.

Electric Conductivity of Hot and Dense Quark Matter in a Magnetic Field with Landau Level Resummation via Kinetic Equations

NASA Astrophysics Data System (ADS)

Fukushima, Kenji; Hidaka, Yoshimasa

2018-04-01

We compute the electric conductivity of quark matter at finite temperature T and a quark chemical potential μ under a magnetic field B beyond the lowest Landau level approximation. The electric conductivity transverse to B is dominated by the Hall conductivity σH. For the longitudinal conductivity σ∥, we need to solve kinetic equations. Then, we numerically find that σ∥ has only a mild dependence on μ and the quark mass mq. Moreover, σ∥ first decreases and then linearly increases as a function of B , leading to an intermediate B region that looks consistent with the experimental signature for the chiral magnetic effect. We also point out that σ∥ at a nonzero B remains within the range of the lattice-QCD estimate at B =0 .

Electric Conductivity of Hot and Dense Quark Matter in a Magnetic Field with Landau Level Resummation via Kinetic Equations.

PubMed

Fukushima, Kenji; Hidaka, Yoshimasa

2018-04-20

We compute the electric conductivity of quark matter at finite temperature T and a quark chemical potential μ under a magnetic field B beyond the lowest Landau level approximation. The electric conductivity transverse to B is dominated by the Hall conductivity σ_{H}. For the longitudinal conductivity σ_{∥}, we need to solve kinetic equations. Then, we numerically find that σ_{∥} has only a mild dependence on μ and the quark mass m_{q}. Moreover, σ_{∥} first decreases and then linearly increases as a function of B, leading to an intermediate B region that looks consistent with the experimental signature for the chiral magnetic effect. We also point out that σ_{∥} at a nonzero B remains within the range of the lattice-QCD estimate at B=0.

Non-abelian factorisation for next-to-leading-power threshold logarithms

NASA Astrophysics Data System (ADS)

Bonocore, D.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C. D.

2016-12-01

Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a nonabelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.

Bloch-Nordsieck thermometers: one-loop exponentiation in finite temperature QED

NASA Astrophysics Data System (ADS)

Gupta, Sourendu; Indumathi, D.; Mathews, Prakash; Ravindran, V.

1996-02-01

We study the scattering of hard external particles in a heat bath in a real-time formalism for finite temperature QED. We investigate the distribution of the 4-momentum difference of initial and final hard particles in a fully covariant manner when the scale of the process, Q, is much larger than the temperature, T. Our computations are valid for all T subject to this constraint. We exponentiate the leading infra-red term at one-loop order through a resummation of soft (thermal) photon emissions and absorptions. For T > 0, we find that tensor structures arise which are not present at T = 0. These cant' thermal signatures. As a result, external particles can serve as thermometers introduced into the heat bath. We investigate the phase space origin of log( Q/ m) and log ( Q/ T) teens.

Parton shower and NLO-matching uncertainties in Higgs boson pair production

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, Stephen; Kuttimalai, Silvan

We perform a detailed study of NLO parton shower matching uncertainties in Higgs boson pair production through gluon fusion at the LHC based on a generic and process independent implementation of NLO subtraction and parton shower matching schemes for loop-induced processes in the Sherpa event generator. We take into account the full top-quark mass dependence in the two-loop virtual corrections and compare the results to an effective theory approximation. In the full calculation, our findings suggest large parton shower matching uncertainties that are absent in the effective theory approximation. Here, we observe large uncertainties even in regions of phase spacemore » where fixed-order calculations are theoretically well motivated and parton shower effects expected to be small. We compare our results to NLO matched parton shower simulations and analytic resummation results that are available in the literature.« less

Parton shower and NLO-matching uncertainties in Higgs boson pair production

DOE PAGES

Jones, Stephen; Kuttimalai, Silvan

2018-02-28

We perform a detailed study of NLO parton shower matching uncertainties in Higgs boson pair production through gluon fusion at the LHC based on a generic and process independent implementation of NLO subtraction and parton shower matching schemes for loop-induced processes in the Sherpa event generator. We take into account the full top-quark mass dependence in the two-loop virtual corrections and compare the results to an effective theory approximation. In the full calculation, our findings suggest large parton shower matching uncertainties that are absent in the effective theory approximation. Here, we observe large uncertainties even in regions of phase spacemore » where fixed-order calculations are theoretically well motivated and parton shower effects expected to be small. We compare our results to NLO matched parton shower simulations and analytic resummation results that are available in the literature.« less

TeV scale dark matter and electroweak radiative corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ciafaloni, Paolo; Urbano, Alfredo

2010-08-15

Recent anomalies in cosmic rays data, namely, from the PAMELA Collaboration, can be interpreted in terms of TeV scale decaying/annihilating dark matter. We analyze the impact of radiative corrections coming from the electroweak sector of the standard model on the spectrum of the final products at the interaction point. As an example, we consider virtual one loop corrections and real gauge bosons emission in the case of a very heavy vector boson annihilating into fermions. We find electroweak corrections that are relevant, but not as big as sometimes found in the literature; we relate this mismatch to the issue ofmore » gauge invariance. At scales much higher than the symmetry breaking scale, one loop electroweak effects are so big that eventually higher orders/resummations have to be considered: we advocate for the inclusion of these effects in parton shower Monte Carlo models aiming at the description of TeV scale physics.« less

Linear response formula for piecewise expanding unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Smania, Daniel

2008-04-01

The average R(t)=\\int \\varphi\\,\\rmd \\mu_t of a smooth function phiv with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839-59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if ft is tangent to the topological class of f, and if ∂t ft|t = 0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series \\sum_{n=0}^\\infty \\int X(y) \\partial_y (\\varphi \\circ f^n)(y)\\,\\rmd \\mu_0(y) given by Ruelle's conjecture. In fact, we show that t map μt is differentiable within Radon measures. Linear response is violated if and only if ft is transversal to the topological class of f.

Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through O(αS4)

NASA Astrophysics Data System (ADS)

Czakon, Michał; Fiedler, Paul; Mitov, Alexander

2013-06-01

We compute the next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) correction to the total cross section for the reaction gg→tt¯+X. Together with the partonic channels we computed previously, the result derived in this Letter completes the set of NNLO QCD corrections to the total top pair-production cross section at hadron colliders. Supplementing the fixed order results with soft-gluon resummation with next-to-next-to-leading logarithmic accuracy, we estimate that the theoretical uncertainty of this observable due to unknown higher order corrections is about 3% at the LHC and 2.2% at the Tevatron. We observe a good agreement between the standard model predictions and the available experimental measurements. The very high theoretical precision of this observable allows a new level of scrutiny in parton distribution functions and new physics searches.

Total top-quark pair-production cross section at hadron colliders through O(αS(4)).

PubMed

Czakon, Michał; Fiedler, Paul; Mitov, Alexander

2013-06-21

We compute the next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) correction to the total cross section for the reaction gg → tt + X. Together with the partonic channels we computed previously, the result derived in this Letter completes the set of NNLO QCD corrections to the total top pair-production cross section at hadron colliders. Supplementing the fixed order results with soft-gluon resummation with next-to-next-to-leading logarithmic accuracy, we estimate that the theoretical uncertainty of this observable due to unknown higher order corrections is about 3% at the LHC and 2.2% at the Tevatron. We observe a good agreement between the standard model predictions and the available experimental measurements. The very high theoretical precision of this observable allows a new level of scrutiny in parton distribution functions and new physics searches.

Soft evolution of multi-jet final states

DOE PAGES

Gerwick, Erik; Schumann, Steffen; Höche, Stefan; ...

2015-02-16

We present a new framework for computing resummed and matched distributions in processes with many hard QCD jets. The intricate color structure of soft gluon emission at large angles renders resummed calculations highly non-trivial in this case. We automate all ingredients necessary for the color evolution of the soft function at next-to-leading-logarithmic accuracy, namely the selection of the color bases and the projections of color operators and Born amplitudes onto those bases. Explicit results for all QCD processes with up to 2 → 5 partons are given. We also devise a new tree-level matching scheme for resummed calculations which exploitsmore » a quasi-local subtraction based on the Catani-Seymour dipole formalism. We implement both resummation and matching in the Sherpa event generator. As a proof of concept, we compute the resummed and matched transverse-thrust distribution for hadronic collisions.« less

Measurement of z boson transverse momentum in proton - anti-proton collisions at √s = 1.96 TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lei

This dissertation describes a measurement of the shape of the boson transverse momentum distribution in pmore » $$\\bar{p}$$ → Z/γ* → e +e - + X events at a center-of-mass energy of 1.96 TeV. The measurement is made for events with electron-positron mass between 70 < M ee < 110 GeV/c 2 and uses 976 pb -1 of data collected at the Fermilab Tevatron collider with the D0 detector. The shape is measured both for the inclusive sample and for the subset of events containing a boson with large rapidity. The large-rapidity distribution shows better agreement with theory when the calculation is done using traditional Collins-Soper-Sterman resummation than when using a recent resummed form factor with modifications in the small-x region.« less

Iterative initial condition reconstruction

NASA Astrophysics Data System (ADS)

Schmittfull, Marcel; Baldauf, Tobias; Zaldarriaga, Matias

2017-07-01

Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter distribution in real space. In our algorithm, objects are first moved back iteratively along estimated potential gradients, with a progressively reduced smoothing scale, until a nearly uniform catalog is obtained. The linear initial density is then estimated as the divergence of the cumulative displacement, with an optional second-order correction. This algorithm should undo nonlinear effects up to one-loop order, including the higher-order infrared resummation piece. We test the method using dark matter simulations in real space. At redshift z =0 , we find that after eight iterations the reconstructed density is more than 95% correlated with the initial density at k ≤0.35 h Mpc-1 . The reconstruction also reduces the power in the difference between reconstructed and initial fields by more than 2 orders of magnitude at k ≤0.2 h Mpc-1 , and it extends the range of scales where the full broadband shape of the power spectrum matches linear theory by a factor of 2-3. As a specific application, we consider measurements of the baryonic acoustic oscillation (BAO) scale that can be improved by reducing the degradation effects of large-scale flows. In our idealized dark matter simulations, the method improves the BAO signal-to-noise ratio by a factor of 2.7 at z =0 and by a factor of 2.5 at z =0.6 , improving standard BAO reconstruction by 70% at z =0 and 30% at z =0.6 , and matching the optimal BAO signal and signal-to-noise ratio of the linear density in the same volume. For BAO, the iterative nature of the reconstruction is the most important aspect.

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation

DOE PAGES

Burgess, C. P.; Holman, R.; Tasinato, G.

2016-01-26

Though simple inflationary models describe the CMB well, their corrections are often plagued by infrared effects that obstruct a reliable calculation of late-time behaviour. Here we adapt to cosmology tools designed to address similar issues in other physical systems with the goal of making reliable late-time inflationary predictions. The main such tool is Open EFTs which reduce in the inflationary case to Stochastic Inflation plus calculable corrections. We apply this to a simple inflationary model that is complicated enough to have dangerous IR behaviour yet simple enough to allow the inference of late-time behaviour. We find corrections to standard Stochasticmore » Inflationary predictions for the noise and drift, and we find these corrections ensure the IR finiteness of both these quantities. The late-time probability distribution, P(Φ), for super-Hubble field fluctuations are obtained as functions of the noise and drift and so these too are IR finite. We compare our results to other methods (such as large-N models) and find they agree when these models are reliable. In all cases we can explore in detail we find IR secular effects describe the slow accumulation of small perturbations to give a big effect: a significant distortion of the late-time probability distribution for the field. But the energy density associated with this is only of order H 4 at late times and so does not generate a dramatic gravitational back-reaction.« less

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burgess, C. P.; Holman, R.; Tasinato, G.

Though simple inflationary models describe the CMB well, their corrections are often plagued by infrared effects that obstruct a reliable calculation of late-time behaviour. Here we adapt to cosmology tools designed to address similar issues in other physical systems with the goal of making reliable late-time inflationary predictions. The main such tool is Open EFTs which reduce in the inflationary case to Stochastic Inflation plus calculable corrections. We apply this to a simple inflationary model that is complicated enough to have dangerous IR behaviour yet simple enough to allow the inference of late-time behaviour. We find corrections to standard Stochasticmore » Inflationary predictions for the noise and drift, and we find these corrections ensure the IR finiteness of both these quantities. The late-time probability distribution, P(Φ), for super-Hubble field fluctuations are obtained as functions of the noise and drift and so these too are IR finite. We compare our results to other methods (such as large-N models) and find they agree when these models are reliable. In all cases we can explore in detail we find IR secular effects describe the slow accumulation of small perturbations to give a big effect: a significant distortion of the late-time probability distribution for the field. But the energy density associated with this is only of order H 4 at late times and so does not generate a dramatic gravitational back-reaction.« less

Integrated analysis of particle interactions at hadron colliders Report of research activities in 2010-2015

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nadolsky, Pavel M.

2015-08-31

The report summarizes research activities of the project ”Integrated analysis of particle interactions” at Southern Methodist University, funded by 2010 DOE Early Career Research Award DE-SC0003870. The goal of the project is to provide state-of-the-art predictions in quantum chromodynamics in order to achieve objectives of the LHC program for studies of electroweak symmetry breaking and new physics searches. We published 19 journal papers focusing on in-depth studies of proton structure and integration of advanced calculations from different areas of particle phenomenology: multi-loop calculations, accurate long-distance hadronic functions, and precise numerical programs. Methods for factorization of QCD cross sections were advancedmore » in order to develop new generations of CTEQ parton distribution functions (PDFs), CT10 and CT14. These distributions provide the core theoretical input for multi-loop perturbative calculations by LHC experimental collaborations. A novel ”PDF meta-analysis” technique was invented to streamline applications of PDFs in numerous LHC simulations and to combine PDFs from various groups using multivariate stochastic sampling of PDF parameters. The meta-analysis will help to bring the LHC perturbative calculations to the new level of accuracy, while reducing computational efforts. The work on parton distributions was complemented by development of advanced perturbative techniques to predict observables dependent on several momentum scales, including production of massive quarks and transverse momentum resummation at the next-to-next-to-leading order in QCD.« less

Conservative self-force correction to the innermost stable circular orbit: Comparison with multiple post-Newtonian-based methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Favata, Marc

2011-01-15

Barack and Sago [Phys. Rev. Lett. 102, 191101 (2009)] have recently computed the shift of the innermost stable circular orbit (ISCO) of the Schwarzschild spacetime due to the conservative self-force that arises from the finite-mass of an orbiting test-particle. This calculation of the ISCO shift is one of the first concrete results of the self-force program, and provides an exact (fully relativistic) point of comparison with approximate post-Newtonian (PN) computations of the ISCO. Here this exact ISCO shift is compared with nearly all known PN-based methods. These include both 'nonresummed' and 'resummed' approaches (the latter reproduce the test-particle limit bymore » construction). The best agreement with the exact (Barack-Sago) result is found when the pseudo-4PN coefficient of the effective-one-body (EOB) metric is fit to numerical relativity simulations. However, if one considers uncalibrated methods based only on the currently known 3PN-order conservative dynamics, the best agreement is found from the gauge-invariant ISCO condition of Blanchet and Iyer [Classical Quantum Gravity 20, 755 (2003)], which relies only on the (nonresummed) 3PN equations of motion. This method reproduces the exact test-particle limit without any resummation. A comparison of PN methods with the ISCO in the equal-mass case (computed via sequences of numerical relativity initial-data sets) is also performed. Here a (different) nonresummed method also performs very well (as was previously shown). These results suggest that the EOB approach - while exactly incorporating the conservative test-particle dynamics and having several other important advantages - does not (in the absence of calibration) incorporate conservative self-force effects more accurately than standard PN methods. I also consider how the conservative self-force ISCO shift, combined in some cases with numerical relativity computations of the ISCO, can be used to constrain our knowledge of (1) the EOB effective metric, (2) phenomenological inspiral-merger-ringdown templates, and (3) 4PN- and 5PN-order terms in the PN orbital energy. These constraints could help in constructing better gravitational-wave templates. Lastly, I suggest a new method to calibrate unknown PN terms in inspiral templates using numerical-relativity calculations.« less

Percent-level-precision physics at the Tevatron: next-to-next-to-leading order QCD corrections to qq¯→tt¯+X.

PubMed

Bärnreuther, Peter; Czakon, Michał; Mitov, Alexander

2012-09-28

We compute the next-to-next-to-leading order QCD corrections to the partonic reaction that dominates top-pair production at the Tevatron. This is the first ever next-to-next-to-leading order calculation of an observable with more than two colored partons and/or massive fermions at hadron colliders. Augmenting our fixed order calculation with soft-gluon resummation through next-to-next-to-leading logarithmic accuracy, we observe that the predicted total inclusive cross section exhibits a very small perturbative uncertainty, estimated at ±2.7%. We expect that once all subdominant partonic reactions are accounted for, and work in this direction is ongoing, the perturbative theoretical uncertainty for this observable could drop below ±2%. Our calculation demonstrates the power of our computational approach and proves it can be successfully applied to all processes at hadron colliders for which high-precision analyses are needed.

Measurements of the [Formula: see text] production cross sections in association with jets with the ATLAS detector.

PubMed

Aad, G; Abbott, B; Abdallah, J; Abdel Khalek, S; Abdinov, O; Aben, R; Abi, B; Abolins, M; AbouZeid, O S; Abramowicz, H; Abreu, H; Abreu, R; Abulaiti, Y; Acharya, B S; Adamczyk, L; Adams, D L; Adelman, J; Adomeit, S; Adye, T; Agatonovic-Jovin, T; Aguilar-Saavedra, J A; Agustoni, M; Ahlen, S P; Ahmadov, F; Aielli, G; Akerstedt, H; Åkesson, T P A; Akimoto, G; Akimov, A V; Alberghi, G L; Albert, J; Albrand, S; Alconada Verzini, M J; Aleksa, M; Aleksandrov, I N; Alexa, C; Alexander, G; Alexandre, G; Alexopoulos, T; Alhroob, M; Alimonti, G; Alio, L; Alison, J; Allbrooke, B M M; Allison, L J; Allport, P P; Almond, J; Aloisio, A; Alonso, A; Alonso, F; Alpigiani, C; Altheimer, A; Alvarez Gonzalez, B; Alviggi, M G; Amako, K; Amaral Coutinho, Y; Amelung, C; Amidei, D; Amor Dos Santos, S P; Amorim, A; Amoroso, S; Amram, N; Amundsen, G; Anastopoulos, C; Ancu, L S; Andari, N; Andeen, T; Anders, C F; Anders, G; Anderson, K J; Andreazza, A; Andrei, V; Anduaga, X S; Angelidakis, S; Angelozzi, I; Anger, P; Angerami, A; Anghinolfi, F; Anisenkov, A V; Anjos, N; Annovi, A; Antonaki, A; Antonelli, M; Antonov, A; Antos, J; Anulli, F; Aoki, M; Aperio Bella, L; Apolle, R; Arabidze, G; Aracena, I; Arai, Y; Araque, J P; Arce, A T H; Arguin, J-F; Argyropoulos, S; Arik, M; Armbruster, A J; Arnaez, O; Arnal, V; Arnold, H; Arratia, M; Arslan, O; Artamonov, A; Artoni, G; Asai, S; Asbah, N; Ashkenazi, A; Åsman, B; Asquith, L; Assamagan, K; Astalos, R; Atkinson, M; Atlay, N B; Auerbach, B; Augsten, K; Aurousseau, M; Avolio, G; Azuelos, G; Azuma, Y; Baak, M A; Baas, A E; Bacci, C; Bachacou, H; Bachas, K; Backes, M; Backhaus, M; Backus Mayes, J; Badescu, E; Bagiacchi, P; Bagnaia, P; Bai, Y; Bain, T; Baines, J T; Baker, O K; Balek, P; Balli, F; Banas, E; Banerjee, Sw; Bannoura, A A E; Bansal, V; Bansil, H S; Barak, L; Baranov, S P; Barberio, E L; Barberis, D; Barbero, M; Barillari, T; Barisonzi, M; Barklow, T; Barlow, N; Barnett, B M; Barnett, R M; Barnovska, Z; Baroncelli, A; Barone, G; Barr, A J; Barreiro, F; Barreiro Guimarães da Costa, J; Bartoldus, R; Barton, A E; Bartos, P; Bartsch, V; Bassalat, A; Basye, A; Bates, R L; Batley, J R; Battaglia, M; Battistin, M; Bauer, F; Bawa, H S; Beattie, M D; Beau, T; Beauchemin, P H; Beccherle, R; Bechtle, P; Beck, H P; Becker, K; Becker, S; Beckingham, M; Becot, C; Beddall, A J; Beddall, A; Bedikian, S; Bednyakov, V A; Bee, C P; Beemster, L J; Beermann, T A; Begel, M; Behr, K; Belanger-Champagne, C; Bell, P J; Bell, W H; Bella, G; Bellagamba, L; Bellerive, A; Bellomo, M; Belotskiy, K; Beltramello, O; Benary, O; Benchekroun, D; Bendtz, K; Benekos, N; Benhammou, Y; Benhar Noccioli, E; Benitez Garcia, J A; Benjamin, D P; Bensinger, J R; Benslama, K; Bentvelsen, S; Berge, D; Bergeaas Kuutmann, E; Berger, N; Berghaus, F; Beringer, J; Bernard, C; Bernat, P; Bernius, C; Bernlochner, F U; Berry, T; Berta, P; Bertella, C; Bertoli, G; Bertolucci, F; Bertsche, C; Bertsche, D; Besana, M I; Besjes, G J; Bessidskaia Bylund, O; Bessner, M; Besson, N; Betancourt, C; 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Brenner, R; Bressler, S; Bristow, K; Bristow, T M; Britton, D; Brochu, F M; Brock, I; Brock, R; Bromberg, C; Bronner, J; Brooijmans, G; Brooks, T; Brooks, W K; Brosamer, J; Brost, E; Brown, J; Bruckman de Renstrom, P A; Bruncko, D; Bruneliere, R; Brunet, S; Bruni, A; Bruni, G; Bruschi, M; Bryngemark, L; Buanes, T; Buat, Q; Bucci, F; Buchholz, P; Buckingham, R M; Buckley, A G; Buda, S I; Budagov, I A; Buehrer, F; Bugge, L; Bugge, M K; Bulekov, O; Bundock, A C; Burckhart, H; Burdin, S; Burghgrave, B; Burke, S; Burmeister, I; Busato, E; Büscher, D; Büscher, V; Bussey, P; Buszello, C P; Butler, B; Butler, J M; Butt, A I; Buttar, C M; Butterworth, J M; Butti, P; Buttinger, W; Buzatu, A; Byszewski, M; Cabrera Urbán, S; Caforio, D; Cakir, O; Calace, N; Calafiura, P; Calandri, A; Calderini, G; Calfayan, P; Calkins, R; Caloba, L P; Calvet, D; Calvet, S; Camacho Toro, R; Camarda, S; Cameron, D; Caminada, L M; Caminal Armadans, R; Campana, S; Campanelli, M; Campoverde, A; Canale, V; Canepa, A; Cano Bret, M; 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This paper presents cross sections for the production of a [Formula: see text] boson in association with jets, measured in proton-proton collisions at [Formula: see text] with the ATLAS experiment at the large hadron collider. With an integrated luminosity of [Formula: see text], this data set allows for an exploration of a large kinematic range, including jet production up to a transverse momentum of [Formula: see text] and multiplicities up to seven associated jets. The production cross sections for [Formula: see text] bosons are measured in both the electron and muon decay channels. Differential cross sections for many observables are also presented including measurements of the jet observables such as the rapidities and the transverse momenta as well as measurements of event observables such as the scalar sums of the transverse momenta of the jets. The measurements are compared to numerous QCD predictions including next-to-leading-order perturbative calculations, resummation calculations and Monte Carlo generators.

Measurement of the φ* η distribution of muon pairs with masses between 30 and 500 GeV in 10.4 fb -1 of pp¯ collisions

DOE PAGES

Abazov, Victor Mukhamedovich

2015-04-06

We present a measurement of the distribution of the variable φ* η for muon pairs with masses between 30 and 500 GeV, using the complete run II data set collected by the D0 detector at the Fermilab Tevatron proton-antiproton collider. This corresponds to an integrated luminosity of 10.4 fb –1 at √s = 1.96 TeV. The data are corrected for detector effects and presented in bins of dimuon rapidity and mass. The variable φ* η probes the same physical effects as the Z/γ* boson transverse momentum, but is less susceptible to the effects of experimental resolution and efficiency. These aremore » the first measurements at any collider of the φ* η distributions for dilepton masses away from the Z → ℓ +ℓ – boson mass peak. As a result, the data are compared to QCD predictions based on the resummation of multiple soft gluons.« less

Percent-Level-Precision Physics at the Tevatron: Next-to-Next-to-Leading Order QCD Corrections to qq¯→tt¯+X

NASA Astrophysics Data System (ADS)

Bärnreuther, Peter; Czakon, Michał; Mitov, Alexander

2012-09-01

We compute the next-to-next-to-leading order QCD corrections to the partonic reaction that dominates top-pair production at the Tevatron. This is the first ever next-to-next-to-leading order calculation of an observable with more than two colored partons and/or massive fermions at hadron colliders. Augmenting our fixed order calculation with soft-gluon resummation through next-to-next-to-leading logarithmic accuracy, we observe that the predicted total inclusive cross section exhibits a very small perturbative uncertainty, estimated at ±2.7%. We expect that once all subdominant partonic reactions are accounted for, and work in this direction is ongoing, the perturbative theoretical uncertainty for this observable could drop below ±2%. Our calculation demonstrates the power of our computational approach and proves it can be successfully applied to all processes at hadron colliders for which high-precision analyses are needed.

Reconciling threshold and subthreshold expansions for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Siemens, D.; Ruiz de Elvira, J.; Epelbaum, E.; Hoferichter, M.; Krebs, H.; Kubis, B.; Meißner, U.-G.

2017-07-01

Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the Δ (1232) as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the Δ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the Δ-less theory the resummation of 1 /mN corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.

Two-body problem in scalar-tensor theories as a deformation of general relativity: An effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis; Deruelle, Nathalie

2017-06-01

In this paper we address the two-body problem in massless scalar-tensor (ST) theories within an effective-one-body (EOB) framework. We focus on the first building block of the EOB approach, that is, mapping the conservative part of the two-body dynamics onto the geodesic motion of a test particle in an effective external metric. To this end, we first deduce the second post-Keplerian (2PK) Hamiltonian of the two-body problem from the known 2PK Lagrangian. We then build, by means of a canonical transformation, a ST deformation of the general relativistic EOB Hamiltonian that allows us to incorporate the scalar-tensor (2PK) corrections to the currently best available general relativity EOB results. This EOB-ST Hamiltonian defines a resummation of the dynamics that may provide information on the strong-field regime, in particular, the ISCO location and associated orbital frequency, and can be compared to, other, e.g., tidal, corrections.

A dispersive treatment of K l4 decays

DOE PAGES

Colangelo, Gilberto; Passemar, Emilie; Stoffer, Peter

2015-04-28

K l4 decays offer several reasons of interest: they allow an accurate measurement of ππ-scattering lengths; they provide the best source for the determination of some low-energy constants of xPT; one form factor is directly related to the chiral anomaly, which can be measured here. We present a dispersive treatment of K l4 decays that provides a resummation of ππ- and K π-rescattering effects. In addition, the free parameters of the dispersion relation are fitted to the data of the high-statistics experiments E865 and NA48/2. The matching to xPT at NLO and NNLO enables us to determine the LECs Lmore » r 1, L r 2 and L r 3. With recently published data from NA48/2, the LEC L r 9 can be determined as well. In contrast to a pure chiral treatment, the dispersion relation describes the observed curvature of one of the form factors, which we understand as a rescattering effect beyond NNLO.« less

Precision corrections to fine tuning in SUSY

DOE PAGES

Buckley, Matthew R.; Monteux, Angelo; Shih, David

2017-06-20

Requiring that the contributions of supersymmetric particles to the Higgs mass are not highly tuned places upper limits on the masses of superpartners — in particular the higgsino, stop, and gluino. We revisit the details of the tuning calculation and introduce a number of improvements, including RGE resummation, two-loop effects, a proper treatment of UV vs. IR masses, and threshold corrections. This improved calculation more accurately connects the tuning measure with the physical masses of the superpartners at LHC-accessible energies. After these refinements, the tuning bound on the stop is now also sensitive to the masses of the 1st andmore » 2nd generation squarks, which limits how far these can be decoupled in Effective SUSY scenarios. We find that, for a fixed level of tuning, our bounds can allow for heavier gluinos and stops than previously considered. Despite this, the natural region of supersymmetry is under pressure from the LHC constraints, with high messenger scales particularly disfavored.« less

Reducing the two-body problem in scalar-tensor theories to the motion of a test particle: A scalar-tensor effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis

2018-01-01

Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a ν deformation (where ν =0 is the test mass limit) of the analytically known ST Hamiltonian of a test particle. This ST-EOB Hamiltonian leads to a simple (yet canonically equivalent) formulation of the conservative 2PK two-body problem, but also defines a resummation of the dynamics which is well-suited to ST regimes that depart strongly from general relativity (GR) and which may provide information on the strong field dynamics; in particular, the ST innermost stable circular orbit location and associated orbital frequency. Results will be compared and contrasted with those deduced from the ST-deformation of the (5PN) GR-EOB Hamiltonian previously obtained in [Phys. Rev. D 95, 124054 (2017), 10.1103/PhysRevD.95.124054].

Open charm production and low x gluons

NASA Astrophysics Data System (ADS)

de Oliveira, E. G.; Martin, A. D.; Ryskin, M. G.

2018-04-01

We compare the rapidity, y , and the beam energy, √{s } , behaviors of the cross section of the data for D meson production in the forward direction that were measured by the LHCb Collaboration. We describe the observed cross sections using NLO perturbative QCD, and choose the optimal factorization scale for the LO contribution which provides the resummation of the large double logarithms. We emphasize the inconsistency observed in the y and √{s } behaviors of the D meson cross sections. The y behavior indicates a very flat x dependence of the gluon PDF in the unexplored low x region around x ˜1 0-5 . However, to describe the √{s } dependence of the data we need a steeper gluon PDF with decreasing x . Moreover, an even steeper behavior is needed to provide an extrapolation which matches on to the well known gluons found in the global PDF analyses for x ˜1 0-3 . The possible role of nonperturbative effects is briefly discussed.

A dispersive treatment of K ι4 decays

DOE PAGES

Stoffer, Peter; Colangelo, Gilberto; Passemar, Emilie

2017-01-01

K ι4 decays have several features of interest: they allow an accurate measurement of ππ-scattering lengths; the decay is the best source for the determination of some low-energy constants of chiral perturbation theory (χPT); one form factor of the decay is connected to the chiral anomaly. Here, we present the results of our dispersive analysis of K ι4 decays, which provides a resummation of ππ- and Kπ-rescattering effects. The free parameters of the dispersion relation are fitted to the data of the high-statistics experiments E865 and NA48/2. By matching to χPT at NLO and NNLO, we determine the low-energy constantsmore » and L r 1, L r 2, and L r 3. In contrast to a pure chiral treatment, the dispersion relation describes the observed curvature of one of the K ι4 form factors, which we understand as an effect of rescattering beyond NNLO.« less

Precision corrections to fine tuning in SUSY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buckley, Matthew R.; Monteux, Angelo; Shih, David

Requiring that the contributions of supersymmetric particles to the Higgs mass are not highly tuned places upper limits on the masses of superpartners — in particular the higgsino, stop, and gluino. We revisit the details of the tuning calculation and introduce a number of improvements, including RGE resummation, two-loop effects, a proper treatment of UV vs. IR masses, and threshold corrections. This improved calculation more accurately connects the tuning measure with the physical masses of the superpartners at LHC-accessible energies. After these refinements, the tuning bound on the stop is now also sensitive to the masses of the 1st andmore » 2nd generation squarks, which limits how far these can be decoupled in Effective SUSY scenarios. We find that, for a fixed level of tuning, our bounds can allow for heavier gluinos and stops than previously considered. Despite this, the natural region of supersymmetry is under pressure from the LHC constraints, with high messenger scales particularly disfavored.« less

Measurements of the W production cross sections in association with jets with the ATLAS detector

DOE PAGES

Aad, G.

2015-02-19

This paper presents cross sections for the production of a W boson in association with jets, measured in proton–proton collisions at \\(\\sqrt{s} = 7\\) TeV with the ATLAS experiment at the large hadron collider. With an integrated luminosity of 4.6fb -1, this data set allows for an exploration of a large kinematic range, including jet production up to a transverse momentum of 1TeV and multiplicities up to seven associated jets. The production cross sections for W bosons are measured in both the electron and muon decay channels. Differential cross sections for many observables are also presented including measurements of themore » jet observables such as the rapidities and the transverse momenta as well as measurements of event observables such as the scalar sums of the transverse momenta of the jets. As a result, the measurements are compared to numerous QCD predictions including next-to-leading-order perturbative calculations, resummation calculations and Monte Carlo generators.« less

Secondary production of massive quarks in thrust

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoang, André H.; Erwin Schrödinger International Institute for Mathematical Physics, University of Vienna, Boltzmanngasse 9, A-1090 Vienna; Mateu, Vicent

2016-01-22

We present a factorization framework that takes into account the production of heavy quarks through gluon splitting in the thrust distribution for e{sup +}e{sup −} → hadrons. The explicit factorization theorems and some numerical results are displayed in the dijet region where the kinematic scales are widely separated, which can be extended systematically to the whole spectrum. We account for the necessary two-loop matrix elements, threshold corrections, and include resummation up to N{sup 3}LL order. We include nonperturbative power corrections through a field theoretical shape function, and remove the O(Λ{sub QCD}) renormalon in the partonic soft function by appropriate mass-dependentmore » subtractions. Our results hold for any value of the quark mass, from an infinitesimally small (merging to the known massless result) to an infinitely large one (achieving the decoupling limit). This is the first example of an application of a variable flavor number scheme to final state jets.« less

Reconciling threshold and subthreshold expansions for pion–nucleon scattering

DOE PAGES

Siemens, D.; Ruiz de Elvira, J.; Epelbaum, E.; ...

2017-04-21

Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion–nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the Δ(1232) as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the Δ indeed reduces the low-energy constants to more natural values and thereby improves consistency betweenmore » threshold and subthreshold kinematics. In addition, even in the Δ-less theory the resummation of 1/m N corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.« less

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

Multiscale Methods for Nuclear Reactor Analysis

NASA Astrophysics Data System (ADS)

Collins, Benjamin S.

The ability to accurately predict local pin powers in nuclear reactors is necessary to understand the mechanisms that cause fuel pin failure during steady state and transient operation. In the research presented here, methods are developed to improve the local solution using high order methods with boundary conditions from a low order global solution. Several different core configurations were tested to determine the improvement in the local pin powers compared to the standard techniques, that use diffusion theory and pin power reconstruction (PPR). Two different multiscale methods were developed and analyzed; the post-refinement multiscale method and the embedded multiscale method. The post-refinement multiscale methods use the global solution to determine boundary conditions for the local solution. The local solution is solved using either a fixed boundary source or an albedo boundary condition; this solution is "post-refinement" and thus has no impact on the global solution. The embedded multiscale method allows the local solver to change the global solution to provide an improved global and local solution. The post-refinement multiscale method is assessed using three core designs. When the local solution has more energy groups, the fixed source method has some difficulties near the interface: however the albedo method works well for all cases. In order to remedy the issue with boundary condition errors for the fixed source method, a buffer region is used to act as a filter, which decreases the sensitivity of the solution to the boundary condition. Both the albedo and fixed source methods benefit from the use of a buffer region. Unlike the post-refinement method, the embedded multiscale method alters the global solution. The ability to change the global solution allows for refinement in areas where the errors in the few group nodal diffusion are typically large. The embedded method is shown to improve the global solution when it is applied to a MOX/LEU assembly interface, the fuel/reflector interface, and assemblies where control rods are inserted. The embedded method also allows for multiple solution levels to be applied in a single calculation. The addition of intermediate levels to the solution improves the accuracy of the method. Both multiscale methods considered here have benefits and drawbacks, but both can provide improvements over the current PPR methodology.

Applications of He's semi-inverse method, ITEM and GGM to the Davey-Stewartson equation

NASA Astrophysics Data System (ADS)

Zinati, Reza Farshbaf; Manafian, Jalil

2017-04-01

We investigate the Davey-Stewartson (DS) equation. Travelling wave solutions were found. In this paper, we demonstrate the effectiveness of the analytical methods, namely, He's semi-inverse variational principle method (SIVPM), the improved tan(φ/2)-expansion method (ITEM) and generalized G'/G-expansion method (GGM) for seeking more exact solutions via the DS equation. These methods are direct, concise and simple to implement compared to other existing methods. The exact solutions containing four types solutions have been achieved. The results demonstrate that the aforementioned methods are more efficient than the Ansatz method applied by Mirzazadeh (2015). Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found by the improved tan(φ/2)-expansion and generalized G'/G-expansion methods. By He's semi-inverse variational principle we have obtained dark and bright soliton wave solutions. Also, the obtained semi-inverse variational principle has profound implications in physical understandings. These solutions might play important role in engineering and physics fields. Moreover, by using Matlab, some graphical simulations were done to see the behavior of these solutions.

Methods of making metal oxide nanostructures and methods of controlling morphology of same

DOEpatents

Wong, Stanislaus S; Hongjun, Zhou

2012-11-27

The present invention includes a method of producing a crystalline metal oxide nanostructure. The method comprises providing a metal salt solution and providing a basic solution; placing a porous membrane between the metal salt solution and the basic solution, wherein metal cations of the metal salt solution and hydroxide ions of the basic solution react, thereby producing a crystalline metal oxide nanostructure.

New exact solutions for a discrete electrical lattice using the analytical methods

NASA Astrophysics Data System (ADS)

Manafian, Jalil; Lakestani, Mehrdad

2018-03-01

This paper retrieves soliton solutions to an equation in nonlinear electrical transmission lines using the semi-inverse variational principle method (SIVPM), the \\exp(-Ω(ξ)) -expansion method (EEM) and the improved tan(φ/2) -expansion method (ITEM), with the aid of the symbolic computation package Maple. As a result, the SIVPM, EEM and ITEM methods are successfully employed and some new exact solitary wave solutions are acquired in terms of kink-singular soliton solution, hyperbolic solution, trigonometric solution, dark and bright soliton solutions. All solutions have been verified back into their corresponding equations with the aid of the Maple package program. We depicted the physical explanation of the extracted solutions with the choice of different parameters by plotting some 2D and 3D illustrations. Finally, we show that the used methods are robust and more efficient than other methods. More importantly, the solutions found in this work can have significant applications in telecommunication systems where solitons are used to codify data.

Method for PE Pipes Fusion Jointing Based on TRIZ Contradictions Theory

NASA Astrophysics Data System (ADS)

Sun, Jianguang; Tan, Runhua; Gao, Jinyong; Wei, Zihui

The core of the TRIZ theories is the contradiction detection and solution. TRIZ provided various methods for the contradiction solution, but all that is not systematized. Combined with the technique system conception, this paper summarizes an integration solution method for contradiction solution based on the TRIZ contradiction theory. According to the method, a flowchart of integration solution method for contradiction is given. As a casestudy, method of fusion jointing PE pipe is analysised.

Method for Non-Invasive Determination of Chemical Properties of Aqueous Solutions

NASA Technical Reports Server (NTRS)

Jones, Alan (Inventor); Thomas, Nathan A. (Inventor); Todd, Paul W. (Inventor)

2016-01-01

A method for non-invasively determining a chemical property of an aqueous solution is provided. The method provides the steps of providing a colored solute having a light absorbance spectrum and transmitting light through the colored solute at two different wavelengths. The method further provides the steps of measuring light absorbance of the colored solute at the two different transmitted light wavelengths, and comparing the light absorbance of the colored solute at the two different wavelengths to determine a chemical property of an aqueous solution.

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions

NASA Astrophysics Data System (ADS)

Foroutan, Mohammadreza; Zamanpour, Isa; Manafian, Jalil

2017-10-01

This paper presents a number of new solutions obtained for solving a complex nonlinear equation describing dynamics of nonlinear chains of atoms via the improved Bernoulli sub-ODE method (IBSOM) and the extended trial equation method (ETEM). The proposed solutions are kink solitons, anti-kink solitons, soliton solutions, hyperbolic solutions, trigonometric solutions, and bellshaped soliton solutions. Then our new results are compared with the well-known results. The methods used here are very simple and succinct and can be also applied to other nonlinear models. The balance number of these methods is not constant contrary to other methods. The proposed methods also allow us to establish many new types of exact solutions. By utilizing the Maple software package, we show that all obtained solutions satisfy the conditions of the studied model. More importantly, the solutions found in this work can have significant applications in Hamilton's equations and generalized momentum where solitons are used for long-range interactions.

A new solution method for wheel/rail rolling contact.

PubMed

Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

2016-01-01

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

Solution of plane cascade flow using improved surface singularity methods. [application of panel method to internal aerodynamics

NASA Technical Reports Server (NTRS)

Mcfarland, E. R.

1981-01-01

A solution method was developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

Boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain, with both a crack singularity and a corner singularity. Also an analysis of partial solutions near the singular points is provided. These methods are easy to apply, have good stability properties, and lead to highly accurate solutions. Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

PubMed Central

Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

2014-01-01

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327

F-expansion method and new exact solutions of the Schrödinger-KdV equation.

PubMed

Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

2014-01-01

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

Solution of plane cascade flow using improved surface singularity methods

NASA Technical Reports Server (NTRS)

Mcfarland, E. R.

1981-01-01

A solution method has been developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those found in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.

New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

NASA Astrophysics Data System (ADS)

Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

2018-03-01

In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Metal sulfide and rare-earth phosphate nanostructures and methods of making same

DOEpatents

Wong, Stanislaus; Zhang, Fen

2016-06-28

The present invention provides a method of producing a crystalline rare earth phosphate nanostructure. The method comprising: providing a rare earth metal precursor solution and providing a phosphate precursor solution; placing a porous membrane between the metal precursor solution and the phosphate precursor solution, wherein metal cations of the metal precursor solution and phosphate ions of the phosphate precursor solution react, thereby producing a crystalline rare earth metal phosphate nanostructure.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

PubMed

Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng

2014-01-01

We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2 (z) and simply periodic solutions us,2-6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

Study on a Multi-Frequency Homotopy Analysis Method for Period-Doubling Solutions of Nonlinear Systems

NASA Astrophysics Data System (ADS)

Fu, H. X.; Qian, Y. H.

In this paper, a modification of homotopy analysis method (HAM) is applied to study the two-degree-of-freedom coupled Duffing system. Firstly, the process of calculating the two-degree-of-freedom coupled Duffing system is presented. Secondly, the single periodic solutions and double periodic solutions are obtained by solving the constructed nonlinear algebraic equations. Finally, comparing the periodic solutions obtained by the multi-frequency homotopy analysis method (MFHAM) and the fourth-order Runge-Kutta method, it is found that the approximate solution agrees well with the numerical solution.

Fundamental solution of the problem of linear programming and method of its determination

NASA Technical Reports Server (NTRS)

Petrunin, S. V.

1978-01-01

The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Kookjin; Carlberg, Kevin; Elman, Howard C.

Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weightedmore » $$\\ell^2$$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $$\\ell^2$$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.« less

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

Method of precipitating uranium from an aqueous solution and/or sediment

DOEpatents

Tokunaga, Tetsu K; Kim, Yongman; Wan, Jiamin

2013-08-20

A method for precipitating uranium from an aqueous solution and/or sediment comprising uranium and/or vanadium is presented. The method includes precipitating uranium as a uranyl vanadate through mixing an aqueous solution and/or sediment comprising uranium and/or vanadium and a solution comprising a monovalent or divalent cation to form the corresponding cation uranyl vanadate precipitate. The method also provides a pathway for extraction of uranium and vanadium from an aqueous solution and/or sediment.

Low energy probes of PeV scale sfermions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Altmannshofer, Wolfgang; Harnik, Roni; Zupan, Jure

2013-11-27

We derive bounds on squark and slepton masses in mini-split supersymmetry scenario using low energy experiments. In this setup gauginos are at the TeV scale, while sfermions are heavier by a loop factor. We cover the most sensitive low energy probes including electric dipole moments (EDMs), meson oscillations and charged lepton flavor violation (LFV) transitions. A leading log resummation of the large logs of gluino to sfermion mass ratio is performed. A sensitivity to PeV squark masses is obtained at present from kaon mixing measurements. A number of observables, including neutron EDMs, mu->e transitions and charmed meson mixing, will startmore » probing sfermion masses in the 100 TeV-1000 TeV range with the projected improvements in the experimental sensitivities. We also discuss the implications of our results for a variety of models that address the flavor hierarchy of quarks and leptons. We find that EDM searches will be a robust probe of models in which fermion masses are generated radiatively, while LFV searches remain sensitive to simple-texture based flavor models.« less

Soft gluon evolution and non-global logarithms

NASA Astrophysics Data System (ADS)

Martínez, René Ángeles; De Angelis, Matthew; Forshaw, Jeffrey R.; Plätzer, Simon; Seymour, Michael H.

2018-05-01

We consider soft-gluon evolution at the amplitude level. Our evolution algorithm applies to generic hard-scattering processes involving any number of coloured partons and we present a reformulation of the algorithm in such a way as to make the cancellation of infrared divergences explicit. We also emphasise the special role played by a Lorentz-invariant evolution variable, which coincides with the transverse momentum of the latest emission in a suitably defined dipole zero-momentum frame. Handling large colour matrices presents the most significant challenge to numerical implementations and we present a means to expand systematically about the leading colour approximation. Specifically, we present a systematic procedure to calculate the resulting colour traces, which is based on the colour flow basis. Identifying the leading contribution leads us to re-derive the Banfi-Marchesini-Smye equation. However, our formalism is more general and can systematically perform resummation of contributions enhanced by the t'Hooft coupling α s N ˜ 1, along with successive perturbations that are parametrically suppressed by powers of 1 /N . We also discuss how our approach relates to earlier work.

Abelian non-global logarithms from soft gluon clustering

NASA Astrophysics Data System (ADS)

Kelley, Randall; Walsh, Jonathan R.; Zuberi, Saba

2012-09-01

Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to previously identified correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections, which are known as clustering logarithms. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution. Using the framework of Soft Collinear Effective Theory (SCET), we show that new clustering effects contributing at NLL arise at each order. While numerical resummation of clustering logs is possible, it is unlikely that they can be analytically resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power suppressed. They can arise in Abelian and non-Abelian terms, and we calculate the Abelian clustering logarithms at O ( {α_s^2} ) for the jet mass distribution using the Cambridge/Aachen and kT algorithms, including jet radius dependence, which extends previous results. We find that clustering logarithms can be naturally thought of as a class of non-global logarithms, which have traditionally been tied to non-Abelian correlations in soft gluon emission.

A Lagrangian effective field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlah, Zvonimir; White, Martin; Aviles, Alejandro

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less

A Lagrangian effective field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlah, Zvonimir; White, Martin; Aviles, Alejandro, E-mail: zvlah@stanford.edu, E-mail: mwhite@berkeley.edu, E-mail: aviles@berkeley.edu

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.« less

A Lagrangian effective field theory

DOE PAGES

Vlah, Zvonimir; White, Martin; Aviles, Alejandro

2015-09-02

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less

Controlled fabrication of semiconductor-metal hybrid nano-heterostructures via site-selective metal photodeposition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vela Becerra, Javier; Ruberu, T. Purnima A.

A method of synthesizing colloidal semiconductor-metal hybrid heterostructures is disclosed. The method includes dissolving semiconductor nanorods in a solvent to form a nanorod solution, and adding a precursor solution to the nanorod solution. The precursor solution contains a metal. The method further includes illuminating the combined precursor and nanorod solutions with light of a specific wavelength. The illumination causes the deposition of the metal in the precursor solution onto the surface of the semiconductor nanorods.

Methods of producing cesium-131

DOEpatents

Meikrantz, David H; Snyder, John R

2012-09-18

Methods of producing cesium-131. The method comprises dissolving at least one non-irradiated barium source in water or a nitric acid solution to produce a barium target solution. The barium target solution is irradiated with neutron radiation to produce cesium-131, which is removed from the barium target solution. The cesium-131 is complexed with a calixarene compound to separate the cesium-131 from the barium target solution. A liquid:liquid extraction device or extraction column is used to separate the cesium-131 from the barium target solution.

Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed

In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.

Technetium recovery from high alkaline solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nash, Charles A.

2016-07-12

Disclosed are methods for recovering technetium from a highly alkaline solution. The highly alkaline solution can be a liquid waste solution from a nuclear waste processing system. Methods can include combining the solution with a reductant capable of reducing technetium at the high pH of the solution and adding to or forming in the solution an adsorbent capable of adsorbing the precipitated technetium at the high pH of the solution.

Soliton solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas

NASA Astrophysics Data System (ADS)

Sindi, Cevat Teymuri; Manafian, Jalil

2017-02-01

In this paper, we extended the improved tan(φ/2)-expansion method (ITEM) and the generalized G'/G-expansion method (GGEM) proposed by Manafian and Fazli (Opt. Quantum Electron. 48, 413 (2016)) to construct new types of soliton wave solutions of nonlinear partial differential equations (NPDEs). Moreover, we use of the improvement of the Exp-function method (IEFM) proposed by Jahani and Manafian (Eur. Phys. J. Plus 131, 54 (2016)) for obtaining solutions of NPDEs. The merit of the presented three methods is they can find further solutions to the considered problems, including soliton, periodic, kink, kink-singular wave solutions. This paper studies the quantum Zakharov-Kuznetsov (QZK) equation by the aid of the improved tan(φ/2)-expansion method, the generalized G'/G-expansion method and the improvement of the Exp-function method. Moreover, the 1-soliton solution of the modified QZK equation with power law nonlinearity is obtained by the aid of traveling wave hypothesis with the necessary constraints in place for the existence of the soliton. Comparing our new results with Ebadi et al. results (Astrophys. Space Sci. 341, 507 (2012)), namely, G'/G-expansion method, exp-function method, modified F-expansion method, shows that our results give further solutions. Finally, these solutions might play an important role in engineering, physics and applied mathematics fields.

Some new exact solitary wave solutions of the van der Waals model arising in nature

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Ahmed, Naveed; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-06-01

This work proposes two well-known methods, namely, Exponential rational function method (ERFM) and Generalized Kudryashov method (GKM) to seek new exact solutions of the van der Waals normal form for the fluidized granular matter, linked with natural phenomena and industrial applications. New soliton solutions such as kink, periodic and solitary wave solutions are established coupled with 2D and 3D graphical patterns for clarity of physical features. Our comparison reveals that the said methods excel several existing methods. The worked-out solutions show that the suggested methods are simple and reliable as compared to many other approaches which tackle nonlinear equations stemming from applied sciences.

The block adaptive multigrid method applied to the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Pantelelis, Nikos

1993-01-01

In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.

Accuracy, Precision, Ease-Of-Use, and Cost of Methods to Test Ebola-Relevant Chlorine Solutions

PubMed Central

Wells, Emma; Wolfe, Marlene K.; Murray, Anna; Lantagne, Daniele

2016-01-01

To prevent transmission in Ebola Virus Disease (EVD) outbreaks, it is recommended to disinfect living things (hands and people) with 0.05% chlorine solution and non-living things (surfaces, personal protective equipment, dead bodies) with 0.5% chlorine solution. In the current West African EVD outbreak, these solutions (manufactured from calcium hypochlorite (HTH), sodium dichloroisocyanurate (NaDCC), and sodium hypochlorite (NaOCl)) have been widely used in both Ebola Treatment Unit and community settings. To ensure solution quality, testing is necessary, however test method appropriateness for these Ebola-relevant concentrations has not previously been evaluated. We identified fourteen commercially-available methods to test Ebola-relevant chlorine solution concentrations, including two titration methods, four DPD dilution methods, and six test strips. We assessed these methods by: 1) determining accuracy and precision by measuring in quintuplicate five different 0.05% and 0.5% chlorine solutions manufactured from NaDCC, HTH, and NaOCl; 2) conducting volunteer testing to assess ease-of-use; and, 3) determining costs. Accuracy was greatest in titration methods (reference-12.4% error compared to reference method), then DPD dilution methods (2.4–19% error), then test strips (5.2–48% error); precision followed this same trend. Two methods had an accuracy of <10% error across all five chlorine solutions with good precision: Hach digital titration for 0.05% and 0.5% solutions (recommended for contexts with trained personnel and financial resources), and Serim test strips for 0.05% solutions (recommended for contexts where rapid, inexpensive, and low-training burden testing is needed). Measurement error from test methods not including pH adjustment varied significantly across the five chlorine solutions, which had pH values 5–11. Volunteers found test strip easiest and titration hardest; costs per 100 tests were $14–37 for test strips and $33–609 for titration. Given the ease-of-use and cost benefits of test strips, we recommend further development of test strips robust to pH variation and appropriate for Ebola-relevant chlorine solution concentrations. PMID:27243817

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

UXDs-Driven Transferring Method from TRIZ Solution to Domain Solution

NASA Astrophysics Data System (ADS)

Ma, Lihui; Cao, Guozhong; Chang, Yunxia; Wei, Zihui; Ma, Kai

The translation process from TRIZ solutions to domain solutions is an analogy-based process. TRIZ solutions, such as 40 inventive principles and the related cases, are medium-solutions for domain problems. Unexpected discoveries (UXDs) are the key factors to trigger designers to generate new ideas for domain solutions. The Algorithm of UXD resolving based on Means-Ends Analysis(MEA) is studied and an UXDs-driven transferring method from TRIZ solution to domain solution is formed. A case study shows the application of the process.

Method for preparing salt solutions having desired properties

DOEpatents

Ally, Moonis R.; Braunstein, Jerry

1994-01-01

The specification discloses a method for preparing salt solutions which exhibit desired thermodynamic properties. The method enables prediction of the value of the thermodynamic properties for single and multiple salt solutions over a wide range of conditions from activity data and constants which are independent of concentration and temperature. A particular application of the invention is in the control of salt solutions in a process to provide a salt solution which exhibits the desired properties.

Method and Apparatus for Powered Descent Guidance

NASA Technical Reports Server (NTRS)

Acikmese, Behcet (Inventor); Blackmore, James C. L. (Inventor); Scharf, Daniel P. (Inventor)

2013-01-01

A method and apparatus for landing a spacecraft having thrusters with non-convex constraints is described. The method first computes a solution to a minimum error landing problem for a convexified constraints, then applies that solution to a minimum fuel landing problem for convexified constraints. The result is a solution that is a minimum error and minimum fuel solution that is also a feasible solution to the analogous system with non-convex thruster constraints.

Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

NASA Astrophysics Data System (ADS)

Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.

2017-12-01

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Impact of Complex-Valued Energy Function Singularities on the Behaviour of RAYLEIGH-SCHRöDINGER Perturbation Series. H_2CO Molecule Vibrational Energy Spectrum.

NASA Astrophysics Data System (ADS)

Duchko, Andrey; Bykov, Alexandr

2015-06-01

Nowadays the task of spectra processing is as relevant as ever in molecular spectroscopy. Nevertheless, existing techniques of vibrational energy levels and wave functions computation often come to a dead-lock. Application of standard quantum-mechanical approaches often faces inextricable difficulties. Variational method requires unimaginable computational performance. On the other hand perturbational approaches beat against divergent series. That's why this problem faces an urgent need in application of specific resummation techniques. In this research Rayleigh-Schrödinger perturbation theory is applied to vibrational energy levels calculation of excited vibrational states of H_2CO. It is known that perturbation series diverge in the case of anharmonic resonance coupling between vibrational states [1]. Nevertheless, application of advanced divergent series summation techniques makes it possible to calculate the value of energy with high precision (more than 10 true digits) even for highly excited states of the molecule [2]. For this purposes we have applied several summation techniques based on high-order Pade-Hermite approximations. Our research shows that series behaviour completely depends on the singularities of complex energy function inside unit circle. That's why choosing an approximation function modelling this singularities allows to calculate the sum of divergent series. Our calculations for formaldehyde molecule show that the efficiency of each summation technique depends on the resonant type. REFERENCES 1. J. Cizek, V. Spirko, and O. Bludsky, ON THE USE OF DIVERGENT SERIES IN VIBRATIONAL SPECTROSCOPY. TWO- AND THREE-DIMENSIONAL OSCILLATORS, J. Chem. Phys. 99, 7331 (1993). 2. A. V. Sergeev and D. Z. Goodson, SINGULARITY ANALYSIS OF FOURTH-ORDER MöLLER-PLESSET PERTURBATION THEORY, J. Chem. Phys. 124, 4111 (2006).

Stochastic study of solute transport in a nonstationary medium.

PubMed

Hu, Bill X

2006-01-01

A Lagrangian stochastic approach is applied to develop a method of moment for solute transport in a physically and chemically nonstationary medium. Stochastic governing equations for mean solute flux and solute covariance are analytically obtained in the first-order accuracy of log conductivity and/or chemical sorption variances and solved numerically using the finite-difference method. The developed method, the numerical method of moments (NMM), is used to predict radionuclide solute transport processes in the saturated zone below the Yucca Mountain project area. The mean, variance, and upper bound of the radionuclide mass flux through a control plane 5 km downstream of the footprint of the repository are calculated. According to their chemical sorption capacities, the various radionuclear chemicals are grouped as nonreactive, weakly sorbing, and strongly sorbing chemicals. The NMM method is used to study their transport processes and influence factors. To verify the method of moments, a Monte Carlo simulation is conducted for nonreactive chemical transport. Results indicate the results from the two methods are consistent, but the NMM method is computationally more efficient than the Monte Carlo method. This study adds to the ongoing debate in the literature on the effect of heterogeneity on solute transport prediction, especially on prediction uncertainty, by showing that the standard derivation of solute flux is larger than the mean solute flux even when the hydraulic conductivity within each geological layer is mild. This study provides a method that may become an efficient calculation tool for many environmental projects.

Electrodialytic in-line preconcentration for ionic solute analysis.

PubMed

Ohira, Shin-Ichi; Yamasaki, Takayuki; Koda, Takumi; Kodama, Yuko; Toda, Kei

2018-04-01

Preconcentration is an effective way to improve analytical sensitivity. Many types of methods are used for enrichment of ionic solute analytes. However, current methods are batchwise and include procedures such as trapping and elution. In this manuscript, we propose in-line electrodialytic enrichment of ionic solutes. The method can enrich ionic solutes within seconds by quantitative transfer of analytes from the sample solution to the acceptor solution under an electric field. Because of quantitative ion transfer, the enrichment factor (the ratio of the concentration in the sample and to that in the obtained acceptor solution) only depends on the flow rate ratio of the sample solution to the acceptor solution. The ratios of the concentrations and flow rates are equal for ratios up to 70, 20, and 70 for the tested ionic solutes of inorganic cations, inorganic anions, and heavy metal ions, respectively. The sensitivity of ionic solute determinations is also improved based on the enrichment factor. The method can also simultaneously achieve matrix isolation and enrichment. The method was successively applied to determine the concentrations of trace amounts of chloroacetic acids in tap water. The regulated concentration levels cannot be determined by conventional high-performance liquid chromatography with ultraviolet detection (HPLC-UV) without enrichment. However, enrichment with the present method is effective for determination of tap water quality by improving the limits of detection of HPLC-UV. The standard addition test with real tap water samples shows good recoveries (94.9-109.6%). Copyright © 2017 Elsevier B.V. All rights reserved.

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

NASA Technical Reports Server (NTRS)

Cockrell, C. R.

1989-01-01

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

PubMed Central

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

Study of analytical method to seek for exact solutions of variant Boussinesq equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali

2014-01-01

In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. 35 K99; 35P05; 35P99.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Larsen, E.W.

A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.

Burton-Miller-type singular boundary method for acoustic radiation and scattering

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Gu, Yan

2014-08-01

This paper proposes the singular boundary method (SBM) in conjunction with Burton and Miller's formulation for acoustic radiation and scattering. The SBM is a strong-form collocation boundary discretization technique using the singular fundamental solutions, which is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors (SIFs) to eliminate the singularities of the fundamental solutions. Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS). In the present method, we derive the SIFs of exterior Helmholtz equation by means of the SIFs of exterior Laplace equation owing to the same order of singularities between the Laplace and Helmholtz fundamental solutions. In conjunction with the Burton-Miller formulation, the SBM enhances the quality of the solution, particularly in the vicinity of the corresponding interior eigenfrequencies. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on some benchmark examples under 2D and 3D unbounded domains in comparison with the analytical solutions, the boundary element solutions and Dirichlet-to-Neumann finite element solutions.

Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moridis, G.

1992-03-01

The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.

Method for chemically analyzing a solution by acoustic means

DOEpatents

Beller, Laurence S.

1997-01-01

A method and apparatus for determining a type of solution and the concention of that solution by acoustic means. Generally stated, the method consists of: immersing a sound focusing transducer within a first liquid filled container; locating a separately contained specimen solution at a sound focal point within the first container; locating a sound probe adjacent to the specimen, generating a variable intensity sound signal from the transducer; measuring fundamental and multiple harmonic sound signal amplitudes; and then comparing a plot of a specimen sound response with a known solution sound response, thereby determining the solution type and concentration.

A direct method of solution for the Fokas-Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions

NASA Astrophysics Data System (ADS)

Matsuno, Yoshimasa

2012-06-01

We develop a direct method of solution for finding the bright N-soliton solution of the Fokas-Lenells derivative nonlinear Schrödinger equation. The construction of the solution is performed by means of a purely algebraic procedure using an elementary theory of determinants and does not rely on the inverse scattering transform method. We present two different expressions of the solution both of which are expressed as a ratio of determinants. We then investigate the properties of the solutions and find several new features. Specifically, we derive the formula for the phase shift caused by the collisions of bright solitons.

Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods.

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

Containerless synthesis of amorphous and nanophase organic materials

DOEpatents

Benmore, Chris J.; Weber, Johann R.

2016-05-03

The invention provides a method for producing a mixture of amorphous compounds, the method comprising supplying a solution containing the compounds; and allowing at least a portion of the solvent of the solution to evaporate while preventing the solute of the solution from contacting a nucleation point. Also provided is a method for transforming solids to amorphous material, the method comprising heating the solids in an environment to form a melt, wherein the environment contains no nucleation points; and cooling the melt in the environment.

Method for fabricating apatite crystals and ceramics

DOEpatents

Soules, Thomas F.; Schaffers, Kathleen I.; Tassano, Jr., John B.; Hollingsworth, Joel P.

2013-09-10

The present invention provides a method of crystallizing Yb:C-FAP [Yb.sup.3+:Ca.sub.5(PO.sub.4).sub.3F], by dissolving the Yb:C-FAP in an acidic solution, following by neutralizing the solution. The present invention also provides a method of forming crystalline Yb:C-FAP by dissolving the component ingredients in an acidic solution, followed by forming a supersaturated solution.

Unidirectional growth of benzil crystal from solution by Sankaranarayanan-Ramasamy method and its characterization

NASA Astrophysics Data System (ADS)

Rajalakshmi, M.; Shyju, T. S.; Indirajith, R.; Gopalakrishnan, R.

2012-02-01

Good quality <1 0 0> benzil single crystal with a diameter 18 mm and length 75 mm was successfully grown from solution by the unidirectional growth method of Sankaranarayanan-Ramasamy (SR) for the first time in the literature. The seed crystals have been harvested from conventional solution growth technique and subsequently used for unidirectional growth. The grown crystal was subjected to various characterization studies. The results of UV-vis spectral analysis, photoluminescence, etching and microhardness studies were compared with conventional solution grown crystal to that of SR method grown crystal. The quality of SR method grown benzil crystal is better than conventional solution grown crystal.

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Determining osmotic pressure of drug solutions by air humidity in equilibrium method.

PubMed

Zhan, Xiancheng; Li, Hui; Yu, Lan; Wei, Guocui; Li, Chengrong

2014-06-01

To establish a new osmotic pressure measuring method with a wide measuring range. The osmotic pressure of drug solutions is determined by measuring the relative air humidity in equilibrium with the solution. The freezing point osmometry is used as a control. The data obtained by the proposed method are comparable to those by the control method, and the measuring range of the proposed method is significantly wider than that of the control method. The proposed method is performed in an isothermal and equilibrium state, so it overcomes the defects of the freezing point and dew point osmometries which result from the heterothermal process in the measurement, and therefore is not limited to diluted solutions.

Application of chiral critical clusters to assymetric synthesis

DOEpatents

Ferrieri, Richard A.

2002-01-01

Disclosed is a composition, a method of making and a method of using critical clusters for asymmetric synthesis using substantially optically-pure chiral solvent molecules in a supercritical fluid. The solvent molecules are capable of forming a multipoint hydrogen bonded solvate as they encage at least one solute molecule. The encaged solute molecule is capable of reacting to form an optically active chiral center. In another aspect, there is disclosed a method of directing the position of bonding between a solute molecule and a ligand involving encaging the solute molecule and the ligand with polar solvent molecules in a supercritical fluid under conditions of temperature and pressure sufficient to change electric charge distribution in the solute molecule. In yet another aspect, disclosed is a method of making pharmaceutical compounds involving encaging a solute molecule, which is capable of forming a chiral center, and a ligand with polar solvent molecules in a supercritical fluid under conditions of temperature and pressure sufficient to change electric charge distribution of the solute molecule. The solute molecule and ligand are then reacted whereby the ligand bonds to the solute molecule forming a chiral center. Also disclosed is a method for racemic resolution using critical clusters involving encaging racemic mixtures of solute molecules with substantially optically-pure chiral solvent molecules in a supercritical fluid under conditions of temperature and pressure sufficient to form critical clusters. The solvent molecules are capable of multipoint hydrogen bonding with the solute molecules. The encaged solute molecules are then nonenzymatically reacted to enhance the optical purity of the solute molecules.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

NASA Astrophysics Data System (ADS)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-12-22

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly setmore » negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.« less

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly setmore » negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.« less

PROCESS OF RECOVERING URANIUM

DOEpatents

Kilner, S.B.

1959-12-29

A method is presented for separating and recovering uranium from a complex mixure of impurities. The uranium is dissolved to produce an aqueous acidic solution including various impurities. In accordance with one method, with the uranium in the uranyl state, hydrogen cyanide is introduced into the solution to complex the impurities. Subsequently, ammonia is added to the solution to precipitate the uraniunn as ammonium diuranate away from the impurities in the solution. Alternatively, the uranium is precipitated by adding an alkaline metal hydroxide. In accordance with the second method, the uranium is reduced to the uranous state in the solution. The reduced solution is then treated with solid alkali metal cyanide sufficient to render the solution about 0.1 to 1.0 N in cyanide ions whereat cyanide complex ions of the metal impurities are produced and the uranium is simultaneously precipituted as uranous hydroxide. Alternatively, hydrogen cyanide may be added to the reduced solution and the uranium precipitated subsequently by adding ammonium hydroxide or an alkali metal hydroxide. Other refinements of the method are also disclosed.

A simple high performance liquid chromatography method for analyzing paraquat in soil solution samples.

PubMed

Ouyang, Ying; Mansell, Robert S; Nkedi-Kizza, Peter

2004-01-01

A high performance liquid chromatography (HPLC) method with UV detection was developed to analyze paraquat (1,1'-dimethyl-4,4'-dipyridinium dichloride) herbicide content in soil solution samples. The analytical method was compared with the liquid scintillation counting (LSC) method using 14C-paraquat. Agreement obtained between the two methods was reasonable. However, the detection limit for paraquat analysis was 0.5 mg L(-1) by the HPLC method and 0.05 mg L(-1) by the LSC method. The LSC method was, therefore, 10 times more precise than the HPLC method for solution concentrations less than 1 mg L(-1). In spite of the high detection limit, the UC (nonradioactive) HPLC method provides an inexpensive and environmentally safe means for determining paraquat concentration in soil solution compared with the 14C-LSC method.

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

A Simple Method for Decreasing the Liquid Junction Potential in a Flow-through-Type Differential pH Sensor Probe Consisting of pH-FETs by Exerting Spatiotemporal Control of the Liquid Junction

PubMed Central

Yamada, Akira; Mohri, Satoshi; Nakamura, Michihiro; Naruse, Keiji

2015-01-01

The liquid junction potential (LJP), the phenomenon that occurs when two electrolyte solutions of different composition come into contact, prevents accurate measurements in potentiometry. The effect of the LJP is usually remarkable in measurements of diluted solutions with low buffering capacities or low ion concentrations. Our group has constructed a simple method to eliminate the LJP by exerting spatiotemporal control of a liquid junction (LJ) formed between two solutions, a sample solution and a baseline solution (BLS), in a flow-through-type differential pH sensor probe. The method was contrived based on microfluidics. The sensor probe is a differential measurement system composed of two ion-sensitive field-effect transistors (ISFETs) and one Ag/AgCl electrode. With our new method, the border region of the sample solution and BLS is vibrated in order to mix solutions and suppress the overshoot after the sample solution is suctioned into the sensor probe. Compared to the conventional method without vibration, our method shortened the settling time from over two min to 15 s and reduced the measurement error by 86% to within 0.060 pH. This new method will be useful for improving the response characteristics and decreasing the measurement error of many apparatuses that use LJs. PMID:25835300

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Effect of mint solution concentration on the absorption spectra of silver nanoparticles in thulium ions presence

NASA Astrophysics Data System (ADS)

Rasmagin, S. I.; Krasovskii, V. I.; Apresyan, L. A.; Novikov, I. K.; Krystob, V. I.; Kazaryan, M. A.

2018-04-01

By the method of green synthesis, silver nanoparticles were obtained in colloidal solutions. The solutions were modified with thulium ions. Using the method of electron microscopy and optical method, the properties of silver nanoparticles obtained are studied. The influence of change in concentration of the solution of mint and thulium ions on the properties of colloidal silver nanoparticles was studied.

Metal sulfide and rare-earth phosphate nanostructures and methods of making same

DOEpatents

Wong, Stanislaus; Zhang, Fen

2014-05-13

The present invention provides a method of producing a crystalline metal sulfide nanostructure. The metal is a transitional metal or a Group IV metal. In the method, a porous membrane is placed between a metal precursor solution and a sulfur precursor solution. The metal cations of the metal precursor solution and sulfur ions of the sulfur precursor solution react, thereby producing a crystalline metal sulfide nanostructure.

A Multipurpose Apparatus to Measure Viscosity and Surface Tension of Solutions: The Measurement of the Molecular Cross-Sectional Area of N-Proposal

ERIC Educational Resources Information Center

Xin Zhang; Shouxin Liu; Booxin Li; Na An; Fan Zhang

2004-01-01

A multipurpose apparatus that can be used to measure the viscosity of solution by the Ostwald method and the surface tension of solution by the drop-weight method or by the capillary-rise method is developed. The apparatus is convenient for in-situ preparation of solutions of different concentrations and avoids the error that frothing of the…

Analysis of the Multiple-Solution Response of a Flexible Rotor Supported on Non-Linear Squeeze Film Dampers

NASA Astrophysics Data System (ADS)

ZHU, C. S.; ROBB, D. A.; EWINS, D. J.

2002-05-01

The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.

Method for chemically analyzing a solution by acoustic means

DOEpatents

Beller, L.S.

1997-04-22

A method and apparatus are disclosed for determining a type of solution and the concentration of that solution by acoustic means. Generally stated, the method consists of: immersing a sound focusing transducer within a first liquid filled container; locating a separately contained specimen solution at a sound focal point within the first container; locating a sound probe adjacent to the specimen, generating a variable intensity sound signal from the transducer; measuring fundamental and multiple harmonic sound signal amplitudes; and then comparing a plot of a specimen sound response with a known solution sound response, thereby determining the solution type and concentration. 10 figs.

Removal of uranium from aqueous HF solutions

DOEpatents

Pulley, Howard; Seltzer, Steven F.

1980-01-01

This invention is a simple and effective method for removing uranium from aqueous HF solutions containing trace quantities of the same. The method comprises contacting the solution with particulate calcium fluoride to form uranium-bearing particulates, permitting the particulates to settle, and separting the solution from the settled particulates. The CaF.sub.2 is selected to have a nitrogen surface area in a selected range and is employed in an amount providing a calcium fluoride/uranium weight ratio in a selected range. As applied to dilute HF solutions containing 120 ppm uranium, the method removes at least 92% of the uranium, without introducing contaminants to the product solution.

Geometrical and Graphical Solutions of Quadratic Equations.

ERIC Educational Resources Information Center

Hornsby, E. John, Jr.

1990-01-01

Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

Angular spectral framework to test full corrections of paraxial solutions.

PubMed

Mahillo-Isla, R; González-Morales, M J

2015-07-01

Different correction methods for paraxial solutions have been used when such solutions extend out of the paraxial regime. The authors have used correction methods guided by either their experience or some educated hypothesis pertinent to the particular problem that they were tackling. This article provides a framework so as to classify full wave correction schemes. Thus, for a given solution of the paraxial wave equation, we can select the best correction scheme of those available. Some common correction methods are considered and evaluated under the proposed scope. Another remarkable contribution is obtained by giving the necessary conditions that two solutions of the Helmholtz equation must accomplish to accept a common solution of the parabolic wave equation as a paraxial approximation of both solutions.

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

NASA Technical Reports Server (NTRS)

Atluri, Satya N.; Shen, Shengping

2002-01-01

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

The L sub 1 finite element method for pure convection problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1991-01-01

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

Inattentive Drivers: Making the Solution Method the Model

ERIC Educational Resources Information Center

McCartney, Mark

2003-01-01

A simple car following model based on the solution of coupled ordinary differential equations is considered. The model is solved using Euler's method and this method of solution is itself interpreted as a mathematical model for car following. Examples of possible classroom use are given. (Contains 6 figures.)

Optimal homotopy asymptotic method for flow and heat transfer of a viscoelastic fluid in an axisymmetric channel with a porous wall.

PubMed

Mabood, Fazle; Khan, Waqar A; Ismail, Ahmad Izani Md

2013-01-01

In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.

Global Search Capabilities of Indirect Methods for Impulsive Transfers

NASA Astrophysics Data System (ADS)

Shen, Hong-Xin; Casalino, Lorenzo; Luo, Ya-Zhong

2015-09-01

An optimization method which combines an indirect method with homotopic approach is proposed and applied to impulsive trajectories. Minimum-fuel, multiple-impulse solutions, with either fixed or open time are obtained. The homotopic approach at hand is relatively straightforward to implement and does not require an initial guess of adjoints, unlike previous adjoints estimation methods. A multiple-revolution Lambert solver is used to find multiple starting solutions for the homotopic procedure; this approach can guarantee to obtain multiple local solutions without relying on the user's intuition, thus efficiently exploring the solution space to find the global optimum. The indirect/homotopic approach proves to be quite effective and efficient in finding optimal solutions, and outperforms the joint use of evolutionary algorithms and deterministic methods in the test cases.

Optimal Homotopy Asymptotic Method for Flow and Heat Transfer of a Viscoelastic Fluid in an Axisymmetric Channel with a Porous Wall

PubMed Central

Mabood, Fazle; Khan, Waqar A.; Ismail, Ahmad Izani

2013-01-01

In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena. PMID:24376722

Unidirectional growth of benzil crystal from solution by Sankaranarayanan-Ramasamy method and its characterization.

PubMed

Rajalakshmi, M; Shyju, T S; Indirajith, R; Gopalakrishnan, R

2012-02-01

Good quality <100> benzil single crystal with a diameter 18 mm and length 75 mm was successfully grown from solution by the unidirectional growth method of Sankaranarayanan-Ramasamy (SR) for the first time in the literature. The seed crystals have been harvested from conventional solution growth technique and subsequently used for unidirectional growth. The grown crystal was subjected to various characterization studies. The results of UV-vis spectral analysis, photoluminescence, etching and microhardness studies were compared with conventional solution grown crystal to that of SR method grown crystal. The quality of SR method grown benzil crystal is better than conventional solution grown crystal. Copyright © 2011 Elsevier B.V. All rights reserved.

CTE method and interaction solutions for the Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Ren, Bo

2017-02-01

The consistent tanh expansion method is applied to the Kadomtsev-Petviashvili equation. The interaction solutions among one soliton and other types of solitary waves, such as multiple resonant soliton solutions and cnoidal waves, are explicitly given. Some special concrete interaction solutions are discussed both in analytical and graphical ways.

Active Solution Space and Search on Job-shop Scheduling Problem

NASA Astrophysics Data System (ADS)

Watanabe, Masato; Ida, Kenichi; Gen, Mitsuo

In this paper we propose a new searching method of Genetic Algorithm for Job-shop scheduling problem (JSP). The coding method that represent job number in order to decide a priority to arrange a job to Gannt Chart (called the ordinal representation with a priority) in JSP, an active schedule is created by using left shift. We define an active solution at first. It is solution which can create an active schedule without using left shift, and set of its defined an active solution space. Next, we propose an algorithm named Genetic Algorithm with active solution space search (GA-asol) which can create an active solution while solution is evaluated, in order to search the active solution space effectively. We applied it for some benchmark problems to compare with other method. The experimental results show good performance.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

A combined physicochemical-biological method of NaCl extraction from the irrigation solution in the BTLSS

NASA Astrophysics Data System (ADS)

Trifonov, Sergey V.; Tikhomirov, Alexander A.; Ushakova, Sofya; Tikhomirova, Natalia

2016-07-01

The use of processed human wastes as a source of minerals for plants in closed biotechnical life support systems (BTLSS) leads to high salt levels in the irrigation solution, as urine contains high concentrations of NaCl. It is important to develop a process that would effectively decrease NaCl concentration in the irrigation solution and return this salt to the crew's diet. The salt-tolerant plants (Salicornia europea) used to reduce NaCl concentration in the irrigation solution require higher salt concentrations than those of the solution, and this problem cannot be resolved by concentrating the solution. At the same time, NaCl extracted from mineralized wastes by physicochemical methods is not pure enough to be included in the crew's diet. This study describes an original physicochemical method of NaCl extraction from the solution, which is intended to be used in combination with the biological method of NaCl extraction by using saltwort plants. The physicochemical method produces solutions with high NaCl concentrations, and saltwort plants serve as a biological filter in the final phase, to produce table salt. The study reports the order in which physicochemical and biological methods of NaCl extraction from the irrigation solution should be used to enable rapid and effective inclusion of NaCl into the cycling of the BTLSS with humans. This study was carried out in the IBP SB RAS and supported by the grant of the Russian Science Foundation (Project No. 14-14-00599).

Computationally efficient control allocation

NASA Technical Reports Server (NTRS)

Durham, Wayne (Inventor)

2001-01-01

A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.

Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

NASA Astrophysics Data System (ADS)

Yuan, Na

2018-04-01

With the aid of the symbolic computation, we present an improved ( G ‧ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef

2013-01-01

The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.

Dynamic one-dimensional modeling of secondary settling tanks and system robustness evaluation.

PubMed

Li, Ben; Stenstrom, M K

2014-01-01

One-dimensional secondary settling tank models are widely used in current engineering practice for design and optimization, and usually can be expressed as a nonlinear hyperbolic or nonlinear strongly degenerate parabolic partial differential equation (PDE). Reliable numerical methods are needed to produce approximate solutions that converge to the exact analytical solutions. In this study, we introduced a reliable numerical technique, the Yee-Roe-Davis (YRD) method as the governing PDE solver, and compared its reliability with the prevalent Stenstrom-Vitasovic-Takács (SVT) method by assessing their simulation results at various operating conditions. The YRD method also produced a similar solution to the previously developed Method G and Enquist-Osher method. The YRD and SVT methods were also used for a time-to-failure evaluation, and the results show that the choice of numerical method can greatly impact the solution. Reliable numerical methods, such as the YRD method, are strongly recommended.

Students' Use of "Look Back" Strategies in Multiple Solution Methods

ERIC Educational Resources Information Center

Lee, Shin-Yi

2016-01-01

The purpose of this study was to investigate the relationship between both 9th-grade and 1st-year undergraduate students' use of "look back" strategies and problem solving performance in multiple solution methods, the difference in their use of look back strategies and problem solving performance in multiple solution methods, and the…

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel

2010-09-01

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by gluing together WKB and Airy solutions of corresponding one-dimensional Schrödinger equations. Our method is motivated by, and has applications to, the analysis of linear wave equations in the geometry of a rotating black hole.

Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

PubMed

Gu, Yongyi; Qi, Jianming

2017-01-01

In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the [Formula: see text]-expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

How Does the Low-Rank Matrix Decomposition Help Internal and External Learnings for Super-Resolution.

PubMed

Wang, Shuang; Yue, Bo; Liang, Xuefeng; Jiao, Licheng

2018-03-01

Wisely utilizing the internal and external learning methods is a new challenge in super-resolution problem. To address this issue, we analyze the attributes of two methodologies and find two observations of their recovered details: 1) they are complementary in both feature space and image plane and 2) they distribute sparsely in the spatial space. These inspire us to propose a low-rank solution which effectively integrates two learning methods and then achieves a superior result. To fit this solution, the internal learning method and the external learning method are tailored to produce multiple preliminary results. Our theoretical analysis and experiment prove that the proposed low-rank solution does not require massive inputs to guarantee the performance, and thereby simplifying the design of two learning methods for the solution. Intensive experiments show the proposed solution improves the single learning method in both qualitative and quantitative assessments. Surprisingly, it shows more superior capability on noisy images and outperforms state-of-the-art methods.

PLUTONIUM-CUPFERRON COMPLEX AND METHOD OF REMOVING PLUTONIUM FROM SOLUTION

DOEpatents

Potratz, H.A.

1959-01-13

A method is presented for separating plutonium from fission products present in solutions of neutronirradiated uranium. The process consists in treating such acidic solutions with cupferron so that the cupferron reacts with the plutonium present to form an insoluble complex. This plutonium cupferride precipitates and may then be separated from the solution.

Method for removing metals from a cleaning solution

DOEpatents

Deacon, Lewis E.

2002-01-01

A method for removing accumulated metals from a cleaning solution is provided. After removal of the metals, the cleaning solution can be discharged or recycled. The process manipulates the pH levels of the solution as a means of precipitating solids. Preferably a dual phase separation at two different pH levels is utilized.

Method for the recovery of silver from waste photographic fixer solutions

DOEpatents

Posey, F.A.; Palko, A.A.

The method of the present invention is directed to the recovery of silver from spent photographic fixer solutions and for providing an effluent essentially silver-free that is suitable for discharge into commercial sewage systems. The present method involves the steps of introducing the spent photographic fixer solution into an alkaline hypochlorite solution. The oxidizing conditions of the alkaline hypochlorite solution are maintained during the addition of the fixer solution so that the silver ion complexing agents of thiosulfate and sulfite ions are effectively destroyed. Hydrazine monohydrate is then added to the oxidizing solution to form a reducing solution to effect the formation of a precipitate of silver which can be readily removed by filtration of decanting. Experimental tests indicate that greater than 99.99% of the original silver in the spent photographic fixer can be efficiently removed by practicing the present method. Also, the chemical and biological oxygen demand of the remaining effluent is significantly reduced so as to permit the discharge thereof into sewage systems at levels in compliance with federal and state environmental standards.

Method for the recovery of silver from waste photographic fixer solutions

DOEpatents

Posey, Franz A.; Palko, Aloysius A.

1984-01-01

The method of the present invention is directed to the recovery of silver from spent photographic fixer solutions and for providing an effluent essentially silver-free that is suitable for discharge into commercial sewage systems. The present method involves the steps of introducing the spent photographic fixer solution into an alkaline hypochlorite solution. The oxidizing conditions of the alkaline hypochlorite solution are maintained during the addition of the fixer solution so that the silver ion complexing agents of thiosulfate and sulfite ions are effectively destroyed. Hydrazine monohydrate is then added to the oxidizing solution to form a reducing solution to effect the formation of a precipitate of silver which can be readily removed by filtration or decanting. Experimental tests indicate that greater than 99.99% of the original silver in the spent photographic fixer can be efficiently removed by practicing the present method. Also, the chemical and biological oxygen demand of the remaining effluent is significantly reduced so as to permit the discharge thereof into sewage systems at levels in compliance with federal and state environmental standards.

Coupled bending-torsion steady-state response of pretwisted, nonuniform rotating beams using a transfer-matrix method

NASA Technical Reports Server (NTRS)

Gray, Carl E., Jr.

1988-01-01

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.

Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.

2017-07-01

The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.

Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains

NASA Astrophysics Data System (ADS)

Belyaev, V. A.; Shapeev, V. P.

2017-10-01

New versions of the collocations and least squares method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for the biharmonic equation in non-canonical domains. The solution of the biharmonic equation is used for simulating the stress-strain state of an isotropic plate under the action of transverse load. The differential problem is projected into a space of fourth-degree polynomials by the CLS method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLS method are implemented on the grids which are constructed in two different ways. It is shown that the approximate solution of problems converges with high order. Thus it matches with high accuracy with the analytical solution of the test problems in the case of known solution in the numerical experiments on the convergence of the solution of various problems on a sequence of grids.

Note on the coupled oscillator model solutions in crystalline optical activity

NASA Astrophysics Data System (ADS)

Vyšín, I.; Ríha, J.; Svácková, K.

2006-06-01

Many methods have been used in the crystalline optical activity solution, among them the traditional method of coupled oscillators. The two coupled oscillator model was first solved by Chandrasekhar, and the most general dispersion relations for the crystalline optical activity can be obtained from its next extensions. However, the Chandrasekhar solution method seems to be based on a mistake in the computations. For this reason, the solution of a more complicated model of coupled oscillators which better corresponds to the structure of real crystals using the Condon relations is presented. This solution leads to the conclusion that, although it is possible to object to the Chandrasekhar solution method, the form of his final dispersion relations is correct. On the other hand, the dispersion relations following from the solution of more complicated coupled oscillator models are more convenient for the interpretation of the crystalline optical activity experimental data, which is demonstrated in examples of crystals of tellurium and benzil.

Transport of reacting solutes subject to a moving dissolution boundary: Numerical methods and solutions

USGS Publications Warehouse

Willis, Catherine; Rubin, Jacob

1987-01-01

A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters. Although the water flow rate does not explicitly appear in the equation for the velocity of the moving boundary, the speed of the boundary depends more on the flux rate than on the dispersion coefficient. The discontinuity in the gradient of the solute concentration profile at the boundary increases with convection and with the initial concentration of the mineral. Our implicit method is extended to allow participation of the solutes in complexation reactions as well as the precipitation-dissolution reaction. This extension is easily made and does not change the basic method.

A Spectral Method for Color Quantitation of a Protein Drug Solution.

PubMed

Swartz, Trevor E; Yin, Jian; Patapoff, Thomas W; Horst, Travis; Skieresz, Susan M; Leggett, Gordon; Morgan, Charles J; Rahimi, Kimia; Marhoul, Joseph; Kabakoff, Bruce

2016-01-01

Color is an important quality attribute for biotherapeutics. In the biotechnology industry, a visual method is most commonly utilized for color characterization of liquid drug protein solutions. The color testing method is used for both batch release and on stability testing for quality control. Using that method, an analyst visually determines the color of the sample by choosing the closest matching European Pharmacopeia reference color solution. The requirement to judge the best match makes it a subjective method. Furthermore, the visual method does not capture data on hue or chroma that would allow for improved product characterization and the ability to detect subtle differences between samples. To overcome these challenges, we describe a quantitative method for color determination that greatly reduces the variability in measuring color and allows for a more precise understanding of color differences. Following color industry standards established by International Commission on Illumination, this method converts a protein solution's visible absorption spectra to L*a*b* color space. Color matching is achieved within the L*a*b* color space, a practice that is already widely used in other industries. The work performed here is to facilitate the adoption and transition for the traditional visual assessment method to a quantitative spectral method. We describe here the algorithm used such that the quantitative spectral method correlates with the currently used visual method. In addition, we provide the L*a*b* values for the European Pharmacopeia reference color solutions required for the quantitative method. We have determined these L*a*b* values by gravimetrically preparing and measuring multiple lots of the reference color solutions. We demonstrate that the visual assessment and the quantitative spectral method are comparable using both low- and high-concentration antibody solutions and solutions with varying turbidity. In the biotechnology industry, a visual assessment is the most commonly used method for color characterization, batch release, and stability testing of liquid protein drug solutions. Using this method, an analyst visually determines the color of the sample by choosing the closest match to a standard color series. This visual method can be subjective because it requires an analyst to make a judgment of the best match of color of the sample to the standard color series, and it does not capture data on hue and chroma that would allow for improved product characterization and the ability to detect subtle differences between samples. To overcome these challenges, we developed a quantitative spectral method for color determination that greatly reduces the variability in measuring color and allows for a more precise understanding of color differences. The details of the spectral quantitative method are described. A comparison between the visual assessment method and spectral quantitative method is presented. This study supports the transition to a quantitative spectral method from the visual assessment method for quality testing of protein solutions. © PDA, Inc. 2016.

A deterministic particle method for one-dimensional reaction-diffusion equations

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Solution identification and quantitative analysis of fiber-capacitive drop analyzer based on multivariate statistical methods

NASA Astrophysics Data System (ADS)

Chen, Zhe; Qiu, Zurong; Huo, Xinming; Fan, Yuming; Li, Xinghua

2017-03-01

A fiber-capacitive drop analyzer is an instrument which monitors a growing droplet to produce a capacitive opto-tensiotrace (COT). Each COT is an integration of fiber light intensity signals and capacitance signals and can reflect the unique physicochemical property of a liquid. In this study, we propose a solution analytical and concentration quantitative method based on multivariate statistical methods. Eight characteristic values are extracted from each COT. A series of COT characteristic values of training solutions at different concentrations compose a data library of this kind of solution. A two-stage linear discriminant analysis is applied to analyze different solution libraries and establish discriminant functions. Test solutions can be discriminated by these functions. After determining the variety of test solutions, Spearman correlation test and principal components analysis are used to filter and reduce dimensions of eight characteristic values, producing a new representative parameter. A cubic spline interpolation function is built between the parameters and concentrations, based on which we can calculate the concentration of the test solution. Methanol, ethanol, n-propanol, and saline solutions are taken as experimental subjects in this paper. For each solution, nine or ten different concentrations are chosen to be the standard library, and the other two concentrations compose the test group. By using the methods mentioned above, all eight test solutions are correctly identified and the average relative error of quantitative analysis is 1.11%. The method proposed is feasible which enlarges the applicable scope of recognizing liquids based on the COT and improves the concentration quantitative precision, as well.

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

2014-01-01

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

B+ L violation at colliders and new physics

NASA Astrophysics Data System (ADS)

Cerdeño, David G.; Reimitz, Peter; Sakurai, Kazuki; Tamarit, Carlos

2018-04-01

Chiral electroweak anomalies predict baryon ( B) and lepton ( L) violating fermion interactions, which can be dressed with large numbers of Higgs and gauge bosons. The estimation of the total B + L-violating rate from an initial two-particle state — potentially observable at colliders — has been the subject of an intense discussion, mainly centered on the resummation of boson emission, which is believed to contribute to the cross-section with an exponential function of the energy, yet with an exponent (the "holy-grail" function) which is not fully known in the energy range of interest. In this article we focus instead on the effect of fermions beyond the Standard-Model (SM) in the polynomial contributions to the rate. It is shown that B + L processes involving the new fermions have a polynomial contribution that can be several orders of magnitude greater than in the SM, for high centre-of-mass energies and light enough masses. We also present calculations that hint at a simple dependence of the holy grail function on the heavy fermion masses. Thus, if anomalous B + L violating interactions are ever detected at high-energy colliders, they could be associated with new physics.

Multipoint propagators in cosmological gravitational instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernardeau, Francis; Crocce, Martin; Scoccimarro, Roman

2008-11-15

We introduce the concept of multipoint propagators between linear cosmic fields and their nonlinear counterparts in the context of cosmological perturbation theory. Such functions express how a nonlinearly evolved Fourier mode depends on the full ensemble of modes in the initial density field. We identify and resum the dominant diagrams in the large-k limit, showing explicitly that multipoint propagators decay into the nonlinear regime at the same rate as the two-point propagator. These analytic results generalize the large-k limit behavior of the two-point propagator to arbitrary order. We measure the three-point propagator as a function of triangle shape in numericalmore » simulations and confirm the results of our high-k resummation. We show that any n-point spectrum can be reconstructed from multipoint propagators, which leads to a physical connection between nonlinear corrections to the power spectrum at small scales and higher-order correlations at large scales. As a first application of these results, we calculate the reduced bispectrum at one loop in renormalized perturbation theory and show that we can predict the decrease in its dependence on triangle shape at redshift zero, when standard perturbation theory is least successful.« less

Failure of Breit-Wigner and success of dispersive descriptions of the τ- → K-ηντ decays

NASA Astrophysics Data System (ADS)

Roig, Pablo

2015-11-01

The τ- → K-ηντ decays have been studied using Chiral Perturbation Theory extended by including resonances as active fields. We have found that the treatment of final state interactions is crucial to provide a good description of the data. The Breit-Wigner approximation does not resum them and neglects the real part of the corresponding chiral loop functions, which violates analyticity and leads to a failure in the confrontation with the data. On the contrary, its resummation by means of an Omnes-like exponentiation of through a dispersive representation provides a successful explanation of the measurements. These results illustrate the fact that Breit-Wigner parametrizations of hadronic data, although simple and easy to handle, lack a link with the underlying strong interaction theory and should be avoided. As a result of our analysis we determine the properties of the K* (1410) resonance with a precision competitive to its traditional extraction using τ- → (Kπ)-ντ decays, albeit the much limited statistics accumulated for the τ- → K-ηντ channel. We also predict the soon discovery of the τ- → K-η'ντ decays.

Implications of improved Higgs mass calculations for supersymmetric models.

PubMed

Buchmueller, O; Dolan, M J; Ellis, J; Hahn, T; Heinemeyer, S; Hollik, W; Marrouche, J; Olive, K A; Rzehak, H; de Vries, K J; Weiglein, G

We discuss the allowed parameter spaces of supersymmetric scenarios in light of improved Higgs mass predictions provided by FeynHiggs 2.10.0. The Higgs mass predictions combine Feynman-diagrammatic results with a resummation of leading and subleading logarithmic corrections from the stop/top sector, which yield a significant improvement in the region of large stop masses. Scans in the pMSSM parameter space show that, for given values of the soft supersymmetry-breaking parameters, the new logarithmic contributions beyond the two-loop order implemented in FeynHiggs tend to give larger values of the light CP-even Higgs mass, [Formula: see text], in the region of large stop masses than previous predictions that were based on a fixed-order Feynman-diagrammatic result, though the differences are generally consistent with the previous estimates of theoretical uncertainties. We re-analyse the parameter spaces of the CMSSM, NUHM1 and NUHM2, taking into account also the constraints from CMS and LHCb measurements of [Formula: see text]and ATLAS searches for [Formula: see text] events using 20/fb of LHC data at 8 TeV. Within the CMSSM, the Higgs mass constraint disfavours [Formula: see text], though not in the NUHM1 or NUHM2.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model.

PubMed

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-28

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

NASA Astrophysics Data System (ADS)

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-01

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Farhi, David; Feige, Ilya; Freytsis, Marat

Some of the most arduous and error-prone aspects of precision resummed calculations are related to the partonic hard process, having nothing to do with the resummation. In particular, interfacing to parton-distribution functions, combining various channels, and performing the phase space integration can be limiting factors in completing calculations. Conveniently, however, most of these tasks are already automated in many Monte Carlo programs, such as MadGraph [1], Alpgen [2] or Sherpa [3]. In this paper, we show how such programs can be used to produce distributions of partonic kinematics with associated color structures representing the hard factor in a resummed distribution.more » These distributions can then be used to weight convolutions of jet, soft and beam functions producing a complete resummed calculation. In fact, only around 1000 unweighted events are necessary to produce precise distributions. A number of examples and checks are provided, including e +e – two- and four-jet event shapes, n-jettiness and jet-mass related observables at hadron colliders at next-to-leading-log (NLL) matched to leading order (LO). Furthermore, the attached code can be used to modify MadGraph to export the relevant LO hard functions and color structures for arbitrary processes.« less

2-vertex Lorentzian spin foam amplitudes for dipole transitions

NASA Astrophysics Data System (ADS)

Sarno, Giorgio; Speziale, Simone; Stagno, Gabriele V.

2018-04-01

We compute transition amplitudes between two spin networks with dipole graphs, using the Lorentzian EPRL model with up to two (non-simplicial) vertices. We find power-law decreasing amplitudes in the large spin limit, decreasing faster as the complexity of the foam increases. There are no oscillations nor asymptotic Regge actions at the order considered, nonetheless the amplitudes still induce non-trivial correlations. Spin correlations between the two dipoles appear only when one internal face is present in the foam. We compute them within a mini-superspace description, finding positive correlations, decreasing in value with the Immirzi parameter. The paper also provides an explicit guide to computing Lorentzian amplitudes using the factorisation property of SL(2,C) Clebsch-Gordan coefficients in terms of SU(2) ones. We discuss some of the difficulties of non-simplicial foams, and provide a specific criterion to partially limit the proliferation of diagrams. We systematically compare the results with the simplified EPRLs model, much faster to evaluate, to learn evidence on when it provides reliable approximations of the full amplitudes. Finally, we comment on implications of our results for the physics of non-simplicial spin foams and their resummation.

Heavy-flavor parton distributions without heavy-flavor matching prescriptions

NASA Astrophysics Data System (ADS)

Bertone, Valerio; Glazov, Alexandre; Mitov, Alexander; Papanastasiou, Andrew S.; Ubiali, Maria

2018-04-01

We show that the well-known obstacle for working with the zero-mass variable flavor number scheme, namely, the omission of O(1) mass power corrections close to the conventional heavy flavor matching point (HFMP) μ b = m, can be easily overcome. For this it is sufficient to take advantage of the freedom in choosing the position of the HFMP. We demonstrate that by choosing a sufficiently large HFMP, which could be as large as 10 times the mass of the heavy quark, one can achieve the following improvements: 1) above the HFMP the size of missing power corrections O(m) is restricted by the value of μ b and, therefore, the error associated with their omission can be made negligible; 2) additional prescriptions for the definition of cross-sections are not required; 3) the resummation accuracy is maintained and 4) contrary to the common lore we find that the discontinuity of α s and pdfs across thresholds leads to improved continuity in predictions for observables. We have considered a large set of proton-proton and electron-proton collider processes, many through NNLO QCD, that demonstrate the broad applicability of our proposal.

Streamlining resummed QCD calculations using Monte Carlo integration

DOE PAGES

Farhi, David; Feige, Ilya; Freytsis, Marat; ...

2016-08-18

Some of the most arduous and error-prone aspects of precision resummed calculations are related to the partonic hard process, having nothing to do with the resummation. In particular, interfacing to parton-distribution functions, combining various channels, and performing the phase space integration can be limiting factors in completing calculations. Conveniently, however, most of these tasks are already automated in many Monte Carlo programs, such as MadGraph [1], Alpgen [2] or Sherpa [3]. In this paper, we show how such programs can be used to produce distributions of partonic kinematics with associated color structures representing the hard factor in a resummed distribution.more » These distributions can then be used to weight convolutions of jet, soft and beam functions producing a complete resummed calculation. In fact, only around 1000 unweighted events are necessary to produce precise distributions. A number of examples and checks are provided, including e +e – two- and four-jet event shapes, n-jettiness and jet-mass related observables at hadron colliders at next-to-leading-log (NLL) matched to leading order (LO). Furthermore, the attached code can be used to modify MadGraph to export the relevant LO hard functions and color structures for arbitrary processes.« less

Hard matching for boosted tops at two loops

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoang, Andre H.; Pathak, Aditya; Pietrulewicz, Piotr

2015-12-10

Here, cross sections for top quarks provide very interesting physics opportunities, being both sensitive to new physics and also perturbatively tractable due to the large top quark mass. Rigorous factorization theorems for top cross sections can be derived in several kinematic scenarios, including the boosted regime in the peak region that we consider here. In the context of the corresponding factorization theorem for e +e – collisions we extract the last missing ingredient that is needed to evaluate the cross section differential in the jet-mass at two-loop order, namely the matching coefficient at the scale μ≃m t. Our extraction alsomore » yields the final ingredients needed to carry out logarithmic re-summation at next-to-next-to-leading logarithmic order (or N 3LL if we ignore the missing 4-loop cusp anomalous dimension). This coefficient exhibits an amplitude level rapidity logarithm starting at O(α 2 s) due to virtual top quark loops, which we treat using rapidity renormalization group (RG) evolution. Interestingly, this rapidity RG evolution appears in the matching coefficient between two effective theories around the heavy quark mass scale μ ≃ m t.« less

Molecular dynamics study of salt-solution interface: solubility and surface charge of salt in water.

PubMed

Kobayashi, Kazuya; Liang, Yunfeng; Sakka, Tetsuo; Matsuoka, Toshifumi

2014-04-14

The NaCl salt-solution interface often serves as an example of an uncharged surface. However, recent laser-Doppler electrophoresis has shown some evidence that the NaCl crystal is positively charged in its saturated solution. Using molecular dynamics (MD) simulations, we have investigated the NaCl salt-solution interface system, and calculated the solubility of the salt using the direct method and free energy calculations, which are kinetic and thermodynamic approaches, respectively. The direct method calculation uses a salt-solution combined system. When the system is equilibrated, the concentration in the solution area is the solubility. In the free energy calculation, we separately calculate the chemical potential of NaCl in two systems, the solid and the solution, using thermodynamic integration with MD simulations. When the chemical potential of NaCl in the solution phase is equal to the chemical potential of the solid phase, the concentration of the solution system is the solubility. The advantage of using two different methods is that the computational methods can be mutually verified. We found that a relatively good estimate of the solubility of the system can be obtained through comparison of the two methods. Furthermore, we found using microsecond time-scale MD simulations that the positively charged NaCl surface was induced by a combination of a sodium-rich surface and the orientation of the interfacial water molecules.

Molecular dynamics study of salt–solution interface: Solubility and surface charge of salt in water

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kobayashi, Kazuya; Liang, Yunfeng, E-mail: y-liang@earth.kumst.kyoto-u.ac.jp, E-mail: matsuoka@earth.kumst.kyoto-u.ac.jp; Matsuoka, Toshifumi, E-mail: y-liang@earth.kumst.kyoto-u.ac.jp, E-mail: matsuoka@earth.kumst.kyoto-u.ac.jp

2014-04-14

The NaCl salt–solution interface often serves as an example of an uncharged surface. However, recent laser-Doppler electrophoresis has shown some evidence that the NaCl crystal is positively charged in its saturated solution. Using molecular dynamics (MD) simulations, we have investigated the NaCl salt–solution interface system, and calculated the solubility of the salt using the direct method and free energy calculations, which are kinetic and thermodynamic approaches, respectively. The direct method calculation uses a salt–solution combined system. When the system is equilibrated, the concentration in the solution area is the solubility. In the free energy calculation, we separately calculate the chemicalmore » potential of NaCl in two systems, the solid and the solution, using thermodynamic integration with MD simulations. When the chemical potential of NaCl in the solution phase is equal to the chemical potential of the solid phase, the concentration of the solution system is the solubility. The advantage of using two different methods is that the computational methods can be mutually verified. We found that a relatively good estimate of the solubility of the system can be obtained through comparison of the two methods. Furthermore, we found using microsecond time-scale MD simulations that the positively charged NaCl surface was induced by a combination of a sodium-rich surface and the orientation of the interfacial water molecules.« less

Methods of producing adsorption media including a metal oxide

DOEpatents

Mann, Nicholas R; Tranter, Troy J

2014-03-04

Methods of producing a metal oxide are disclosed. The method comprises dissolving a metal salt in a reaction solvent to form a metal salt/reaction solvent solution. The metal salt is converted to a metal oxide and a caustic solution is added to the metal oxide/reaction solvent solution to adjust the pH of the metal oxide/reaction solvent solution to less than approximately 7.0. The metal oxide is precipitated and recovered. A method of producing adsorption media including the metal oxide is also disclosed, as is a precursor of an active component including particles of a metal oxide.

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The development, validation and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems are discussed. A solution method that combines a finite-volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries was previously developed for fixed-grids. In the present research effort, this solution method is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Solution of time fractional Black-Scholes European option pricing equation arising in financial market

NASA Astrophysics Data System (ADS)

Ravi Kanth, A. S. V.; Aruna, K.

2016-12-01

In this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation. The method finds the solution without any discretization, transformation, or restrictive assumptions with the use of appropriate initial or boundary conditions. The efficiency and exactitude of the proposed methods are tested by means of three examples.

Perturbational blowup solutions to the compressible Euler equations with damping.

PubMed

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Sol-gel preparation of lead magnesium niobate (PMN) powders and thin films

DOEpatents

Boyle, T.J.

1999-01-12

A method of preparing a lead magnesium niobium oxide (PMN), Pb(Mg{sub 1/3}Nb{sub 2/3})O{sub 3}, precursor solution by a solvent method wherein a liquid solution of a lead-complex PMN precursor is combined with a liquid solution of a niobium-complex PMN precursor, the combined lead- and niobium-complex liquid solutions are reacted with a magnesium-alkyl solution, forming a PMN precursor solution and a lead-based precipitate, and the precipitate is separated from the reacted liquid PMN precursor solution to form a precipitate-free PMN precursor solution. This precursor solution can be processed to form both ferroelectric powders and thin films. 3 figs.

Sol-Gel Preparation Of Lead Magnesium Ni Obate (Pmn) Powdersand Thin Films

DOEpatents

Boyle, Timothy J.

1999-01-12

A method of preparing a lead magnesium niobium oxide (PMN), Pb(Mg.sub.1/3 Nb.sub.2/3)O.sub.3, precursor solution by a solvent method wherein a liquid solution of a lead-complex PMN precursor is combined with a liquid solution of a niobium-complex PMN precursor, the combined lead- and niobium-complex liquid solutions are reacted with a magnesium-alkyl solution, forming a PMN precursor solution and a lead-based precipitate, and the precipitate is separated from the reacted liquid PMN precursor solution to form a precipitate-free PMN precursor solution. This precursor solution can be processed to form both ferroelectric powders and thin films.

Methods of synthesizing carbon-magnetite nanocomposites from renewable resource materials and application of same

DOEpatents

Viswanathan, Tito

2014-07-29

A method of synthesizing carbon-magnetite nanocomposites. In one embodiment, the method includes the steps of (a) dissolving a first amount of an alkali salt of lignosulfonate in water to form a first solution, (b) heating the first solution to a first temperature, (c) adding a second amount of iron sulfate (FeSO.sub.4) to the first solution to form a second solution, (d) heating the second solution at a second temperature for a first duration of time effective to form a third solution of iron lignosulfonate, (e) adding a third amount of 1N sodium hydroxide (NaOH) to the third solution of iron lignosulfonate to form a fourth solution with a first pH level, (f) heating the fourth solution at a third temperature for a second duration of time to form a first sample, and (g) subjecting the first sample to a microwave radiation for a third duration of time effective to form a second sample containing a plurality of carbon-magnetite nanocomposites.

METHOD OF INHIBITING CORROSION IN URANYL SULFATE SOLUTIONS

DOEpatents

Bohlmann, E.G.; Griess, J.C. Jr.

1960-08-23

A method is given for treating a uranyl sulfate solution to inhibit the corrosiveness of the solution and elevate the phase separation temperature of the solution. Lithium sulfate is added to the solution in an amount ranging from 0.25 to 1.3 times the uranyl sulfate concentration. The corrosiveness of the solution with respect to stainless steel is substantially decreased by this means. This treatment also serves to raise the phase separation temperature of the solution (above 250 deg C), at which time the uranyl sulfate solution separates into two liquid phases of unequal uranium concentration and thus becomes unsuitable as nuclear reactor fuel.

Synthesis and Microstructure of Highly Oriented PbTiO3 Thin Films Prepared by a Sol-Gel Method

DTIC Science & Technology

1989-06-01

lead acetate with titanium isopropoxide * in 2-methoxyethanol,* in a method similar to that reported by Gurkovitch and Blum." The resulting yellow-gold...orientation by a sol-gel processing method. EXPERIMENTAL Precursor Solution Preparation Stock solutions of complex Pb-Ti alkoxide were prepared by reacting... solution had an equivalent PbTiO 3 concentration of approximately 66 wt%. The alkoxide solutions were handled as moisture-sensitive reagents and, as

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chatterjee, Anupam; Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076; Higham, Jonathan

A range of methods are presented to calculate a solute’s hydration shell from computer simulations of dilute solutions of monatomic ions and noble gas atoms. The methods are designed to be parameter-free and instantaneous so as to make them more general, accurate, and consequently applicable to disordered systems. One method is a modified nearest-neighbor method, another considers solute-water Lennard-Jones overlap followed by hydrogen-bond rearrangement, while three methods compare various combinations of water-solute and water-water forces. The methods are tested on a series of monatomic ions and solutes and compared with the values from cutoffs in the radial distribution function, themore » nearest-neighbor distribution functions, and the strongest-acceptor hydrogen bond definition for anions. The Lennard-Jones overlap method and one of the force-comparison methods are found to give a hydration shell for cations which is in reasonable agreement with that using a cutoff in the radial distribution function. Further modifications would be required, though, to make them capture the neighboring water molecules of noble-gas solutes if these weakly interacting molecules are considered to constitute the hydration shell.« less

Extended Hansen solubility approach: naphthalene in individual solvents.

PubMed

Martin, A; Wu, P L; Adjei, A; Beerbower, A; Prausnitz, J M

1981-11-01

A multiple regression method using Hansen partial solubility parameters, delta D, delta p, and delta H, was used to reproduce the solubilities of naphthalene in pure polar and nonpolar solvents and to predict its solubility in untested solvents. The method, called the extended Hansen approach, was compared with the extended Hildebrand solubility approach and the universal-functional-group-activity-coefficient (UNIFAC) method. The Hildebrand regular solution theory was also used to calculate naphthalene solubility. Naphthalene, an aromatic molecule having no side chains or functional groups, is "well-behaved', i.e., its solubility in active solvents known to interact with drug molecules is fairly regular. Because of its simplicity, naphthalene is a suitable solute with which to initiate the difficult study of solubility phenomena. The three methods tested (Hildebrand regular solution theory was introduced only for comparison of solubilities in regular solution) yielded similar results, reproducing naphthalene solubilities within approximately 30% of literature values. In some cases, however, the error was considerably greater. The UNIFAC calculation is superior in that it requires only the solute's heat of fusion, the melting point, and a knowledge of chemical structures of solute and solvent. The extended Hansen and extended Hildebrand methods need experimental solubility data on which to carry out regression analysis. The extended Hansen approach was the method of second choice because of its adaptability to solutes and solvents from various classes. Sample calculations are included to illustrate methods of predicting solubilities in untested solvents at various temperatures. The UNIFAC method was successful in this regard.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Iodine retention during evaporative volume reduction

DOEpatents

Godbee, H.W.; Cathers, G.I.; Blanco, R.E.

1975-11-18

An improved method for retaining radioactive iodine in aqueous waste solutions during volume reduction is disclosed. The method applies to evaporative volume reduction processes whereby the decontaminated (evaporated) water can be returned safely to the environment. The method generally comprises isotopically diluting the waste solution with a nonradioactive iodide and maintaining the solution at a high pH during evaporation.

An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

Automatic Annotation Method on Learners' Opinions in Case Method Discussion

ERIC Educational Resources Information Center

Samejima, Masaki; Hisakane, Daichi; Komoda, Norihisa

2015-01-01

Purpose: The purpose of this paper is to annotate an attribute of a problem, a solution or no annotation on learners' opinions automatically for supporting the learners' discussion without a facilitator. The case method aims at discussing problems and solutions in a target case. However, the learners miss discussing some of problems and solutions.…

Historical Notes. A Madness in the Methods. Cubic and Quartic Equations: Are the General Solving Techniques Still Important?

ERIC Educational Resources Information Center

Francis, Richard L.

1991-01-01

Described is an outline for a school mathematics project dealing with the theory of equations, specifically solutions to polynomials of the third and of the fourth degree. Cardano's method for solution of cubic equations and Ferrari's method for solution of quartic equations are included with examples. (JJK)

Combined multireference configuration interaction/ molecular dynamics approach for calculating solvatochromic shifts: application to the n(O) --> pi* electronic transition of formaldehyde.

PubMed

Xu, ZongRong; Matsika, Spiridoula

2006-11-02

A combined quantum mechanics/molecular mechanics method is described here for considering the solvatochromic shift of excited states in solution. The quantum mechanical solute is described using high level multireference configuration interaction methods (MRCI), while molecular dynamics is used for obtaining the structure of the solvent around the solute. The electrostatic effect of the solvent is included in the quantum description of the solute in an averaged way. This method is used to study solvent effects on the n(O) --> pi* electronic transition of formaldehyde in aqueous solution. The effects of solute polarization, basis sets, and dynamical correlation on the solvatochromic shift, and on dipole moments, have been investigated.

Newton-like methods for Navier-Stokes solution

NASA Astrophysics Data System (ADS)

Qin, N.; Xu, X.; Richards, B. E.

1992-12-01

The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.

Method for recovering palladium and technetium values from nuclear fuel reprocessing waste solutions

DOEpatents

Horwitz, E. Philip; Delphin, Walter H.

1979-07-24

A method for recovering palladium and technetium values from nuclear fuel reprocessing waste solutions containing these and other values by contacting the waste solution with an extractant of tricaprylmethylammonium nitrate in an inert hydrocarbon diluent which extracts the palladium and technetium values from the waste solution. The palladium and technetium values are recovered from the extractant and from any other coextracted values with a strong nitric acid strip solution.

A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

NASA Astrophysics Data System (ADS)

Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.

2017-09-01

Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.

Method for low temperature preparation of a noble metal alloy

DOEpatents

Even, Jr., William R.

2002-01-01

A method for producing fine, essentially contamination free, noble metal alloys is disclosed. The alloys comprise particles in a size range of 5 to 500 nm. The method comprises 1. A method for preparing a noble metal alloy at low temperature, the method comprising the steps of forming solution of organometallic compounds by dissolving the compounds into a quantity of a compatible solvent medium capable of solvating the organometallic, mixing a portion of each solution to provide a desired molarity ratio of ions in the mixed solution, adding a support material, rapidly quenching droplets of the mixed solution to initiate a solute-solvent phase separation as the solvent freezes, removing said liquid cryogen, collecting and freezing drying the frozen droplets to produce a dry powder, and finally reducing the powder to a metal by flowing dry hydrogen over the powder while warming the powder to a temperature of about 150.degree. C.

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

Development and application of ab initio QM/MM methods for mechanistic simulation of reactions in solution and in enzymes

PubMed Central

Hu, Hao; Yang, Weitao

2013-01-01

Determining the free energies and mechanisms of chemical reactions in solution and enzymes is a major challenge. For such complex reaction processes, combined quantum mechanics/molecular mechanics (QM/MM) method is the most effective simulation method to provide an accurate and efficient theoretical description of the molecular system. The computational costs of ab initio QM methods, however, have limited the application of ab initio QM/MM methods. Recent advances in ab initio QM/MM methods allowed the accurate simulation of the free energies for reactions in solution and in enzymes and thus paved the way for broader application of the ab initio QM/MM methods. We review here the theoretical developments and applications of the ab initio QM/MM methods, focusing on the determination of reaction path and the free energies of the reaction processes in solution and enzymes. PMID:24146439

Method and means for dynamic measurement of rates of adsorption from solutions

DOEpatents

Slomka, Bogdan J.; Buttermore, William H.

1992-05-05

A method and apparatus for dynamic measurement of rates of absorption from solutions. The method has the advantage of avoiding the use of solvent normally used to establish a baseline. The method involves pre-evacuating the adsorbent contained in an adsorbent cell and thereafter rapidly contacting the adsorbent with analytical solution, all without prior exposure of adsorbent to pure solvent. The result is a sharp characteristic adsorption line.

Finding Dantzig Selectors with a Proximity Operator based Fixed-point Algorithm

DTIC Science & Technology

2014-11-01

experiments showed that this method usually outperforms the method in [2] in terms of CPU time while producing solutions of comparable quality. The... method proposed in [19]. To alleviate the difficulty caused by the subprob- lem without a closed form solution , a linearized ADM was proposed for the...a closed form solution , but the β-related subproblem does not and is solved approximately by using the nonmonotone gradient method in [18]. The

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garn, Troy G; Law, Jack D; Greenhalgh, Mitchell R

A composite media including at least one crystalline aluminosilicate material in polyacrylonitrile. A method of forming a composite media is also disclosed. The method comprises dissolving polyacrylonitrile in an organic solvent to form a matrix solution. At least one crystalline aluminosilicate material is combined with the matrix solution to form a composite media solution. The organic solvent present in the composite media solution is diluted. The composite media solution is solidified. In addition, a method of processing a fluid stream is disclosed. The method comprises providing a beads of a composite media comprising at least one crystalline aluminosilicate material dispersedmore » in a polyacrylonitrile matrix. The beads of the composite media are contacted with a fluid stream comprising at least one constituent. The at least one constituent is substantially removed from the fluid stream.« less

Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

NASA Astrophysics Data System (ADS)

Ali, Asghar; Seadawy, Aly R.; Lu, Dianchen

2018-05-01

The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

NASA Technical Reports Server (NTRS)

Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

1992-01-01

The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

Method of synthesizing pyrite nanocrystals

DOEpatents

Wadia, Cyrus; Wu, Yue

2013-04-23

A method of synthesizing pyrite nanocrystals is disclosed which in one embodiment includes forming a solution of iron (III) diethyl dithiophosphate and tetra-alkyl-ammonium halide in water. The solution is heated under pressure. Pyrite nanocrystal particles are then recovered from the solution.

The covariance matrix for the solution vector of an equality-constrained least-squares problem

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1976-01-01

Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.'

The method of averages applied to the KS differential equations

NASA Technical Reports Server (NTRS)

Graf, O. F., Jr.; Mueller, A. C.; Starke, S. E.

1977-01-01

A new approach for the solution of artificial satellite trajectory problems is proposed. The basic idea is to apply an analytical solution method (the method of averages) to an appropriate formulation of the orbital mechanics equations of motion (the KS-element differential equations). The result is a set of transformed equations of motion that are more amenable to numerical solution.

Method and apparatus for the production of metal oxide powder

DOEpatents

Harris, Michael T.; Scott, Timothy C.; Byers, Charles H.

1993-01-01

The present invention provides a method for preparing metal oxide powder. A first solution, which is substantially organic, is prepared. A second solution, which is an aqueous solution substantially immiscible in the first solution, is prepared and delivered as drops to the first solution. The drops of the second solution are atomized by a pulsed electric field forming micro-drops of the second solution. Reagents in the first solution diffuse into and react with reactants in the micro-drops of the second solution forming metal hydroxide or oxalate particles. The metal hydroxide or metal oxalate particles are then recovered and dried to produce the metal oxide powder. An apparatus for preparing a metal oxide powder is also disclosed.

Method and apparatus for the production of metal oxide powder

DOEpatents

Harris, Michael T.; Scott, Timothy C.; Byers, Charles H.

1992-01-01

The present invention provides a method for preparing metal oxide powder. A first solution, which is substantially organic, is prepared. A second solution, which is an aqueous solution substantially immiscible in the first solution, is prepared and delivered as drops to the first solution. The drops of the second solution are atomized by a pulsed electric field forming micro-drops of the second solution. Reagents in the first solution diffuse into and react with reactants in the micro-drops of the second solution forming metal hydroxide or oxalate particles. The metal hydroxide or metal oxalate particles are then recovered and dried to produce the metal oxide powder. An apparatus for preparing a metal oxide powder is also disclosed.

Method and apparatus for the production of metal oxide powder

DOEpatents

Harris, M.T.; Scott, T.C.; Byers, C.H.

1992-06-16

The present invention provides a method for preparing metal oxide powder. A first solution, which is substantially organic, is prepared. A second solution, which is an aqueous solution substantially immiscible in the first solution, is prepared and delivered as drops to the first solution. The drops of the second solution are atomized by a pulsed electric field forming micro-drops of the second solution. Reagents in the first solution diffuse into and react with reactants in the micro-drops of the second solution forming metal hydroxide or oxalate particles. The metal hydroxide or metal oxalate particles are then recovered and dried to produce the metal oxide powder. An apparatus for preparing a metal oxide powder is also disclosed. 2 figs.

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

PubMed

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

An efficient computational method for the approximate solution of nonlinear Lane-Emden type equations arising in astrophysics

NASA Astrophysics Data System (ADS)

Singh, Harendra

2018-04-01

The key purpose of this article is to introduce an efficient computational method for the approximate solution of the homogeneous as well as non-homogeneous nonlinear Lane-Emden type equations. Using proposed computational method given nonlinear equation is converted into a set of nonlinear algebraic equations whose solution gives the approximate solution to the Lane-Emden type equation. Various nonlinear cases of Lane-Emden type equations like standard Lane-Emden equation, the isothermal gas spheres equation and white-dwarf equation are discussed. Results are compared with some well-known numerical methods and it is observed that our results are more accurate.

Simple method to make a supersaturated oxygen fluid.

PubMed

Tange, Yoshihiro; Yoshitake, Shigenori; Takesawa, Shingo

2018-01-22

Intravenous oxygenation has demonstrated significant increase in partial pressure of oxygen (PO 2 ) in animal models. A highly dissolved oxygen solution might be able to provide a sufficient level of oxygen delivery to the tissues and organs in patients with hypoxia. However, conventional fluid oxygenation methods have required the use of original devices. If simpler oxygenation of a solution is possible, it will be a useful strategy for application in clinical practice. We simply developed its administration by injection of either air or oxygen gas into conventional saline. We determined the PO 2 values in the solutions in comparison with conventional saline in vitro. To examine the effects of the administration of the new solutions on the blood gas profile, we diluted bovine blood with either conventional or the new solutions and analyzed PO 2 , oxygen saturation (SO 2 ) and total oxygen content. PO 2 levels in the blood and new solution mixture significantly increased with each additional injected gas volume. Significant increases in the PO 2 and SO 2 of the bovine blood were found in those blood samples with the new solution, as compared with those with the control solution. These results suggest that this solution promotes oxygen delivery to the hypoxic tissue and recovery from hypoxia. This method is simpler and easier than previous methods.

A solution quality assessment method for swarm intelligence optimization algorithms.

PubMed

Zhang, Zhaojun; Wang, Gai-Ge; Zou, Kuansheng; Zhang, Jianhua

2014-01-01

Nowadays, swarm intelligence optimization has become an important optimization tool and wildly used in many fields of application. In contrast to many successful applications, the theoretical foundation is rather weak. Therefore, there are still many problems to be solved. One problem is how to quantify the performance of algorithm in finite time, that is, how to evaluate the solution quality got by algorithm for practical problems. It greatly limits the application in practical problems. A solution quality assessment method for intelligent optimization is proposed in this paper. It is an experimental analysis method based on the analysis of search space and characteristic of algorithm itself. Instead of "value performance," the "ordinal performance" is used as evaluation criteria in this method. The feasible solutions were clustered according to distance to divide solution samples into several parts. Then, solution space and "good enough" set can be decomposed based on the clustering results. Last, using relative knowledge of statistics, the evaluation result can be got. To validate the proposed method, some intelligent algorithms such as ant colony optimization (ACO), particle swarm optimization (PSO), and artificial fish swarm algorithm (AFS) were taken to solve traveling salesman problem. Computational results indicate the feasibility of proposed method.

Method for liquid chromatographic extraction of strontium from acid solutions

DOEpatents

Horwitz, E. Philip; Dietz, Mark L.

1992-01-01

A method and apparatus for extracting strontium and technetium values from biological, industrial and environmental sample solutions using a chromatographic column is described. An extractant medium for the column is prepared by generating a solution of a diluent containing a Crown ether and dispersing the solution on a resin substrate material. The sample solution is highly acidic and is introduced directed to the chromatographic column and strontium or technetium is eluted using deionized water.

Effective calculation of power system low-voltage solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Overbye, T.J.; Klump, R.P.

1996-02-01

This paper develops a method for reliably determining the set of low-voltage solutions which are closest to the operable power flow solution. These solutions are often used in conjunction with techniques such as energy methods and the voltage instability proximity index (VIPI) for assessing system voltage stability. This paper presents an algorithm which provides good initial guesses for these solutions. The results are demonstrated on a small system and on larger systems with up to 2,000 buses.

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

Multiple steady states in atmospheric chemistry

NASA Technical Reports Server (NTRS)

Stewart, Richard W.

1993-01-01

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

Sonic wave separation of invertase from a dilute solution to generated droplets.

PubMed

Tanner, R D; Ko, S; Loha, V; Prokop, A

2000-01-01

It has previously been shown that a droplet fractionation process, simulated by shaking a separatory funnel containing a dilute protein solution, can generate droplets richer in protein than present in the original dilute solution. In this article, we describe an alternative method that can increase the amount of protein transferred to the droplets. The new method uses ultrasonic waves, enhanced by a bubble gas stream to create the droplets. The amount of protein in these droplets increases by about 50%. In this method, the top layer of the dilute protein solution (of the solution-air interface) becomes enriched in protein when air is bubbled into the solution. This concentrating procedure is called bubble fractionation. Once the protein has passed through the initial buildup, this enriched protein layer is transferred into droplets with the aid of a vacuum above the solution at the same time that ultrasonic waves are introduced. The droplets are then carried over to a condenser and coalesced. We found that this new method provides an easier way to remove the protein-enriched top layer of the dilute solution and generates more droplets within a shorter period than the separatory funnel droplet generation method. The added air creates the bubbles and carries the droplets, and the vacuum helps remove the effluent airstream from the condenser. The maximum partition coefficient, the ratio of the protein concentration in the droplets to that in the residual solution (approx 8.5), occurred at pH 5.0.

Abundant closed form solutions of the conformable time fractional Sawada-Kotera-Ito equation using (G‧ / G) -expansion method

NASA Astrophysics Data System (ADS)

Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.

2018-06-01

In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chng, Brenda; Mann, Robert; Department of Physics, University of Waterloo 200 University Avenue West, Waterloo, Ontario N2L 3G1

We construct new solutions of the vacuum Einstein field equations in four dimensions via a solution-generating method utilizing the SL(2,R) symmetry of the reduced Lagrangian. We apply the method to an accelerating version of the Zipoy-Voorhees solution and generate new solutions which we interpret to be the accelerating versions of the Zipoy-Voorhees generalization of the Taub-NUT solution (with Lorentzian signature) and the Zipoy-Voorhees generalization of the Eguchi-Hanson solitons (with Euclidean signature). As an intermediary in the solution-generating process we obtain charged versions of the accelerated Zipoy-Voorhees-like families of solutions. Finally we present the accelerating version of the Taub-NUT solution andmore » discuss its properties.« less

Hybrid Weighted Minimum Norm Method A new method based LORETA to solve EEG inverse problem.

PubMed

Song, C; Zhuang, T; Wu, Q

2005-01-01

This Paper brings forward a new method to solve EEG inverse problem. Based on following physiological characteristic of neural electrical activity source: first, the neighboring neurons are prone to active synchronously; second, the distribution of source space is sparse; third, the active intensity of the sources are high centralized, we take these prior knowledge as prerequisite condition to develop the inverse solution of EEG, and not assume other characteristic of inverse solution to realize the most commonly 3D EEG reconstruction map. The proposed algorithm takes advantage of LORETA's low resolution method which emphasizes particularly on 'localization' and FOCUSS's high resolution method which emphasizes particularly on 'separability'. The method is still under the frame of the weighted minimum norm method. The keystone is to construct a weighted matrix which takes reference from the existing smoothness operator, competition mechanism and study algorithm. The basic processing is to obtain an initial solution's estimation firstly, then construct a new estimation using the initial solution's information, repeat this process until the solutions under last two estimate processing is keeping unchanged.

Fidelity of the Integrated Force Method Solution

NASA Technical Reports Server (NTRS)

Hopkins, Dale; Halford, Gary; Coroneos, Rula; Patnaik, Surya

2002-01-01

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

An analysis of shock coalescence including three-dimensional effects with application to sonic boom extrapolation. Ph.D. Thesis - George Washington Univ.

NASA Technical Reports Server (NTRS)

Darden, C. M.

1984-01-01

A method for analyzing shock coalescence which includes three dimensional effects was developed. The method is based on an extension of the axisymmetric solution, with asymmetric effects introduced through an additional set of governing equations, derived by taking the second circumferential derivative of the standard shock equations in the plane of symmetry. The coalescence method is consistent with and has been combined with a nonlinear sonic boom extrapolation program which is based on the method of characteristics. The extrapolation program, is able to extrapolate pressure signatures which include embedded shocks from an initial data line in the plane of symmetry at approximately one body length from the axis of the aircraft to the ground. The axisymmetric shock coalescence solution, the asymmetric shock coalescence solution, the method of incorporating these solutions into the extrapolation program, and the methods used to determine spatial derivatives needed in the coalescence solution are described. Results of the method are shown for a body of revolution at a small, positive angle of attack.

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

NASA Astrophysics Data System (ADS)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

A gradient system solution to Potts mean field equations and its electronic implementation.

PubMed

Urahama, K; Ueno, S

1993-03-01

A gradient system solution method is presented for solving Potts mean field equations for combinatorial optimization problems subject to winner-take-all constraints. In the proposed solution method the optimum solution is searched by using gradient descent differential equations whose trajectory is confined within the feasible solution space of optimization problems. This gradient system is proven theoretically to always produce a legal local optimum solution of combinatorial optimization problems. An elementary analog electronic circuit implementing the presented method is designed on the basis of current-mode subthreshold MOS technologies. The core constituent of the circuit is the winner-take-all circuit developed by Lazzaro et al. Correct functioning of the presented circuit is exemplified with simulations of the circuits implementing the scheme for solving the shortest path problems.

SEPARATION OF TECHNETIUM FROM AQUEOUS SOLUTIONS BY COPRECIPITATION WITH MAGNETITE

DOEpatents

Rimshaw, S.J.

1961-10-24

A method of separating technetium in the 4+ oxidation state from an aqueous basic solution containing products of uranium fission is described. The method consists of contacting the solution with finely divided magnetite and recovering a technetium-bearing precipitate. (AEC)

Wet-chemical systems and methods for producing black silicon substrates

DOEpatents

Yost, Vernon; Yuan, Hao-Chih; Page, Matthew

2015-05-19

A wet-chemical method of producing a black silicon substrate. The method comprising soaking single crystalline silicon wafers in a predetermined volume of a diluted inorganic compound solution. The substrate is combined with an etchant solution that forms a uniform noble metal nanoparticle induced Black Etch of the silicon wafer, resulting in a nanoparticle that is kinetically stabilized. The method comprising combining with an etchant solution having equal volumes acetonitrile/acetic acid:hydrofluoric acid:hydrogen peroxide.

Method and means for dynamic measurement of rates of adsorption from solutions

DOEpatents

Slomka, B.J.; Buttermore, W.H.

1992-05-05

A method and apparatus are described for the dynamic measurement of rates of absorption from solutions. The method has the advantage of avoiding the use of solvent normally used to establish a baseline. The method involves pre-evacuating the adsorbent contained in an adsorbent cell and thereafter rapidly contacting the adsorbent with analytical solution, all without prior exposure of adsorbent to pure solvent. The result is a sharp characteristic adsorption line. 5 figs.

Erosion of water-based cements evaluated by volumetric and gravimetric methods.

PubMed

Nomoto, Rie; Uchida, Keiko; Momoi, Yasuko; McCabe, John F

2003-05-01

To compare the erosion of glass ionomer, zinc phosphate and polycarboxylate cements using volumetric and gravimetric methods. For the volumetric method, the eroded depth of cement placed in a cylindrical cavity in PMMA was measured using a dial gauge after immersion in an eroding solution. For the gravimetric method, the weight of the residue of a solution in which a cylindrical specimen had been immersed was measured. 0.02 M lactic acid solution (0.02 M acid) and 0.1 M lactic acid/sodium lactate buffer solution (0.1 M buffer) were used as eroding solutions. The pH of both solutions was 2.74 and the test period was 24 h. Ranking of eroded depth and weight of residue was polycarboxylate>zinc phosphate>glass ionomers. Differences in erosion were more clearly defined by differences in eroded depth than differences in weight of residue. In 0.02 M acid, the erosion of glass ionomer using the volumetric method was effected by the hygroscopic expansion. In 0.1 M buffer, the erosion for polycarboxylate and zinc phosphate using the volumetric method was much greater than that using the gravimetric method. This is explained by cryo-SEM images which show many holes in the surface of specimens after erosion. It appears that zinc oxide is dissolved leaving a spongy matrix which easily collapses under the force applied to the dial gauge during measurement. The volumetric method that employs eroded depth of cement using a 0.1 M buffer solution is able to quantify erosion and to make material comparisons.

Optical limiting device and method of preparation thereof

DOEpatents

Wang, Hsing-Lin; Xu, Su; McBranch, Duncan W.

2003-01-01

Optical limiting device and method of preparation thereof. The optical limiting device includes a transparent substrate and at least one homogeneous layer of an RSA material in polyvinylbutyral attached to the substrate. The device may be produced by preparing a solution of an RSA material, preferably a metallophthalocyanine complex, and a solution of polyvinylbutyral, and then mixing the two solutions together to remove air bubbles. The resulting solution is layered onto the substrate and the solvent is evaporated. The method can be used to produce a dual tandem optical limiting device.

On the exact solutions of high order wave equations of KdV type (I)

NASA Astrophysics Data System (ADS)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

METHOD OF SEPARATING PLUTONIUM FROM LANTHANUM FLUORIDE CARRIER

DOEpatents

Watt, G.W.; Goeckermann, R.H.

1958-06-10

An improvement in oxidation-reduction type methods of separating plutoniunn from elements associated with it in a neutron-irradiated uranium solution is described. The method relates to the separating of plutonium from lanthanum ions in an aqueous 0.5 to 2.5 N nitric acid solution by 'treating the solution, at room temperature, with ammonium sulfite in an amount sufficient to reduce the hexavalent plutonium present to a lower valence state, and then treating the solution with H/sub 2/O/sub 2/ thereby forming a tetravalent plutonium peroxide precipitate.

Method for converting sucrose to .beta.-D-glucose

DOEpatents

Simmons, Blake A [San Francisco, CA; Volponi, Joanne V [Livermore, CA; Ingersoll, David [Albuquerque, NM; Walker, Andrew [Woodinville, WA

2009-07-07

Disclosed is an apparatus and method for continuously converting sucrose to .beta.-D-glucose. The method comprises a three-stage enzymatic reactor in which an aqueous solution of sucrose is first converted into a solution of fructose and .alpha.-D-glucose by passing it through a porous, packed column containing an inert media on which invertase is immobilized. This solution is then sent through a second packed column containing glucose isomerase and finally a third packed column containing mutarotase. Solution temperature and pH are adjusted to maximize glucose output.

A boundary element alternating method for two-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Krishnamurthy, T.

1992-01-01

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

Algorithms for the computation of solutions of the Ornstein-Zernike equation.

PubMed

Peplow, A T; Beardmore, R E; Bresme, F

2006-10-01

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

Evaluation of a Pair-Wise Conflict Detection and Resolution Algorithm in a Multiple Aircraft Scenario

NASA Technical Reports Server (NTRS)

Carreno, Victor A.

2002-01-01

The KB3D algorithm is a pairwise conflict detection and resolution (CD&R) algorithm. It detects and generates trajectory vectoring for an aircraft which has been predicted to be in an airspace minima violation within a given look-ahead time. It has been proven, using mechanized theorem proving techniques, that for a pair of aircraft, KB3D produces at least one vectoring solution and that all solutions produced are correct. Although solutions produced by the algorithm are mathematically correct, they might not be physically executable by an aircraft or might not solve multiple aircraft conflicts. This paper describes a simple solution selection method which assesses all solutions generated by KB3D and determines the solution to be executed. The solution selection method and KB3D are evaluated using a simulation in which N aircraft fly in a free-flight environment and each aircraft in the simulation uses KB3D to maintain separation. Specifically, the solution selection method filters KB3D solutions which are procedurally undesirable or physically not executable and uses a predetermined criteria for selection.

Numerical solution of the electron transport equation

NASA Astrophysics Data System (ADS)

Woods, Mark

The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

Multiple solution of linear algebraic systems by an iterative method with recomputed preconditioner in the analysis of microstrip structures

NASA Astrophysics Data System (ADS)

Ahunov, Roman R.; Kuksenko, Sergey P.; Gazizov, Talgat R.

2016-06-01

A multiple solution of linear algebraic systems with dense matrix by iterative methods is considered. To accelerate the process, the recomputing of the preconditioning matrix is used. A priory condition of the recomputing based on change of the arithmetic mean of the current solution time during the multiple solution is proposed. To confirm the effectiveness of the proposed approach, the numerical experiments using iterative methods BiCGStab and CGS for four different sets of matrices on two examples of microstrip structures are carried out. For solution of 100 linear systems the acceleration up to 1.6 times, compared to the approach without recomputing, is obtained.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Soliton and periodic solutions for time-dependent coefficient non-linear equation

NASA Astrophysics Data System (ADS)

Guner, Ozkan

2016-01-01

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev-Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of ? functions and the modified sine-cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

Soliton and quasi-periodic wave solutions for b-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Singh, Manjit; Gupta, R. K.

2017-11-01

In this paper, truncated Laurent expansion is used to obtain the bilinear equation of a nonlinear evolution equation. As an application of Hirota's method, multisoliton solutions are constructed from the bilinear equation. Extending the application of Hirota's method and employing multidimensional Riemann theta function, one and two-periodic wave solutions are also obtained in a straightforward manner. The asymptotic behavior of one and two-periodic wave solutions under small amplitude limits is presented, and their relations with soliton solutions are also demonstrated.

Preparation of transition metal nanoparticles and surfaces modified with (CO)polymers synthesized by RAFT

DOEpatents

McCormick, III., Charles L.; Lowe, Andrew B.; Sumerlin, Brent S.

2006-11-21

A new, facile, general one-phase method of generating thio-functionalized transition metal nanoparticles and surfaces modified by (co)polymers synthesized by the RAFT method is described. The method includes the stops of forming a (co)polymer in aqueous solution using the RAFT methodology, forming a colloidal transition metal precursor solution from an appropriate transition metal; adding the metal precursor solution or surface to the (co)polymer solution, adding a reducing agent into the solution to reduce the metal colloid in situ to produce the stabilized nanoparticles or surface, and isolating the stabilized nanoparticles or surface in a manner such that aggregation is minimized. The functionalized surfaces generated using these methods can further undergo planar surface modifications, such as functionalization with a variety of different chemical groups, expanding their utility and application.

Preparation of transition metal nanoparticles and surfaces modified with (co)polymers synthesized by RAFT

DOEpatents

McCormick, III, Charles L.; Lowe, Andrew B [Hattiesburg, MS; Sumerlin, Brent S [Pittsburgh, PA

2011-12-27

A new, facile, general one-phase method of generating thiol-functionalized transition metal nanoparticles and surfaces modified by (co)polymers synthesized by the RAFT method is described. The method includes the steps of forming a (co)polymer in aqueous solution using the RAFT methodology, forming a colloidal transition metal precursor solution from an appropriate transition metal; adding the metal precursor solution or surface to the (co)polymer solution, adding a reducing agent into the solution to reduce the metal colloid in situ to produce the stabilized nanoparticles or surface, and isolating the stabilized nanoparticles or surface in a manner such that aggregation is minimized. The functionalized surfaces generated using these methods can further undergo planar surface modifications, such as functionalization with a variety of different chemical groups, expanding their utility and application.

Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics.

Membrane contactor assisted water extraction system for separating hydrogen peroxide from a working solution, and method thereof

DOEpatents

Snyder, Seth W [Lincolnwood, IL; Lin, Yupo J [Naperville, IL; Hestekin', Jamie A [Fayetteville, AR; Henry, Michael P [Batavia, IL; Pujado, Peter [Kildeer, IL; Oroskar, Anil [Oak Brook, IL; Kulprathipanja, Santi [Inverness, IL; Randhava, Sarabjit [Evanston, IL

2010-09-21

The present invention relates to a membrane contactor assisted extraction system and method for extracting a single phase species from multi-phase working solutions. More specifically one preferred embodiment of the invention relates to a method and system for membrane contactor assisted water (MCAWE) extraction of hydrogen peroxide (H.sub.2O.sub.2) from a working solution.

An algebraic equation solution process formulated in anticipation of banded linear equations.

DOT National Transportation Integrated Search

1971-01-01

A general method for the solution of large, sparsely banded, positive-definite, coefficient matrices is presented. The goal in developing the method was to produce an efficient and reliable solution process and to provide the user-programmer with a p...

New analytical methodology for analysing S(IV) species at low pH solutions by one stage titration method (bichromatometry) with a clear colour change. Could potentially replace the state-of-art-method iodometry at low pH analysis due higher accuracy

PubMed Central

Galfi, Istvan; Virtanen, Jorma; Gasik, Michael M.

2017-01-01

A new, faster and more reliable analytical methodology for S(IV) species analysis at low pH solutions by bichromatometry is proposed. For decades the state of the art methodology has been iodometry that is still well justified method for neutral solutions, thus at low pH media possess various side reactions increasing inaccuracy. In contrast, the new methodology has no side reactions at low pH media, requires only one titration step and provides a clear color change if S(IV) species are present in the solution. The method is validated using model solutions with known concentrations and applied to analyses of gaseous SO2 from purged solution in low pH media samples. The results indicate that bichromatometry can accurately analyze SO2 from liquid samples having pH even below 0 relevant to metallurgical industrial processes. PMID:29145479

Multifunctional nanocomposites of carbon nanotubes and nanoparticles formed via vacuum filtration

DOEpatents

Hersam, Mark C; Ostojic, Gordana; Liang, Yu Teng

2013-10-22

In one aspect, the present invention provides a method of forming a film of nanocomposites of carbon nanotubes (CNTs) and platinum (Pt) nanoparticles. In one embodiment, the method includes the steps of (a) providing a first solution that contains a plurality of CNTs, (b) providing a second solution that contains a plurality of Pt nanoparticles, (c) combining the first solution and the second solution to form a third solution, and (d) filtering the third solution through a nanoporous membrane using vacuum filtration to obtain a film of nanocomposites of CNTs and Pt nanoparticles.

Formulation and application of optimal homotopty asymptotic method to coupled differential-difference equations.

PubMed

Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

2015-01-01

In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.

Formulation and Application of Optimal Homotopty Asymptotic Method to Coupled Differential - Difference Equations

PubMed Central

Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

2015-01-01

In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit. PMID:25874457

Methods of Functionalization of Carbon Nanotubes by Photooxidation

NASA Technical Reports Server (NTRS)

Lebron-Colon, Marisabel (Inventor); Meador, Michael A. (Inventor)

2016-01-01

A method of photooxidizing carbon nanotubes, such as single-walled and multi-walled carbon nanotubes. The nanotubes are purified and dispersed in a solvent, such as n-methyl pyrrolidinone or dimethylformamide. A singlet oxygen sensitizer like Rose Bengal is added to the solution. Oxygen gas is continuously supplied while irradiating the solution while irradiating the solution with ultraviolet light to produce singlet oxygen to oxidize the single-walled carbon nanotubes. Advantageously, the method significantly increases the level of oxidation compared with prior art methods.

A conservative staggered-grid Chebyshev multidomain method for compressible flows

NASA Technical Reports Server (NTRS)

Kopriva, David A.; Kolias, John H.

1995-01-01

We present a new multidomain spectral collocation method that uses staggered grids for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute.

Topological soliton solutions for three shallow water waves models

NASA Astrophysics Data System (ADS)

Liu, Jiangen; Zhang, Yufeng; Wang, Yan

2018-07-01

In this article, we investigate three distinct physical structures for shallow water waves models by the improved ansatz method. The method was improved and can be used to obtain more generalized form topological soliton solutions than the original method. As a result, some new exact solutions of the shallow water equations are successfully established and the obtained results are exhibited graphically. The results showed that the improved ansatz method can be applied to solve other nonlinear differential equations arising from mathematical physics.

Predictive Sampling of Rare Conformational Events in Aqueous Solution: Designing a Generalized Orthogonal Space Tempering Method.

PubMed

Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei

2016-01-12

In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment analysis suggests that because essential conformational events are mainly driven by the compensating fluctuations of essential solute-solvent and solute-solute interactions, commonly employed "predictive" sampling methods are unlikely to be effective on this seemingly "simple" system. The gOST development presented in this paper illustrates how to employ the OSS scheme for physics-based sampling method designs.

A simplified analytic form for generation of axisymmetric plasma boundaries

DOE PAGES

Luce, Timothy C.

2017-02-23

An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less

A simplified analytic form for generation of axisymmetric plasma boundaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luce, Timothy C.

An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extendedmore » to cases that are more general and may be useful for benchmarking purposes.« less

The origin of spurious solutions in computational electromagnetics

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Wu, Jie; Povinelli, L. A.

1995-01-01

The origin of spurious solutions in computational electromagnetics, which violate the divergence equations, is deeply rooted in a misconception about the first-order Maxwell's equations and in an incorrect derivation and use of the curl-curl equations. The divergence equations must be always included in the first-order Maxwell's equations to maintain the ellipticity of the system in the space domain and to guarantee the uniqueness of the solution and/or the accuracy of the numerical solutions. The div-curl method and the least-squares method provide rigorous derivation of the equivalent second-order Maxwell's equations and their boundary conditions. The node-based least-squares finite element method (LSFEM) is recommended for solving the first-order full Maxwell equations directly. Examples of the numerical solutions by LSFEM for time-harmonic problems are given to demonstrate that the LSFEM is free of spurious solutions.

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

Path Following in the Exact Penalty Method of Convex Programming.

PubMed

Zhou, Hua; Lange, Kenneth

2015-07-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.

Path Following in the Exact Penalty Method of Convex Programming

PubMed Central

Zhou, Hua; Lange, Kenneth

2015-01-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044

Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

PubMed

Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo

2016-05-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

PubMed Central

Sun, Hui; Zhou, Shenggao; Moore, David K.; Cheng, Li-Tien; Li, Bo

2015-01-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems. PMID:27365866

A thin-shock-layer solution for nonequilibrium, inviscid hypersonic flows in earth, Martian, and Venusian atmospheres

NASA Technical Reports Server (NTRS)

Grose, W. L.

1971-01-01

An approximate inverse solution is presented for the nonequilibrium flow in the inviscid shock layer about a vehicle in hypersonic flight. The method is based upon a thin-shock-layer approximation and has the advantage of being applicable to both subsonic and supersonic regions of the shock layer. The relative simplicity of the method makes it ideally suited for programming on a digital computer with a significant reduction in storage capacity and computing time required by other more exact methods. Comparison of nonequilibrium solutions for an air mixture obtained by the present method is made with solutions obtained by two other methods. Additional cases are presented for entry of spherical nose cones into representative Venusian and Martian atmospheres. A digital computer program written in FORTRAN language is presented that permits an arbitrary gas mixture to be employed in the solution. The effects of vibration, dissociation, recombination, electronic excitation, and ionization are included in the program.

Integral method for transient He II heat transfer in a semi-infinite domain

NASA Astrophysics Data System (ADS)

Baudouy, B.

2002-05-01

Integral methods are suited to solve a non-linear system of differential equations where the non-linearity can be found either in the differential equations or in the boundary conditions. Though they are approximate methods, they have proven to give simple solutions with acceptable accuracy for transient heat transfer in He II. Taking in account the temperature dependence of thermal properties, direct solutions are found without the need of adjusting a parameter. Previously, we have presented a solution for the clamped heat flux and in the present study this method is used to accommodate the clamped-temperature problem. In the case of constant thermal properties, this method yields results that are within a few percent of the exact solution for the heat flux at the axis origin. We applied this solution to analyze recovery from burnout and find an agreement within 10% at low heat flux, whereas at high heat flux the model deviates from the experimental data suggesting the need for a more refined thermal model.

Time-periodic solutions of the Benjamin-Ono equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ambrose , D.M.; Wilkening, Jon

2008-04-01

We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one ofmore » the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.« less

The Shortlist Method for fast computation of the Earth Mover's Distance and finding optimal solutions to transportation problems.

PubMed

Gottschlich, Carsten; Schuhmacher, Dominic

2014-01-01

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method.

The Shortlist Method for Fast Computation of the Earth Mover's Distance and Finding Optimal Solutions to Transportation Problems

PubMed Central

Gottschlich, Carsten; Schuhmacher, Dominic

2014-01-01

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method. PMID:25310106

The effect of explanations on mathematical reasoning tasks

NASA Astrophysics Data System (ADS)

Norqvist, Mathias

2018-01-01

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in follow up tests than students that are given a solution method and engage in algorithmic reasoning. However, teachers and textbooks, at least occasionally, provide explanations together with an algorithmic method, and this could possibly be more efficient than creative reasoning. In this study, three matched groups practiced with either creative, algorithmic, or explained algorithmic tasks. The main finding was that students that practiced with creative tasks did, outperform the students that practiced with explained algorithmic tasks in a post-test, despite a much lower practice score. The two groups that got a solution method presented, performed similarly in both practice and post-test, even though one group got an explanation to the given solution method. Additionally, there were some differences between the groups in which variables predicted the post-test score.

Numerical Solution of the Flow of a Perfect Gas Over A Circular Cylinder at Infinite Mach Number

NASA Technical Reports Server (NTRS)

Hamaker, Frank M.

1959-01-01

A solution for the two-dimensional flow of an inviscid perfect gas over a circular cylinder at infinite Mach number is obtained by numerical methods of analysis. Nonisentropic conditions of curved shock waves and vorticity are included in the solution. The analysis is divided into two distinct regions, the subsonic region which is analyzed by the relaxation method of Southwell and the supersonic region which was treated by the method of characteristics. Both these methods of analysis are inapplicable on the sonic line which is therefore considered separately. The shapes of the sonic line and the shock wave are obtained by iteration techniques. The striking result of the solution is the strong curvature of the sonic line and of the other lines of constant Mach number. Because of this the influence of the supersonic flow on the sonic line is negligible. On comparison with Newtonian flow methods, it is found that the approximate methods show a larger variation of surface pressure than is given by the present solution.

A Quantitative Study of a Software Tool that Supports a Part-Complete Solution Method on Learning Outcomes

ERIC Educational Resources Information Center

Garner, Stuart

2009-01-01

This paper reports on the findings from a quantitative research study into the use of a software tool that was built to support a part-complete solution method (PCSM) for the learning of computer programming. The use of part-complete solutions to programming problems is one of the methods that can be used to reduce the cognitive load that students…

Multi-layer articles and methods of making same

DOEpatents

Fritzemeier, Leslie G.; Zhang, Wei; Palm, Walter C.; Rupich, Martin W.

2005-05-17

The invention relates to superconductor articles, and compositions and methods for making superconductor articles. The methods can include using a precursor solution having a relatively small concentration of total free acid. The articles can include more than one layer of superconductor material in which at least one layer of superconductor material can be formed by a solution process, such as a solution process involving the use of metalorganic precursors.

Two Novel Methods and Multi-Mode Periodic Solutions for the Fermi-Pasta-Ulam Model

NASA Astrophysics Data System (ADS)

Arioli, Gianni; Koch, Hans; Terracini, Susanna

2005-04-01

We introduce two novel methods for studying periodic solutions of the FPU β-model, both numerically and rigorously. One is a variational approach, based on the dual formulation of the problem, and the other involves computer-assisted proofs. These methods are used e.g. to construct a new type of solutions, whose energy is spread among several modes, associated with closely spaced resonances.

Dynamically controlled crystallization method and apparatus and crystals obtained thereby

NASA Technical Reports Server (NTRS)

Arnowitz, Leonard (Inventor); Steinberg, Emanuel (Inventor)

1999-01-01

A method and apparatus for dynamically controlling the crystallization of proteins including a crystallization chamber or chambers for holding a protein in a salt solution, one or more salt solution chambers, two communication passages respectively coupling the crystallization chamber with each of the salt solution chambers, and transfer mechanisms configured to respectively transfer salt solution between each of the salt solution chambers and the crystallization chamber. The transfer mechanisms are interlocked to maintain the volume of salt solution in the crystallization chamber substantially constant. Salt solution of different concentrations is transferred into and out of the crystallization chamber to adjust the salt concentration in the crystallization chamber to achieve precise control of the crystallization process.

Nucleation of Crystals From Solution in Microgravity (USML-1 Glovebox (GBX) Investigation)

NASA Technical Reports Server (NTRS)

Kroes, Roger L.; Reiss, Donald A.; Lehoczky, Sandor L.

1994-01-01

A new method for initiating nucleation from solutions in microgravity which avoids nucleation on container walls and other surfaces is described. This method consists of injecting a small quantity of highly concentrated, heated solution into the interior of a lightly supersaturated, cooler host gowth solution. It was tested successfully on USML-I, producing a large number of LAP crystals whose longest dimension averaged 1 mm.

The solution of Cauchy's problem for the Toda lattice with limit periodic initial data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khanmamedov, A Kh

Cauchy's problem for Toda lattices with initial data equal to the sum of a periodic and a rapidly decreasing sequence is solved with the use of the inverse scattering method. A method allowing one to find a limit periodic solution of the Toda lattice from a known periodic solution is described. The existence and uniqueness of a limit periodic solution is proved. Bibliography: 17 titles.

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

PubMed

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

A study on Marangoni convection by the variational iteration method

NASA Astrophysics Data System (ADS)

Karaoǧlu, Onur; Oturanç, Galip

2012-09-01

In this paper, we will consider the use of the variational iteration method and Padé approximant for finding approximate solutions for a Marangoni convection induced flow over a free surface due to an imposed temperature gradient. The solutions are compared with the numerical (fourth-order Runge Kutta) solutions.

Remediation of arsenic-contaminated soils and groundwaters

DOEpatents

Peters, Robert W.; Frank, James R.; Feng, Xiandong

1998-01-01

An in situ method for extraction of arsenic contaminants from a soil medium and remediation of the medium including contacting the medium with an extractant solution, directing the solution within and through the medium, and collecting the solution and contaminants. The method can also be used for arsenate and/or arsenite removal.

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

NASA Technical Reports Server (NTRS)

Agapov, A. V.; Kolosov, B. I.

1979-01-01

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Method of producing solution-derived metal oxide thin films

DOEpatents

Boyle, Timothy J.; Ingersoll, David

2000-01-01

A method of preparing metal oxide thin films by a solution method. A .beta.-metal .beta.-diketonate or carboxylate compound, where the metal is selected from groups 8, 9, 10, 11, and 12 of the Periodic Table, is solubilized in a strong Lewis base to form a homogeneous solution. This precursor solution forms within minutes and can be deposited on a substrate in a single layer or a multiple layers to form a metal oxide thin film. The substrate with the deposited thin film is heated to change the film from an amorphous phase to a ceramic metal oxide and cooled.

Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels

NASA Technical Reports Server (NTRS)

Coffee, Thomas M.; Anderson, Rodney L.; Lo, Martin W.

2011-01-01

We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.

Method for loading resin beds

DOEpatents

Notz, Karl J.; Rainey, Robert H.; Greene, Charles W.; Shockley, William E.

1978-01-01

An improved method of preparing nuclear reactor fuel by carbonizing a uranium loaded cation exchange resin provided by contacting a H.sup.+ loaded resin with a uranyl nitrate solution deficient in nitrate, comprises providing the nitrate deficient solution by a method comprising the steps of reacting in a reaction zone maintained between about 145.degree.-200.degree. C, a first aqueous component comprising a uranyl nitrate solution having a boiling point of at least 145.degree. C with a second aqueous component to provide a gaseous phase containing HNO.sub.3 and a reaction product comprising an aqueous uranyl nitrate solution deficient in nitrate.

Short-Chain Polysaccharide Analysis in Ethanol-Water Solutions.

PubMed

Yan, Xun

2017-07-01

This study demonstrates that short-chain polysaccharides, or oligosaccharides, could be sufficiently separated with hydrophilic interaction LC (HILIC) conditions and quantified by evaporative light-scattering detection (ELSD). The multianalyte calibration approach improved the efficiency of calibrating the nonlinear detector response. The method allowed easy quantification of short-chain carbohydrates. Using the HILIC method, the oligosaccharide solubility and its profile in water/alcohol solutions at room temperature were able to be quantified. The results showed that the polysaccharide solubility in ethanol-water solutions decreased as ethanol content increased. The results also showed oligosaccharides to have minimal solubility in pure ethanol. In a saturated maltodextrin ethanol (80%) solution, oligosaccharide components with a degree of polymerization >12 were practically insoluble and contributed less than 0.2% to the total solute dry weight. The HILIC-ELSD method allows for the identification and quantification of low-MW carbohydrates individually and served as an alternative method to current gel permeation chromatography procedures.

A method to approximate a closest loadability limit using multiple load flow solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yorino, Naoto; Harada, Shigemi; Cheng, Haozhong

A new method is proposed to approximate a closest loadability limit (CLL), or closest saddle node bifurcation point, using a pair of multiple load flow solutions. More strictly, the obtainable points by the method are the stationary points including not only CLL but also farthest and saddle points. An operating solution and a low voltage load flow solution are used to efficiently estimate the node injections at a CLL as well as the left and right eigenvectors corresponding to the zero eigenvalue of the load flow Jacobian. They can be used in monitoring loadability margin, in identification of weak spotsmore » in a power system and in the examination of an optimal control against voltage collapse. Most of the computation time of the proposed method is taken in calculating the load flow solution pair. The remaining computation time is less than that of an ordinary load flow.« less

Inverse solutions for electrical impedance tomography based on conjugate gradients methods

NASA Astrophysics Data System (ADS)

Wang, M.

2002-01-01

A multistep inverse solution for two-dimensional electric field distribution is developed to deal with the nonlinear inverse problem of electric field distribution in relation to its boundary condition and the problem of divergence due to errors introduced by the ill-conditioned sensitivity matrix and the noise produced by electrode modelling and instruments. This solution is based on a normalized linear approximation method where the change in mutual impedance is derived from the sensitivity theorem and a method of error vector decomposition. This paper presents an algebraic solution of the linear equations at each inverse step, using a generalized conjugate gradients method. Limiting the number of iterations in the generalized conjugate gradients method controls the artificial errors introduced by the assumption of linearity and the ill-conditioned sensitivity matrix. The solution of the nonlinear problem is approached using a multistep inversion. This paper also reviews the mathematical and physical definitions of the sensitivity back-projection algorithm based on the sensitivity theorem. Simulations and discussion based on the multistep algorithm, the sensitivity coefficient back-projection method and the Newton-Raphson method are given. Examples of imaging gas-liquid mixing and a human hand in brine are presented.

A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries

PubMed Central

Secomb, Timothy W.

2016-01-01

A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10–30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume. PMID:26443811

Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function. Ph.D. Thesis - Houston Univ.

NASA Technical Reports Server (NTRS)

Garcia, F., Jr.

1974-01-01

A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.

Identification of the connections in biologically inspired neural networks

NASA Technical Reports Server (NTRS)

Demuth, H.; Leung, K.; Beale, M.; Hicklin, J.

1990-01-01

We developed an identification method to find the strength of the connections between neurons from their behavior in small biologically-inspired artificial neural networks. That is, given the network external inputs and the temporal firing pattern of the neurons, we can calculate a solution for the strengths of the connections between neurons and the initial neuron activations if a solution exists. The method determines directly if there is a solution to a particular neural network problem. No training of the network is required. It should be noted that this is a first pass at the solution of a difficult problem. The neuron and network models chosen are related to biology but do not contain all of its complexities, some of which we hope to add to the model in future work. A variety of new results have been obtained. First, the method has been tailored to produce connection weight matrix solutions for networks with important features of biological neural (bioneural) networks. Second, a computationally efficient method of finding a robust central solution has been developed. This later method also enables us to find the most consistent solution in the presence of noisy data. Prospects of applying our method to identify bioneural network connections are exciting because such connections are almost impossible to measure in the laboratory. Knowledge of such connections would facilitate an understanding of bioneural networks and would allow the construction of the electronic counterparts of bioneural networks on very large scale integrated (VLSI) circuits.

Compositions and methods for treating nuclear fuel

DOEpatents

Soderquist, Chuck Z; Johnsen, Amanda M; McNamara, Bruce K; Hanson, Brady D; Smith, Steven C; Peper, Shane M

2013-08-13

Compositions are provided that include nuclear fuel. Methods for treating nuclear fuel are provided which can include exposing the fuel to a carbonate-peroxide solution. Methods can also include exposing the fuel to an ammonium solution. Methods for acquiring molybdenum from a uranium comprising material are provided.

Compositions and methods for treating nuclear fuel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soderquist, Chuck Z; Johnsen, Amanda M; McNamara, Bruce K

Compositions are provided that include nuclear fuel. Methods for treating nuclear fuel are provided which can include exposing the fuel to a carbonate-peroxide solution. Methods can also include exposing the fuel to an ammonium solution. Methods for acquiring molybdenum from a uranium comprising material are provided.

Method for producing rapid pH changes

DOEpatents

Clark, John H.; Campillo, Anthony J.; Shapiro, Stanley L.; Winn, Kenneth R.

1981-01-01

A method of initiating a rapid pH change in a solution by irradiating the solution with an intense flux of electromagnetic radiation of a frequency which produces a substantial pK change to a compound in solution. To optimize the resulting pH change, the compound being irradiated in solution should have an excited state lifetime substantially longer than the time required to establish an excited state acid-base equilibrium in the solution. Desired pH changes can be accomplished in nanoseconds or less by means of picosecond pulses of laser radiation.

Method for producing rapid pH changes

DOEpatents

Clark, J.H.; Campillo, A.J.; Shapiro, S.L.; Winn, K.R.

A method of initiating a rapid pH change in a solution comprises irradiating the solution with an intense flux of electromagnetic radiation of a frequency which produces a substantial pK change to a compound in solution. To optimize the resulting pH change, the compound being irradiated in solution should have an excited state lifetime substantially longer than the time required to establish an excited state acid-base equilibrium in the solution. Desired pH changes can be accomplished in nanoseconds or less by means of picosecond pulses of laser radiation.

Method for single crystal growth of photovoltaic perovskite material and devices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Jinsong; Dong, Qingfeng

Systems and methods for perovskite single crystal growth include using a low temperature solution process that employs a temperature gradient in a perovskite solution in a container, also including at least one small perovskite single crystal, and a substrate in the solution upon which substrate a perovskite crystal nucleates and grows, in part due to the temperature gradient in the solution and in part due to a temperature gradient in the substrate. For example, a top portion of the substrate external to the solution may be cooled.

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

PubMed

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Optical solitons, complexitons, Gaussian soliton and power series solutions of a generalized Hirota equation

NASA Astrophysics Data System (ADS)

Mao, Jin-Jin; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

2018-05-01

In this paper, we consider a generalized Hirota equation with a bounded potential, which can be used to describe the propagation properties of optical soliton solutions. By employing the hypothetical method and the sub-equation method, we construct the bright soliton, dark soliton, complexitons and Gaussian soliton solutions of the Hirota equation. Moreover, we explicitly derive the power series solutions with their convergence analysis. Finally, we provide the graphical analysis of such soliton solutions in order to better understand their dynamical behavior.

Method of separating thorium from plutonium

DOEpatents

Clifton, David G.; Blum, Thomas W.

1984-01-01

A method of chemically separating plutonium from thorium. Plutonium and thorium to be separated are dissolved in an aqueous feed solution, preferably as the nitrate salts. The feed solution is acidified and sodium nitrite is added to the solution to adjust the valence of the plutonium to the +4 state. A chloride salt, preferably sodium chloride, is then added to the solution to induce formation of an anionic plutonium chloride complex. The anionic plutonium chloride complex and the thorium in solution are then separated by ion exchange on a strong base anion exchange column.

Method of separating thorium from plutonium

DOEpatents

Clifton, D.G.; Blum, T.W.

A method of chemically separating plutonium from thorium is claimed. Plutonium and thorium to be separated are dissolved in an aqueous feed solution, preferably as the nitrate salts. The feed solution is acidified and sodium nitrite is added to the solution to adjust the valence of the plutonium to the +4 state. A chloride salt, preferably sodium chloride, is then added to the solution to induce formation of an anionic plutonium chloride complex. The anionic plutonium chloride complex and the thorium in solution are then separated by ion exchange on a strong base anion exchange column.

Method of separating thorium from plutonium

DOEpatents

Clifton, D.G.; Blum, T.W.

1984-07-10

A method is described for chemically separating plutonium from thorium. Plutonium and thorium to be separated are dissolved in an aqueous feed solution, preferably as the nitrate salts. The feed solution is acidified and sodium nitrite is added to the solution to adjust the valence of the plutonium to the +4 state. A chloride salt, preferably sodium chloride, is then added to the solution to induce formation of an anionic plutonium chloride complex. The anionic plutonium chloride complex and the thorium in solution are then separated by ion exchange on a strong base anion exchange column.

Analytical solutions for solute transport in groundwater and riverine flow using Green's Function Method and pertinent coordinate transformation method

NASA Astrophysics Data System (ADS)

Sanskrityayn, Abhishek; Suk, Heejun; Kumar, Naveen

2017-04-01

In this study, analytical solutions of one-dimensional pollutant transport originating from instantaneous and continuous point sources were developed in groundwater and riverine flow using both Green's Function Method (GFM) and pertinent coordinate transformation method. Dispersion coefficient and flow velocity are considered spatially and temporally dependent. The spatial dependence of the velocity is linear, non-homogeneous and that of dispersion coefficient is square of that of velocity, while the temporal dependence is considered linear, exponentially and asymptotically decelerating and accelerating. Our proposed analytical solutions are derived for three different situations depending on variations of dispersion coefficient and velocity, respectively which can represent real physical processes occurring in groundwater and riverine systems. First case refers to steady solute transport situation in steady flow in which dispersion coefficient and velocity are only spatially dependent. The second case represents transient solute transport in steady flow in which dispersion coefficient is spatially and temporally dependent while the velocity is spatially dependent. Finally, the third case indicates transient solute transport in unsteady flow in which both dispersion coefficient and velocity are spatially and temporally dependent. The present paper demonstrates the concentration distribution behavior from a point source in realistically occurring flow domains of hydrological systems including groundwater and riverine water in which the dispersivity of pollutant's mass is affected by heterogeneity of the medium as well as by other factors like velocity fluctuations, while velocity is influenced by water table slope and recharge rate. Such capabilities give the proposed method's superiority about application of various hydrological problems to be solved over other previously existing analytical solutions. Especially, to author's knowledge, any other solution doesn't exist for both spatially and temporally variations of dispersion coefficient and velocity. In this study, the existing analytical solutions from previous widely known studies are used for comparison as validation tools to verify the proposed analytical solution as well as the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) code and the developed 1D finite difference code (FDM). All such solutions show perfect match with the respective proposed solutions.

Dynamically controlled crystallization method and apparatus and crystals obtained thereby

NASA Technical Reports Server (NTRS)

Arnowitz, Leonard (Inventor); Steinberg, Emanuel (Inventor)

2003-01-01

A method and apparatus for dynamically controlling the crystallization of molecules including a crystallization chamber (14) or chambers for holding molecules in a precipitant solution, one or more precipitant solution reservoirs (16, 18), communication passages (17, 19) respectively coupling the crystallization chamber(s) with each of the precipitant solution reservoirs, and transfer mechanisms (20, 21, 22, 24, 26, 28) configured to respectively transfer precipitant solution between each of the precipitant solution reservoirs and the crystallization chamber(s). The transfer mechanisms are interlocked to maintain a constant volume of precipitant solution in the crystallization chamber(s). Precipitant solutions of different concentrations are transferred into and out of the crystallization chamber(s) to adjust the concentration of precipitant in the crystallization chamber(s) to achieve precise control of the crystallization process. The method and apparatus can be used effectively to grow crystals under reduced gravity conditions such as microgravity conditions of space, and under conditions of reduced or enhanced effective gravity as induced by a powerful magnetic field.

Discrimination of Mixed Taste Solutions using Ultrasonic Wave and Soft Computing

NASA Astrophysics Data System (ADS)

Kojima, Yohichiro; Kimura, Futoshi; Mikami, Tsuyoshi; Kitama, Masataka

In this study, ultrasonic wave acoustic properties of mixed taste solutions were investigated, and the possibility of taste sensing based on the acoustical properties obtained was examined. In previous studies, properties of solutions were discriminated based on sound velocity, amplitude and frequency characteristics of ultrasonic waves propagating through the five basic taste solutions and marketed beverages. However, to make this method applicable to beverages that contain many taste substances, further studies are required. In this paper, the waveform of an ultrasonic wave with frequency of approximately 5 MHz propagating through mixed solutions composed of sweet and salty substance was measured. As a result, differences among solutions were clearly observed as differences in their properties. Furthermore, these mixed solutions were discriminated by a self-organizing neural network. The ratio of volume in their mixed solutions was estimated by a distance-type fuzzy reasoning method. Therefore, the possibility of taste sensing was shown by using ultrasonic wave acoustic properties and the soft computing, such as the self-organizing neural network and the distance-type fuzzy reasoning method.

Constructing exact symmetric informationally complete measurements from numerical solutions

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

An induced current method for measuring zeta potential of electrolyte solution-air interface.

PubMed

Song, Yongxin; Zhao, Kai; Wang, Junsheng; Wu, Xudong; Pan, Xinxiang; Sun, Yeqing; Li, Dongqing

2014-02-15

This paper reports a novel and very simple method for measuring the zeta potential of electrolyte solution-air interface. When a measuring electrode contacts the electrolyte solution-air interface, an electrical current will be generated due to the potential difference between the electrode-air surface and the electrolyte solution-air interface. The amplitude of the measured electric signal is linearly proportional to this potential difference; and depends only on the zeta potential at the electrolyte solution-air interface, regardless of the types and concentrations of the electrolyte. A correlation between the zeta potential and the measured voltage signal is obtained based on the experimental data. Using this equation, the zeta potential of any electrolyte solution-air interface can be evaluated quickly and easily by inserting an electrode through the electrolyte solution-air interface and measuring the electrical signal amplitude. This method was verified by comparing the obtained results of NaCl, MgCl2 and CaCl2 solutions of different pH values and concentrations with the zeta potential data reported in the published journal papers. Copyright © 2013 Elsevier Inc. All rights reserved.

Characterization of a new candidate isotopic reference material for natural Pb using primary measurement method.

PubMed

Nonose, Naoko; Suzuki, Toshihiro; Shin, Ki-Cheol; Miura, Tsutomu; Hioki, Akiharu

2017-06-29

A lead isotopic standard solution with natural abundance has been developed by applying a mixture of a solution of enriched 208 Pb and a solution of enriched 204 Pb ( 208 Pb- 204 Pb double spike solution) as bracketing method. The amount-of-substance ratio of 208 Pb: 204 Pb in this solution is accurately measured by applying EDTA titrimetry, which is one of the primary measurement methods, to each enriched Pb isotope solution. Also metal impurities affecting EDTA titration and minor lead isotopes contained in each enriched Pb isotope solution are quantified by ICP-SF-MS. The amount-of-substance ratio of 208 Pb: 204 Pb in the 208 Pb- 204 Pb double spike solution is 0.961959 ± 0.000056 (combined standard uncertainty; k = 1). Both the measurement of lead isotope ratios in a candidate isotopic standard solution and the correction of mass discrimination in MC-ICP-MS are carried out by coupling of a bracketing method with the 208 Pb- 204 Pb double spike solution and a thallium internal addition method, where thallium solution is added to the standard and the sample. The measured lead isotope ratios and their expanded uncertainties (k = 2) in the candidate isotopic standard solution are 18.0900 ± 0.0046 for 206 Pb: 204 Pb, 15.6278 ± 0.0036 for 207 Pb: 204 Pb, 38.0626 ± 0.0089 for 208 Pb: 204 Pb, 2.104406 ± 0.00013 for 208 Pb: 206 Pb, and 0.863888 ± 0.000036 for 207 Pb: 206 Pb. The expanded uncertainties are about one half of the stated uncertainty for NIST SRM 981, for 208 Pb: 204 Pb, 207 Pb: 204 Pb and 206 Pb: 204 Pb, or one eighth, for 208 Pb: 206 Pb and 207 Pb: 206 Pb, The combined uncertainty consists of the uncertainties due to lead isotope ratio measurements and the remaining time-drift effect of mass discrimination in MC-ICP-MS, which is not removed by the coupled correction method. In the measurement of 208 Pb: 204 Pb, 207 Pb: 204 Pb and 206 Pb: 204 Pb, the latter contribution is two or three times larger than the former. When the coupling of a bracketing method with the 208 Pb- 204 Pb double spike solution and a thallium internal addition method is applied to the analysis of NIST SRM 981, the measured lead isotope ratios are in good agreement with its certified values. This proves that the developed method is not only consistent with the conventional one by NIST SRM 981 but also enables measurement of the lead isotope ratios with higher precision. Copyright © 2017 Elsevier B.V. All rights reserved.

Method of forming a foamed thermoplastic polymer

DOEpatents

Duchane, David V.; Cash, David L.

1986-01-01

A method of forming a foamed thermoplastic polymer. A solid thermoplastic lymer is immersed in an immersant solution comprising a compatible carrier solvent and an infusant solution containing an incompatible liquid blowing agent for a time sufficient for the immersant solution to infuse into the polymer. The carrier solvent is then selectively extracted, preferably by a solvent exchange process in which the immersant solution is gradually diluted with and replaced by the infusant solution, so as to selectively leave behind the infusant solution permanently entrapped in the polymer. The polymer is then heated to volatilize the blowing agent and expand the polymer into a foamed state.

A stopping criterion for the iterative solution of partial differential equations

NASA Astrophysics Data System (ADS)

Rao, Kaustubh; Malan, Paul; Perot, J. Blair

2018-01-01

A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

METHOD FOR DISSOLVING ZIRCONIUM-URANIUM COMPOSITIONS

DOEpatents

Gens, T.A.

1961-07-18

A method is descrioed for treating a zirconium-- uranium composition to form a stable solution from which uranium and other values may be extracted by contacting the composition with at least a 4 molar aqueous solution of ammonium fluoride at a temperature of about 100 deg C, adding a peroxide, in incremental amounts, to the heated solution throughout the period of dissolution until all of the uranium is converted to soluble uranyl salt, adding nitric acid to the resultant solution to form a solvent extraction feed solution to convert the uranyl salt to a solvent extractable state, and thereafter recovering the uranium and other desired values from the feed solution by solvent extraction.

Method for selectively reducing plutonium values by a photochemical process

DOEpatents

Friedman, Horace A.; Toth, Louis M.; Bell, Jimmy T.

1978-01-01

The rate of reduction of Pu(IV) to Pu(III) in nitric acid solution containing a reducing agent is enhanced by exposing the solution to 200-500 nm electromagnetic radiation. Pu values are recovered from an organic extractant solution containing Pu(IV) values and U(VI) values by the method of contacting the extractant solution with an aqueous nitric acid solution in the presence of a reducing agent and exposing the aqueous solution to electromagnetic radiation having a wavelength of 200-500 nm. Under these conditions, Pu values preferentially distribute to the aqueous phase and U values preferentially distribute to the organic phase.

Calixarene crown ether solvent composition and use thereof for extraction of cesium from alkaline waste solutions

DOEpatents

Moyer, Bruce A.; Sachleben, Richard A.; Bonnesen, Peter V.; Presley, Derek J.

2001-01-01

A solvent composition and corresponding method for extracting cesium (Cs) from aqueous neutral and alkaline solutions containing Cs and perhaps other competing metal ions is described. The method entails contacting an aqueous Cs-containing solution with a solvent consisting of a specific class of lipophilic calix[4]arene-crown ether extractants dissolved in a hydrocarbon-based diluent containing a specific class of alkyl-aromatic ether alcohols as modifiers. The cesium values are subsequently recovered from the extractant, and the solvent subsequently recycled, by contacting the Cs-containing organic solution with an aqueous stripping solution. This combined extraction and stripping method is especially useful as a process for removal of the radionuclide cesium-137 from highly alkaline waste solutions which are also very concentrated in sodium and potassium. No pre-treatment of the waste solution is necessary, and the cesium can be recovered using a safe and inexpensive stripping process using water, dilute (millimolar) acid solutions, or dilute (millimolar) salt solutions. An important application for this invention would be treatment of alkaline nuclear tank wastes. Alternatively, the invention could be applied to decontamination of acidic reprocessing wastes containing cesium-137.

Shaped nanocrystal particles and methods for making the same

DOEpatents

Alivisatos, A Paul [Oakland, CA; Scher, Erik C [Menlo Park, CA; Manna, Liberato [Berkeley, CA

2011-11-22

Shaped nanocrystal particles and methods for making shaped nanocrystal particles are disclosed. One embodiment includes a method for forming a branched, nanocrystal particle. It includes (a) forming a core having a first crystal structure in a solution, (b) forming a first arm extending from the core having a second crystal structure in the solution, and (c) forming a second arm extending from the core having the second crystal structure in the solution.