Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks

DOE PAGES

Park, Jong-Kyu; Logan, Nikolas C.

2017-03-01

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly formore » each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.« less

Self-consistent adjoint analysis for topology optimization of electromagnetic waves

NASA Astrophysics Data System (ADS)

Deng, Yongbo; Korvink, Jan G.

2018-05-01

In topology optimization of electromagnetic waves, the Gâteaux differentiability of the conjugate operator to the complex field variable results in the complexity of the adjoint sensitivity, which evolves the original real-valued design variable to be complex during the iterative solution procedure. Therefore, the self-inconsistency of the adjoint sensitivity is presented. To enforce the self-consistency, the real part operator has been used to extract the real part of the sensitivity to keep the real-value property of the design variable. However, this enforced self-consistency can cause the problem that the derived structural topology has unreasonable dependence on the phase of the incident wave. To solve this problem, this article focuses on the self-consistent adjoint analysis of the topology optimization problems for electromagnetic waves. This self-consistent adjoint analysis is implemented by splitting the complex variables of the wave equations into the corresponding real parts and imaginary parts, sequentially substituting the split complex variables into the wave equations with deriving the coupled equations equivalent to the original wave equations, where the infinite free space is truncated by the perfectly matched layers. Then, the topology optimization problems of electromagnetic waves are transformed into the forms defined on real functional spaces instead of complex functional spaces; the adjoint analysis of the topology optimization problems is implemented on real functional spaces with removing the variational of the conjugate operator; the self-consistent adjoint sensitivity is derived, and the phase-dependence problem is avoided for the derived structural topology. Several numerical examples are implemented to demonstrate the robustness of the derived self-consistent adjoint analysis.

On the role of self-adjointness in the continuum formulation of topological quantum phases

NASA Astrophysics Data System (ADS)

Tanhayi Ahari, Mostafa; Ortiz, Gerardo; Seradjeh, Babak

2016-11-01

Topological quantum phases of matter are characterized by an intimate relationship between the Hamiltonian dynamics away from the edges and the appearance of bound states localized at the edges of the system. Elucidating this correspondence in the continuum formulation of topological phases, even in the simplest case of a one-dimensional system, touches upon fundamental concepts and methods in quantum mechanics that are not commonly discussed in textbooks, in particular the self-adjoint extensions of a Hermitian operator. We show how such topological bound states can be derived in a prototypical one-dimensional system. Along the way, we provide a pedagogical exposition of the self-adjoint extension method as well as the role of symmetries in correctly formulating the continuum, field-theory description of topological matter with boundaries. Moreover, we show that self-adjoint extensions can be characterized generally in terms of a conserved local current associated with the self-adjoint operator.

Operator pencil passing through a given operator

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

Biggs, A., E-mail: khudian@manchester.ac.uk, E-mail: adam.biggs@student.manchester.ac.uk; Khudaverdian, H. M., E-mail: khudian@manchester.ac.uk, E-mail: adam.biggs@student.manchester.ac.uk

Let Δ be a linear differential operator acting on the space of densities of a given weight λ{sub 0} on a manifold M. One can consider a pencil of operators Π-circumflex(Δ)=(Δ{sub λ}) passing through the operator Δ such that any Δ{sub λ} is a linear differential operator acting on densities of weight λ. This pencil can be identified with a linear differential operator Δ-circumflex acting on the algebra of densities of all weights. The existence of an invariant scalar product in the algebra of densities implies a natural decomposition of operators, i.e., pencils of self-adjoint and anti-self-adjoint operators. We studymore » lifting maps that are on one hand equivariant with respect to divergenceless vector fields, and, on the other hand, with values in self-adjoint or anti-self-adjoint operators. In particular, we analyze the relation between these two concepts, and apply it to the study of diff (M)-equivariant liftings. Finally, we briefly consider the case of liftings equivariant with respect to the algebra of projective transformations and describe all regular self-adjoint and anti-self-adjoint liftings. Our constructions can be considered as a generalisation of equivariant quantisation.« less

On the theory of self-adjoint extensions of symmetric operators and its applications to quantum physics

NASA Astrophysics Data System (ADS)

Ibort, A.; Pérez-Pardo, J. M.

2015-04-01

This is a series of five lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory of self-adjoint extensions of symmetric operators on Hilbert spaces and their applications to a few specific problems in Quantum Mechanics.

An adjoint view on flux consistency and strong wall boundary conditions to the Navier–Stokes equations

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

Stück, Arthur, E-mail: arthur.stueck@dlr.de

2015-11-15

Inconsistent discrete expressions in the boundary treatment of Navier–Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection–diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yieldsmore » second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier–Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.« less

Adjoint-based optimization of PDEs in moving domains

NASA Astrophysics Data System (ADS)

Protas, Bartosz; Liao, Wenyuan

2008-02-01

In this investigation we address the problem of adjoint-based optimization of PDE systems in moving domains. As an example we consider the one-dimensional heat equation with prescribed boundary temperatures and heat fluxes. We discuss two methods of deriving an adjoint system necessary to obtain a gradient of a cost functional. In the first approach we derive the adjoint system after mapping the problem to a fixed domain, whereas in the second approach we derive the adjoint directly in the moving domain by employing methods of the noncylindrical calculus. We show that the operations of transforming the system from a variable to a fixed domain and deriving the adjoint do not commute and that, while the gradient information contained in both systems is the same, the second approach results in an adjoint problem with a simpler structure which is therefore easier to implement numerically. This approach is then used to solve a moving boundary optimization problem for our model system.

Continuous energy adjoint transport for photons in PHITS

NASA Astrophysics Data System (ADS)

Malins, Alex; Machida, Masahiko; Niita, Koji

2017-09-01

Adjoint Monte Carlo can be an effcient algorithm for solving photon transport problems where the size of the tally is relatively small compared to the source. Such problems are typical in environmental radioactivity calculations, where natural or fallout radionuclides spread over a large area contribute to the air dose rate at a particular location. Moreover photon transport with continuous energy representation is vital for accurately calculating radiation protection quantities. Here we describe the incorporation of an adjoint Monte Carlo capability for continuous energy photon transport into the Particle and Heavy Ion Transport code System (PHITS). An adjoint cross section library for photon interactions was developed based on the JENDL- 4.0 library, by adding cross sections for adjoint incoherent scattering and pair production. PHITS reads in the library and implements the adjoint transport algorithm by Hoogenboom. Adjoint pseudo-photons are spawned within the forward tally volume and transported through space. Currently pseudo-photons can undergo coherent and incoherent scattering within the PHITS adjoint function. Photoelectric absorption is treated implicitly. The calculation result is recovered from the pseudo-photon flux calculated over the true source volume. A new adjoint tally function facilitates this conversion. This paper gives an overview of the new function and discusses potential future developments.

Sensitivity analysis of a model of CO2 exchange in tundra ecosystems by the adjoint method

NASA Technical Reports Server (NTRS)

Waelbroek, C.; Louis, J.-F.

1995-01-01

A model of net primary production (NPP), decomposition, and nitrogen cycling in tundra ecosystems has been developed. The adjoint technique is used to study the sensitivity of the computed annual net CO2 flux to perturbation in initial conditions, climatic inputs, and model's main parameters describing current seasonal CO2 exchange in wet sedge tundra at Barrow, Alaska. The results show that net CO2 flux is most sensitive to parameters characterizing litter chemical composition and more sensitive to decomposition parameters than to NPP parameters. This underlines the fact that in nutrient-limited ecosystems, decomposition drives net CO2 exchange by controlling mineralization of main nutrients. The results also indicate that the short-term (1 year) response of wet sedge tundra to CO2-induced warming is a significant increase in CO2 emission, creating a positive feedback to atmosphreic CO2 accumulation. However, a cloudiness increase during the same year can severely alter this response and lead to either a slight decrease or a strong increase in emitted CO2, depending on its exact timing. These results demonstrate that the adjoint method is well suited to study systems encountering regime changes, as a single run of the adjoint model provides sensitivities of the net CO2 flux to perturbations in all parameters and variables at any time of the year. Moreover, it is shown that large errors due to the presence of thresholds can be avoided by first delimiting the range of applicability of the adjoint results.

An Adjoint-Based Analysis of the Sampling Footprints of Tall Tower, Aircraft and Potential Future Lidar Observations of CO2

NASA Technical Reports Server (NTRS)

Andrews, Arlyn; Kawa, Randy; Zhu, Zhengxin; Burris, John; Abshire, Jim

2004-01-01

A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.

Reduction by symmetries in singular quantum-mechanical problems: General scheme and application to Aharonov-Bohm model

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

Smirnov, A. G., E-mail: smirnov@lpi.ru

2015-12-15

We develop a general technique for finding self-adjoint extensions of a symmetric operator that respects a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schrödinger operators with singular potentials. The approach is based on constructing a unitary transformation diagonalizing the symmetries and reducing the initial operator to the direct integral of a suitable family of partial operators. We prove that symmetry preserving self-adjoint extensions of the initial operator are in a one-to-one correspondence with measurable families of self-adjoint extensions of partial operators obtained by reduction. The general scheme is applied to themore » three-dimensional Aharonov-Bohm Hamiltonian describing the electron in the magnetic field of an infinitely thin solenoid. We construct all self-adjoint extensions of this Hamiltonian, invariant under translations along the solenoid and rotations around it, and explicitly find their eigenfunction expansions.« less

Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

DOE PAGES

Burke, Timothy P.; Kiedrowski, Brian C.

2017-12-11

Here, Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivitiesmore » of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and 3σ of reference solutions obtained using direct perturbations with central differences for the majority of test problems.« less

Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei

NASA Astrophysics Data System (ADS)

Gallone, Matteo; Michelangeli, Alessandro

2018-02-01

We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the Kreĭn-Višik-Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neumann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the extension, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.

The Gauss-Bonnet operator of an infinite graph

NASA Astrophysics Data System (ADS)

Anné, Colette; Torki-Hamza, Nabila

2015-06-01

We propose a general condition, to ensure essential self-adjointness for the Gauss-Bonnet operator , based on a notion of completeness as Chernoff. This gives essential self-adjointness of the Laplace operator both for functions and 1-forms on infinite graphs. This is used to extend Flanders result concerning solutions of Kirchhoff's laws.

Technical Note: Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework (RETRO-TOM)

NASA Astrophysics Data System (ADS)

Haines, P. E.; Esler, J. G.; Carver, G. D.

2014-06-01

A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model, RETRO-TOM. The Eulerian backtracking method is used, allowing the forward advection scheme (Prather's second-order moments) to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time symmetric, suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" formulation with the accuracy of an "adjoint of finite difference" formulation.

Technical Note: Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework (RETRO-TOM)

NASA Astrophysics Data System (ADS)

Haines, P. E.; Esler, J. G.; Carver, G. D.

2014-01-01

A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model RETRO-TOM. The Eulerian backtracking method is used, allowing the forward advection scheme (Prather's second-order moments), to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time-symmetric suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux-limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" formulation with the accuracy of an "adjoint of finite difference" formulation.

Stratospheric Water Vapor and the Asian Monsoon: An Adjoint Model Investigation

NASA Technical Reports Server (NTRS)

Olsen, Mark A.; Andrews, Arlyn E.

2003-01-01

A new adjoint model of the Goddard Parameterized Chemistry and Transport Model is used to investigate the role that the Asian monsoon plays in transporting water to the stratosphere. The adjoint model provides a unique perspective compared to non-diffusive and non-mixing Lagrangian trajectory analysis. The quantity of water vapor transported from the monsoon and the pathways into the stratosphere are examined. The emphasis is on the amount of water originating from the monsoon that contributes to the tropical tape recorder signal. The cross-tropopause flux of water from the monsoon to the midlatitude lower stratosphere will also be discussed.

On the symmetry of the boundary conditions of the volume potential

NASA Astrophysics Data System (ADS)

Kal'menov, Tynysbek Sh.; Arepova, Gaukhar; Suragan, Durvudkhan

2017-09-01

It is well known that the volume potential determines the mass or the charge distributed over the domain with density f. The volume potential is extensively used in function theory and embedding theorems. It is also well known that the volume potential gives a solution to an inhomogeneous equation. And it generates a linear self-adjoint operator. It is known that self-adjoint differential operators are generated by boundary conditions. In our previous papers for an arbitrary domain a boundary condition on the volume potential is given. In the past, it was not possible to prove the self-adjointness of these obtained boundary conditions. In the present paper, we prove the symmetry of boundary condition for the volume potential.

Nodal weighting factor method for ex-core fast neutron fluence evaluation

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

Chiang, R. T.

The nodal weighting factor method is developed for evaluating ex-core fast neutron flux in a nuclear reactor by utilizing adjoint neutron flux, a fictitious unit detector cross section for neutron energy above 1 or 0.1 MeV, the unit fission source, and relative assembly nodal powers. The method determines each nodal weighting factor for ex-core neutron fast flux evaluation by solving the steady-state adjoint neutron transport equation with a fictitious unit detector cross section for neutron energy above 1 or 0.1 MeV as the adjoint source, by integrating the unit fission source with a typical fission spectrum to the solved adjointmore » flux over all energies, all angles and given nodal volume, and by dividing it with the sum of all nodal weighting factors, which is a normalization factor. Then, the fast neutron flux can be obtained by summing the various relative nodal powers times the corresponding nodal weighting factors of the adjacent significantly contributed peripheral assembly nodes and times a proper fast neutron attenuation coefficient over an operating period. A generic set of nodal weighting factors can be used to evaluate neutron fluence at the same location for similar core design and fuel cycles, but the set of nodal weighting factors needs to be re-calibrated for a transition-fuel-cycle. This newly developed nodal weighting factor method should be a useful and simplified tool for evaluating fast neutron fluence at selected locations of interest in ex-core components of contemporary nuclear power reactors. (authors)« less

MPACT Subgroup Self-Shielding Efficiency Improvements

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

Stimpson, Shane; Liu, Yuxuan; Collins, Benjamin S.

Recent developments to improve the efficiency of the MOC solvers in MPACT have yielded effective kernels that loop over several energy groups at once, rather that looping over one group at a time. These kernels have produced roughly a 2x speedup on the MOC sweeping time during eigenvalue calculation. However, the self-shielding subgroup calculation had not been reevaluated to take advantage of these new kernels, which typically requires substantial solve time. The improvements covered in this report start by integrating the multigroup kernel concepts into the subgroup calculation, which are then used as the basis for further extensions. The nextmore » improvement that is covered is what is currently being termed as “Lumped Parameter MOC”. Because the subgroup calculation is a purely fixed source problem and multiple sweeps are performed only to update the boundary angular fluxes, the sweep procedure can be condensed to allow for the instantaneous propagation of the flux across a spatial domain, without the need to sweep along all segments in a ray. Once the boundary angular fluxes are considered to be converged, an additional sweep that will tally the scalar flux is completed. The last improvement that is investigated is the possible reduction of the number of azimuthal angles per octant in the shielding sweep. Typically 16 azimuthal angles per octant are used for self-shielding and eigenvalue calculations, but it is possible that the self-shielding sweeps are less sensitive to the number of angles than the full eigenvalue calculation.« less

Spectral monodromy of non-self-adjoint operators

NASA Astrophysics Data System (ADS)

Phan, Quang Sang

2014-01-01

In the present paper, we build a combinatorial invariant, called the "spectral monodromy" from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc ["Quantum monodromy in integrable systems," Commun. Math. Phys. 203(2), 465-479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat ["On global action-angle coordinates," Commun. Pure Appl. Math. 33(6), 687-706 (1980)].

Adjoint-Based Climate Model Tuning: Application to the Planet Simulator

NASA Astrophysics Data System (ADS)

Lyu, Guokun; Köhl, Armin; Matei, Ion; Stammer, Detlef

2018-01-01

The adjoint method is used to calibrate the medium complexity climate model "Planet Simulator" through parameter estimation. Identical twin experiments demonstrate that this method can retrieve default values of the control parameters when using a long assimilation window of the order of 2 months. Chaos synchronization through nudging, required to overcome limits in the temporal assimilation window in the adjoint method, is employed successfully to reach this assimilation window length. When assimilating ERA-Interim reanalysis data, the observations of air temperature and the radiative fluxes are the most important data for adjusting the control parameters. The global mean net longwave fluxes at the surface and at the top of the atmosphere are significantly improved by tuning two model parameters controlling the absorption of clouds and water vapor. The global mean net shortwave radiation at the surface is improved by optimizing three model parameters controlling cloud optical properties. The optimized parameters improve the free model (without nudging terms) simulation in a way similar to that in the assimilation experiments. Results suggest a promising way for tuning uncertain parameters in nonlinear coupled climate models.

Determination of the self-adjoint matrix Schrödinger operators without the bound state data

NASA Astrophysics Data System (ADS)

Xu, Xiao-Chuan; Yang, Chuan-Fu

2018-06-01

(i) For the matrix Schrödinger operator on the half line, it is shown that the scattering data, which consists of the scattering matrix and the bound state data, uniquely determines the potential and the boundary condition. It is also shown that only the scattering matrix uniquely determines the self-adjoint potential and the boundary condition if either the potential exponentially decreases fast enough or the potential is known a priori on (), where a is an any fixed positive number. (ii) For the matrix Schrödinger operator on the full line, it is shown that the left (or right) reflection coefficient uniquely determine the self-adjoint potential if either the potential exponentially decreases fast enough or the potential is known a priori on (or ()), where b is an any fixed number.

Sensitivity Analysis for Steady State Groundwater Flow Using Adjoint Operators

NASA Astrophysics Data System (ADS)

Sykes, J. F.; Wilson, J. L.; Andrews, R. W.

1985-03-01

Adjoint sensitivity theory is currently being considered as a potential method for calculating the sensitivity of nuclear waste repository performance measures to the parameters of the system. For groundwater flow systems, performance measures of interest include piezometric heads in the vicinity of a waste site, velocities or travel time in aquifers, and mass discharge to biosphere points. The parameters include recharge-discharge rates, prescribed boundary heads or fluxes, formation thicknesses, and hydraulic conductivities. The derivative of a performance measure with respect to the system parameters is usually taken as a measure of sensitivity. To calculate sensitivities, adjoint sensitivity equations are formulated from the equations describing the primary problem. The solution of the primary problem and the adjoint sensitivity problem enables the determination of all of the required derivatives and hence related sensitivity coefficients. In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Alternatively, local velocity related performance measures are more sensitive to hydraulic conductivities.

Crypto-Unitary Forms of Quantum Evolution Operators

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2013-06-01

The description of quantum evolution using unitary operator {u}(t)=exp(-i{h}t) requires that the underlying self-adjoint quantum Hamiltonian {h} remains time-independent. In a way extending the so called {PT}-symmetric quantum mechanics to the models with manifestly time-dependent "charge" {C}(t) we propose and describe an extension of such an exponential-operator approach to evolution to the manifestly time-dependent self-adjoint quantum Hamiltonians {h}(t).

Advanced Variance Reduction Strategies for Optimizing Mesh Tallies in MAVRIC

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

Peplow, Douglas E.; Blakeman, Edward D; Wagner, John C

2007-01-01

More often than in the past, Monte Carlo methods are being used to compute fluxes or doses over large areas using mesh tallies (a set of region tallies defined on a mesh that overlays the geometry). For problems that demand that the uncertainty in each mesh cell be less than some set maximum, computation time is controlled by the cell with the largest uncertainty. This issue becomes quite troublesome in deep-penetration problems, and advanced variance reduction techniques are required to obtain reasonable uncertainties over large areas. The CADIS (Consistent Adjoint Driven Importance Sampling) methodology has been shown to very efficientlymore » optimize the calculation of a response (flux or dose) for a single point or a small region using weight windows and a biased source based on the adjoint of that response. This has been incorporated into codes such as ADVANTG (based on MCNP) and the new sequence MAVRIC, which will be available in the next release of SCALE. In an effort to compute lower uncertainties everywhere in the problem, Larsen's group has also developed several methods to help distribute particles more evenly, based on forward estimates of flux. This paper focuses on the use of a forward estimate to weight the placement of the source in the adjoint calculation used by CADIS, which we refer to as a forward-weighted CADIS (FW-CADIS).« less

Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces

NASA Astrophysics Data System (ADS)

Mantile, Andrea; Posilicano, Andrea; Sini, Mourad

2016-07-01

The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the ;free; operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.

Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger's equation with repulsive delta potential

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-11-01

In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrödinger's equation with repulsive delta potential (δ-NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the δ-NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented.

A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165

Toward a Comprehensive Carbon Budget for North America: Potential Applications of Adjoint Methods with Diverse Datasets

NASA Technical Reports Server (NTRS)

Andrews, A.

2002-01-01

A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future COS levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an "inverse problem," where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from long-term surface monitoring stations with data from intensive field campaigns and with proposed future satellite observations. A major advantage of the adjoint approach is that meteorological and surface data, as well as data for other atmospheric constituents and pollutants can be efficiently included in addition to observations of CO2 mixing ratios. This presentation will provide an overview of potentially useful datasets for carbon cycle research in general with an emphasis on planning for the North American Carbon Project. Areas of overlap with ongoing and proposed work on air quality/air pollution issues will be highlighted.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation.

PubMed

Marcotte, Christopher D; Grigoriev, Roman O

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation

NASA Astrophysics Data System (ADS)

Marcotte, Christopher D.; Grigoriev, Roman O.

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

Adjoint-based constant-mass partial derivatives

DOE PAGES

Favorite, Jeffrey A.

2017-09-01

In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, k effmore » of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.« less

Development of CO2 inversion system based on the adjoint of the global coupled transport model

NASA Astrophysics Data System (ADS)

Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon

2014-05-01

We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) Eulerian transport model (TM) and the Lagrangian plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the Lagrangian model FLEXPART. The Lagrangian component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the Lagrangian part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to Eulerian part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of Lagrangian model is required, making it applicable to combination of global NIES TM and any Lagrangian model; 2. Once run, the Lagrangian output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over limited regions close to the monitoring sites (using the LPDM part), and at coarse resolution for the rest of the globe (using the Eulerian part), minimizing aggregation errors and computation cost. The adjoint of the coupled high-resolution Eulerian-Lagrangian model will be incorporated into the PYVAR CO2 variational inverse system (Chevallier et al., 2005). Chevallier, F., Fisher, M., Peylin, P., Serrar, S., Bousquet, P., Bréon, F.-M., Chédin, A., and Ciais, P.: Inferring CO2 sources and sinks from satellite observations: method and application to TOVS data, J. Geophys. Res., 110, D24309, doi:10.1029/2005JD006390, 2005.

Magnetic braking in young late-type stars. The effect of polar spots

NASA Astrophysics Data System (ADS)

Aibéo, A.; Ferreira, J. M.; Lima, J. J. G.

2007-10-01

Context: The existence of rapidly rotating cool stars in young clusters implies a reduction of angular momentum loss rate for a certain period of the star's early life. Recently, the concentration of magnetic flux near the poles of these stars has been proposed as an alternative mechanism to dynamo saturation in order to explain the saturation of angular momentum loss. Aims: In this work we study the effect of magnetic surface flux distribution on the coronal field topology and angular momentum loss rate. We investigate if magnetic flux concentration towards the pole is a reasonable alternative to dynamo saturation. Methods: We construct a 1D wind model and also apply a 2-D self-similar analytical model, to evaluate how the surface field distribution affects the angular momentum loss of the rotating star. Results: From the 1D model we find that, in a magnetically dominated low corona, the concentrated polar surface field rapidly expands to regions of low magnetic pressure resulting in a coronal field with small latitudinal variation. We also find that the angular momentum loss rate due to a uniform field or a concentrated field with equal total magnetic flux is very similar. From the 2D wind model we show that there are several relevant factors to take into account when studying the angular momentum loss from a star. In particular, we show that the inclusion of force balance across the field in a wind model is fundamental if realistic conclusions are to be drawn from the effect of non-uniform surface field distribution on magnetic braking. This model predicts that a magnetic field concentrated at high latitudes leads to larger Alfvén radii and larger braking rates than a smoother field distribution. Conclusions: From the results obtained, we argue that the magnetic surface field distribution towards the pole does not directly limit the braking efficiency of the wind.

Comparative Study of Three Data Assimilation Methods for Ice Sheet Model Initialisation

NASA Astrophysics Data System (ADS)

Mosbeux, Cyrille; Gillet-Chaulet, Fabien; Gagliardini, Olivier

2015-04-01

The current global warming has direct consequences on ice-sheet mass loss contributing to sea level rise. This loss is generally driven by an acceleration of some coastal outlet glaciers and reproducing these mechanisms is one of the major issues in ice-sheet and ice flow modelling. The construction of an initial state, as close as possible to current observations, is required as a prerequisite before producing any reliable projection of the evolution of ice-sheets. For this step, inverse methods are often used to infer badly known or unknown parameters. For instance, the adjoint inverse method has been implemented and applied with success by different authors in different ice flow models in order to infer the basal drag [ Schafer et al., 2012; Gillet-chauletet al., 2012; Morlighem et al., 2010]. Others data fields, such as ice surface and bedrock topography, are easily measurable with more or less uncertainty but only locally along tracks and interpolated on finer model grid. All these approximations lead to errors on the data elevation model and give rise to an ill-posed problem inducing non-physical anomalies in flux divergence [Seroussi et al, 2011]. A solution to dissipate these divergences of flux is to conduct a surface relaxation step at the expense of the accuracy of the modelled surface [Gillet-Chaulet et al., 2012]. Other solutions, based on the inversion of ice thickness and basal drag were proposed [Perego et al., 2014; Pralong & Gudmundsson, 2011]. In this study, we create a twin experiment to compare three different assimilation algorithms based on inverse methods and nudging to constrain the bedrock friction and the bedrock elevation: (i) cyclic inversion of friction parameter and bedrock topography using adjoint method, (ii) cycles coupling inversion of friction parameter using adjoint method and nudging of bedrock topography, (iii) one step inversion of both parameters with adjoint method. The three methods show a clear improvement in parameters knowledge leading to a significant reduction of flux divergence of the model before forecasting.

Self-similar Hot Accretion Flow onto a Neutron Star

NASA Astrophysics Data System (ADS)

Medvedev, Mikhail V.; Narayan, Ramesh

2001-06-01

We consider hot, two-temperature, viscous accretion onto a rotating, unmagnetized neutron star. We assume Coulomb coupling between the protons and electrons, as well as free-free cooling from the electrons. We show that the accretion flow has an extended settling region that can be described by means of two analytical self-similar solutions: a two-temperature solution that is valid in an inner zone, r<~102.5, where r is the radius in Schwarzschild units; and a one-temperature solution that is valid in an outer zone, r>~102.5. In both zones the density varies as ρ~r-2 and the angular velocity as Ω~r-3/2. We solve the flow equations numerically and confirm that the analytical solutions are accurate. Except for the radial velocity, all gas properties in the self-similar settling zone, such as density, angular velocity, temperature, luminosity, and angular momentum flux, are independent of the mass accretion rate; these quantities do depend sensitively on the spin of the neutron star. The angular momentum flux is outward under most conditions; therefore, the central star is nearly always spun down. The luminosity of the settling zone arises from the rotational energy that is released as the star is braked by viscosity, and the contribution from gravity is small; hence, the radiative efficiency, η=Lacc/Mc2, is arbitrarily large at low M. For reasonable values of the gas adiabatic index γ, the Bernoulli parameter is negative; therefore, in the absence of dynamically important magnetic fields, a strong outflow or wind is not expected. The flow is also convectively stable but may be thermally unstable. The described solution is not advection dominated; however, when the spin of the star is small enough, the flow transforms smoothly to an advection-dominated branch of solution.

Banach Synaptic Algebras

NASA Astrophysics Data System (ADS)

Foulis, David J.; Pulmannov, Sylvia

2018-04-01

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

Elementary operators on self-adjoint operators

NASA Astrophysics Data System (ADS)

Molnar, Lajos; Semrl, Peter

2007-03-01

Let H be a Hilbert space and let and be standard *-operator algebras on H. Denote by and the set of all self-adjoint operators in and , respectively. Assume that and are surjective maps such that M(AM*(B)A)=M(A)BM(A) and M*(BM(A)B)=M*(B)AM*(B) for every pair , . Then there exist an invertible bounded linear or conjugate-linear operator and a constant c[set membership, variant]{-1,1} such that M(A)=cTAT*, , and M*(B)=cT*BT, .

Subcritical saturation of the magnetorotational instability through mean magnetic field generation

NASA Astrophysics Data System (ADS)

Xie, Jin-Han; Julien, Keith; Knobloch, Edgar

2018-03-01

The magnetorotational instability is widely believed to be responsible for outward angular momentum transport in astrophysical accretion discs. The efficiency of this transport depends on the amplitude of this instability in the saturated state. We employ an asymptotic expansion based on an explicit, astrophysically motivated time-scale separation between the orbital period, Alfvén crossing time and viscous or resistive dissipation time-scales, originally proposed by Knobloch and Julien, to formulate a semi-analytical description of the saturated state in an incompressible disc. In our approach a Keplerian shear flow is maintained by the central mass but the instability saturates via the generation of a mean vertical magnetic field. The theory assumes that the time-averaged angular momentum flux and the radial magnetic flux are constant and determines both self-consistently. The results predict that, depending on parameters, steady saturation may be supercritical or subcritical, and in the latter case that the upper (lower) solution branch is always stable (unstable). The angular momentum flux is always outward, consistent with the presence of accretion, and for fixed wavenumber peaks in the subcritical regime. The limit of infinite Reynolds number at large but finite magnetic Reynolds number is also discussed.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

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

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

Doppler Temperature Coefficient Calculations Using Adjoint-Weighted Tallies and Continuous Energy Cross Sections in MCNP6

NASA Astrophysics Data System (ADS)

Gonzales, Matthew Alejandro

The calculation of the thermal neutron Doppler temperature reactivity feedback co-efficient, a key parameter in the design and safe operation of advanced reactors, using first order perturbation theory in continuous energy Monte Carlo codes is challenging as the continuous energy adjoint flux is not readily available. Traditional approaches of obtaining the adjoint flux attempt to invert the random walk process as well as require data corresponding to all temperatures and their respective temperature derivatives within the system in order to accurately calculate the Doppler temperature feedback. A new method has been developed using adjoint-weighted tallies and On-The-Fly (OTF) generated continuous energy cross sections within the Monte Carlo N-Particle (MCNP6) transport code. The adjoint-weighted tallies are generated during the continuous energy k-eigenvalue Monte Carlo calculation. The weighting is based upon the iterated fission probability interpretation of the adjoint flux, which is the steady state population in a critical nuclear reactor caused by a neutron introduced at that point in phase space. The adjoint-weighted tallies are produced in a forward calculation and do not require an inversion of the random walk. The OTF cross section database uses a high order functional expansion between points on a user-defined energy-temperature mesh in which the coefficients with respect to a polynomial fitting in temperature are stored. The coefficients of the fits are generated before run- time and called upon during the simulation to produce cross sections at any given energy and temperature. The polynomial form of the OTF cross sections allows the possibility of obtaining temperature derivatives of the cross sections on-the-fly. The use of Monte Carlo sampling of adjoint-weighted tallies and the capability of computing derivatives of continuous energy cross sections with respect to temperature are used to calculate the Doppler temperature coefficient in a research version of MCNP6. Temperature feedback results from the cross sections themselves, changes in the probability density functions, as well as changes in the density of the materials. The focus of this work is specific to the Doppler temperature feedback which result from Doppler broadening of cross sections as well as changes in the probability density function within the scattering kernel. This method is compared against published results using Mosteller's numerical benchmark to show accurate evaluations of the Doppler temperature coefficient, fuel assembly calculations, and a benchmark solution based on the heavy gas model for free-gas elastic scattering. An infinite medium benchmark for neutron free gas elastic scattering for large scattering ratios and constant absorption cross section has been developed using the heavy gas model. An exact closed form solution for the neutron energy spectrum is obtained in terms of the confluent hypergeometric function and compared against spectra for the free gas scattering model in MCNP6. Results show a quick increase in convergence of the analytic energy spectrum to the MCNP6 code with increasing target size, showing absolute relative differences of less than 5% for neutrons scattering with carbon. The analytic solution has been generalized to accommodate piecewise constant in energy absorption cross section to produce temperature feedback. Results reinforce the constraints in which heavy gas theory may be applied resulting in a significant target size to accommodate increasing cross section structure. The energy dependent piecewise constant cross section heavy gas model was used to produce a benchmark calculation of the Doppler temperature coefficient to show accurate calculations when using the adjoint-weighted method. Results show the Doppler temperature coefficient using adjoint weighting and cross section derivatives accurately obtains the correct solution within statistics as well as reduce computer runtimes by a factor of 50.

Quasi-stationary states and fermion pair creation from a vacuum in supercritical Coulomb field

NASA Astrophysics Data System (ADS)

Khalilov, V. R.

2017-12-01

Creation of charged fermion pair from a vacuum in so-called supercritical Coulomb potential is examined for the case when fermions can move only in the same (one) plane. In which case, quantum dynamics of charged massive or massless fermions can be described by the two-dimensional Dirac Hamiltonians with an usual (-a/r) Coulomb potential. These Hamiltonians are singular and require the additional definition in order for them to be treated as self-adjoint quantum-mechanical operators. We construct the self-adjoint two-dimensional Dirac Hamiltonians with a Coulomb potential and determine the quantum-mechanical states for such Hamiltonians in the corresponding Hilbert spaces of square-integrable functions. We determine the scattering amplitude in which the self-adjoint extension parameter is incorporated and then obtain equations implicitly defining possible discrete energy spectra of the self-adjoint Dirac Hamiltonians with a Coulomb potential. It is shown that this quantum system becomes unstable in the presence of a supercritical Coulomb potential which manifests in the appearance of quasi-stationary states in the lower (negative) energy continuum. The energy spectrum of those states is quasi-discrete, consists of broadened levels with widths related to the inverse lifetimes of the quasi-stationary states as well as the probability of creation of charged fermion pair by a supercritical Coulomb field. Explicit analytical expressions for the creation probabilities of charged (massive or massless) fermion pair are obtained in a supercritical Coulomb field.

PRODUCTION OF SOUND BY UNSTEADY THROTTLING OF FLOW INTO A RESONANT CAVITY, WITH APPLICATION TO VOICED SPEECH

PubMed Central

Howe, M. S.; McGowan, R. S.

2011-01-01

An analysis is made of the sound generated by the time-dependent throttling of a nominally steady stream of air through a small orifice into a flow-through resonant cavity. This is exemplified by the production of voiced speech, where air from the lungs enters the vocal tract through the glottis at a time variable volume flow rate Q(t) controlled by oscillations of the glottis cross-section. Voicing theory has hitherto determined Q from a heuristic, reduced complexity ‘Fant’ differential equation (G. Fant, Acoustic Theory of Speech Production, 1960). A new self-consistent, integro-differential form of this equation is derived in this paper using the theory of aerodynamic sound, with full account taken of the back-reaction of the resonant tract on the glottal flux Q. The theory involves an aeroacoustic Green’s function (G) for flow-surface interactions in a time-dependent glottis, so making the problem non-self-adjoint. In complex problems of this type it is not usually possible to obtain G in an explicit analytic form. The principal objective of the paper is to show how the Fant equation can still be derived in such cases from a consideration of the equation of aerodynamic sound and from the adjoint of the equation governing G in the neighbourhood of the ‘throttle’. The theory is illustrated by application to the canonical problem of throttled flow into a Helmholtz resonator. PMID:21666824

Development of the WRF-CO2 4D-Var assimilation system v1.0

NASA Astrophysics Data System (ADS)

Zheng, Tao; French, Nancy H. F.; Baxter, Martin

2018-05-01

Regional atmospheric CO2 inversions commonly use Lagrangian particle trajectory model simulations to calculate the required influence function, which quantifies the sensitivity of a receptor to flux sources. In this paper, an adjoint-based four-dimensional variational (4D-Var) assimilation system, WRF-CO2 4D-Var, is developed to provide an alternative approach. This system is developed based on the Weather Research and Forecasting (WRF) modeling system, including the system coupled to chemistry (WRF-Chem), with tangent linear and adjoint codes (WRFPLUS), and with data assimilation (WRFDA), all in version 3.6. In WRF-CO2 4D-Var, CO2 is modeled as a tracer and its feedback to meteorology is ignored. This configuration allows most WRF physical parameterizations to be used in the assimilation system without incurring a large amount of code development. WRF-CO2 4D-Var solves for the optimized CO2 flux scaling factors in a Bayesian framework. Two variational optimization schemes are implemented for the system: the first uses the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization algorithm (L-BFGS-B) and the second uses the Lanczos conjugate gradient (CG) in an incremental approach. WRFPLUS forward, tangent linear, and adjoint models are modified to include the physical and dynamical processes involved in the atmospheric transport of CO2. The system is tested by simulations over a domain covering the continental United States at 48 km × 48 km grid spacing. The accuracy of the tangent linear and adjoint models is assessed by comparing against finite difference sensitivity. The system's effectiveness for CO2 inverse modeling is tested using pseudo-observation data. The results of the sensitivity and inverse modeling tests demonstrate the potential usefulness of WRF-CO2 4D-Var for regional CO2 inversions.

Adjoint-Based Implicit Uncertainty Analysis for Figures of Merit in a Laser Inertial Fusion Engine

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

Seifried, J E; Fratoni, M; Kramer, K J

A primary purpose of computational models is to inform design decisions and, in order to make those decisions reliably, the confidence in the results of such models must be estimated. Monte Carlo neutron transport models are common tools for reactor designers. These types of models contain several sources of uncertainty that propagate onto the model predictions. Two uncertainties worthy of note are (1) experimental and evaluation uncertainties of nuclear data that inform all neutron transport models and (2) statistical counting precision, which all results of a Monte Carlo codes contain. Adjoint-based implicit uncertainty analyses allow for the consideration of anymore » number of uncertain input quantities and their effects upon the confidence of figures of merit with only a handful of forward and adjoint transport calculations. When considering a rich set of uncertain inputs, adjoint-based methods remain hundreds of times more computationally efficient than Direct Monte-Carlo methods. The LIFE (Laser Inertial Fusion Energy) engine is a concept being developed at Lawrence Livermore National Laboratory. Various options exist for the LIFE blanket, depending on the mission of the design. The depleted uranium hybrid LIFE blanket design strives to close the fission fuel cycle without enrichment or reprocessing, while simultaneously achieving high discharge burnups with reduced proliferation concerns. Neutron transport results that are central to the operation of the design are tritium production for fusion fuel, fission of fissile isotopes for energy multiplication, and production of fissile isotopes for sustained power. In previous work, explicit cross-sectional uncertainty analyses were performed for reaction rates related to the figures of merit for the depleted uranium hybrid LIFE blanket. Counting precision was also quantified for both the figures of merit themselves and the cross-sectional uncertainty estimates to gauge the validity of the analysis. All cross-sectional uncertainties were small (0.1-0.8%), bounded counting uncertainties, and were precise with regard to counting precision. Adjoint/importance distributions were generated for the same reaction rates. The current work leverages those adjoint distributions to transition from explicit sensitivities, in which the neutron flux is constrained, to implicit sensitivities, in which the neutron flux responds to input perturbations. This treatment vastly expands the set of data that contribute to uncertainties to produce larger, more physically accurate uncertainty estimates.« less

Greenland Regional and Ice Sheet-wide Geometry Sensitivity to Boundary and Initial conditions

NASA Astrophysics Data System (ADS)

Logan, L. C.; Narayanan, S. H. K.; Greve, R.; Heimbach, P.

2017-12-01

Ice sheet and glacier model outputs require inputs from uncertainly known initial and boundary conditions, and other parameters. Conservation and constitutive equations formalize the relationship between model inputs and outputs, and the sensitivity of model-derived quantities of interest (e.g., ice sheet volume above floatation) to model variables can be obtained via the adjoint model of an ice sheet. We show how one particular ice sheet model, SICOPOLIS (SImulation COde for POLythermal Ice Sheets), depends on these inputs through comprehensive adjoint-based sensitivity analyses. SICOPOLIS discretizes the shallow-ice and shallow-shelf approximations for ice flow, and is well-suited for paleo-studies of Greenland and Antarctica, among other computational domains. The adjoint model of SICOPOLIS was developed via algorithmic differentiation, facilitated by the source transformation tool OpenAD (developed at Argonne National Lab). While model sensitivity to various inputs can be computed by costly methods involving input perturbation simulations, the time-dependent adjoint model of SICOPOLIS delivers model sensitivities to initial and boundary conditions throughout time at lower cost. Here, we explore both the sensitivities of the Greenland Ice Sheet's entire and regional volumes to: initial ice thickness, precipitation, basal sliding, and geothermal flux over the Holocene epoch. Sensitivity studies such as described here are now accessible to the modeling community, based on the latest version of SICOPOLIS that has been adapted for OpenAD to generate correct and efficient adjoint code.

Estimation of Turbulent Heat Fluxes by Assimilation of Land Surface Temperature Observations From GOES Satellites Into an Ensemble Kalman Smoother Framework

NASA Astrophysics Data System (ADS)

Xu, Tongren; Bateni, S. M.; Neale, C. M. U.; Auligne, T.; Liu, Shaomin

2018-03-01

In different studies, land surface temperature (LST) observations have been assimilated into the variational data assimilation (VDA) approaches to estimate turbulent heat fluxes. The VDA methods yield accurate turbulent heat fluxes, but they need an adjoint model, which is difficult to derive and code. They also cannot directly calculate the uncertainty of their estimates. To overcome the abovementioned drawbacks, this study assimilates LST data from Geostationary Operational Environmental Satellite into the ensemble Kalman smoother (EnKS) data assimilation system to estimate turbulent heat fluxes. EnKS does not need to derive the adjoint term and directly generates statistical information on the accuracy of its predictions. It uses the heat diffusion equation to simulate LST. EnKS with the state augmentation approach finds the optimal values for the unknown parameters (i.e., evaporative fraction and neutral bulk heat transfer coefficient, CHN) by minimizing the misfit between LST observations from Geostationary Operational Environmental Satellite and LST estimations from the heat diffusion equation. The augmented EnKS scheme is tested over six Ameriflux sites with a wide range of hydrological and vegetative conditions. The results show that EnKS can predict not only the model parameters and turbulent heat fluxes but also their uncertainties over a variety of land surface conditions. Compared to the variational method, EnKS yields suboptimal turbulent heat fluxes. However, suboptimality of EnKS is small, and its results are comparable to those of the VDA method. Overall, EnKS is a feasible and reliable method for estimation of turbulent heat fluxes.

Geometry of quantum dynamics in infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana

2018-04-01

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

FW-CADIS Method for Global and Semi-Global Variance Reduction of Monte Carlo Radiation Transport Calculations

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

Wagner, John C; Peplow, Douglas E.; Mosher, Scott W

2014-01-01

This paper presents a new hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as responses at multiple localized detectors and spectra. This method, referred to as Forward-Weighted CADIS (FW-CADIS), is an extension of the Consistent Adjoint Driven Importance Sampling (CADIS) method, which has been used for more than a decade to very effectively improve the efficiency of Monte Carlo calculations of localized quantities, e.g., flux, dose, or reaction rate at a specific location. The basis of this method is the development ofmore » an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. Implementation of this method utilizes the results from a forward deterministic calculation to develop a forward-weighted source for a deterministic adjoint calculation. The resulting adjoint function is then used to generate consistent space- and energy-dependent source biasing parameters and weight windows that are used in a forward Monte Carlo calculation to obtain more uniform statistical uncertainties in the desired tally regions. The FW-CADIS method has been implemented and demonstrated within the MAVRIC sequence of SCALE and the ADVANTG/MCNP framework. Application of the method to representative, real-world problems, including calculation of dose rate and energy dependent flux throughout the problem space, dose rates in specific areas, and energy spectra at multiple detectors, is presented and discussed. Results of the FW-CADIS method and other recently developed global variance reduction approaches are also compared, and the FW-CADIS method outperformed the other methods in all cases considered.« less

Year End Progress Report on Rattlesnake Improvements

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

Wang, Yaqi; DeHart, Mark David; Gleicher, Frederick Nathan

Rattlesnake is a MOOSE-based radiation transport application developed at INL to support modern multi-physics simulations. At the beginning of the last year, Rattlesnake was able to perform steady-state, transient and eigenvalue calculations for the multigroup radiation transport equations. Various discretization schemes, including continuous finite element method (FEM) with discrete ordinates method (SN) and spherical harmonics expansion method (PN) for the self-adjoint angular flux (SAAF) formulation, continuous FEM (CFEM) with SN for the least square (LS) formulation, diffusion approximation with CFEM and discontinuous FEM (DFEM), have been implemented. A separate toolkit, YAKXS, for multigroup cross section management was developed to supportmore » Rattlesnake calculations with feedback both from changes in the field variables, such as fuel temperature, coolant density, and etc., and in isotope inventory. The framework for doing nonlinear diffusion acceleration (NDA) within Rattlesnake has been set up, and both NDA calculations with SAAF-SN-CFEM scheme and Monte Carlo with OpenMC have been performed. It was also used for coupling BISON and RELAP-7 for the full-core multiphysics simulations. Within the last fiscal year, significant improvements have been made in Rattlesnake. Rattlesnake development was migrated into our internal GITLAB development environment at the end of year 2014. Since then total 369 merge requests has been accepted into Rattlesnake. It is noted that the MOOSE framework that Rattlesnake is based on is under continuous developments. Improvements made in MOOSE can improve the Rattlesnake. It is acknowledged that MOOSE developers spent efforts on patching Rattlesnake for the improvements made on the framework side. This report will not cover the code restructuring for better readability and modularity and documentation improvements, which we have spent tremendous effort on. It only details some of improvements in the following sections.« less

Metabolic Flux Analysis in Isotope Labeling Experiments Using the Adjoint Approach.

PubMed

Mottelet, Stephane; Gaullier, Gil; Sadaka, Georges

2017-01-01

Comprehension of metabolic pathways is considerably enhanced by metabolic flux analysis (MFA-ILE) in isotope labeling experiments. The balance equations are given by hundreds of algebraic (stationary MFA) or ordinary differential equations (nonstationary MFA), and reducing the number of operations is therefore a crucial part of reducing the computation cost. The main bottleneck for deterministic algorithms is the computation of derivatives, particularly for nonstationary MFA. In this article, we explain how the overall identification process may be speeded up by using the adjoint approach to compute the gradient of the residual sum of squares. The proposed approach shows significant improvements in terms of complexity and computation time when it is compared with the usual (direct) approach. Numerical results are obtained for the central metabolic pathways of Escherichia coli and are validated against reference software in the stationary case. The methods and algorithms described in this paper are included in the sysmetab software package distributed under an Open Source license at http://forge.scilab.org/index.php/p/sysmetab/.

Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation

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

Goffin, Mark A., E-mail: mark.a.goffin@gmail.com; Buchan, Andrew G.; Dargaville, Steven

2015-01-15

A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specifiedmore » functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.« less

Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods

NASA Astrophysics Data System (ADS)

Liu, Qinya; Tromp, Jeroen

2008-07-01

We determine adjoint equations and Fréchet kernels for global seismic wave propagation based upon a Lagrange multiplier method. We start from the equations of motion for a rotating, self-gravitating earth model initially in hydrostatic equilibrium, and derive the corresponding adjoint equations that involve motions on an earth model that rotates in the opposite direction. Variations in the misfit function χ then may be expressed as , where δlnm = δm/m denotes relative model perturbations in the volume V, δlnd denotes relative topographic variations on solid-solid or fluid-solid boundaries Σ, and ∇Σδlnd denotes surface gradients in relative topographic variations on fluid-solid boundaries ΣFS. The 3-D Fréchet kernel Km determines the sensitivity to model perturbations δlnm, and the 2-D kernels Kd and Kd determine the sensitivity to topographic variations δlnd. We demonstrate also how anelasticity may be incorporated within the framework of adjoint methods. Finite-frequency sensitivity kernels are calculated by simultaneously computing the adjoint wavefield forward in time and reconstructing the regular wavefield backward in time. Both the forward and adjoint simulations are based upon a spectral-element method. We apply the adjoint technique to generate finite-frequency traveltime kernels for global seismic phases (P, Pdiff, PKP, S, SKS, depth phases, surface-reflected phases, surface waves, etc.) in both 1-D and 3-D earth models. For 1-D models these adjoint-generated kernels generally agree well with results obtained from ray-based methods. However, adjoint methods do not have the same theoretical limitations as ray-based methods, and can produce sensitivity kernels for any given phase in any 3-D earth model. The Fréchet kernels presented in this paper illustrate the sensitivity of seismic observations to structural parameters and topography on internal discontinuities. These kernels form the basis of future 3-D tomographic inversions.

Classical gluon and graviton radiation from the bi-adjoint scalar double copy

NASA Astrophysics Data System (ADS)

Goldberger, Walter D.; Prabhu, Siddharth G.; Thompson, Jedidiah O.

2017-09-01

We find double-copy relations between classical radiating solutions in Yang-Mills theory coupled to dynamical color charges and their counterparts in a cubic bi-adjoint scalar field theory which interacts linearly with particles carrying bi-adjoint charge. The particular color-to-kinematics replacements we employ are motivated by the Bern-Carrasco-Johansson double-copy correspondence for on-shell amplitudes in gauge and gravity theories. They are identical to those recently used to establish relations between classical radiating solutions in gauge theory and in dilaton gravity. Our explicit bi-adjoint solutions are constructed to second order in a perturbative expansion, and map under the double copy onto gauge theory solutions which involve at most cubic gluon self-interactions. If the correspondence is found to persist to higher orders in perturbation theory, our results suggest the possibility of calculating gravitational radiation from colliding compact objects, directly from a scalar field with vastly simpler (purely cubic) Feynman vertices.

Transmutation approximations for the application of hybrid Monte Carlo/deterministic neutron transport to shutdown dose rate analysis

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

Biondo, Elliott D.; Wilson, Paul P. H.

In fusion energy systems (FES) neutrons born from burning plasma activate system components. The photon dose rate after shutdown from resulting radionuclides must be quantified. This shutdown dose rate (SDR) is calculated by coupling neutron transport, activation analysis, and photon transport. The size, complexity, and attenuating configuration of FES motivate the use of hybrid Monte Carlo (MC)/deterministic neutron transport. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) method can be used to optimize MC neutron transport for coupled multiphysics problems, including SDR analysis, using deterministic estimates of adjoint flux distributions. When used for SDR analysis, MS-CADIS requires the formulation ofmore » an adjoint neutron source that approximates the transmutation process. In this work, transmutation approximations are used to derive a solution for this adjoint neutron source. It is shown that these approximations are reasonably met for typical FES neutron spectra and materials over a range of irradiation scenarios. When these approximations are met, the Groupwise Transmutation (GT)-CADIS method, proposed here, can be used effectively. GT-CADIS is an implementation of the MS-CADIS method for SDR analysis that uses a series of single-energy-group irradiations to calculate the adjoint neutron source. For a simple SDR problem, GT-CADIS provides speedups of 200 100 relative to global variance reduction with the Forward-Weighted (FW)-CADIS method and 9 ± 5 • 104 relative to analog. As a result, this work shows that GT-CADIS is broadly applicable to FES problems and will significantly reduce the computational resources necessary for SDR analysis.« less

Transmutation approximations for the application of hybrid Monte Carlo/deterministic neutron transport to shutdown dose rate analysis

DOE PAGES

Biondo, Elliott D.; Wilson, Paul P. H.

2017-05-08

In fusion energy systems (FES) neutrons born from burning plasma activate system components. The photon dose rate after shutdown from resulting radionuclides must be quantified. This shutdown dose rate (SDR) is calculated by coupling neutron transport, activation analysis, and photon transport. The size, complexity, and attenuating configuration of FES motivate the use of hybrid Monte Carlo (MC)/deterministic neutron transport. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) method can be used to optimize MC neutron transport for coupled multiphysics problems, including SDR analysis, using deterministic estimates of adjoint flux distributions. When used for SDR analysis, MS-CADIS requires the formulation ofmore » an adjoint neutron source that approximates the transmutation process. In this work, transmutation approximations are used to derive a solution for this adjoint neutron source. It is shown that these approximations are reasonably met for typical FES neutron spectra and materials over a range of irradiation scenarios. When these approximations are met, the Groupwise Transmutation (GT)-CADIS method, proposed here, can be used effectively. GT-CADIS is an implementation of the MS-CADIS method for SDR analysis that uses a series of single-energy-group irradiations to calculate the adjoint neutron source. For a simple SDR problem, GT-CADIS provides speedups of 200 100 relative to global variance reduction with the Forward-Weighted (FW)-CADIS method and 9 ± 5 • 104 relative to analog. As a result, this work shows that GT-CADIS is broadly applicable to FES problems and will significantly reduce the computational resources necessary for SDR analysis.« less

Quadratic Finite Element Method for 1D Deterministic Transport

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

Tolar, Jr., D R; Ferguson, J M

2004-01-06

In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

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

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

A time-dependent neutron transport method of characteristics formulation with time derivative propagation

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

Hoffman, Adam J., E-mail: adamhoff@umich.edu; Lee, John C., E-mail: jcl@umich.edu

2016-02-15

A new time-dependent Method of Characteristics (MOC) formulation for nuclear reactor kinetics was developed utilizing angular flux time-derivative propagation. This method avoids the requirement of storing the angular flux at previous points in time to represent a discretized time derivative; instead, an equation for the angular flux time derivative along 1D spatial characteristics is derived and solved concurrently with the 1D transport characteristic equation. This approach allows the angular flux time derivative to be recast principally in terms of the neutron source time derivatives, which are approximated to high-order accuracy using the backward differentiation formula (BDF). This approach, called Sourcemore » Derivative Propagation (SDP), drastically reduces the memory requirements of time-dependent MOC relative to methods that require storing the angular flux. An SDP method was developed for 2D and 3D applications and implemented in the computer code DeCART in 2D. DeCART was used to model two reactor transient benchmarks: a modified TWIGL problem and a C5G7 transient. The SDP method accurately and efficiently replicated the solution of the conventional time-dependent MOC method using two orders of magnitude less memory.« less

The three-dimensional angular widths of CMEs and their relations to the source regions

NASA Astrophysics Data System (ADS)

Zhao, X.; Feng, X. S.

2017-12-01

The angular width of a coronal mass ejection (CME) is an important factor to determine whether the corresponding interplanetary CME (ICME) and its preceding shock will reach our Earth. However, very few studies are involved to study the decisive factors of the CME's angular width. In this study, we use the three-dimensional (3D) angular width of CMEs obtained from the Graduated Cylindrical Shell (GCS) model based on observations of Solar Terrestrial Relations Observatory (STEREO) to study the relations between the CME's 3D width and characteristics of the CME's source region. We find that for the CMEs produced by active regions (ARs), the CME width has some correlations with the AR's area and flux, but these correlations are not strong. The magnetic flux contained in the CME seems to come from only part of the AR's total flux. For the CMEs produced by flare regions, the correlations between the CME angular width and the flare region's area and flux are strong. The magnetic flux within those CMEs seems to totally (even not enough) come from the flare region. Our findings prefer to support that the CME's 3D angular width can be generally estimated based on observations of Solar Dynamics Observatory (SDO) for its source region instead of the observations from coronagraphs onboard Solar and Heliospheric Observatory (SOHO) and STEREO.

Gauge transformations for twisted spectral triples

NASA Astrophysics Data System (ADS)

Landi, Giovanni; Martinetti, Pierre

2018-05-01

It is extended to twisted spectral triples the fluctuations of the metric as bounded perturbations of the Dirac operator that arises when a spectral triple is exported between Morita equivalent algebras, as well as gauge transformations which are obtained by the action of the unitary endomorphisms of the module implementing the Morita equivalence. It is firstly shown that the twisted-gauged Dirac operators, previously introduced to generate an extra scalar field in the spectral description of the standard model of elementary particles, in fact follow from Morita equivalence between twisted spectral triples. The law of transformation of the gauge potentials turns out to be twisted in a natural way. In contrast with the non-twisted case, twisted fluctuations do not necessarily preserve the self-adjointness of the Dirac operator. For a self-Morita equivalence, conditions are obtained in order to maintain self-adjointness that are solved explicitly for the minimal twist of a Riemannian manifold.

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

Favorite, Jeffrey A.

In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, k effmore » of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.« less

Dependence of the Peak Fluxes of Solar Energetic Particles on CME 3D Parameters from STEREO and SOHO

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

Park, Jinhye; Moon, Y.-J.; Lee, Harim, E-mail: jinhye@khu.ac.kr

We investigate the relationships between the peak fluxes of 18 solar energetic particle (SEP) events and associated coronal mass ejection (CME) 3D parameters (speed, angular width, and separation angle) obtained from SOHO , and STEREO-A / B for the period from 2010 August to 2013 June. We apply the STEREO CME Analysis Tool (StereoCAT) to the SEP-associated CMEs to obtain 3D speeds and 3D angular widths. The separation angles are determined as the longitudinal angles between flaring regions and magnetic footpoints of the spacecraft, which are calculated by the assumption of a Parker spiral field. The main results are asmore » follows. (1) We find that the dependence of the SEP peak fluxes on CME 3D speed from multiple spacecraft is similar to that on CME 2D speed. (2) There is a positive correlation between SEP peak flux and 3D angular width from multiple spacecraft, which is much more evident than the relationship between SEP peak flux and 2D angular width. (3) There is a noticeable anti-correlation ( r = −0.62) between SEP peak flux and separation angle. (4) The multiple-regression method between SEP peak fluxes and CME 3D parameters shows that the longitudinal separation angle is the most important parameter, and the CME 3D speed is secondary on SEP peak flux.« less

Time Operator in Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

Khorasani, Sina

2017-07-01

It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

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

Bagarello, F., E-mail: fabio.bagarello@unipa.it

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we willmore » find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.« less

Modal expansions for infrasound propagation and their implications for ground-to-ground propagation.

PubMed

Waxler, Roger; Assink, Jelle; Velea, Doru

2017-02-01

The use of expansions in vertical eigenmodes for long range infrasound propagation modeling in the effective sound speed approximation is investigated. The question of convergence of such expansions is related to the maximum elevation angles that are required. Including atmospheric attenuation leads to a non-self-adjoint vertical eigenvalue problem. The use of leading order perturbation theory for the modal attenuation is compared to the results of numerical solutions to the non-self-adjoint eigenvalue problem and conditions under which the perturbative result is expected to be valid are obtained. Modal expansions are obtained in the frequency domain; broadband signals must be modeled through Fourier reconstruction. Such broadband signal reconstruction is investigated and the relation between bandwidth, wavetrain duration, and frequency sampling is discussed.

Assimilation of seasonal chlorophyll and nutrient data into an adjoint three-dimensional ocean carbon cycle model: Sensitivity analysis and ecosystem parameter optimization

NASA Astrophysics Data System (ADS)

Tjiputra, Jerry F.; Polzin, Dierk; Winguth, Arne M. E.

2007-03-01

An adjoint method is applied to a three-dimensional global ocean biogeochemical cycle model to optimize the ecosystem parameters on the basis of SeaWiFS surface chlorophyll observation. We showed with identical twin experiments that the model simulated chlorophyll concentration is sensitive to perturbation of phytoplankton and zooplankton exudation, herbivore egestion as fecal pellets, zooplankton grazing, and the assimilation efficiency parameters. The assimilation of SeaWiFS chlorophyll data significantly improved the prediction of chlorophyll concentration, especially in the high-latitude regions. Experiments that considered regional variations of parameters yielded a high seasonal variance of ecosystem parameters in the high latitudes, but a low variance in the tropical regions. These experiments indicate that the adjoint model is, despite the many uncertainties, generally capable to optimize sensitive parameters and carbon fluxes in the euphotic zone. The best fit regional parameters predict a global net primary production of 36 Pg C yr-1, which lies within the range suggested by Antoine et al. (1996). Additional constraints of nutrient data from the World Ocean Atlas showed further reduction in the model-data misfit and that assimilation with extensive data sets is necessary.

Gradient-based Optimization for Poroelastic and Viscoelastic MR Elastography

PubMed Central

Tan, Likun; McGarry, Matthew D.J.; Van Houten, Elijah E.W.; Ji, Ming; Solamen, Ligin; Weaver, John B.

2017-01-01

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized ‘adjoint method’ based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation. PMID:27608454

Time-dependent polar distribution of outgassing from a spacecraft

NASA Technical Reports Server (NTRS)

Scialdone, J. J.

1974-01-01

A technique has been developed to obtain a characterization of the self-generated environment of a spacecraft and its variation with time, angular position, and distance. The density, pressure, outgassing flux, total weight loss, and other important parameters were obtained from data provided by two mass measuring crystal microbalances, mounted back to back, at distance of 1 m from the spacecraft equivalent surface. A major outgassing source existed at an angular position of 300 deg to 340 deg, near the rocket motor, while the weakest source was at the antennas. The strongest source appeared to be caused by a material diffusion process which produced a directional density at 1 m distance of about 1.6 x 10 to the 11th power molecules/cu cm after 1 hr in vacuum and decayed to 1.6 x 10 to the 9th power molecules/cu cm after 200 hr. The total average outgassing flux at the same distance and during the same time span changed from 1.2 x 10 to the minus 7th power to 1.4 x to the minus 10th power g/sq cm/s. These values are three times as large at the spacecraft surface. Total weight loss was 537 g after 10 hr and about 833 g after 200 hr. Self-contamination of the spacecraft was equivalent to that in orbit at about 300-km altitude.

Asymptotic, multigroup flux reconstruction and consistent discontinuity factors

DOE PAGES

Trahan, Travis J.; Larsen, Edward W.

2015-05-12

Recent theoretical work has led to an asymptotically derived expression for reconstructing the neutron flux from lattice functions and multigroup diffusion solutions. The leading-order asymptotic term is the standard expression for flux reconstruction, i.e., it is the product of a shape function, obtained through a lattice calculation, and the multigroup diffusion solution. The first-order asymptotic correction term is significant only where the gradient of the diffusion solution is not small. Inclusion of this first-order correction term can significantly improve the accuracy of the reconstructed flux. One may define discontinuity factors (DFs) to make certain angular moments of the reconstructed fluxmore » continuous across interfaces between assemblies in 1-D. Indeed, the standard assembly discontinuity factors make the zeroth moment (scalar flux) of the reconstructed flux continuous. The inclusion of the correction term in the flux reconstruction provides an additional degree of freedom that can be used to make two angular moments of the reconstructed flux continuous across interfaces by using current DFs in addition to flux DFs. Thus, numerical results demonstrate that using flux and current DFs together can be more accurate than using only flux DFs, and that making the second angular moment continuous can be more accurate than making the zeroth moment continuous.« less

Correlation between Angular Widths of CMEs and Characteristics of Their Source Regions

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

Zhao, X. H.; Feng, X. S.; Feng, H. Q.

The angular width of a coronal mass ejection (CME) is an important factor in determining whether the corresponding interplanetary CME (ICME) and its preceding shock will reach Earth. However, there have been very few studies of the decisive factors of the CME’s angular width. In this study, we use the three-dimensional (3D) angular width of CMEs obtained from the Graduated Cylindrical Shell model based on observations of Solar Terrestrial Relations Observatory ( STEREO ) to study the relations between the CME’s 3D width and characteristics of the CME’s source region. We find that for the CMEs produced by active regionsmore » (ARs), the CME width has some correlations with the AR’s area and flux, but these correlations are not strong. The magnetic flux contained in the CME seems to come from only part of the AR’s total flux. For the CMEs produced by flare regions, the correlations between the CME angular width and the flare region’s area and flux are strong. The magnetic flux within those CMEs seems to come from the whole flare region or even from a larger region than the flare. Our findings show that the CME’s 3D angular width can be generally estimated based on observations of Solar Dynamics Observatory for the CME’s source region instead of the observations from coronagraphs on board the Solar and Heliospheric Observatory and STEREO if the two foot points of the CME stay in the same places with no expansion of the CME in the transverse direction until reaching Earth.« less

Numerical Study of Hydrothermal Wave Suppression in Thermocapillary Flow Using a Predictive Control Method

NASA Astrophysics Data System (ADS)

Muldoon, F. H.

2018-04-01

Hydrothermal waves in flows driven by thermocapillary and buoyancy effects are suppressed by applying a predictive control method. Hydrothermal waves arise in the manufacturing of crystals, including the "open boat" crystal growth process, and lead to undesirable impurities in crystals. The open boat process is modeled using the two-dimensional unsteady incompressible Navier-Stokes equations under the Boussinesq approximation and the linear approximation of the surface thermocapillary force. The flow is controlled by a spatially and temporally varying heat flux density through the free surface. The heat flux density is determined by a conjugate gradient optimization algorithm. The gradient of the objective function with respect to the heat flux density is found by solving adjoint equations derived from the Navier-Stokes ones in the Boussinesq approximation. Special attention is given to heat flux density distributions over small free-surface areas and to the maximum admissible heat flux density.

Partitioning technique for open systems

NASA Astrophysics Data System (ADS)

Brändas, Erkki J.

2010-11-01

The focus of the present contribution is essentially confined to three research areas carried out during the author's turns as visiting (assistant, associate and full) professor at the University of Florida's Quantum Theory Project, QTP. The first two topics relate to perturbation theory and spectral theory for self-adjoint operators in Hilbert space. The third subject concerns analytic extensions to non-self-adjoint problems, where particular consequences of the occurrence of continuous energy spectra are measured. In these studies general partitioning methods serve as general cover for perturbation-, variational- and general matrix theory. In addition we follow up associated inferences for the time dependent problem as well as recent results and conclusions of a rather general yet surprising character. Although the author spent most of his times at QTP during visits in the 1970s and 1980s, collaborations with department members and shorter stays continued through later decades. Nevertheless the impact must be somewhat fragmentary, yet it is hoped that the present account is sufficiently self-contained to be realistic and constructive.

Self similar flow behind an exponential shock wave in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux

NASA Astrophysics Data System (ADS)

Bajargaan, Ruchi; Patel, Arvind

2018-04-01

One-dimensional unsteady adiabatic flow behind an exponential shock wave propagating in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux, which has exponentially varying azimuthal and axial fluid velocities, is investigated. The shock wave is driven out by a piston moving with time according to an exponential law. The dusty gas is taken to be a mixture of a non-ideal gas and small solid particles. The density of the ambient medium is assumed to be constant. The equilibrium flow conditions are maintained and energy is varying exponentially, which is continuously supplied by the piston. The heat conduction is expressed in the terms of Fourier's law, and the radiation is assumed of diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density according to a power law. The effects of the variation of heat transfer parameters, gravitation parameter and dusty gas parameters on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail. It is interesting to note that the similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the self gravitation, heat conduction and radiation heat flux.

Analysis of Seasonal Chlorophyll-a Using An Adjoint Three-Dimensional Ocean Carbon Cycle Model

NASA Astrophysics Data System (ADS)

Tjiputra, J.; Winguth, A.; Polzin, D.

2004-12-01

The misfit between numerical ocean model and observations can be reduced using data assimilation. This can be achieved by optimizing the model parameter values using adjoint model. The adjoint model minimizes the model-data misfit by estimating the sensitivity or gradient of the cost function with respect to initial condition, boundary condition, or parameters. The adjoint technique was used to assimilate seasonal chlorophyll-a data from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) satellite to a marine biogeochemical model HAMOCC5.1. An Identical Twin Experiment (ITE) was conducted to test the robustness of the model and the non-linearity level of the forward model. The ITE experiment successfully recovered most of the perturbed parameter to their initial values, and identified the most sensitive ecosystem parameters, which contribute significantly to model-data bias. The regional assimilations of SeaWiFS chlorophyll-a data into the model were able to reduce the model-data misfit (i.e. the cost function) significantly. The cost function reduction mostly occurred in the high latitudes (e.g. the model-data misfit in the northern region during summer season was reduced by 54%). On the other hand, the equatorial regions appear to be relatively stable with no strong reduction in cost function. The optimized parameter set is used to forecast the carbon fluxes between marine ecosystem compartments (e.g. Phytoplankton, Zooplankton, Nutrients, Particulate Organic Carbon, and Dissolved Organic Carbon). The a posteriori model run using the regional best-fit parameterization yields approximately 36 PgC/yr of global net primary productions in the euphotic zone.

Multimodel methods for optimal control of aeroacoustics.

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

Chen, Guoquan; Collis, Samuel Scott

2005-01-01

A new multidomain/multiphysics computational framework for optimal control of aeroacoustic noise has been developed based on a near-field compressible Navier-Stokes solver coupled with a far-field linearized Euler solver both based on a discontinuous Galerkin formulation. In this approach, the coupling of near- and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources. For optimal control, gradient information is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far-field to the near-field. This computational framework has been successfully appliedmore » to study optimal boundary-control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing. In the model-problem presented here, the noise propagated toward the ground is reduced by 12dB.« less

Automated variance reduction for MCNP using deterministic methods.

PubMed

Sweezy, J; Brown, F; Booth, T; Chiaramonte, J; Preeg, B

2005-01-01

In order to reduce the user's time and the computer time needed to solve deep penetration problems, an automated variance reduction capability has been developed for the MCNP Monte Carlo transport code. This new variance reduction capability developed for MCNP5 employs the PARTISN multigroup discrete ordinates code to generate mesh-based weight windows. The technique of using deterministic methods to generate importance maps has been widely used to increase the efficiency of deep penetration Monte Carlo calculations. The application of this method in MCNP uses the existing mesh-based weight window feature to translate the MCNP geometry into geometry suitable for PARTISN. The adjoint flux, which is calculated with PARTISN, is used to generate mesh-based weight windows for MCNP. Additionally, the MCNP source energy spectrum can be biased based on the adjoint energy spectrum at the source location. This method can also use angle-dependent weight windows.

The current impact flux on Mars and its seasonal variation

NASA Astrophysics Data System (ADS)

JeongAhn, Youngmin; Malhotra, Renu

2015-12-01

We calculate the present-day impact flux on Mars and its variation over the martian year, using the current data on the orbital distribution of known Mars-crossing minor planets. We adapt the Öpik-Wetherill formulation for calculating collision probabilities, paying careful attention to the non-uniform distribution of the perihelion longitude and the argument of perihelion owed to secular planetary perturbations. We find that, at the current epoch, the Mars crossers have an axial distribution of the argument of perihelion, and the mean direction of their eccentricity vectors is nearly aligned with Mars' eccentricity vector. These previously neglected angular non-uniformities have the effect of depressing the mean annual impact flux by a factor of about 2 compared to the estimate based on a uniform random distribution of the angular elements of Mars-crossers; the amplitude of the seasonal variation of the impact flux is likewise depressed by a factor of about 4-5. We estimate that the flux of large impactors (of absolute magnitude H < 16) within ±30° of Mars' aphelion is about three times larger than when the planet is near perihelion. Extrapolation of our results to a model population of meter-size Mars-crossers shows that if these small impactors have a uniform distribution of their angular elements, then their aphelion-to-perihelion impact flux ratio would be 11-15, but if they track the orbital distribution of the large impactors, including their non-uniform angular elements, then this ratio would be about 3. Comparison of our results with the current dataset of fresh impact craters on Mars (detected with Mars-orbiting spacecraft) appears to rule out the uniform distribution of angular elements.

Axisymmetric problem of fretting wear for a foundation with a nonuniform coating and rough punch

NASA Astrophysics Data System (ADS)

Manzhirov, A. V.; Kazakov, K. E.

2018-05-01

The axisymmetric contact problem with fretting wear for an elastic foundation with a longitudinally nonuniform (surface nonuniform) coating and a rigid punch with a rough foundation has been solved for the first time. The case of linear wear is considered. The nonuniformity of the coating and punch roughness are described by a different rapidly changing functions. This strong nonuniformity arises when coatings are deposited using modern additive manufacturing technologies. The problem is reduced the solution of an integral equation with two different integral operators: a compact self-adjoint positively defined operator with respect to the coordinate and the non-self-adjoint integral Volterra operator with respect to time. The solution is obtained in series using the projection method of the authors. The efficiency of the proposed approach for constructing a high-accuracy approximate solution to the problem (with only a few expansion terms retained) is demonstrated.

Periodic differential equations with self-adjoint monodromy operator

NASA Astrophysics Data System (ADS)

Yudovich, V. I.

2001-04-01

A linear differential equation \\dot u=A(t)u with p-periodic (generally speaking, unbounded) operator coefficient in a Euclidean or a Hilbert space \\mathbb H is considered. It is proved under natural constraints that the monodromy operator U_p is self-adjoint and strictly positive if A^*(-t)=A(t) for all t\\in\\mathbb R.It is shown that Hamiltonian systems in the class under consideration are usually unstable and, if they are stable, then the operator U_p reduces to the identity and all solutions are p-periodic.For higher frequencies averaged equations are derived. Remarkably, high-frequency modulation may double the number of critical values.General results are applied to rotational flows with cylindrical components of the velocity a_r=a_z=0, a_\\theta=\\lambda c(t)r^\\beta, \\beta<-1, c(t) is an even p-periodic function, and also to several problems of free gravitational convection of fluids in periodic fields.

Quantum space and quantum completeness

NASA Astrophysics Data System (ADS)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Receptivity of a precessing vortex core to open-loop forcing in a swirling jet and its predictability by linear stability adjoint theory

NASA Astrophysics Data System (ADS)

Müller, Jens; Lückoff, Finn; Oberleithner, Kilian

2017-11-01

The precessing vortex core (PVC) is a dominant coherent structure which occurs in swirling jets such as in swirl-stabilised gas turbine combustors. It stems from a global hydrodynamic instability caused by an internal feedback mechanism within the jet core. In this work, open-loop forcing is applied to a generic non-reacting swirling jet to investigate its receptivity to external actuation regarding lock-in behaviour of the PVC for different streamwise positions and Reynolds numbers. The forcing is periodically exerted by zero net mass flux synthetic jets which are introduced radially through slits inside the duct walls upstream of the swirling jet's exit plane. Time-resolved pressure measurements are conducted to identify the PVC frequency and stereo PIV combined with proper orthogonal decomposition in the duct and free field is used to extract the mean flow and the PVC mode. The data is used in a global linear stability framework to gain the adjoint of the PVC which reveals the regions of highest receptivity to periodic forcing based on mean flow input only. This theoretical receptivity model is compared with the experimentally obtained receptivity results and the validity and applicability of the adjoint model for the prediction of optimal forcing positions is discussed.

Improving the Fit of a Land-Surface Model to Data Using its Adjoint

NASA Astrophysics Data System (ADS)

Raoult, N.; Jupp, T. E.; Cox, P. M.; Luke, C.

2015-12-01

Land-surface models (LSMs) are of growing importance in the world of climate prediction. They are crucial components of larger Earth system models that are aimed at understanding the effects of land surface processes on the global carbon cycle. The Joint UK Land Environment Simulator (JULES) is the land-surface model used by the UK Met Office. It has been automatically differentiated using commercial software from FastOpt, resulting in an analytical gradient, or 'adjoint', of the model. Using this adjoint, the adJULES parameter estimation system has been developed, to search for locally optimum parameter sets by calibrating against observations. adJULES presents an opportunity to confront JULES with many different observations, and make improvements to the model parameterisation. In the newest version of adJULES, multiple sites can be used in the calibration, to giving a generic set of parameters that can be generalised over plant functional types. We present an introduction to the adJULES system and its applications to data from a variety of flux tower sites. We show that calculation of the 2nd derivative of JULES allows us to produce posterior probability density functions of the parameters and how knowledge of parameter values is constrained by observations.

New biorthogonality relations for inhomogeneous biisotropic planar waveguides

NASA Astrophysics Data System (ADS)

Topa, Antonio L.; Paiva, Carlos R.; Barbosa, Afonso M.

1994-04-01

Using a linear operator formalism this paper presents new biorthogonality relations for the hybrid modes supported by planar waveguides inhomogeneously filled with general biisotropic media. In the special case of lossless biisotropic media, the linear operator is self-adjoint, the original and adjoint waveguides are identical, and new orthogonality relations can be derived. As an example of application, the radiation modes of a grounded nonreciprocal and lossless biisotropic slab waveguide are analyzed in terms of a pair of incident transverse electric (ITE) and incident transverse magnetic (ITM) continuous modes, which have the advantage of being mutually orthogonal and of having a clear physical interpretation.

The fast neutron fluence and the activation detector activity calculations using the effective source method and the adjoint function

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

Hep, J.; Konecna, A.; Krysl, V.

2011-07-01

This paper describes the application of effective source in forward calculations and the adjoint method to the solution of fast neutron fluence and activation detector activities in the reactor pressure vessel (RPV) and RPV cavity of a VVER-440 reactor. Its objective is the demonstration of both methods on a practical task. The effective source method applies the Boltzmann transport operator to time integrated source data in order to obtain neutron fluence and detector activities. By weighting the source data by time dependent decay of the detector activity, the result of the calculation is the detector activity. Alternatively, if the weightingmore » is uniform with respect to time, the result is the fluence. The approach works because of the inherent linearity of radiation transport in non-multiplying time-invariant media. Integrated in this way, the source data are referred to as the effective source. The effective source in the forward calculations method thereby enables the analyst to replace numerous intensive transport calculations with a single transport calculation in which the time dependence and magnitude of the source are correctly represented. In this work, the effective source method has been expanded slightly in the following way: neutron source data were performed with few group method calculation using the active core calculation code MOBY-DICK. The follow-up neutron transport calculation was performed using the neutron transport code TORT to perform multigroup calculations. For comparison, an alternative method of calculation has been used based upon adjoint functions of the Boltzmann transport equation. Calculation of the three-dimensional (3-D) adjoint function for each required computational outcome has been obtained using the deterministic code TORT and the cross section library BGL440. Adjoint functions appropriate to the required fast neutron flux density and neutron reaction rates have been calculated for several significant points within the RPV and RPV cavity of the VVER-440 reacto rand located axially at the position of maximum power and at the position of the weld. Both of these methods (the effective source and the adjoint function) are briefly described in the present paper. The paper also describes their application to the solution of fast neutron fluence and detectors activities for the VVER-440 reactor. (authors)« less

PWR Facility Dose Modeling Using MCNP5 and the CADIS/ADVANTG Variance-Reduction Methodology

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

Blakeman, Edward D; Peplow, Douglas E.; Wagner, John C

2007-09-01

The feasibility of modeling a pressurized-water-reactor (PWR) facility and calculating dose rates at all locations within the containment and adjoining structures using MCNP5 with mesh tallies is presented. Calculations of dose rates resulting from neutron and photon sources from the reactor (operating and shut down for various periods) and the spent fuel pool, as well as for the photon source from the primary coolant loop, were all of interest. Identification of the PWR facility, development of the MCNP-based model and automation of the run process, calculation of the various sources, and development of methods for visually examining mesh tally filesmore » and extracting dose rates were all a significant part of the project. Advanced variance reduction, which was required because of the size of the model and the large amount of shielding, was performed via the CADIS/ADVANTG approach. This methodology uses an automatically generated three-dimensional discrete ordinates model to calculate adjoint fluxes from which MCNP weight windows and source bias parameters are generated. Investigative calculations were performed using a simple block model and a simplified full-scale model of the PWR containment, in which the adjoint source was placed in various regions. In general, it was shown that placement of the adjoint source on the periphery of the model provided adequate results for regions reasonably close to the source (e.g., within the containment structure for the reactor source). A modification to the CADIS/ADVANTG methodology was also studied in which a global adjoint source is weighted by the reciprocal of the dose response calculated by an earlier forward discrete ordinates calculation. This method showed improved results over those using the standard CADIS/ADVANTG approach, and its further investigation is recommended for future efforts.« less

A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics

NASA Technical Reports Server (NTRS)

Gingold, H.

1991-01-01

A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.

Ammonia emissions in the United States, European Union, and China derived by high-resolution inversion of ammonium wet deposition data: Interpretation with a new agricultural emissions inventory (MASAGE_NH3)

EPA Science Inventory

We use the adjoint of a global 3-D chemical transport model (GEOS-Chem) to optimizeammonia (NH_{3+4 wet deposition fluxes. Optimized emissions are derive...}

Top-of-atmosphere radiative fluxes - Validation of ERBE scanner inversion algorithm using Nimbus-7 ERB data

NASA Technical Reports Server (NTRS)

Suttles, John T.; Wielicki, Bruce A.; Vemury, Sastri

1992-01-01

The ERBE algorithm is applied to the Nimbus-7 earth radiation budget (ERB) scanner data for June 1979 to analyze the performance of an inversion method in deriving top-of-atmosphere albedos and longwave radiative fluxes. The performance is assessed by comparing ERBE algorithm results with appropriate results derived using the sorting-by-angular-bins (SAB) method, the ERB MATRIX algorithm, and the 'new-cloud ERB' (NCLE) algorithm. Comparisons are made for top-of-atmosphere albedos, longwave fluxes, viewing zenith-angle dependence of derived albedos and longwave fluxes, and cloud fractional coverage. Using the SAB method as a reference, the rms accuracy of monthly average ERBE-derived results are estimated to be 0.0165 (5.6 W/sq m) for albedos (shortwave fluxes) and 3.0 W/sq m for longwave fluxes. The ERBE-derived results were found to depend systematically on the viewing zenith angle, varying from near nadir to near the limb by about 10 percent for albedos and by 6-7 percent for longwave fluxes. Analyses indicated that the ERBE angular models are the most likely source of the systematic angular dependences. Comparison of the ERBE-derived cloud fractions, based on a maximum-likelihood estimation method, with results from the NCLE showed agreement within about 10 percent.

Empirical Bolometric Fluxes and Angular Diameters of 1.6 Million Tycho-2 Stars and Radii of 350,000 Stars with Gaia DR1 Parallaxes

NASA Astrophysics Data System (ADS)

Stevens, Daniel J.; Stassun, Keivan G.; Gaudi, B. Scott

2017-12-01

We present bolometric fluxes and angular diameters for over 1.6 million stars in the Tycho-2 catalog, determined using previously determined empirical color-temperature and color-flux relations. We vet these relations via full fits to the full broadband spectral energy distributions for a subset of benchmark stars and perform quality checks against the large set of stars for which spectroscopically determined parameters are available from LAMOST, RAVE, and/or APOGEE. We then estimate radii for the 355,502 Tycho-2 stars in our sample whose Gaia DR1 parallaxes are precise to ≲ 10 % . For these stars, we achieve effective temperature, bolometric flux, and angular diameter uncertainties of the order of 1%-2% and radius uncertainties of order 8%, and we explore the effect that imposing spectroscopic effective temperature priors has on these uncertainties. These stellar parameters are shown to be reliable for stars with {T}{eff} ≲ 7000 K. The over half a million bolometric fluxes and angular diameters presented here will serve as an immediate trove of empirical stellar radii with the Gaia second data release, at which point effective temperature uncertainties will dominate the radius uncertainties. Already, dwarf, subgiant, and giant populations are readily identifiable in our purely empirical luminosity-effective temperature (theoretical) Hertzsprung-Russell diagrams.

Empirical effective temperatures and bolometric corrections for early-type stars

NASA Technical Reports Server (NTRS)

Code, A. D.; Bless, R. C.; Davis, J.; Brown, R. H.

1976-01-01

An empirical effective temperature for a star can be found by measuring its apparent angular diameter and absolute flux distribution. The angular diameters of 32 bright stars in the spectral range O5f to F8 have recently been measured with the stellar interferometer at Narrabri Observatory, and their absolute flux distributions have been found by combining observations of ultraviolet flux from the Orbiting Astronomical Observatory (OAO-2) with ground-based photometry. In this paper, these data have been combined to derive empirical effective temperatures and bolometric corrections for these 32 stars.

Reynolds number scaling of the influence of boundary layers on the global behavior of laboratory quasi-Keplerian flows

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

Edlund, E. M.; Ji, H.

2015-10-06

Here, we present fluid velocity measurements in a modified Taylor-Couette device operated in the quasi-Keplerian regime, where it is observed that nearly ideal flows exhibit self-similarity under scaling of the Reynolds number. In contrast, nonideal flows show progressive departure from ideal Couette as the Reynolds number is increased. We present a model that describes the observed departures from ideal Couette rotation as a function of the fluxes of angular momentum across the boundaries, capturing the dependence on Reynolds number and boundary conditions.

Reynolds number scaling of the influence of boundary layers on the global behavior of laboratory quasi-Keplerian flows.

PubMed

Edlund, E M; Ji, H

2015-10-01

We present fluid velocity measurements in a modified Taylor-Couette device operated in the quasi-Keplerian regime, where it is observed that nearly ideal flows exhibit self-similarity under scaling of the Reynolds number. In contrast, nonideal flows show progressive departure from ideal Couette as the Reynolds number is increased. We present a model that describes the observed departures from ideal Couette rotation as a function of the fluxes of angular momentum across the boundaries, capturing the dependence on Reynolds number and boundary conditions.

Ring-Gaussian laser pulse filamentation in a self-induced diffraction waveguide

NASA Astrophysics Data System (ADS)

Geints, Yu E.; Zemlyanov, A. A.

2017-10-01

Self-action in air of a high-power femtosecond laser pulse with the spatial form of a ring-Gaussian beam (‘dressed’ beam) is studied theoretically. Pulse self-focusing and filamentation is analyzed in detail through the numerical solution of the spectral propagation equation, taking into account medium optical nonlinearity and plasma generation. Pulse propagation dynamics and energy fluxes inside the beam are visualized by means of averaged diffraction ray tracing. We clearly show that, in terms of diffraction optics, the outer ring forms a specific nonmaterial diffractive waveguide, favoring long-range self-channeling of the central part of a beam by delivering optical energy to a filament. The spatial robustness and stability of such diffractive waveguides strongly depends on the energy stored in the ring, as well as on its position relative to the beam axis. The striking advantage of such ‘dressed’ beams is their reduced angular divergence during plasma-free (post-filamentation) evolution.

A new approach for developing adjoint models

NASA Astrophysics Data System (ADS)

Farrell, P. E.; Funke, S. W.

2011-12-01

Many data assimilation algorithms rely on the availability of gradients of misfit functionals, which can be efficiently computed with adjoint models. However, the development of an adjoint model for a complex geophysical code is generally very difficult. Algorithmic differentiation (AD, also called automatic differentiation) offers one strategy for simplifying this task: it takes the abstraction that a model is a sequence of primitive instructions, each of which may be differentiated in turn. While extremely successful, this low-level abstraction runs into time-consuming difficulties when applied to the whole codebase of a model, such as differentiating through linear solves, model I/O, calls to external libraries, language features that are unsupported by the AD tool, and the use of multiple programming languages. While these difficulties can be overcome, it requires a large amount of technical expertise and an intimate familiarity with both the AD tool and the model. An alternative to applying the AD tool to the whole codebase is to assemble the discrete adjoint equations and use these to compute the necessary gradients. With this approach, the AD tool must be applied to the nonlinear assembly operators, which are typically small, self-contained units of the codebase. The disadvantage of this approach is that the assembly of the discrete adjoint equations is still very difficult to perform correctly, especially for complex multiphysics models that perform temporal integration; as it stands, this approach is as difficult and time-consuming as applying AD to the whole model. In this work, we have developed a library which greatly simplifies and automates the alternate approach of assembling the discrete adjoint equations. We propose a complementary, higher-level abstraction to that of AD: that a model is a sequence of linear solves. The developer annotates model source code with library calls that build a 'tape' of the operators involved and their dependencies, and supplies callbacks to compute the action of these operators. The library, called libadjoint, is then capable of symbolically manipulating the forward annotation to automatically assemble the adjoint equations. Libadjoint is open source, and is explicitly designed to be bolted-on to an existing discrete model. It can be applied to any discretisation, steady or time-dependent problems, and both linear and nonlinear systems. Using libadjoint has several advantages. It requires the application of an AD tool only to small pieces of code, making the use of AD far more tractable. As libadjoint derives the adjoint equations, the expertise required to develop an adjoint model is greatly diminished. One major advantage of this approach is that the model developer is freed from implementing complex checkpointing strategies for the adjoint model: libadjoint has sufficient information about the forward model to re-play the entire forward solve when necessary, and thus the checkpointing algorithm can be implemented entirely within the library itself. Examples are shown using the Fluidity/ICOM framework, a complex ocean model under development at Imperial College London.

Numerical Computation of Sensitivities and the Adjoint Approach

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael

1997-01-01

We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.

Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

NASA Technical Reports Server (NTRS)

Webb, G. M.; Jokipii, J. R.; Morfill, G. E.

1994-01-01

Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and truncated power-law sources. We conclude that it is possible to accelerate particles beyond the knee by galactic rotation, but not in sufficient number to adequately explain the observed spectrum.

Improving the Fit of a Land-Surface Model to Data Using its Adjoint

NASA Astrophysics Data System (ADS)

Raoult, Nina; Jupp, Tim; Cox, Peter; Luke, Catherine

2016-04-01

Land-surface models (LSMs) are crucial components of the Earth System Models (ESMs) which are used to make coupled climate-carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. In this study, JULES is automatically differentiated using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimation system has been developed, to search for locally optimum parameter sets by calibrating against observations. We present an introduction to the adJULES system and demonstrate its ability to improve the model-data fit using eddy covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the 5 Plant Functional Types (PFTS) in JULES. The optimised PFT-specific parameters improve the performance of JULES over 90% of the FLUXNET sites used in the study. These reductions in error are shown and compared to reductions found due to site-specific optimisations. Finally, we show that calculation of the 2nd derivative of JULES allows us to produce posterior probability density functions of the parameters and how knowledge of parameter values is constrained by observations.

Introduction to Adjoint Models

NASA Technical Reports Server (NTRS)

Errico, Ronald M.

2015-01-01

In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

Analytical solution for the advection-dispersion transport equation in layered media

USDA-ARS?s Scientific Manuscript database

The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...

Elliptic complexes over C∗-algebras of compact operators

NASA Astrophysics Data System (ADS)

Krýsl, Svatopluk

2016-03-01

For a C∗-algebra A of compact operators and a compact manifold M, we prove that the Hodge theory holds for A-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective A-Hilbert bundles over M. For these C∗-algebras and manifolds, we get a topological isomorphism between the cohomology groups of an A-elliptic complex and the space of harmonic elements of the complex. Consequently, the cohomology groups appear to be finitely generated projective C∗-Hilbert modules and especially, Banach spaces. We also prove that in the category of Hilbert A-modules and continuous adjointable Hilbert A-module homomorphisms, the property of a complex of being self-adjoint parametrix possessing characterizes the complexes of Hodge type.

Simultaneous Retrievals of Aerosol Properties Using Airborne Sun Photometer, Solar Flux Radiometer, and Satellite Radiance Data

NASA Astrophysics Data System (ADS)

Houben, H.; Bergstrom, R. W.; Russell, P. B.; Pilewskie, P.

2006-12-01

Characterization of atmospheric aerosols and their climatic effects frequently requires more information than can be gathered by a single instrument. Considerable effort must be devoted to assembling a suite of complementary instruments to make the required measurements and to the production of computational tools that can fuse the data into a coherent description of the aerosols. The twin turboprop Sky Research Jetstream-31 (J-31) has participated in a number of recent field campaigns (Intex A/ICARTT, Intex B/Milagro) with goals that include column closure studies of atmospheric radiation and satellite validation. Among the instruments on board were the 14-channel NASA Ames Airborne Tracking Sunphotometer (AATS-14, which measures the transmission of the solar beam in 14 narrow spectral channels from 354 nm to 2139 nm with bandwidths between 2 and 6 nm for most channels) and the Solar Spectral Flux Radiometer (SSFR, a moderate resolution flux [irradiance] spectrometer with a hemispheric field of view which makes simultaneous zenith and nadir measurements in the wavelength range from 300 nm to 2200 nm with spectral resolution 8--12 nm). To retrieve the data we have developed a new adjointed radiative transfer model which simultaneously predicts the direct solar beam, upwelling and downwelling fluxes at the J-31 level, and satellite radiances. The code is based on an adding-doubling formulation, with an arbitrary number of streams and azimuths. The matrix form of the model allows for straightforward (though complicated) linearized and adjoint versions. We are thus able to use data assimilation techniques to determine best-fit aerosol properties above and below the J-31 (and ocean surface albedo), based on approximately 25 independent measurements from the aircraft alone. The presence of both flux and extinction data allow the ready identification of absorbing and scattering aerosols. When column closure spirals are flown, or surface or satellite data are available, a more detailed description of the aerosol and its vertical distribution can be obtained. We believe the J-31 platform and the new radiation code constitute an important facility for the validation of satellite aerosol observations.

Pseudospectra in non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

2015-10-01

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Semi-classical analysis and pseudo-spectra

NASA Astrophysics Data System (ADS)

Davies, E. B.

We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second-order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudo-spectra and boundary conditions in the semi-classical limit.

Generalized Heisenberg algebra and (non linear) pseudo-bosons

NASA Astrophysics Data System (ADS)

Bagarello, F.; Curado, E. M. F.; Gazeau, J. P.

2018-04-01

We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given physical system. We also discuss relations with nonlinear pseudo-bosons. Several examples are discussed.

Linear Characteristic Spatial Quadrature for Discrete Ordinates Neutral Particle Transport on Arbitrary Triangles

DTIC Science & Technology

1993-06-01

1•) + ) •,(v)(•,L) = ()(Q)+ sEXT (F). (4) The scalar flux, 0, is related to the angular flux, W, by (F)= f (dQ Vh) (5) and the particle current, J...J," v,p’) u +at(U, v) w(u, U, p’)= as(u, v) O(u, v) + SEXT (uv)] (92) 0 Ul,(V) I Assuming the area of the triangle is sufficiently small that cross...M + SEXT () (98) Wvn and WoUT are angular flux averages along the input and output edges, respectively, and are defined by WD Iv = f- ds. V(s.v) (99

Adjoint affine fusion and tadpoles

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

Urichuk, Andrew, E-mail: andrew.urichuk@uleth.ca; Walton, Mark A., E-mail: walton@uleth.ca; International School for Advanced Studies

2016-06-15

We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are writtenmore » for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.« less

The Aharonov–Bohm effect in scattering theory

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

Sitenko, Yu.A., E-mail: yusitenko@bitp.kiev.ua; Vlasii, N.D.

2013-12-15

The Aharonov–Bohm effect is considered as a scattering event with nonrelativistic charged particles of the wavelength which is less than the transverse size of an impenetrable magnetic vortex. The quasiclassical WKB method is shown to be efficient in solving this scattering problem. We find that the scattering cross section consists of two terms, one describing the classical phenomenon of elastic reflection and another one describing the quantum phenomenon of diffraction; the Aharonov–Bohm effect is manifested as a fringe shift in the diffraction pattern. Both the classical and the quantum phenomena are independent of the choice of a boundary condition atmore » the vortex edge, providing that probability is conserved. We show that a propagation of charged particles can be controlled by altering the flux of a magnetic vortex placed on their way. -- Highlights: •Aharonov–Bohm effect as a scattering event. •Impenetrable magnetic vortex of nonzero transverse size. •Scattering cross section is independent of a self-adjoint extension employed. •Classical phenomenon of elastic reflection and quantum phenomenon of diffraction. •Aharonov–Bohm effect as a fringe shift in the diffraction pattern.« less

Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver

NASA Astrophysics Data System (ADS)

Paige, Cody

The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward mode ADjoint is a combination of an adjoint sensitivity analysis method with a forward mode automatic differentiation (AD) and is a modification of the reverse mode ADjoint method proposed by Mader et al.[1]. A colouring acceleration technique is presented to reduce the computational cost increase associated with forward mode AD. The forward mode AD facilitates the implementation of the laminar Navier-Stokes (NS) equations. The forward mode ADjoint method is applied to a three-dimensional computational fluid dynamics solver. The resulting Euler and viscous ADjoint sensitivities are compared to the reverse mode Euler ADjoint derivatives and a complex-step method to demonstrate the reduced computational cost and accuracy. Both comparisons demonstrate the benefits of the colouring method and the practicality of using a forward mode AD. [1] Mader, C.A., Martins, J.R.R.A., Alonso, J.J., and van der Weide, E. (2008) ADjoint: An approach for the rapid development of discrete adjoint solvers. AIAA Journal, 46(4):863-873. doi:10.2514/1.29123.

Growth dependent magnetization reversal in Co2MnAl full Heusler alloy thin films

NASA Astrophysics Data System (ADS)

Barwal, Vineet; Husain, Sajid; Behera, Nilamani; Goyat, Ekta; Chaudhary, Sujeet

2018-02-01

Angular dependent magnetization reversal has been investigated in Co2MnAl (CMA) full Heusler alloy thin films grown on Si(100) at different growth temperatures (Ts) by DC-magnetron sputtering. An M -shaped curve is observed in the in-plane angular (0°-360°) dependent coercivity (ADC) by magneto-optical Kerr effect measurements. The dependence of the magnetization reversal on Ts is investigated in detail to bring out the structure-property correlation with regards to ADC in these polycrystalline CMA thin films. This magnetization reversal ( M -shaped ADC behavior) is well described by the two-phase model, which is a combination of Kondorsky (domain wall motion) and Stoner Wohlfarth (coherent rotation) models. In this model, magnetization reversal starts with depinning of domain walls, with their gradual displacement explained by the Kondorsky model, and at a higher field (when the domain walls merge), the system follows coherent rotation before reaching its saturation following the Stoner Wohlfarth model. Further, the analysis of angular dependent squareness ratio (Mr/Ms) indicates that our films clearly exhibited twofold uniaxial anisotropy, which is related to self-steering effect arising due to the obliquely incident flux during the film-growth.

Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates

NASA Astrophysics Data System (ADS)

Wang, Mengze; Mons, Vincent; Zaki, Tamer

2017-11-01

Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak & Vinokur. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542).

Angular sensitivities of scintillator slab configurations for location of gamma ray bursts

NASA Technical Reports Server (NTRS)

Gregory, J. C.

1976-01-01

Thin flat scintillator slabs are a useful means of measuring the angular location of gamma ray fluxes of astronomical interest. A statistical estimate of position error was made of two scintillator systems suitable for gamma ray burst location from a balloon or satellite platform. A single rotating scintillator with associated flux monitor is compared with a pair of stationary orthogonal scintillators. Position error for a strong burst is of the order of a few arcmin if systematic errors are ignored.

The discrete adjoint method for parameter identification in multibody system dynamics.

PubMed

Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

2018-01-01

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

A new approach to three-dimensional neutron transport solution based on the method of characteristics and linear axial approximation

NASA Astrophysics Data System (ADS)

Zheng, Youqi; Choi, Sooyoung; Lee, Deokjung

2017-12-01

A new approach based on the method of characteristics (MOC) is proposed to solve the neutron transport equation. A new three-dimensional (3D) spatial discretization is applied to avoid the instability issue of the transverse leakage iteration of the traditional 2D/1D approach. In this new approach, the axial and radial variables are discretized in two different ways: the linear expansion is performed in the axial direction, then, the 3D solution of the angular flux is transformed to be the planar solution of 2D angular expansion moments, which are solved by the planar MOC sweeping. Based on the boundary and interface continuity conditions, the 2D expansion moment solution is equivalently transformed to be the solution of the axially averaged angular flux. Using the piecewise averaged angular flux at the top and bottom surfaces of 3D meshes, the planes are coupled to give the 3D angular flux distribution. The 3D CMFD linear system is established from the surface net current of every 3D pin-mesh to accelerate the convergence of power iteration. The STREAM code is extended to be capable of handling 3D problems based on the new approach. Several benchmarks are tested to verify its feasibility and accuracy, including the 3D homogeneous benchmarks and heterogeneous benchmarks. The computational sensitivity is discussed. The results show good accuracy in all tests. With the CMFD acceleration, the convergence is stable. In addition, a pin-cell problem with void gap is calculated. This shows the advantage compared to the traditional 2D/1D MOC methods.

Robust X-ray angular correlations for the study of meso-structures

DOE PAGES

Lhermitte, Julien R.; Tian, Cheng; Stein, Aaron; ...

2017-05-08

As self-assembling nanomaterials become more sophisticated, it is becoming increasingly important to measure the structural order of finite-sized assemblies of nano-objects. These mesoscale clusters represent an acute challenge to conventional structural probes, owing to the range of implicated size scales (10 nm to several micrometres), the weak scattering signal and the dynamic nature of meso-clusters in native solution environments. The high X-ray flux and coherence of modern synchrotrons present an opportunity to extract structural information from these challenging systems, but conventional ensemble X-ray scattering averages out crucial information about local particle configurations. Conversely, a single meso-cluster scatters too weakly tomore » recover the full diffraction pattern. Using X-ray angular cross-correlation analysis, it is possible to combine multiple noisy measurements to obtain robust structural information. This paper explores the key theoretical limits and experimental challenges that constrain the application of these methods to probing structural order in real nanomaterials. A metric is presented to quantify the signal-to-noise ratio of angular correlations, and it is used to identify several experimental artifacts that arise. In particular, it is found that background scattering, data masking and inter-cluster interference profoundly affect the quality of correlation analyses. A robust workflow is demonstrated for mitigating these effects and extracting reliable angular correlations from realistic experimental data.« less

Fast neutrino flavor conversions near the supernova core with realistic flavor-dependent angular distributions

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

Dasgupta, Basudeb; Sen, Manibrata; Mirizzi, Alessandro, E-mail: bdasgupta@theory.tifr.res.in, E-mail: alessandro.mirizzi@ba.infn.it, E-mail: manibrata.sen@gmail.com

2017-02-01

It has been recently pointed out that neutrino fluxes from a supernova can show substantial flavor conversions almost immediately above the core. Using linear stability analyses and numerical solutions of the fully nonlinear equations of motion, we perform a detailed study of these fast conversions , focussing on the region just above the supernova core. We carefully specify the instabilities for evolution in space or time, and find that neutrinos travelling towards the core make fast conversions more generic, i.e., possible for a wider range of flux ratios and angular asymmetries that produce a crossing between the zenith-angle spectra ofmore » ν {sub e} and ν-bar {sub e} . Using fluxes and angular distributions predicted by supernova simulations, we find that fast conversions can occur within tens of nanoseconds, only a few meters away from the putative neutrinospheres. If these fast flavor conversions indeed take place, they would have important implications for the supernova explosion mechanism and nucleosynthesis.« less

Frequency Domain Design of Robust Controllers for Space Structures

DTIC Science & Technology

1989-08-01

A natural assumption for structural problems [1] is that A0 is self -adjoint with compact resolvent and discrete (real) spectrum which is bounded from...the same controller using only 256 points. The curves are very similiar, but in both cases, the low frequency end of the respose is under-sampled due

Multigrid methods for bifurcation problems: The self adjoint case

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1987-01-01

This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.

Hairy black hole stability in AdS, quantum mechanics on the half-line and holography

NASA Astrophysics Data System (ADS)

Anabalón, Andrés; Astefanesei, Dumitru; Oliva, Julio

2015-10-01

We consider the linear stability of 4-dimensional hairy black holes with mixed boundary conditions in Anti-de Sitter spacetime. We focus on the mass of scalar fields around the maximally supersymmetric vacuum of the gauged N=8 supergravity in four dimensions, m 2 = -2 l -2. It is shown that the Schrödinger operator on the half-line, governing the S 2, H 2 or {{R}}^2 invariant mode around the hairy black hole, allows for non-trivial self-adjoint extensions and each of them corresponds to a class of mixed boundary conditions in the gravitational theory. Discarding the self-adjoint extensions with a negative mode impose a restriction on these boundary conditions. The restriction is given in terms of an integral of the potential in the Schrödinger operator resembling the estimate of Simon for Schrödinger operators on the real line. In the context of AdS/CFT duality, our result has a natural interpretation in terms of the field theory dual effective potential.

Constructing the spectral web of rotating plasmas

NASA Astrophysics Data System (ADS)

Goedbloed, Hans

2012-10-01

Rotating plasmas are ubiquitous in nature. The theory of MHD stability of such plasmas, initiated a long time ago, has severely suffered from the wide spread misunderstanding that it necessarily involves non-self-adjoint operators. It has been shown (J.P. Goedbloed, PPCF 16, 074001, 2011; Goedbloed, Keppens and Poedts, Advanced Magnetohydrodynamics, Cambridge, 2010) that, on the contrary, spectral theory of moving plasmas can be constructed entirely on the basis of energy conservation and self-adjointness of the occurring operators. The spectral web is a further development along this line. It involves the construction of a network of curves in the complex omega-plane associated with the complex complementary energy, which is the energy needed to maintain harmonic time dependence in an open system. Vanishing of that energy, at the intersections of the mentioned curves, yields the eigenvalues of the closed system. This permits to consider the enormous diversity of MHD instabilities of rotating tokamaks, accretion disks about compact objects, and jets emitted from those objects, from a single view point. This will be illustrated with results obtained with a new spectral code (ROC).

On quantum integrability of the Landau-Lifshitz model

NASA Astrophysics Data System (ADS)

Melikyan, A.; Pinzul, A.

2009-10-01

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Characterization of measurements in quantum communication. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chan, V. W. S.

1975-01-01

A characterization of quantum measurements by operator valued measures is presented. The generalized measurements include simultaneous approximate measurement of noncommuting observables. This characterization is suitable for solving problems in quantum communication. Two realizations of such measurements are discussed. The first is by adjoining an apparatus to the system under observation and performing a measurement corresponding to a self-adjoint operator in the tensor-product Hilbert space of the system and apparatus spaces. The second realization is by performing, on the system alone, sequential measurements that correspond to self-adjoint operators, basing the choice of each measurement on the outcomes of previous measurements. Simultaneous generalized measurements are found to be equivalent to a single finer grain generalized measurement, and hence it is sufficient to consider the set of single measurements. An alternative characterization of generalized measurement is proposed. It is shown to be equivalent to the characterization by operator-values measures, but it is potentially more suitable for the treatment of estimation problems. Finally, a study of the interaction between the information-carrying system and a measurement apparatus provides clues for the physical realizations of abstractly characterized quantum measurements.

Correlation between X-ray flux and rotational acceleration in Vela X-1

NASA Technical Reports Server (NTRS)

Deeter, J. E.; Boynton, P. E.; Shibazaki, N.; Hayakawa, S.; Nagase, F.

1989-01-01

The results of a search for correlations between X-ray flux and angular acceleration for the accreting binary pulsar Vela X-1 are presented. Results are based on data obtained with the Hakucho satellite during the interval 1982 to 1984. In undertaking this correlation analysis, it was necessary to modify the usual statistical method to deal with conditions imposed by generally unavoidable satellite observing constraints, most notably a mismatch in sampling between the two variables. The results are suggestive of a correlation between flux and the absolute value of the angular acceleration, at a significance level of 96 percent. The implications of the methods and results for future observations and analysis are discussed.

Surface Pressure Dependencies in the GEOS-Chem-Adjoint System and the Impact of the GEOS-5 Surface Pressure on CO2 Model Forecast

NASA Technical Reports Server (NTRS)

Lee, Meemong; Weidner, Richard

2016-01-01

In the GEOS-Chem Adjoint (GCA) system, the total (wet) surface pressure of the GEOS meteorology is employed as dry surface pressure, ignoring the presence of water vapor. The Jet Propulsion Laboratory (JPL) Carbon Monitoring System (CMS) research team has been evaluating the impact of the above discrepancy on the CO2 model forecast and the CO2 flux inversion. The JPL CMS research utilizes a multi-mission assimilation framework developed by the Multi-Mission Observation Operator (M2O2) research team at JPL extending the GCA system. The GCA-M2O2 framework facilitates mission-generic 3D and 4D-variational assimilations streamlining the interfaces to the satellite data products and prior emission inventories. The GCA-M2O2 framework currently integrates the GCA system version 35h and provides a dry surface pressure setup to allow the CO2 model forecast to be performed with the GEOS-5 surface pressure directly or after converting it to dry surface pressure.

Surface Pressure Dependencies in the Geos-Chem-Adjoint System and the Impact of the GEOS-5 Surface Pressure on CO2 Model Forecast

NASA Technical Reports Server (NTRS)

Lee, Meemong; Weidner, Richard

2016-01-01

In the GEOS-Chem Adjoint (GCA) system, the total (wet) surface pressure of the GEOS meteorology is employed as dry surface pressure, ignoring the presence of water vapor. The Jet Propulsion Laboratory (JPL) Carbon Monitoring System (CMS) research team has been evaluating the impact of the above discrepancy on the CO2 model forecast and the CO2 flux inversion. The JPL CMS research utilizes a multi-mission assimilation framework developed by the Multi-Mission Observation Operator (M2O2) research team at JPL extending the GCA system. The GCA-M2O2 framework facilitates mission-generic 3D and 4D-variational assimilations streamlining the interfaces to the satellite data products and prior emission inventories. The GCA-M2O2 framework currently integrates the GCA system version 35h and provides a dry surface pressure setup to allow the CO2 model forecast to be performed with the GEOS-5 surface pressure directly or after converting it to dry surface pressure.

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

Favorite, Jeffrey A.; Gonzalez, Esteban

Adjoint-based first-order perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate first-order approximation of a flux or reaction rate within a radioactive system when the boundary is perturbed. When the response of interest is the flux or leakage current on the boundary, the Roussopoulos perturbation estimate has long been used. The Rahnema and Roussopoulos estimates differ in one term. Our paper shows that the Rahnema and Roussopoulos estimates can be derived consistently, using different responses, from a single variational functional (due to Gheorghiu and Rahnema), resolving any apparent contradiction. In analyticmore » test problems, Rahnema’s estimate and the Roussopoulos estimate produce exact first derivatives of the response of interest when appropriately applied. We also present a realistic, nonanalytic test problem.« less

Stellar dynamics around a massive black hole - III. Resonant relaxation of razor-thin axisymmetric discs

NASA Astrophysics Data System (ADS)

Sridhar, S.; Touma, Jihad R.

2017-02-01

We study the resonant relaxation (RR) of an axisymmetric, low-mass (or Keplerian) stellar disc orbiting a more massive black hole (MBH). Our recent work on the general kinetic theory of RR is simplified in the standard manner by the neglect of 'gravitational polarization' and applied to a razor-thin axisymmetric disc. The wake of a stellar orbit is expressed in terms of the angular momenta exchanged with other orbits, and used to derive a kinetic equation for RR under the combined actions of self-gravity, 1 PN and 1.5 PN general relativistic effects of the MBH and an arbitrary external axisymmetric potential. This is a Fokker-Planck equation for the stellar distribution function (DF), wherein the diffusion coefficients are given self-consistently in terms of contributions from apsidal resonances between pairs of stellar orbits. The physical kinetics is studied for the two main cases of interest. (1) 'Lossless' discs in which the MBH is not a sink of stars, and disc mass, angular momentum and energy are conserved: we prove that general H-functions can increase or decrease during RR, but the Boltzmann entropy is (essentially) unique in being a non-decreasing function of time. Therefore, secular thermal equilibria are maximum entropy states, with DFs of the Boltzmann form; the two-ring correlation function at equilibrium is computed. (2) Discs that lose stars to the MBH through an 'empty loss cone': we derive expressions for the MBH feeding rates of mass, angular momentum and energy in terms of the diffusive fluxes at the loss-cone boundaries.

Toward a Self-Consistent Dynamical Model of the NSSL

NASA Astrophysics Data System (ADS)

Matilsky, Loren

2018-01-01

The advent of helioseismology has revealed in detail the internal differential rotation profile of the Sun. In particular, the presence of two boundary layers, the tachocline at the bottom of the convection zone (CZ) and the Near Surface Shear Layer (NSSL) at the top of the CZ, has remained a mystery. These two boundary layers may have significant consequences for the internal dynamo that operates the Sun's magnetic field, and so understanding their dynamics is an important step in solar physics and in the theory of solar-like stellar structure in general. In this talk, we analyze three numerical models of hydrodynamic convection in rotating spherical shells with varying degrees of stratification in order to understand the dynamical balance of the solar near-surface shear layer (NSSL). We find that with sufficient stratification, a boundary layer with some characteristics of the NSSL develops at high latitudes, and it is maintained purely an inertial balance of torques in which the viscosity is negligible. An inward radial flux of angular momentum from the Reynold's stress (as has been predicted by theory) is balanced by the poleward latitudinal flux of angular momentum due to the meridional circulation. We analyze the similarities of the near surface shear in our models to that of the Sun, and find that the solar NSSL is most likely maintained by the inertial balance our simulations display at high latitudes, but with a modified upper boundary condition.

Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.

2017-11-01

This paper presents a discrete adjoint version of the recently developed non-intrusive least squares shadowing (NILSS) algorithm, which circumvents the instability that conventional adjoint methods encounter for chaotic systems. The NILSS approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers. Adjoint NILSS is demonstrated on a small chaotic ODE, a one-dimensional scalar PDE, and a direct numerical simulation (DNS) of the minimal flow unit, a turbulent channel flow on a small spatial domain. This is the first application of an adjoint shadowing-based algorithm to a three-dimensional turbulent flow.

A dynamical stabilizer in the climate system: a mechanism suggested by a simple model

NASA Astrophysics Data System (ADS)

Bates, J. R.

1999-05-01

A simple zonally averaged hemispheric model of the climate system is constructed, based on energy equations for two ocean basins separated at 30° latitude with the surface fluxes calculated explicitly. A combination of empirical input and theoretical calculation is used to determine an annual mean equilibrium climate for the model and to study its stability with respect to small perturbations. The insolation, the mean albedos and the equilibrium temperatures for the two model zones are prescribed from observation. The principal agent of interaction between the zones is the vertically integrated poleward transport of atmospheric angular momentum across their common boundary. This is parameterized using an empirical formula derived from a multiyear atmospheric data set. The surface winds are derived from the angular momentum transport assuming the atmosphere to be in a state of dynamic balance on the climatic timescales of interest. A further assumption that the air sea temperature difference and low level relative humidity remain fixed at their mean observed values then allows the surface fluxes of latent and sensible heat to be calculated. Results from a radiative model, which show a positive lower tropospheric water vapour/infrared radiative feedback on SST perturbations in both zones, are used to calculate the net upward infrared radiative fluxes at the surface. In the model's equilibrium climate, the principal processes balancing the solar radiation absorbed at the surface are evaporation in the tropical zone and net infrared radiation in the extratropical zone. The stability of small perturbations about the equilibrium is studied using a linearized form of the ocean energy equations. Ice-albedo and cloud feedbacks are omitted and attention is focussed on the competing effects of the water vapour/infrared radiative feedback and the turbulent surface flux and oceanic heat transport feedbacks associated with the angular momentum cycle. The perturbation equations involve inter-zone coupling and have coefficients dependent on the values of the equilibrium fluxes and the sensitivity of the angular momentum transport. Analytical solutions for the perturbations are obtained. These provide criteria for the stability of the equilibrium climate. If the evaporative feedback on SST perturbations is omitted, the equilibrium climate is unstable due to the influence of the water vapour/infrared radiative feedback, which dominates over the effects of the sensible heat and ocean heat transport feedbacks. The inclusion of evaporation gives a negative feedback which is of sufficient strength to stabilize the system. The stabilizing mechanism involves wind and humidity factors in the evaporative fluxes that are of comparable magnitude. Both factors involve the angular momentum transport. In including angular momentum and calculating the surface fluxes explicitly, the model presented here differs from the many simple climate models based on the Budyko Sellers formulation. In that formulation, an atmospheric energy balance equation is used to eliminate surface fluxes in favour of top-of-the-atmosphere radiative fluxes and meridional atmospheric energy transports. In the resulting models, infrared radiation appears as a stabilizing influence on SST perturbations and the dynamical stabilizing mechanism found here cannot be identified.

Angular radiation models for earth-atmosphere system. Volume 2: Longwave radiation

NASA Technical Reports Server (NTRS)

Suttles, J. T.; Green, R. N.; Smith, G. L.; Wielicki, B. A.; Walker, I. J.; Taylor, V. R.; Stowe, L. L.

1989-01-01

The longwave angular radiation models that are required for analysis of satellite measurements of Earth radiation, such as those from the Earth Radiation Budget Experiment (ERBE) are presented. The models contain limb-darkening characteristics and mean fluxes. Limb-darkening characteristics are the longwave anisotropic factor and the standard deviation of the longwave radiance. Derivation of these models from the Nimbus 7 ERB (Earth Radiation Budget) data set is described. Tabulated values and computer-generated plots are included for the limb-darkening and mean-flux models.

Brownian self-driven particles on the surface of a sphere

NASA Astrophysics Data System (ADS)

Apaza, Leonardo; Sandoval, Mario

2017-08-01

We present the dynamics of overdamped Brownian self-propelled particles moving on the surface of a sphere. The effect of self-propulsion on the diffusion of these particles is elucidated by determining their angular (azimuthal and polar) mean-square displacement. Short- and long-times analytical expressions for their angular mean-square displacement are offered. Finally, the particles' steady marginal angular probability density functions are also elucidated.

Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2009-01-01

.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

New insights gained on mechanisms of low-energy proton-induced SEUs by minimizing energy straggle

DOE PAGES

Dodds, Nathaniel Anson; Dodd, Paul E.; Shaneyfelt, Marty R.; ...

2015-12-01

In this study, we present low-energy proton single-event upset (SEU) data on a 65 nm SOI SRAM whose substrate has been completely removed. Since the protons only had to penetrate a very thin buried oxide layer, these measurements were affected by far less energy loss, energy straggle, flux attrition, and angular scattering than previous datasets. The minimization of these common sources of experimental interference allows more direct interpretation of the data and deeper insight into SEU mechanisms. The results show a strong angular dependence, demonstrate that energy straggle, flux attrition, and angular scattering affect the measured SEU cross sections, andmore » prove that proton direct ionization is the dominant mechanism for low-energy proton-induced SEUs in these circuits.« less

Self-dual monopoles and toda molecules

NASA Astrophysics Data System (ADS)

Ganoulis, N.; Goddard, P.; Olive, D.

1982-07-01

Stable static solutions to a gauge field theory with a Higgs field in the adjoint representation and with vanishing self-coupling are self-dual in the sense of Bogomolny. Leznov and Saveliev showed that a specific form of spherical symmetry reduces these equations to a modified form of the Toda molecule equations associated with the overall gauge symmetry G. Values of the constants of integration are found in terms of the distant Higgs field, guaranteeing regularity of the solution at the origin. The expressions hold for any simple Lie group G, depending on G via its root system.

On the Implementation and Performance of Iterative Methods for Computational Electromagnetics

DTIC Science & Technology

1985-12-01

based on F3 only if L is self-adjoint and positive definite in the sense of Griffel [651. Each of the above functionals gives rise to a different...New York: Wiley, 1960. [65] D. H. Griffel , Applied Functional Analysis. New York: Wiley, 1981. [661 R. Fletcher and C. M. Reeves, "Functional

What confines the rings of Saturn?

NASA Astrophysics Data System (ADS)

Tajeddine, Radwan; Nicholson, Philip D.; El Moutamid, Maryame; Longaretti, Pierre-Yves; Burns, Joseph A.

2017-10-01

The viscous spreading of planetary rings is believed to be counteracted by satellite torques, either through an individual resonance or through overlapping resonances (when the satellite is close to the ring edge). For the A ring of Saturn, it has been commonly believed that the satellite Janus alone can prevent the ring from spreading via its 7:6 Lindblad resonance. We discuss this common misconception and show that, in reality, the A ring is confined by the contributions from the group of satellites Pan, Atlas, Prometheus, Pandora, Janus, Epimetheus, and Mimas, whose resonances gradually decrease the angular momentum flux transported outward through the ring via density and bending waves. We further argue that this decrease in angular momentum flux occurs through the mechanism of ‘flux reversal’.We find that the Janus 7:6 torque is relatively feeble, as is the comparable torque of the nearby small satellite Atlas, each amounting to less than one-tenth of the angular momentum transport carried by the A ring. But the cumulative torques of the many other satellite resonances in the A ring sufficiently reduce the angular momentum flux through the rings so that the torques due to Janus and Atlas are effective in confining the outer edge of the ring.Furthermore, we use the magnitude of the satellites’ resonance torques to estimate the effective viscosity profile across the A ring, showing that it decreases from ~50 cm2 s-1 at the inner edge to less than ~11 cm2 s-1 at the outer edge. The gradual estimated decrease of the angular momentum flux and effective viscosity are roughly consistent with results obtained by balancing the shepherding torques from Pan and Daphnis with the viscous torque at the edges of the Encke and Keeler gaps, as well as the edge of the A ring.On the other hand, the Mimas 2:1 Lindblad resonance alone seems to be capable of confining the edge of the B ring, and contrary to the situation in the A ring, we show that the effective viscosity across the B ring is relatively constant at ~24-30 cm2 s-1.

Angular dependence models for radiance to flux conversion

NASA Technical Reports Server (NTRS)

Green, Richard N.; Suttles, John T.; Wielicki, Bruce A.

1990-01-01

Angular dependence models (ADM) used for converting the measured radiance to flux at the top of the atmosphere are reviewed, and emphasis is placed on the measure of their effectiveness and the implications of requiring the ADMs to satisfy reciprocity. The overall significance of the ADMs is figured out by analyzing the same satellite data with a single Lambertian model, single mean model, and the 12 Earth Radiation Budget Experiment (ERBE) ADMs. It is shown that the Lambertian ADM is inadequate, while the mean ADM results in nearly unbiased fluxes but creates substantial differences for individual pixel fluxes. The standard ERBE ADM works well except for a 10-pct to 15-pct albedo growth across the scan; a modified ADM based on the standard ERBE ADM but forced to satisfy the principle of reciprocity increases the limb brightening and reduces the albedo growth but does not improve the scanner and nonscanner intercomparison.

Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation.

PubMed

Chen, Rui-Pin; Chen, Zhaozhong; Chew, Khian-Hooi; Li, Pei-Gang; Yu, Zhongliang; Ding, Jianping; He, Sailing

2015-05-29

A caustic vector vortex optical field is experimentally generated and demonstrated by a caustic-based approach. The desired caustic with arbitrary acceleration trajectories, as well as the structured states of polarization (SoP) and vortex orders located in different positions in the field cross-section, is generated by imposing the corresponding spatial phase function in a vector vortex optical field. Our study reveals that different spin and orbital angular momentum flux distributions (including opposite directions) in different positions in the cross-section of a caustic vector vortex optical field can be dynamically managed during propagation by intentionally choosing the initial polarization and vortex topological charges, as a result of the modulation of the caustic phase. We find that the SoP in the field cross-section rotates during propagation due to the existence of the vortex. The unique structured feature of the caustic vector vortex optical field opens the possibility of multi-manipulation of optical angular momentum fluxes and SoP, leading to more complex manipulation of the optical field scenarios. Thus this approach further expands the functionality of an optical system.

Unsteady adjoint for large eddy simulation of a coupled turbine stator-rotor system

NASA Astrophysics Data System (ADS)

Talnikar, Chaitanya; Wang, Qiqi; Laskowski, Gregory

2016-11-01

Unsteady fluid flow simulations like large eddy simulation are crucial in capturing key physics in turbomachinery applications like separation and wake formation in flow over a turbine vane with a downstream blade. To determine how sensitive the design objectives of the coupled system are to control parameters, an unsteady adjoint is needed. It enables the computation of the gradient of an objective with respect to a large number of inputs in a computationally efficient manner. In this paper we present unsteady adjoint solutions for a coupled turbine stator-rotor system. As the transonic fluid flows over the stator vane, the boundary layer transitions to turbulence. The turbulent wake then impinges on the rotor blades, causing early separation. This coupled system exhibits chaotic dynamics which causes conventional adjoint solutions to diverge exponentially, resulting in the corruption of the sensitivities obtained from the adjoint solutions for long-time simulations. In this presentation, adjoint solutions for aerothermal objectives are obtained through a localized adjoint viscosity injection method which aims to stabilize the adjoint solution and maintain accurate sensitivities. Preliminary results obtained from the supercomputer Mira will be shown in the presentation.

Brownian self-propelled particles on a sphere

NASA Astrophysics Data System (ADS)

Apaza-Pilco, Leonardo Felix; Sandoval, Mario

We present the dynamics of a Brownian self-propelled particle at low Reynolds number moving on the surface of a sphere. The effects of curvature and self-propulsion on the diffusion of the particle are elucidated by determining (numerically) the mean-square displacement of the particle's angular (azimuthal and polar) coordinates. The results show that the long time behavior of its angular mean-square displacement is linear in time. We also see that the slope of the angular MSD is proportional to the propulsion velocity and inverse to the curvature of the sphere. The angular probability distribution function (PDF) of the particle is also obtained by numerically solving its respective Smoluchowski equation.

Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems

DOE PAGES

Favorite, Jeffrey A.; Gonzalez, Esteban

2017-03-10

Adjoint-based first-order perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate first-order approximation of a flux or reaction rate within a radioactive system when the boundary is perturbed. When the response of interest is the flux or leakage current on the boundary, the Roussopoulos perturbation estimate has long been used. The Rahnema and Roussopoulos estimates differ in one term. Our paper shows that the Rahnema and Roussopoulos estimates can be derived consistently, using different responses, from a single variational functional (due to Gheorghiu and Rahnema), resolving any apparent contradiction. In analyticmore » test problems, Rahnema’s estimate and the Roussopoulos estimate produce exact first derivatives of the response of interest when appropriately applied. We also present a realistic, nonanalytic test problem.« less

Source Parameter Estimation using the Second-order Closure Integrated Puff Model

DTIC Science & Technology

The sensor measurements are categorized as triggered and non-triggered based on the recorded concentration measurements and a threshold...concentration value. Using each measured value, sources of adjoint material are created from the triggered and non-triggered sensors, and the adjoint transport...equations are solved to predict the adjoint concentration fields. The adjoint source strength is inversely proportional to the concentration measurement

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

Schnack, D.D.; Lottati, I.; Mikic, Z.

The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.

Trotter's limit formula for the Schrödinger equation with singular potential

NASA Astrophysics Data System (ADS)

Nathanson, Ekaterina S.; Jørgensen, Palle E. T.

2017-12-01

We discuss the Schrödinger equation with singular potentials. Our focus is non-relativistic Schrödinger operators H with scalar potentials V defined on R d, hence covering such quantum systems as atoms, molecules, and subatomic particles whether free, bound, or localized. By a "singular potential" V, we refer to the case when the corresponding Schrödinger operators H, with their natural minimal domain in L2(R d), are not essentially self-adjoint. Since V is assumed real valued, the corresponding Hermitian symmetric operator H commutes with the conjugation in L2(R d), and so (by von Neumann's theorem), H has deficiency indices (n, n). The case of singular potentials V refers to when n > 0. Hence, by von Neumann's theory, we know the full variety of all the self-adjoint extensions. Since the Trotter formula is restricted to the case when n = 0, and here n > 0, two questions arise: (i) existence of the Trotter limit and (ii) the nature of this limit. We answer (i) affirmatively. Our answer to (ii) is that when n > 0, the Trotter limit is a strongly continuous contraction semigroup; so it is not time-reversible.

Quantum motion of a point particle in the presence of the Aharonov–Bohm potential in curved space

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

Silva, Edilberto O., E-mail: edilbertoo@gmail.com; Ulhoa, Sérgio C., E-mail: sc.ulhoa@gmail.com; Andrade, Fabiano M., E-mail: f.andrade@ucl.ac.uk

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov–Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The geometry of this line element establishes that the motion of the particle can occur on the surface of a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also because of two-dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in suchmore » a context. Because of the presence of the geometric potential, which contains a singular term, we use the self-adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions. -- Highlights: •Motion of particle under the influence of magnetic field in curved space. •Bound state for Aharonov–Bohm problem. •Particle describing a circular path. •Determination of the self-adjoint extension parameter.« less

Variational approach to stability boundary for the Taylor-Goldstein equation

NASA Astrophysics Data System (ADS)

Hirota, Makoto; Morrison, Philip J.

2015-11-01

Linear stability of inviscid stratified shear flow is studied by developing an efficient method for finding neutral (i.e., marginally stable) solutions of the Taylor-Goldstein equation. The classical Miles-Howard criterion states that stratified shear flow is stable if the local Richardson number JR is greater than 1/4 everywhere. In this work, the case of JR > 0 everywhere is considered by assuming strictly monotonic and smooth profiles of the ambient shear flow and density. It is shown that singular neutral modes that are embedded in the continuous spectrum can be found by solving one-parameter families of self-adjoint eigenvalue problems. The unstable ranges of wavenumber are searched for accurately and efficiently by adopting this method in a numerical algorithm. Because the problems are self-adjoint, the variational method can be applied to ascertain the existence of singular neutral modes. For certain shear flow and density profiles, linear stability can be proven by showing the non-existence of a singular neutral mode. New sufficient conditions, extensions of the Rayleigh-Fjortoft stability criterion for unstratified shear flows, are derived in this manner. This work was supported by JSPS Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation # 55053270.

Gravitational self-force on generic bound geodesics in Kerr spacetime

NASA Astrophysics Data System (ADS)

van de Meent, Maarten

2018-05-01

In this work we present the first calculation of the gravitational self-force on generic bound geodesics in Kerr spacetime to first order in the mass ratio. That is, the local correction to equations of motion for a compact object orbiting a larger rotating black hole due to its own impact on the gravitational field. This includes both dissipative and conservative effects. Our method builds on and extends earlier methods for calculating the gravitational self-force on equatorial orbits. In particular we reconstruct the local metric perturbation in the outgoing radiation gauge from the Weyl scalar ψ4 , which in turn is obtained by solving the Teukolsky equation using semianalytical frequency domain methods. The gravitational self-force is subsequently obtained using (spherical) l -mode regularization. We test our implementation by comparing the large l -behavior against the analytically known regularization parameters. In addition we validate our results by comparing the long-term average changes to the energy, angular momentum, and Carter constant to changes to these constants of motion inferred from the gravitational wave flux to infinity and down the horizon.

Sensitivity kernels for viscoelastic loading based on adjoint methods

NASA Astrophysics Data System (ADS)

Al-Attar, David; Tromp, Jeroen

2014-01-01

Observations of glacial isostatic adjustment (GIA) allow for inferences to be made about mantle viscosity, ice sheet history and other related parameters. Typically, this inverse problem can be formulated as minimizing the misfit between the given observations and a corresponding set of synthetic data. When the number of parameters is large, solution of such optimization problems can be computationally challenging. A practical, albeit non-ideal, solution is to use gradient-based optimization. Although the gradient of the misfit required in such methods could be calculated approximately using finite differences, the necessary computation time grows linearly with the number of model parameters, and so this is often infeasible. A far better approach is to apply the `adjoint method', which allows the exact gradient to be calculated from a single solution of the forward problem, along with one solution of the associated adjoint problem. As a first step towards applying the adjoint method to the GIA inverse problem, we consider its application to a simpler viscoelastic loading problem in which gravitationally self-consistent ocean loading is neglected. The earth model considered is non-rotating, self-gravitating, compressible, hydrostatically pre-stressed, laterally heterogeneous and possesses a Maxwell solid rheology. We determine adjoint equations and Fréchet kernels for this problem based on a Lagrange multiplier method. Given an objective functional J defined in terms of the surface deformation fields, we show that its first-order perturbation can be written δ J = int _{MS}K_{η }δ ln η dV +int _{t0}^{t1}int _{partial M}K_{dot{σ }} δ dot{σ } dS dt, where δ ln η = δη/η denotes relative viscosity variations in solid regions MS, dV is the volume element, δ dot{σ } is the perturbation to the time derivative of the surface load which is defined on the earth model's surface ∂M and for times [t0, t1] and dS is the surface element on ∂M. The `viscosity kernel' Kη determines the linearized sensitivity of J to viscosity perturbations defined with respect to a laterally heterogeneous reference earth model, while the `rate-of-loading kernel' K_{dot{σ }} determines the sensitivity to variations in the time derivative of the surface load. By restricting attention to spherically symmetric viscosity perturbations, we also obtain a `radial viscosity kernel' overline{K}_{η } such that the associated contribution to δJ can be written int _{IS}overline{K}_{η }δ ln η dr, where IS denotes the subset of radii lying in solid regions. In order to illustrate this theory, we describe its numerical implementation in the case of a spherically symmetric earth model using a 1-D spectral element method, and calculate sensitivity kernels for a range of realistic observables.

Analysis and development of adjoint-based h-adaptive direct discontinuous Galerkin method for the compressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Cheng, Jian; Yue, Huiqiang; Yu, Shengjiao; Liu, Tiegang

2018-06-01

In this paper, an adjoint-based high-order h-adaptive direct discontinuous Galerkin method is developed and analyzed for the two dimensional steady state compressible Navier-Stokes equations. Particular emphasis is devoted to the analysis of the adjoint consistency for three different direct discontinuous Galerkin discretizations: including the original direct discontinuous Galerkin method (DDG), the direct discontinuous Galerkin method with interface correction (DDG(IC)) and the symmetric direct discontinuous Galerkin method (SDDG). Theoretical analysis shows the extra interface correction term adopted in the DDG(IC) method and the SDDG method plays a key role in preserving the adjoint consistency. To be specific, for the model problem considered in this work, we prove that the original DDG method is not adjoint consistent, while the DDG(IC) method and the SDDG method can be adjoint consistent with appropriate treatment of boundary conditions and correct modifications towards the underlying output functionals. The performance of those three DDG methods is carefully investigated and evaluated through typical test cases. Based on the theoretical analysis, an adjoint-based h-adaptive DDG(IC) method is further developed and evaluated, numerical experiment shows its potential in the applications of adjoint-based adaptation for simulating compressible flows.

Adjoint-Based Aerodynamic Design of Complex Aerospace Configurations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.

2016-01-01

An overview of twenty years of adjoint-based aerodynamic design research at NASA Langley Research Center is presented. Adjoint-based algorithms provide a powerful tool for efficient sensitivity analysis of complex large-scale computational fluid dynamics (CFD) simulations. Unlike alternative approaches for which computational expense generally scales with the number of design parameters, adjoint techniques yield sensitivity derivatives of a simulation output with respect to all input parameters at the cost of a single additional simulation. With modern large-scale CFD applications often requiring millions of compute hours for a single analysis, the efficiency afforded by adjoint methods is critical in realizing a computationally tractable design optimization capability for such applications.

Project to Study Soil Electromagnetic Properties

DTIC Science & Technology

2007-09-30

transmitter loops (these may be one and the same physical loop or any combinations of loops) and w is angular frequency. M is the magnetic flux that...space, and w is angular frequency used by the sensor. In this case sensor response is frequency-dependent, even if the layer variables are real and...Consider a transmitter current in a single turn coil with angular frequency wand amplitude I. This produces a receiver voltage V (a complex phasor) in the

Universal Racah matrices and adjoint knot polynomials: Arborescent knots

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2016-04-01

By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.

Effects of a parallel electric field and the geomagnetic field in the topside ionosphere on auroral and photoelectron energy distributions

NASA Technical Reports Server (NTRS)

Min, Q.-L.; Lummerzheim, D.; Rees, M. H.; Stamnes, K.

1993-01-01

The consequences of electric field acceleration and an inhomogeneous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one-dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogeneous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of O(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function is investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogeneous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.

Effects of a Parallel Electric Field and the Geomagnetic Field in the Topside Ionosphere on Auroral and Photoelectron Energy Distributions

NASA Technical Reports Server (NTRS)

Min, Q.-L.; Lummerzheim, D.; Rees, M. H.; Stamnes, K.

1993-01-01

The consequences of electric field acceleration and an inhomogencous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one- dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogencous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of 0(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function in investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogencous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.

The Galactic Isotropic γ-ray Background and Implications for Dark Matter

NASA Astrophysics Data System (ADS)

Campbell, Sheldon S.; Kwa, Anna; Kaplinghat, Manoj

2018-06-01

We present an analysis of the radial angular profile of the galacto-isotropic (GI) γ-ray flux-the statistically uniform flux in angular annuli centred on the Galactic centre. Two different approaches are used to measure the GI flux profile in 85 months of Fermi-LAT data: the BDS statistical method which identifies spatial correlations, and a new Poisson ordered-pixel method which identifies non-Poisson contributions. Both methods produce similar GI flux profiles. The GI flux profile is well-described by an existing model of bremsstrahlung, π0 production, inverse Compton scattering, and the isotropic background. Discrepancies with data in our full-sky model are not present in the GI component, and are therefore due to mis-modelling of the non-GI emission. Dark matter annihilation constraints based solely on the observed GI profile are close to the thermal WIMP cross section below 100 GeV, for fixed models of the dark matter density profile and astrophysical γ-ray foregrounds. Refined measurements of the GI profile are expected to improve these constraints by a factor of a few.

Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1992-01-01

A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

Magnetogasdynamics shock waves in a rotational axisymmetric non-ideal gas with increasing energy and conductive and radiative heat-fluxes

NASA Astrophysics Data System (ADS)

Nath, Gorakh

2016-07-01

Self-similar solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamics cylindrical shock wave propagating in a rotational axisymmetric non ideal gas with increasing energy and conductive and radiative heat fluxes in presence of an azimuthal magnetic field. The fluid velocities and the azimuthal magnetic field in the ambient medium are assume to be varying and obeying power laws. In order to find the similarity solutions the angular velocity of the ambient medium is taken to be decreasing as the distance from the axis increases. The heat conduction is expressed in terms of Fourier's law and the radiation is considered to be the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density. The effects of the presence of radiation and conduction, the non-idealness of the gas and the magnetic field on the shock propagation and the flow behind the shock are investigated.

Fully automatic adjoints: a robust and efficient mechanism for generating adjoint ocean models

NASA Astrophysics Data System (ADS)

Ham, D. A.; Farrell, P. E.; Funke, S. W.; Rognes, M. E.

2012-04-01

The problem of generating and maintaining adjoint models is sufficiently difficult that typically only the most advanced and well-resourced community ocean models achieve it. There are two current technologies which each suffer from their own limitations. Algorithmic differentiation, also called automatic differentiation, is employed by models such as the MITGCM [2] and the Alfred Wegener Institute model FESOM [3]. This technique is very difficult to apply to existing code, and requires a major initial investment to prepare the code for automatic adjoint generation. AD tools may also have difficulty with code employing modern software constructs such as derived data types. An alternative is to formulate the adjoint differential equation and to discretise this separately. This approach, known as the continuous adjoint and employed in ROMS [4], has the disadvantage that two different model code bases must be maintained and manually kept synchronised as the model develops. The discretisation of the continuous adjoint is not automatically consistent with that of the forward model, producing an additional source of error. The alternative presented here is to formulate the flow model in the high level language UFL (Unified Form Language) and to automatically generate the model using the software of the FEniCS project. In this approach it is the high level code specification which is differentiated, a task very similar to the formulation of the continuous adjoint [5]. However since the forward and adjoint models are generated automatically, the difficulty of maintaining them vanishes and the software engineering process is therefore robust. The scheduling and execution of the adjoint model, including the application of an appropriate checkpointing strategy is managed by libadjoint [1]. In contrast to the conventional algorithmic differentiation description of a model as a series of primitive mathematical operations, libadjoint employs a new abstraction of the simulation process as a sequence of discrete equations which are assembled and solved. It is the coupling of the respective abstractions employed by libadjoint and the FEniCS project which produces the adjoint model automatically, without further intervention from the model developer. This presentation will demonstrate this new technology through linear and non-linear shallow water test cases. The exceptionally simple model syntax will be highlighted and the correctness of the resulting adjoint simulations will be demonstrated using rigorous convergence tests.

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2004-01-01

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Sensitivity of Lumped Constraints Using the Adjoint Method

NASA Technical Reports Server (NTRS)

Akgun, Mehmet A.; Haftka, Raphael T.; Wu, K. Chauncey; Walsh, Joanne L.

1999-01-01

Adjoint sensitivity calculation of stress, buckling and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. Adjoint stress and displacement sensitivities are available in the literature. Expressions for local buckling sensitivity of isotropic plate elements are derived in this study. Computational efficiency of the adjoint method is sensitive to the number of constraints and, therefore, the method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser (KS) function is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a simple HSCT wing model, and a large HSCT model. These sensitivity derivatives are then used in optimization.

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

Energy transfer from a pulsed thermal source to He II below 0.3 K.

NASA Technical Reports Server (NTRS)

Pfeifer, C. D.; Luszczynski, K.

1973-01-01

Results of measurements of the angular distribution of the energy flux radiated from a pulsed heater immersed in He II at low temperatures (around 230 mK). It is shown that the energy transfer from a pulsed carbon heater at a relatively high temperature to ambient liquid helium maintained at low temperature cannot be adequately described by the phonon-coupling models. The experimental data on the velocity and angular distribution of the energy flux radiated from the plane of the heater indicate that the energy from the heater is transferred to a layer of hot helium adjacent to the surface of the heater and that this layer acts as the effective source of excitations radiated into the ambient liquid helium. The extent and shape of this source depend on the total energy flux produced by the heater.

Higher order derivatives of R-Jacobi polynomials

NASA Astrophysics Data System (ADS)

Das, Sourav; Swaminathan, A.

2016-06-01

In this work, the R-Jacobi polynomials defined on the nonnegative real axis related to F-distribution are considered. Using their Sturm-Liouville system higher order derivatives are constructed. Orthogonality property of these higher ordered R-Jacobi polynomials are obtained besides their normal form, self-adjoint form and hypergeometric representation. Interesting results on the Interpolation formula and Gaussian quadrature formulae are obtained with numerical examples.

Development and Applications of the FV3 GEOS-5 Adjoint Modeling System

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kim, Jong G.; Lin, Shian-Jiann; Errico, Ron; Gelaro, Ron; Kent, James; Coy, Larry; Doyle, Jim; Goldstein, Alex

2017-01-01

GMAO has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR. In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system.

Spectral-Element Seismic Wave Propagation Codes for both Forward Modeling in Complex Media and Adjoint Tomography

NASA Astrophysics Data System (ADS)

Smith, J. A.; Peter, D. B.; Tromp, J.; Komatitsch, D.; Lefebvre, M. P.

2015-12-01

We present both SPECFEM3D_Cartesian and SPECFEM3D_GLOBE open-source codes, representing high-performance numerical wave solvers simulating seismic wave propagation for local-, regional-, and global-scale application. These codes are suitable for both forward propagation in complex media and tomographic imaging. Both solvers compute highly accurate seismic wave fields using the continuous Galerkin spectral-element method on unstructured meshes. Lateral variations in compressional- and shear-wave speeds, density, as well as 3D attenuation Q models, topography and fluid-solid coupling are all readily included in both codes. For global simulations, effects due to rotation, ellipticity, the oceans, 3D crustal models, and self-gravitation are additionally included. Both packages provide forward and adjoint functionality suitable for adjoint tomography on high-performance computing architectures. We highlight the most recent release of the global version which includes improved performance, simultaneous MPI runs, OpenCL and CUDA support via an automatic source-to-source transformation library (BOAST), parallel I/O readers and writers for databases using ADIOS and seismograms using the recently developed Adaptable Seismic Data Format (ASDF) with built-in provenance. This makes our spectral-element solvers current state-of-the-art, open-source community codes for high-performance seismic wave propagation on arbitrarily complex 3D models. Together with these solvers, we provide full-waveform inversion tools to image the Earth's interior at unprecedented resolution.

Atomic diffusion in strain fields near solutes

NASA Astrophysics Data System (ADS)

Shropshire, Steven L.; Collins, Gary S.

1993-03-01

Annihilation reactions between mobile self-interstitial defects and complexes of vacancies with111In probe solutes in Au were studied. Measurements were made using the technique of perturbed angular correlations of gamma rays (PAC). Au samples were doped with complexes and plastically deformed at a low temperature to generate fluxes of self-interstitials. Changes in the concentrations of monovacancy (1V) to tetravacancy (4V) complexes induced by annihilation reactions were measured. These are now analysed using a system of coupled first-order equations in order to obtain interstitial annihilation cross sections of the complexes and the fractional amounts of different interstitial clusters in the flux. Relative cross sections obtained for Au are 1.0(1), 3.3(3), 1.2(2) and 7.5(2.5), respectively, for 1V to 4V complexes. The large increase in the cross sections with vacancy number is attributed to a progressive relaxation of the dilatational strain surrounding the oversized In solute as more vacancies are trapped. Also obtained from the analysis are values 0.34(5), 0.66(7), 0.0(1) and 0.0(2), respectively, for the fractions of mobile 1I to 4I clusters in deformed Au, indicating that di-interstitials are produced more readily than mono-interstitials during plastic deformation.

Additional flux of particles and albedo-electrons in upper atmosphere

NASA Technical Reports Server (NTRS)

Aitbaev, F. B.; Dyuisembaev, B. M.; Kolomeets, E. V.

1985-01-01

The results are presented of the Monte Carlo simulation of albedo flux from the dense layers of the Earth's atmosphere and the dependence of angular distribution on the rigidity of geomagnetic cut off and additional flux of particles at the depth in the atmosphere 15-20 g/sq sm. Influence of geomagnetic field on the propagation of charged particles was not taken into account.

Tangent Adjoint Methods In a Higher-Order Space-Time Discontinuous-Galerkin Solver For Turbulent Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo; Murman, Scott; Blonigan, Patrick; Garai, Anirban

2017-01-01

Presented space-time adjoint solver for turbulent compressible flows. Confirmed failure of traditional sensitivity methods for chaotic flows. Assessed rate of exponential growth of adjoint for practical 3D turbulent simulation. Demonstrated failure of short-window sensitivity approximations.

Topology optimization of thermal fluid flows with an adjoint Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Dugast, Florian; Favennec, Yann; Josset, Christophe; Fan, Yilin; Luo, Lingai

2018-07-01

This paper presents an adjoint Lattice Boltzmann Method (LBM) coupled with the Level-Set Method (LSM) for topology optimization of thermal fluid flows. The adjoint-state formulation implies discrete velocity directions in order to take into account the LBM boundary conditions. These boundary conditions are introduced at the beginning of the adjoint-state method as the LBM residuals, so that the adjoint-state boundary conditions can appear directly during the adjoint-state equation formulation. The proposed method is tested with 3 numerical examples concerning thermal fluid flows, but with different objectives: minimization of the mean temperature in the domain, maximization of the heat evacuated by the fluid, and maximization of the heat exchange with heated solid parts. This latter example, treated in several articles, is used to validate our method. In these optimization problems, a limitation of the maximal pressure drop and of the porosity (number of fluid elements) is also applied. The obtained results demonstrate that the method is robust and effective for solving topology optimization of thermal fluid flows.

Adjoint-Based Methodology for Time-Dependent Optimization

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2008-01-01

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Exploring the Flux Tube Paradigm in Solar-like Convection Zones

NASA Astrophysics Data System (ADS)

Weber, Maria A.; Nelson, Nicholas; Browning, Matthew

2017-08-01

In the solar context, important insight into the flux emergence process has been obtained by assuming the magnetism giving rise to sunspots consists partly of idealized flux tubes. Global-scale dynamo models are only now beginning to capture some aspects of flux emergence. In certain regimes, these simulations self-consistently generate magnetic flux structures that rise buoyantly through the computational domain. How similar are these dynamo-generated, rising flux structures to traditional flux tube models? The work we present here is a step toward addressing this question. We utilize the thin flux tube (TFT) approximation to simply model the evolution of flux tubes in a global, three-dimensional geometry. The TFTs are embedded in convective flows taken from a global dynamo simulation of a rapidly rotating Sun within which buoyant flux structures arise naturally from wreaths of magnetism. The initial conditions of the TFTs are informed by rising flux structures identified in the dynamo simulation. We compare the trajectories of the dynamo-generated flux loops with those computed through the TFT approach. We also assess the nature of the relevant forces acting on both sets of flux structures, such as buoyancy, the Coriolis force, and external forces imparted by the surrounding convection. To achieve the fast <15 day rise of the buoyant flux structures, we must suppress the large retrograde flow established inside the TFTs which occurs due to a strong conservation of angular momentum as they move outward. This tendency is common in flux tube models in solar-like convection zones, but is not present to the same degree in the dynamo-generated flux loops. We discuss the mechanisms that may be responsible for suppressing the axial flow inside the flux tube, and consider the implications this has regarding the role of the Coriolis force in explaining sunspot latitudes and the observed Joy’s Law trend of active regions. Our work aims to provide constraints, and possible calibrations, on the traditional flux tube model as it pertains to the Sun and other spotted stars.

Quantifying VOC emissions from East Asia using 10 years of satellite observations

NASA Astrophysics Data System (ADS)

Stavrakou, T.; Muller, J. F.; Bauwens, M.; De Smedt, I.; Van Roozendael, M.; Boersma, F.; van der A, R. J.; Pierre-Francois, C.; Clerbaux, C.

2016-12-01

China's emissions are in the spotlight of efforts to mitigate climate change and improve regional and city-scale air quality. Despite growing efforts to better quantify China's emissions, the current estimates are often poor or inadequate. Complementary to bottom-up inventories, inverse modeling of fluxes has the potential to improve those estimates through the use of atmospheric observations of trace gas compounds. As formaldehyde (HCHO) is a high-yield product in the oxidation of most volatile organic compounds (VOCs) emitted by anthropogenic and natural sources, satellite observations of HCHO hold the potential to inform us on the spatial and temporal variability of the underlying VOC sources. The 10-year record of space-based HCHO column observations from the OMI instrument is used to constrain VOC emission fluxes in East Asia in a source inversion framework built on the IMAGES chemistry-transport model and its adjoint. The interannual and seasonal variability, spatial distribution and potential trends of the top-down VOC fluxes (anthropogenic, pyrogenic and biogenic) are presented and confronted to existing emission inventories, satellite observations of other species (e.g. glyoxal and nitrogen oxides), and past studies.

Helical paths, gravitaxis, and separation phenomena for mass-anisotropic self-propelling colloids: Experiment versus theory

NASA Astrophysics Data System (ADS)

Campbell, Andrew I.; Wittkowski, Raphael; ten Hagen, Borge; Löwen, Hartmut; Ebbens, Stephen J.

2017-08-01

The self-propulsion mechanism of active colloidal particles often generates not only translational but also rotational motion. For particles with an anisotropic mass density under gravity, the motion is usually influenced by a downwards oriented force and an aligning torque. Here we study the trajectories of self-propelled bottom-heavy Janus particles in three spatial dimensions both in experiments and by theory. For a sufficiently large mass anisotropy, the particles typically move along helical trajectories whose axis is oriented either parallel or antiparallel to the direction of gravity (i.e., they show gravitaxis). In contrast, if the mass anisotropy is small and rotational diffusion is dominant, gravitational alignment of the trajectories is not possible. Furthermore, the trajectories depend on the angular self-propulsion velocity of the particles. If this component of the active motion is strong and rotates the direction of translational self-propulsion of the particles, their trajectories have many loops, whereas elongated swimming paths occur if the angular self-propulsion is weak. We show that the observed gravitational alignment mechanism and the dependence of the trajectory shape on the angular self-propulsion can be used to separate active colloidal particles with respect to their mass anisotropy and angular self-propulsion, respectively.

A Jet Source of Event Horizon Telescope Correlated Flux in M87

NASA Astrophysics Data System (ADS)

Punsly, Brian

2017-12-01

Event Horizon Telescope (EHT) observations at 230 GHz are combined with Very Long Baseline Interferometry (VLBI) observations at 86 GHz and high-resolution Hubble Space Telescope optical observations in order to constrain the broadband spectrum of the emission from the base of the jet in M87. The recent VLBI observations of Hada et al. provide much stricter limits on the 86 GHz luminosity and component acceleration in the jet base than were available to previous modelers. They reveal an almost hollow jet on sub-mas scales. Thus, tubular models of the jet base emanating from the innermost accretion disk are considered within the region responsible for the EHT correlated flux. There is substantial synchrotron self-absorbed opacity at 86 GHz. A parametric analysis indicates that the jet dimensions and power depend strongly on the 86 GHz flux density and the black hole spin, but depend weakly on other parameters, such as jet speed, 230 GHz flux density, and optical flux. The entire power budget of the M87 jet, ≲ {10}44 {erg} {{{s}}}-1, can be accommodated by the tubular jet. No invisible, powerful spine is required. Even though this analysis never employs the resolution of the EHT, the spectral shape implies a dimension transverse to the jet direction of 12-21 μ {as} (˜ 24{--}27 μ {as}) for 0.99> a/M> 0.95 (a/M˜ 0.7), where M is the mass and a is the angular momentum per unit mass of the central black hole.

Stellar integrated fluxes for 216 stars in the wavelength range 380 nm-900 NM

NASA Astrophysics Data System (ADS)

Petford, A. D.; Blackwell, D. E.; Booth, A. J.; Haddock, D. J.; Leggett, S. K.; Mountain, C. M.; Selby, M. J.; Arribas, S.

1988-09-01

The paper reports measurements of the integrated fluxes over the wavelength range 380 nm - 900 nm for 216 stars using a Reticon spectrometer in conjunction with the 1 m Kapteyn telescope of the Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. Methods are proposed for deriving visible integrated fluxes from 13-colour photometry, UBVRI and BV photometry. Such fluxes are useful for deriving stellar effective temperatures and angular diameters.

Improved Adjoint-Operator Learning For A Neural Network

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad; Barhen, Jacob

1995-01-01

Improved method of adjoint-operator learning reduces amount of computation and associated computational memory needed to make electronic neural network learn temporally varying pattern (e.g., to recognize moving object in image) in real time. Method extension of method described in "Adjoint-Operator Learning for a Neural Network" (NPO-18352).

Adjoint method and runaway electron avalanche

DOE PAGES

Liu, Chang; Brennan, Dylan P.; Boozer, Allen H.; ...

2016-12-16

The adjoint method for the study of runaway electron dynamics in momentum space Liu et al (2016 Phys. Plasmas 23 010702) is rederived using the Green's function method, for both the runaway probability function (RPF) and the expected loss time (ELT). The RPF and ELT obtained using the adjoint method are presented, both with and without the synchrotron radiation reaction force. In conclusion, the adjoint method is then applied to study the runaway electron avalanche. Both the critical electric field and the growth rate for the avalanche are calculated using this fast and novel approach.

Application of Adjoint Methodology in Various Aspects of Sonic Boom Design

NASA Technical Reports Server (NTRS)

Rallabhandi, Sriram K.

2014-01-01

One of the advances in computational design has been the development of adjoint methods allowing efficient calculation of sensitivities in gradient-based shape optimization. This paper discusses two new applications of adjoint methodology that have been developed to aid in sonic boom mitigation exercises. In the first, equivalent area targets are generated using adjoint sensitivities of selected boom metrics. These targets may then be used to drive the vehicle shape during optimization. The second application is the computation of adjoint sensitivities of boom metrics on the ground with respect to parameters such as flight conditions, propagation sampling rate, and selected inputs to the propagation algorithms. These sensitivities enable the designer to make more informed selections of flight conditions at which the chosen cost functionals are less sensitive.

Sensitivities of Greenland ice sheet volume inferred from an ice sheet adjoint model

NASA Astrophysics Data System (ADS)

Heimbach, P.; Bugnion, V.

2009-04-01

We present a new and original approach to understanding the sensitivity of the Greenland ice sheet to key model parameters and environmental conditions. At the heart of this approach is the use of an adjoint ice sheet model. Since its introduction by MacAyeal (1992), the adjoint method has become widespread to fit ice stream models to the increasing number and diversity of satellite observations, and to estimate uncertain model parameters such as basal conditions. However, no attempt has been made to extend this method to comprehensive ice sheet models. As a first step toward the use of adjoints of comprehensive three-dimensional ice sheet models we have generated an adjoint of the ice sheet model SICOPOLIS of Greve (1997). The adjoint was generated by means of the automatic differentiation (AD) tool TAF. The AD tool generates exact source code representing the tangent linear and adjoint model of the nonlinear parent model provided. Model sensitivities are given by the partial derivatives of a scalar-valued model diagnostic with respect to the controls, and can be efficiently calculated via the adjoint. By way of example, we determine the sensitivity of the total Greenland ice volume to various control variables, such as spatial fields of basal flow parameters, surface and basal forcings, and initial conditions. Reliability of the adjoint was tested through finite-difference perturbation calculations for various control variables and perturbation regions. Besides confirming qualitative aspects of ice sheet sensitivities, such as expected regional variations, we detect regions where model sensitivities are seemingly unexpected or counter-intuitive, albeit ``real'' in the sense of actual model behavior. An example is inferred regions where sensitivities of ice sheet volume to basal sliding coefficient are positive, i.e. where a local increase in basal sliding parameter increases the ice sheet volume. Similarly, positive ice temperature sensitivities in certain parts of the ice sheet are found (in most regions it is negativ, i.e. an increase in temperature decreases ice sheet volume), the detection of which seems highly unlikely if only conventional perturbation experiments had been used. An effort to generate an efficient adjoint with the newly developed open-source AD tool OpenAD is also under way. Available adjoint code generation tools now open up a variety of novel model applications, notably with regard to sensitivity and uncertainty analyses and ice sheet state estimation or data assimilation.

Chain of point-like potentials in Script R3 and infiniteness of the number of bound states

NASA Astrophysics Data System (ADS)

Boitsev, A. A.; Popov, I. Yu; Sokolov, O. V.

2014-10-01

Infinite chain of point-like potentials having the Hamiltonian with infinite number of eigenvalues below the continuous spectrum is constructed. The background of the model is the theory of self-adjoint extensions of symmetric operators in the Hilbert space. The analogous example of the Hamiltonian is obtained for the system of three-dimensional waveguides coupled through point-like windows.

Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source

NASA Astrophysics Data System (ADS)

Nho Hào, Dinh; Van Duc, Nguyen; Van Thang, Nguyen

2018-05-01

Let H be a Hilbert space with the inner product and the norm , a positive self-adjoint unbounded time-dependent operator on H and . We establish stability estimates of Hölder type and propose a regularization method with error estimates of Hölder type for the ill-posed backward semi-linear parabolic equation with the source function f satisfying a local Lipschitz condition.

Observables, measurements and phase operators from a Bohmian perspective

NASA Technical Reports Server (NTRS)

Daumer, Martin; Goldstein, Sheldon

1993-01-01

Bohmian mechanics is a deterministic theory of point particles in motion. While avoiding all the paradoxes of nonrelativistic quantum mechanics, it yields the quantum formalism itself--especially the role of self-adjoint operators--as a macroscopic measurement formalism. As an 'application' it is shown that much of the confusion connected with the phase operator for the electromagnetic field arises from a misunderstanding of the role of operators in quantum theory.

Measurement of high-energy neutron flux above ground utilizing a spallation based multiplicity technique

DOE PAGES

Roecker, Caleb; Bernstein, Adam; Marleau, Peter; ...

2016-11-14

Cosmogenic high-energy neutrons are a ubiquitous, difficult to shield, poorly measured background. Above ground the high-energy neutron energy-dependent flux has been measured, with significantly varying results. Below ground, high-energy neutron fluxes are largely unmeasured. Here we present a reconstruction algorithm to unfold the incident neutron energy-dependent flux measured using the Multiplicity and Recoil Spectrometer (MARS), simulated test cases to verify the algorithm, and provide a new measurement of the above ground high-energy neutron energy-dependent flux with a detailed systematic uncertainty analysis. Uncertainty estimates are provided based upon the measurement statistics, the incident angular distribution, the surrounding environment of the Montemore » Carlo model, and the MARS triggering efficiency. Quantified systematic uncertainty is dominated by the assumed incident neutron angular distribution and surrounding environment of the Monte Carlo model. The energy-dependent neutron flux between 90 MeV and 400 MeV is reported. Between 90 MeV and 250 MeV the MARS results are comparable to previous Bonner sphere measurements. Over the total energy regime measured, the MARS result are located within the span of previous measurements. Lastly, these results demonstrate the feasibility of future below ground measurements with MARS.« less

Measurement of high-energy neutron flux above ground utilizing a spallation based multiplicity technique

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

Roecker, Caleb; Bernstein, Adam; Marleau, Peter

Cosmogenic high-energy neutrons are a ubiquitous, difficult to shield, poorly measured background. Above ground the high-energy neutron energy-dependent flux has been measured, with significantly varying results. Below ground, high-energy neutron fluxes are largely unmeasured. Here we present a reconstruction algorithm to unfold the incident neutron energy-dependent flux measured using the Multiplicity and Recoil Spectrometer (MARS), simulated test cases to verify the algorithm, and provide a new measurement of the above ground high-energy neutron energy-dependent flux with a detailed systematic uncertainty analysis. Uncertainty estimates are provided based upon the measurement statistics, the incident angular distribution, the surrounding environment of the Montemore » Carlo model, and the MARS triggering efficiency. Quantified systematic uncertainty is dominated by the assumed incident neutron angular distribution and surrounding environment of the Monte Carlo model. The energy-dependent neutron flux between 90 MeV and 400 MeV is reported. Between 90 MeV and 250 MeV the MARS results are comparable to previous Bonner sphere measurements. Over the total energy regime measured, the MARS result are located within the span of previous measurements. Lastly, these results demonstrate the feasibility of future below ground measurements with MARS.« less

Self energized air core superconducting (SEAC) motor

NASA Astrophysics Data System (ADS)

Hilal, M. A.; Huang, X.; Lloyd, J. D.; Crapo, A. D.

1991-03-01

The SEAC motor described utilizes superconductive windings both for the stator and the rotor and operates the same way as a conventional motor by supplying power to the stator. The rotor of a simple SEAC motor has a small and a large winding and two switches. The axes of the two rotor windings are normal to each other. The rotor is initially stationary, and the windings are exposed to the rotating stator field. Flux pumping is employed to charge the rotor windings. As the field rotates by 180 deg from being parallel to the axis of the small winding of the rotor, a switch connected in series with the windings automatically opens, allowing the magnetic flux to penetrate the winding. The switch is closed during most of the other half of the cycle. The flux trapped in the small winding is partially transferred to the larger rotor winding by opening another switch, which results in series connection of the two windings. This results in charging the large winding and in accelerating the rotor to reach the rotating field angular velocity. Current decay will not take place, since it will automatically trigger flux pumping and recharging of the windings. The use of superconductive windings will also make it feasible to operate at high magnetic field, thus eliminating the need for using iron laminations to magnetically link the rotor and the stator windings.

On the role of surface friction in tropical cyclone intensification

NASA Astrophysics Data System (ADS)

Wang, Yuqing

2017-04-01

Recent studies have debated on whether surface friction is positive or negative to tropical cyclone intensification in the view on angular momentum budget. That means whether the frictionally induced inward angular momentum transport can overcome the loss of angular momentum to the surface due to surface friction itself. Although this issue is still under debate, this study investigates another implicit dynamical effect, which modifies the radial location and strength of eyewall convection. We found that moderate surface friction is necessary for rapid intensity of tropical cyclones. This is demonstrated first by a simple coupled dynamical system that couples a multi-level boundary layer model and a shallow water equation model above with mass source parameterized by mass flux from the boundary layer model below, and then by a full physics model. The results show that surface friction leads to the inward penetration of inflow under the eyewall, shift the boundary layer mass convergence slightly inside the radius of maximum wind, and enhance the upward mass flux, and thus diabatic heating in the eyewall and intensification rate of a TC. This intensification process is different from the direct angular momentum budget previously used to explain the role of surface friction in tropical cyclone intensification.

Determination of ocean surface heat fluxes by a variational method

NASA Astrophysics Data System (ADS)

Roquet, H.; Planton, S.; Gaspar, P.

1993-06-01

A new technique of determination of the "nonsolar" heat flux (sum of the latent, sensible, and net infrared fluxes) at the ocean surface is proposed. It applies when oceanic advection remains weak and thus relies on a one-dimensional modeling approach. It is based on a variational data assimilation scheme using the adjoint equation formalism. This allows to take advantage of all observed data with their error estimates. Results from experiments performed with station Papa (Gulf of Alaska) and Long-Term Upper Ocean Study (LOTUS, Sargasso Sea) data sets are discussed. The temperature profiles assimilation allows the one-dimensional model to reproduce correctly the temperature evolution at the surface and under the oceanic mixed layer at the two sites. The retrieved fluxes are compared to the fluxes calculated through classical empirical formulae. The diurnal dependence of the fluxes at the LOTUS site is particularly investigated. The results are also compared with those obtained using a simpler technique based on an iterative shooting method and allowing the assimilation of the only sea surface temperature. This second comparison reveals that the variability of the retrieved fluxes is damped when temperature in the inner ocean are assimilated. This is the case for the diurnal cycle at the LOTUS mooring. When the available current data at this site are assimilated, the diurnal variability of the retrieved fluxes is further decreased. This points out a model discrepancy in the representation of mixing processes associated to internal wave activity. The remaining part of the diurnal cycle is significant and could be due to a direct effect of air-sea temperature difference.

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

DOE PAGES

Finn, John M.

2015-03-01

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a 'special divergence-free' property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. Wemore » also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Ref. [11], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Ref. [35], appears to work very well.« less

The relativistic feedback discharge model of terrestrial gamma ray flashes

NASA Astrophysics Data System (ADS)

Dwyer, Joseph R.

2012-02-01

As thunderclouds charge, the large-scale fields may approach the relativistic feedback threshold, above which the production of relativistic runaway electron avalanches becomes self-sustaining through the generation of backward propagating runaway positrons and backscattered X-rays. Positive intracloud (IC) lightning may force the large-scale electric fields inside thunderclouds above the relativistic feedback threshold, causing the number of runaway electrons, and the resulting X-ray and gamma ray emission, to grow exponentially, producing very large fluxes of energetic radiation. As the flux of runaway electrons increases, ionization eventually causes the electric field to discharge, bringing the field below the relativistic feedback threshold again and reducing the flux of runaway electrons. These processes are investigated with a new model that includes the production, propagation, diffusion, and avalanche multiplication of runaway electrons; the production and propagation of X-rays and gamma rays; and the production, propagation, and annihilation of runaway positrons. In this model, referred to as the relativistic feedback discharge model, the large-scale electric fields are calculated self-consistently from the charge motion of the drifting low-energy electrons and ions, produced from the ionization of air by the runaway electrons, including two- and three-body attachment and recombination. Simulation results show that when relativistic feedback is considered, bright gamma ray flashes are a natural consequence of upward +IC lightning propagating in large-scale thundercloud fields. Furthermore, these flashes have the same time structures, including both single and multiple pulses, intensities, angular distributions, current moments, and energy spectra as terrestrial gamma ray flashes, and produce large current moments that should be observable in radio waves.

The creation of photonic orbital angular momentum in electromagnetic waves propagating through turbulence

NASA Astrophysics Data System (ADS)

Sanchez, D. J.; Oesch, D. W.; Reynolds, O. R.

2013-08-01

Context. We have recently shown that the phenomenon known as "branch points" in AO are markers for photons carrying orbital angular momentum (OAM). In doing so, we have demonstrated that atmospheric turbulence creates well defined OAM states in beams propagating through it. Aims: In this paper, we extend our previous research to include any astrophysical turbulent assemblage of molecules or atoms (TAMA), demonstrating that these clouds, similar to Earth's atmosphere, also create photonic orbital angular momentum (POAM) in electromagnetic waves propagating through them. A TAMA is any gaseous cloud with a varying density and therefore variation in its index of refraction, which includes but is not limited to stellar envelopes, circumstellar disks, molecular clouds, planetary atmospheres, and the interstellar medium. Methods: We applied our previous theoretical, simulation, and laboratory results to astrophysical TAMAs. Additionally, we demonstrated how sensors designed for AO can be used to measure this POAM flux. Results: Our results apply to light propagating through any TAMA. Since TAMA are ubiquitous in the cosmos, steady, long lasting POAM fluxes will be ubiquitous as well. Conclusions: Our results, which include theory, benchtop laboratory data, and wave optic simulation, indicate that, under the right conditions, POAM fluxes can reach over 50% of the total photon flux. An initial set of on-sky experimental observations appear to corroborate the laboratory results with two of the five stars, HR 1529 and HR 1577, showing POAM fluxes of 3% ± 1% and 2% ± 1% of the total flux, and a third, HR 1895, with a PAOM flux of up to 17% ± 2% of the total flux. We express our gratitude to the Air Force Office of Scientific Research for their support of this research.Appendices are available in electronic form at http://www.aanda.orgData referred to in measurements are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/556/A130

Bose-Fermi degeneracies in large N adjoint QCD

DOE PAGES

Basar, Gokce; Cherman, Aleksey; McGady, David

2015-07-06

Here, we analyze the large N limit of adjoint QCD, an SU( N) gauge theory with N f flavors of massless adjoint Majorana fermions, compactified on S 3 × S 1. We focus on the weakly-coupled confining small- S 3 regime. If the fermions are given periodic boundary conditions on S 1, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any S 1 size L, even though the bosonicmore » and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any L ~ N 0, explaining how it is able to enjoy large N volume independence for any L. The large N boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite N, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large N limit.« less

Assessing the Impact of Observations on Numerical Weather Forecasts Using the Adjoint Method

NASA Technical Reports Server (NTRS)

Gelaro, Ronald

2012-01-01

The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. This talk provides a general overview of the adjoint method, including the theoretical basis and practical implementation of the technique. Results are presented from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. When performed in conjunction with standard observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies may be important for optimizing the use of the current observational network and defining requirements for future observing systems

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.

2009-01-01

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.

2006-01-01

Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.

Inverse problems in heterogeneous and fractured media using peridynamics

DOE PAGES

Turner, Daniel Z.; van Bloemen Waanders, Bart G.; Parks, Michael L.

2015-12-10

The following work presents an adjoint-based methodology for solving inverse problems in heterogeneous and fractured media using state-based peridynamics. We show that the inner product involving the peridynamic operators is self-adjoint. The proposed method is illustrated for several numerical examples with constant and spatially varying material parameters as well as in the context of fractures. We also present a framework for obtaining material parameters by integrating digital image correlation (DIC) with inverse analysis. This framework is demonstrated by evaluating the bulk and shear moduli for a sample of nuclear graphite using digital photographs taken during the experiment. The resulting measuredmore » values correspond well with other results reported in the literature. Lastly, we show that this framework can be used to determine the load state given observed measurements of a crack opening. Furthermore, this type of analysis has many applications in characterizing subsurface stress-state conditions given fracture patterns in cores of geologic material.« less

Meter-wavelength observations of pulsars using very long baseline interferometry. Ph.D. Thesis - Maryland Univ., College Park; [with particular attention to the Crab nebula

NASA Technical Reports Server (NTRS)

Vandenberg, N. R.

1974-01-01

The results of an investigation of the angular structure imposed on pulsar radiation due to scattering in the interstellar medium are presented. The technique of very-long-baseline interferometry was used to obtain the necessary high angular resolution. The interferometers formed by the Arecibo, NRAO, and Sugar Grove telescopes were used at radio frequencies of 196, 111, and 74 MHz during seven separate observing sessions between November 1971 and February 1973. A crude visibility function for the Crab nebular pulsar was obtained along with the correlated pulse profile. The technique of differential fringe phase was used to show that the pulsar and the compact source in the Crab nebula are coincident to within 0.001 arcsec which corresponds to aproximately 2 a.u. at the distance to the nebula. The ratio of pulsing to total flux, and the fringe visibility of the time-averaged pulsing flux are also discussed, and apparent angular sizes of the pulsars were measured.

Angular Momentum Transport in Thin Magnetically Arrested Disks

NASA Astrophysics Data System (ADS)

Marshall, Megan D.; Avara, Mark J.; McKinney, Jonathan C.

2018-05-01

In accretion disks with large-scale ordered magnetic fields, the magnetorotational instability (MRI) is marginally suppressed, so other processes may drive angular momentum transport leading to accretion. Accretion could then be driven by large-scale magnetic fields via magnetic braking, and large-scale magnetic flux can build-up onto the black hole and within the disk leading to a magnetically-arrested disk (MAD). Such a MAD state is unstable to the magnetic Rayleigh-Taylor (RT) instability, which itself leads to vigorous turbulence and the emergence of low-density highly-magnetized bubbles. This instability was studied in a thin (ratio of half-height H to radius R, H/R ≈ 0.1) MAD simulation, where it has a more dramatic effect on the dynamics of the disk than for thicker disks. Large amounts of flux are pushed off the black hole into the disk, leading to temporary decreases in stress, then this flux is reprocessed as the stress increases again. Throughout this process, we find that the dominant component of the stress is due to turbulent magnetic fields, despite the suppression of the axisymmetric MRI and the dominant presence of large-scale magnetic fields. This suggests that the magnetic RT instability plays a significant role in driving angular momentum transport in MADs.

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

Yin Yunpeng; Sawin, Herbert H.

The impact of etching kinetics and etching chemistries on surface roughening was investigated by etching thermal silicon dioxide and low-k dielectric coral materials in C{sub 4}F{sub 8}/Ar plasma beams in an inductive coupled plasma beam reactor. The etching kinetics, especially the angular etching yield curves, were measured by changing the plasma pressure and the feed gas composition which influence the effective neutral-to-ion flux ratio during etching. At low neutral-to-ion flux ratios, the angular etching yield curves are sputteringlike, with a peak around 60 deg. -70 deg. off-normal angles; the surface at grazing ion incidence angles becomes roughened due to ionmore » scattering related ion-channeling effects. At high neutral-to-ion flux ratios, ion enhanced etching dominates and surface roughening at grazing angles is mainly caused by the local fluorocarbon deposition induced micromasking mechanism. Interestingly, the etched surfaces at grazing angles remain smooth for both films at intermediate neutral-to-ion flux ratio regime. Furthermore, the oxygen addition broadens the region over which the etching without roughening can be performed.« less

Spectral Cauchy characteristic extraction of strain, news and gravitational radiation flux

NASA Astrophysics Data System (ADS)

Handmer, Casey J.; Szilágyi, Béla; Winicour, Jeffrey

2016-11-01

We present a new approach for the Cauchy-characteristic extraction (CCE) of gravitational radiation strain, news function, and the flux of the energy-momentum, supermomentum and angular momentum associated with the Bondi-Metzner-Sachs asymptotic symmetries. In CCE, a characteristic evolution code takes numerical data on an inner worldtube supplied by a Cauchy evolution code, and propagates it outwards to obtain the space-time metric in a neighborhood of null infinity. The metric is first determined in a scrambled form in terms of coordinates determined by the Cauchy formalism. In prior treatments, the waveform is first extracted from this metric and then transformed into an asymptotic inertial coordinate system. This procedure provides the physically proper description of the waveform and the radiated energy but it does not generalize to determine the flux of angular momentum or supermomentum. Here we formulate and implement a new approach which transforms the full metric into an asymptotic inertial frame and provides a uniform treatment of all the radiation fluxes associated with the asymptotic symmetries. Computations are performed and calibrated using the spectral Einstein code.

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

Navarro, Alejandro Bañón, E-mail: banon@physics.ucla.edu; Jenko, Frank, E-mail: jenko@physics.ucla.edu; Teaca, Bogdan, E-mail: bogdan.teaca@coventry.ac.uk

For a Z-pinch geometry, we report on the nonlinear redistribution of free energy across scales perpendicular to the magnetic guide field, for a turbulent plasma described in the framework of gyrokinetics. The analysis is performed using a local flux-surface approximation, in a regime dominated by electrostatic fluctuations driven by the entropy mode, with both ion and electron species being treated kinetically. To explore the anisotropic nature of the free energy redistribution caused by the emergence of zonal flows, we use a polar coordinate representation for the field-perpendicular directions and define an angular density for the scale flux. Positive values formore » the classically defined (angle integrated) scale flux, which denote a direct energy cascade, are shown to be also composed of negative angular sections, a fact that impacts our understanding of the backscatter of energy and the way in which it enters the modeling of sub-grid scales for turbulence. A definition for the flux of free energy across each perpendicular direction is introduced as well, which shows that the redistribution of energy in the presence of zonal flows is highly anisotropic.« less

Gluon correlations from a glasma flux-tube model compared to measured hadron correlations on transverse momentum (p t,p t) and angular differences (η Δ,φ Δ)

DOE PAGES

Trainor, Thomas A.; Ray, R. L.

2011-09-09

A glasma flux-tube model has been proposed to explain strong elongation on pseudorapidity η of the same-side two-dimensional (2D) peak in minimum-bias angular correlations from √( sNN)=200 GeV Au-Au collisions. The same-side peak or “soft ridge” is said to arise from coupling of flux tubes to radial flow whereby gluons radiated transversely from flux tubes are boosted by radial flow to form a narrow structure or ridge on azimuth. In this study we test the theory conjecture by comparing measurements to predictions for particle production, spectra, and correlations from the glasma model and from conventional fragmentation processes. We conclude thatmore » the glasma model is contradicted by measured hadron yields, spectra, and correlations, whereas a two-component model of hadron production, including minimum-bias parton fragmentation, provides a quantitative description of most features of the data, although η elongation of the same-side 2D peak remains undescribed.« less

Measurement of the neutrino component of an antineutrino beam observed by a nonmagnetized detector

NASA Astrophysics Data System (ADS)

Aguilar-Arevalo, A. A.; Anderson, C. E.; Brice, S. J.; Brown, B. C.; Bugel, L.; Conrad, J. M.; Dharmapalan, R.; Djurcic, Z.; Fleming, B. T.; Ford, R.; Garcia, F. G.; Garvey, G. T.; Grange, J.; Green, J. A.; Imlay, R.; Johnson, R. A.; Karagiorgi, G.; Katori, T.; Kobilarcik, T.; Linden, S. K.; Louis, W. C.; Mahn, K. B. M.; Marsh, W.; Mauger, C.; Metcalf, W.; Mills, G. B.; Mirabal, J.; Moore, C. D.; Mousseau, J.; Nelson, R. H.; Nguyen, V.; Nienaber, P.; Nowak, J. A.; Osmanov, B.; Patch, A.; Pavlovic, Z.; Perevalov, D.; Polly, C. C.; Ray, H.; Roe, B. P.; Russell, A. D.; Shaevitz, M. H.; Sorel, M.; Spitz, J.; Stancu, I.; Stefanski, R. J.; Tayloe, R.; Tzanov, M.; van de Water, R. G.; Wascko, M. O.; White, D. H.; Wilking, M. J.; Zeller, G. P.; Zimmerman, E. D.

2011-10-01

Two methods are employed to measure the neutrino flux of the antineutrino-mode beam observed by the MiniBooNE detector. The first method compares data to simulated event rates in a high-purity νμ-induced charged-current single π+ (CC1π+) sample while the second exploits the difference between the angular distributions of muons created in νμ and ν¯μ charged-current quasielastic (CCQE) interactions. The results from both analyses indicate the prediction of the neutrino flux component of the predominately antineutrino beam is overestimated—the CC1π+ analysis indicates the predicted νμ flux should be scaled by 0.76±0.11, while the CCQE angular fit yields 0.65±0.23. The energy spectrum of the flux prediction is checked by repeating the analyses in bins of reconstructed neutrino energy, and the results show that the spectral shape is well-modeled. These analyses are a demonstration of techniques for measuring the neutrino contamination of antineutrino beams observed by future nonmagnetized detectors.

Use of adjoint methods in the probabilistic finite element approach to fracture mechanics

NASA Technical Reports Server (NTRS)

Liu, Wing Kam; Besterfield, Glen; Lawrence, Mark; Belytschko, Ted

1988-01-01

The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.

The Tangent Linear and Adjoint of the FV3 Dynamical Core: Development and Applications

NASA Technical Reports Server (NTRS)

Holdaway, Daniel

2018-01-01

GMAO (NASA's Global Modeling and Assimilation Office) has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR (4-Dimensional Variational Assimilation). In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system.

Four-Dimensional Data Assimilation Using the Adjoint Method

NASA Astrophysics Data System (ADS)

Bao, Jian-Wen

The calculus of variations is used to confirm that variational four-dimensional data assimilation (FDDA) using the adjoint method can be implemented when the numerical model equations have a finite number of first-order discontinuous points. These points represent the on/off switches associated with physical processes, for which the Jacobian matrix of the model equation does not exist. Numerical evidence suggests that, in some situations when the adjoint method is used for FDDA, the temperature field retrieved using horizontal wind data is numerically not unique. A physical interpretation of this type of non-uniqueness of the retrieval is proposed in terms of energetics. The adjoint equations of a numerical model can also be used for model-parameter estimation. A general computational procedure is developed to determine the size and distribution of any internal model parameter. The procedure is then applied to a one-dimensional shallow -fluid model in the context of analysis-nudging FDDA: the weighting coefficients used by the Newtonian nudging technique are determined. The sensitivity of these nudging coefficients to the optimal objectives and constraints is investigated. Experiments of FDDA using the adjoint method are conducted using the dry version of the hydrostatic Penn State/NCAR mesoscale model (MM4) and its adjoint. The minimization procedure converges and the initialization experiment is successful. Temperature-retrieval experiments involving an assimilation of the horizontal wind are also carried out using the adjoint of MM4.

Receptivity of the compressible mixing layer

NASA Astrophysics Data System (ADS)

Barone, Matthew F.; Lele, Sanjiva K.

2005-09-01

Receptivity of compressible mixing layers to general source distributions is examined by a combined theoretical/computational approach. The properties of solutions to the adjoint Navier Stokes equations are exploited to derive expressions for receptivity in terms of the local value of the adjoint solution. The result is a description of receptivity for arbitrary small-amplitude mass, momentum, and heat sources in the vicinity of a mixing-layer flow, including the edge-scattering effects due to the presence of a splitter plate of finite width. The adjoint solutions are examined in detail for a Mach 1.2 mixing-layer flow. The near field of the adjoint solution reveals regions of relatively high receptivity to direct forcing within the mixing layer, with receptivity to nearby acoustic sources depending on the source type and position. Receptivity ‘nodes’ are present at certain locations near the splitter plate edge where the flow is not sensitive to forcing. The presence of the nodes is explained by interpretation of the adjoint solution as the superposition of incident and scattered fields. The adjoint solution within the boundary layer upstream of the splitter-plate trailing edge reveals a mechanism for transfer of energy from boundary-layer stability modes to Kelvin Helmholtz modes. Extension of the adjoint solution to the far field using a Kirchhoff surface gives the receptivity of the mixing layer to incident sound from distant sources.

High speed flux feedback for tuning a universal field oriented controller capable of operating in direct and indirect field orientation modes

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

De Doncker, Rik W. A. A.

The direct (d) and quadrature (q) components of flux, as sensed by flux sensors or determined from voltage and current measurements in a direct field orientation scheme, are processed rapidly and accurately to provide flux amplitude and angular position values for use by the vector rotator of a universal field-oriented (UFO) controller. Flux amplitude (linear or squared) is provided as feedback to tune the UFO controller for operation in direct and indirect field orientation modes and enables smooth transitions from one mode to the other.

High speed flux feedback for tuning a universal field oriented controller capable of operating in direct and indirect field orientation modes

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

De Doncker, R.W.A.A.

The direct (d) and quadrature (q) components of flux, as sensed by flux sensors or determined from voltage and current measurements in a direct field orientation scheme, are processed rapidly and accurately to provide flux amplitude and angular position values for use by the vector rotator of a universal field-oriented (UFO) controller. Flux amplitude (linear or squared) is provided as feedback to tune the UFO controller for operation in direct and indirect field orientation modes and enables smooth transitions from one mode to the other. 3 figs.

High speed flux feedback for tuning a universal field oriented controller capable of operating in direct and indirect field orientation modes

DOEpatents

De Doncker, R.W.A.A.

1992-09-01

The direct (d) and quadrature (q) components of flux, as sensed by flux sensors or determined from voltage and current measurements in a direct field orientation scheme, are processed rapidly and accurately to provide flux amplitude and angular position values for use by the vector rotator of a universal field-oriented (UFO) controller. Flux amplitude (linear or squared) is provided as feedback to tune the UFO controller for operation in direct and indirect field orientation modes and enables smooth transitions from one mode to the other. 3 figs.

Tracking plant physiological properties from multi-angular tower-based remote sensing.

PubMed

Hilker, Thomas; Gitelson, Anatoly; Coops, Nicholas C; Hall, Forrest G; Black, T Andrew

2011-04-01

Imaging spectroscopy is a powerful technique for monitoring the biochemical constituents of vegetation and is critical for understanding the fluxes of carbon and water between the land surface and the atmosphere. However, spectral observations are subject to the sun-observer geometry and canopy structure which impose confounding effects on spectral estimates of leaf pigments. For instance, the sun-observer geometry influences the spectral brightness measured by the sensor. Likewise, when considering pigment distribution at the stand level scale, the pigment content observed from single view angles may not necessarily be representative of stand-level conditions as some constituents vary as a function of the degree of leaf illumination and are therefore not isotropic. As an alternative to mono-angle observations, multi-angular remote sensing can describe the anisotropy of surface reflectance and yield accurate information on canopy structure. These observations can also be used to describe the bi-directional reflectance distribution which then allows the modeling of reflectance independently of the observation geometry. In this paper, we demonstrate a method for estimating pigment contents of chlorophyll and carotenoids continuously over a year from tower-based, multi-angular spectro-radiometer observations. Estimates of chlorophyll and carotenoid content were derived at two flux-tower sites in western Canada. Pigment contents derived from inversion of a CR model (PROSAIL) compared well to those estimated using a semi-analytical approach (r(2) = 0.90 and r(2) = 0.69, P < 0.05 for both sites, respectively). Analysis of the seasonal dynamics indicated that net ecosystem productivity was strongly related to total canopy chlorophyll content at the deciduous site (r(2) = 0.70, P < 0.001), but not at the coniferous site. Similarly, spectral estimates of photosynthetic light-use efficiency showed strong seasonal patterns in the deciduous stand, but not in conifers. We conclude that multi-angular, spectral observations can play a key role in explaining seasonal dynamics of fluxes of carbon and water and provide a valuable addition to flux-tower-based networks.

Self-organization and symmetry-breaking in two-dimensional plasma turbulence

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

Bos, Wouter J. T.; Neffaa, Salah; Schneider, Kai

The spontaneous self-organization of two-dimensional magnetized plasma is investigated within the framework of magnetohydrodynamics with a particular emphasis on the symmetry-breaking induced by the shape of the confining boundaries. This symmetry-breaking is quantified by the angular momentum, which is shown to be generated rapidly and spontaneously from initial conditions free from angular momentum as soon as the geometry lacks axisymmetry. This effect is illustrated by considering circular, square, and elliptical boundaries. It is shown that the generation of angular momentum in nonaxisymmetric geometries can be enhanced by increasing the magnetic pressure. The effect becomes stronger at higher Reynolds numbers. Themore » generation of magnetic angular momentum (or angular field), previously observed at low Reynolds numbers, becomes weaker at larger Reynolds numbers.« less

Tactical Applications (TACAPPS) JavaScript Framework Investigation

DTIC Science & Technology

2017-02-01

frameworks explored were Angular JavaScript (AngularJS), jQuery UI, Meteor, Ember, React JavaScript (ReactJS) and Web Components. The team evaluated the...10 Issues and Risks 11 Web Components 11 Benefits 13 Issues and Risks 13 Conclusions 14 Bibliography 15 Distribution List 19...3 Basic Flux flow 10 4 Shadow DOM tree hierarchy 12 5 Web Components browser support 13 UNCLASSIFIED Approved for

Theory and Performance of AIMS for Active Interrogation

NASA Astrophysics Data System (ADS)

Walters, William J.; Royston, Katherine E. K.; Haghighat, Alireza

2014-06-01

A hybrid Monte Carlo and deterministic methodology has been developed for application to active interrogation systems. The methodology consists of four steps: i) determination of neutron flux distribution due to neutron source transport and subcritical multiplication; ii) generation of gamma source distribution from (n, γ) interactions; iii) determination of gamma current at a detector window; iv) detection of gammas by the detector. This paper discusses the theory and results of the first three steps for the case of a cargo container with a sphere of HEU in third-density water. In the first step, a response-function formulation has been developed to calculate the subcritical multiplication and neutron flux distribution. Response coefficients are pre-calculated using the MCNP5 Monte Carlo code. The second step uses the calculated neutron flux distribution and Bugle-96 (n, γ) cross sections to find the resulting gamma source distribution. Finally, in the third step the gamma source distribution is coupled with a pre-calculated adjoint function to determine the gamma flux at a detector window. A code, AIMS (Active Interrogation for Monitoring Special-Nuclear-materials), has been written to output the gamma current for an source-detector assembly scanning across the cargo using the pre-calculated values and takes significantly less time than a reference MCNP5 calculation.

Comparing mass balance and adjoint methods for inverse modeling of nitrogen dioxide columns for global nitrogen oxide emissions

NASA Astrophysics Data System (ADS)

Cooper, Matthew; Martin, Randall V.; Padmanabhan, Akhila; Henze, Daven K.

2017-04-01

Satellite observations offer information applicable to top-down constraints on emission inventories through inverse modeling. Here we compare two methods of inverse modeling for emissions of nitrogen oxides (NOx) from nitrogen dioxide (NO2) columns using the GEOS-Chem chemical transport model and its adjoint. We treat the adjoint-based 4D-Var modeling approach for estimating top-down emissions as a benchmark against which to evaluate variations on the mass balance method. We use synthetic NO2 columns generated from known NOx emissions to serve as "truth." We find that error in mass balance inversions can be reduced by up to a factor of 2 with an iterative process that uses finite difference calculations of the local sensitivity of NO2 columns to a change in emissions. In a simplified experiment to recover local emission perturbations, horizontal smearing effects due to NOx transport are better resolved by the adjoint approach than by mass balance. For more complex emission changes, or at finer resolution, the iterative finite difference mass balance and adjoint methods produce similar global top-down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3-4. Inversions of simulated satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint method, it offers the prospect of accurately estimating top-down NOx emissions using models that do not have an adjoint.

Adjoint Sensitivity Analysis of Orbital Mechanics: Application to Computations of Observables' Partials with Respect to Harmonics of the Planetary Gravity Fields

NASA Technical Reports Server (NTRS)

Ustinov, Eugene A.; Sunseri, Richard F.

2005-01-01

An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.

Two- and four-dimensional representations of the PT - and CPT -symmetric fermionic algebras

NASA Astrophysics Data System (ADS)

Beygi, Alireza; Klevansky, S. P.; Bender, Carl M.

2018-03-01

Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that T2=-1 for fermionic systems. In PT -symmetric quantum mechanics an operator has both PT and CPT adjoints. Fermionic operators η , which are quadratically nilpotent (η2=0 ), and algebras with PT and CPT adjoints can be constructed. These algebras obey different anticommutation relations: η ηPT+ηPTη =-1 , where ηPT is the PT adjoint of η , and η ηCPT+ηCPTη =1 , where ηCPT is the CPT adjoint of η . This paper presents matrix representations for the operator η and its PT and CPT adjoints in two and four dimensions. A PT -symmetric second-quantized Hamiltonian modeled on quantum electrodynamics that describes a system of interacting fermions and bosons is constructed within this framework and is solved exactly.

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

2013-01-01

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

NASA Technical Reports Server (NTRS)

Arian, Eyal; Salas, Manuel D.

1997-01-01

We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

Adjoint sensitivity analysis of plasmonic structures using the FDTD method.

PubMed

Zhang, Yu; Ahmed, Osman S; Bakr, Mohamed H

2014-05-15

We present an adjoint variable method for estimating the sensitivities of arbitrary responses with respect to the parameters of dispersive discontinuities in nanoplasmonic devices. Our theory is formulated in terms of the electric field components at the vicinity of perturbed discontinuities. The adjoint sensitivities are computed using at most one extra finite-difference time-domain (FDTD) simulation regardless of the number of parameters. Our approach is illustrated through the sensitivity analysis of an add-drop coupler consisting of a square ring resonator between two parallel waveguides. The computed adjoint sensitivities of the scattering parameters are compared with those obtained using the accurate but computationally expensive central finite difference approach.

Solar radiance models for determination of ERBE scanner filter factor

NASA Technical Reports Server (NTRS)

Arduini, R. F.

1985-01-01

Shortwave spectral radiance models for use in the spectral correction algorithms for the ERBE Scanner Instrument are provided. The required data base was delivered to the ERBe Data Reduction Group in October 1984. It consisted of two sets of data files: (1) the spectral bidirectional angular models and (2) the spectral flux modes. The bidirectional models employ the angular characteristics of reflection by the Earth-atmosphere system and were derived from detailed radiance calculations using a finite difference model of the radiative transfer process. The spectral flux models were created through the use of a delta-Eddington model to economically simulate the effects of atmospheric variability. By combining these data sets, a wide range of radiances may be approximated for a number of scene types.

Description of small-scale fluctuations in the diffuse X-ray background.

NASA Technical Reports Server (NTRS)

Cavaliere, A.; Friedland, A.; Gursky, H.; Spada, G.

1973-01-01

An analytical study of the fluctuations on a small angular scale expected in the diffuse X-ray background in the presence of unresolved sources is presented. The source population is described by a function N(S), giving the number of sources per unit solid angle and unit apparent flux S. The distribution of observed flux, s, in each angular resolution element of a complete sky survey is represented by a function Q(s). The analytical relation between the successive, higher-order moments of N(S) and Q(s) is described. The goal of reconstructing the source population from the study of the moments of Q(s) of order higher than the second (i.e., the rms fluctuations) is discussed.

Propagation of neutron-reaction uncertainties through multi-physics models of novel LWR's

NASA Astrophysics Data System (ADS)

Hernandez-Solis, Augusto; Sjöstrand, Henrik; Helgesson, Petter

2017-09-01

The novel design of the renewable boiling water reactor (RBWR) allows a breeding ratio greater than unity and thus, it aims at providing for a self-sustained fuel cycle. The neutron reactions that compose the different microscopic cross-sections and angular distributions are uncertain, so when they are employed in the determination of the spatial distribution of the neutron flux in a nuclear reactor, a methodology should be employed to account for these associated uncertainties. In this work, the Total Monte Carlo (TMC) method is used to propagate the different neutron-reactions (as well as angular distributions) covariances that are part of the TENDL-2014 nuclear data (ND) library. The main objective is to propagate them through coupled neutronic and thermal-hydraulic models in order to assess the uncertainty of important safety parameters related to multi-physics, such as peak cladding temperature along the axial direction of an RBWR fuel assembly. The objective of this study is to quantify the impact that ND covariances of important nuclides such as U-235, U-238, Pu-239 and the thermal scattering of hydrogen in H2O have in the deterministic safety analysis of novel nuclear reactors designs.

Atmospheric nitrogen deposition to the northwestern Pacific: seasonal variation and source attribution

NASA Astrophysics Data System (ADS)

Zhao, Y.; Zhang, L.; Pan, Y.; Wang, Y.; Paulot, F.; Henze, D. K.

2015-09-01

Rapid Asian industrialization has led to increased downwind atmospheric nitrogen deposition threatening the marine environment. We present an analysis of the sources and processes controlling atmospheric nitrogen deposition to the northwestern Pacific, using the GEOS-Chem global chemistry model and its adjoint model at 1/2° × 2/3° horizontal resolution over East Asia and its adjacent oceans. We focus our analyses on the marginal seas: the Yellow Sea and the South China Sea. Asian nitrogen emissions in the model are 28.6 Tg N a-1 as NH3 and 15.7 Tg N a-1 as NOx. China has the largest sources with 12.8 Tg N a-1 as NH3 and 7.9 Tg N a-1 as NOx; the high-NH3 emissions reflect its intensive agricultural activities. We find Asian NH3 emissions are a factor of 3 higher in summer than winter. The model simulation for 2008-2010 is evaluated with NH3 and NO2 column observations from satellite instruments, and wet deposition flux measurements from surface monitoring sites. Simulated atmospheric nitrogen deposition to the northwestern Pacific ranges 0.8-20 kg N ha-1 a-1, decreasing rapidly downwind of the Asian continent. Deposition fluxes average 11.9 kg N ha-1 a-1 (5.0 as reduced nitrogen NHx and 6.9 as oxidized nitrogen NOy) to the Yellow Sea, and 5.6 kg N ha-1 a-1 (2.5 as NHx and 3.1 as NOy) to the South China Sea. Nitrogen sources over the ocean (ship NOx and oceanic NH3) have little contribution to deposition over the Yellow Sea, about 7 % over the South China Sea, and become important (greater than 30 %) further downwind. We find that the seasonality of nitrogen deposition to the northwestern Pacific is determined by variations in meteorology largely controlled by the East Asian monsoon and in nitrogen emissions. The model adjoint further estimates that nitrogen deposition to the Yellow Sea originates from sources over China (92 % contribution) and the Korean peninsula (7 %), and by sectors from fertilizer use (24 %), power plants (22 %), and transportation (18 %). Deposition to the South China Sea shows source contribution from mainland China (66 %), Taiwan (20 %), and the rest (14 %) from the southeast Asian countries and oceanic NH3 emissions. The adjoint analyses also indicate that reducing Asian NH3 emissions would increase NOy dry deposition to the Yellow Sea (28 % offset annually), limiting the effectiveness of NH3 emission controls on reducing nitrogen deposition to the Yellow Sea.

Atmospheric nitrogen deposition to the northwestern Pacific: seasonal variation and source attribution

NASA Astrophysics Data System (ADS)

Zhao, Yuanhong; Zhang, Lin; Pan, Yuepeng; Wang, Yuesi; Paulot, Fabien; Henze, Daven

2016-04-01

Rapid Asian industrialization has lead to increased atmospheric nitrogen deposition downwind threatening the marine environment. We present an analysis of the sources and processes controlling atmospheric nitrogen deposition to the northwestern Pacific, using the GEOS-Chem global chemistry model and its adjoint model at 1/2°× 2/3° horizontal resolution over the East Asia and its adjacent oceans. We focus our analyses on the marginal seas: the Yellow Sea and the South China Sea. Asian nitrogen emissions in the model are 28.6 Tg N a-1 as NH3 and 15.7 Tg N a-1 as NOx. China has the largest sources with 12.8 Tg N a-1 as NH3 and 7.9 Tg N a-1 as NOx; the much higher NH3 emissions reflect its intensive agricultural activities. We improve the seasonality of Asian NH3 emissions; emissions are a factor of 3 higher in summer than winter. The model simulation for 2008-2010 is evaluated with NH3 and NO2 column observations from satellite instruments, and wet deposition flux measurements from surface monitoring sites. Simulated atmospheric nitrogen deposition to the northwestern Pacific ranges 0.8-20 kg N ha-1 a-1, decreasing rapidly downwind the Asian continent. Deposition fluxes average 11.9 kg N ha-1 a-1 (5.0 as reduced nitrogen NHx and 6.9 as oxidized nitrogen NOy) to the Yellow Sea, and 5.6 kg N ha-1 a-1 (2.5 as NHx and 3.1 as NOy) to the South China Sea. Nitrogen sources over the ocean (ship NOx and oceanic NH3) have little contribution to deposition over the Yellow Sea, about 7% over the South China Sea, and become important (greater than 30%) further downwind. We find that the seasonality of nitrogen deposition to the northwestern Pacific is determined by variations in meteorology largely controlled by the East Asian Monsoon and in nitrogen emissions. The model adjoint further points out that nitrogen deposition to the Yellow Sea originates from sources over China (92% contribution) and the Korean peninsula (7%), and by sectors from fertilizer use (24%), power plants (22%), and transportation (18%). Deposition to the South China Sea shows source contribution from Mainland China (64%), Taiwan (21%), and the rest 15% from the Southeast Asian countries and oceanic NH3 emissions. The adjoint analyses also indicate that reducing Asian NH3 emissions would increase NOy dry deposition to the Yellow Sea (28% offset annually), limiting the effectiveness of NH3 emission controls.

What Confines the Rings of Saturn?

NASA Astrophysics Data System (ADS)

Tajeddine, Radwan; Nicholson, Philip D.; Longaretti, Pierre-Yves; El Moutamid, Maryame; Burns, Joseph A.

2017-10-01

The viscous spreading of planetary rings is believed to be counteracted by satellite torques, through either an individual resonance or overlapping resonances. For the A ring of Saturn, it has been commonly believed that the satellite Janus alone can prevent the ring from spreading, via its 7:6 Lindblad resonance. We discuss this common misconception and show that, in reality, the A ring is confined by the contributions from the group of satellites Pan, Atlas, Prometheus, Pandora, Janus, Epimetheus, and Mimas, whose cumulative torques from various resonances gradually decrease the angular momentum flux transported outward through the ring via density and bending waves. We further argue that this decrease in angular momentum flux occurs through “flux reversal.” Furthermore, we use the magnitude of the satellites’ resonance torques to estimate the effective viscosity profile across the A ring, showing that it decreases with radius from ˜50 cm2 s-1 to less than ˜10 cm2 s-1. The gradual estimated decrease of the angular momentum flux and effective viscosity are roughly consistent with results obtained by balancing the shepherding torques from Pan and Daphnis with the viscous torque at the edges of the Encke and Keeler gaps, as well as the edge of the A ring. On the other hand, the Mimas 2:1 Lindblad resonance alone seems to be capable of confining the edge of the B ring, and contrary to the situation in the A ring, we show that the effective viscosity across the B ring is relatively constant at ˜24-30 cm2 s-1.

Heat transfer to throat tubes in a square-chambered rocket engine at the NASA Lewis Research Center

NASA Technical Reports Server (NTRS)

Nesbitt, James A.; Brindley, William J.

1989-01-01

A gaseous H2/O2 rocket engine was constructed at the NASA-Lewis to provide a high heat flux source representative of the heat flux to the blades in the high pressure fuel turbopump (HPFTP) during startup of the space shuttle main engines. The high heat flux source was required to evaluate the durability of thermal barrier coatings being investigated for use on these blades. The heat transfer, and specifically, the heat flux to tubes located at the throat of the test rocket engine was evaluated and compared to the heat flux to the blades in the HPFTP during engine startup. Gas temperatures, pressures and heat transfer coefficients in the test rocket engine were measured. Near surface metal temperatures below thin thermal barrier coatings were also measured at various angular orientations around the throat tube to indicate the angular dependence of the heat transfer coefficients. A finite difference model for a throat tube was developed and a thermal analysis was performed using the measured gas temperatures and the derived heat transfer coefficients to predict metal temperatures in the tube. Near surface metal temperatures of an uncoated throat tube were measured at the stagnation point and showed good agreement with temperatures predicted by the thermal model. The maximum heat flux to the throat tube was calculated and compared to that predicted for the leading edge of an HPFTP blade. It is shown that the heat flux to an uncooled throat tube is slightly greater than the heat flux to an HPFTP blade during engine startup.

Zero modes of the non-relativistic self-dual Chern-Simons vortices on the Toda backgrounds

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

Yoon, Yongsung

The two-dimensional self-dual equations are the governing equations of the static zero-energy vortex solutions for the non-relativistic, non-Abelian Chern-Simons models. The zero modes of the non-relativistic vortices are examined by index calculation for the self-dual equations. The index for the self-dual equations is zero for non-Abelian groups, but a non-zero index is obtained by the Toda Ansatz which reduces the self-dual equations to the Toda equations. The number of zero modes for the non-relativistic Toda vortices is 2 {Sigma}{sub {alpha},{beta}}{sup r}K{sub {alpha}{beta}}Q{sup {beta}} which is twice the total number of isolated zeros of the vortex functions. For the affine Todamore » system, there are additional adjoint zero modes which give a zero index for the SU(N) group.« less

Ambient noise adjoint tomography for a linear array in North China

NASA Astrophysics Data System (ADS)

Zhang, C.; Yao, H.; Liu, Q.; Yuan, Y. O.; Zhang, P.; Feng, J.; Fang, L.

2017-12-01

Ambient noise tomography based on dispersion data and ray theory has been widely utilized for imaging crustal structures. In order to improve the inversion accuracy, ambient noise tomography based on the 3D adjoint approach or full waveform inversion has been developed recently, however, the computational cost is tremendous. In this study we present 2D ambient noise adjoint tomography for a linear array in north China with significant computational efficiency compared to 3D ambient noise adjoint tomography. During the preprocessing, we first convert the observed data in 3D media, i.e., surface-wave empirical Green's functions (EGFs) from ambient noise cross-correlation, to the reconstructed EGFs in 2D media using a 3D/2D transformation scheme. Different from the conventional steps of measuring phase dispersion, the 2D adjoint tomography refines 2D shear wave speeds along the profile directly from the reconstructed Rayleigh wave EGFs in the period band 6-35s. With the 2D initial model extracted from the 3D model from traditional ambient noise tomography, adjoint tomography updates the model by minimizing the frequency-dependent Rayleigh wave traveltime misfits between the reconstructed EGFs and synthetic Green function (SGFs) in 2D media generated by the spectral-element method (SEM), with a preconditioned conjugate gradient method. The multitaper traveltime difference measurement is applied in four period bands during the inversion: 20-35s, 15-30s, 10-20s and 6-15s. The recovered model shows more detailed crustal structures with pronounced low velocity anomaly in the mid-lower crust beneath the junction of Taihang Mountains and Yin-Yan Mountains compared with the initial model. This low velocity structure may imply the possible intense crust-mantle interactions, probably associated with the magmatic underplating during the Mesozoic to Cenozoic evolution of the region. To our knowledge, it's first time that ambient noise adjoint tomography is implemented in 2D media. Considering the intensive computational cost and storage of 3D adjoint tomography, this 2D ambient noise adjoint tomography has potential advantages to get high-resolution 2D crustal structures with limited computational resource.

2D Inviscid and Viscous Inverse Design Using Continuous Adjoint and Lax-Wendroff Formulation

NASA Astrophysics Data System (ADS)

Proctor, Camron Lisle

The continuous adjoint (CA) technique for optimization and/or inverse-design of aerodynamic components has seen nearly 30 years of documented success in academia. The benefits of using CA versus a direct sensitivity analysis are shown repeatedly in the literature. However, the use of CA in industry is relatively unheard-of. The sparseness of industry contributions to the field may be attributed to the tediousness of the derivation and/or to the difficulties in implementation due to the lack of well-documented adjoint numerical methods. The focus of this work has been to thoroughly document the techniques required to build a two-dimensional CA inverse-design tool. To this end, this work begins with a short background on computational fluid dynamics (CFD) and the use of optimization tools in conjunction with CFD tools to solve aerodynamic optimization problems. A thorough derivation of the continuous adjoint equations and the accompanying gradient calculations for inviscid and viscous constraining equations follows the introduction. Next, the numerical techniques used for solving the partial differential equations (PDEs) governing the flow equations and the adjoint equations are described. Numerical techniques for the supplementary equations are discussed briefly. Subsequently, a verification of the efficacy of the inverse design tool, for the inviscid adjoint equations as well as possible numerical implementation pitfalls are discussed. The NACA0012 airfoil is used as an initial airfoil and surface pressure distribution and the NACA16009 is used as the desired pressure and vice versa. Using a Savitsky-Golay gradient filter, convergence (defined as a cost function<1E-5) is reached in approximately 220 design iteration using 121 design variables. The inverse-design using inviscid adjoint equations results are followed by the discussion of the viscous inverse design results and techniques used to further the convergence of the optimizer. The relationship between limiting step-size and convergence in a line-search optimization is shown to slightly decrease the final cost function at significant computational cost. A gradient damping technique is presented and shown to increase the convergence rate for the optimization in viscous problems, at a negligible increase in computational cost, but is insufficient to converge the solution. Systematically including adjacent surface vertices in the perturbation of a design variable, also a surface vertex, is shown to affect the convergence capability of the viscous optimizer. Finally, a comparison of using inviscid adjoint equations, as opposed to viscous adjoint equations, on viscous flow is presented, and the inviscid adjoint paired with viscous flow is found to reduce the cost function further than the viscous adjoint for the presented problem.

Quantum damped oscillator I: Dissipation and resonances

NASA Astrophysics Data System (ADS)

Chruściński, Dariusz; Jurkowski, Jacek

2006-04-01

Quantization of a damped harmonic oscillator leads to so called Bateman’s dual system. The corresponding Bateman’s Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.

A new least-squares transport equation compatible with voids

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

Hansen, J. B.; Morel, J. E.

2013-07-01

We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

Estimating stellar effective temperatures and detected angular parameters using stochastic particle swarm optimization

NASA Astrophysics Data System (ADS)

Zhang, Chuan-Xin; Yuan, Yuan; Zhang, Hao-Wei; Shuai, Yong; Tan, He-Ping

2016-09-01

Considering features of stellar spectral radiation and sky surveys, we established a computational model for stellar effective temperatures, detected angular parameters and gray rates. Using known stellar flux data in some bands, we estimated stellar effective temperatures and detected angular parameters using stochastic particle swarm optimization (SPSO). We first verified the reliability of SPSO, and then determined reasonable parameters that produced highly accurate estimates under certain gray deviation levels. Finally, we calculated 177 860 stellar effective temperatures and detected angular parameters using data from the Midcourse Space Experiment (MSX) catalog. These derived stellar effective temperatures were accurate when we compared them to known values from literatures. This research makes full use of catalog data and presents an original technique for studying stellar characteristics. It proposes a novel method for calculating stellar effective temperatures and detecting angular parameters, and provides theoretical and practical data for finding information about radiation in any band.

Running coupling from gluon and ghost propagators in the Landau gauge: Yang-Mills theories with adjoint fermions

NASA Astrophysics Data System (ADS)

Bergner, Georg; Piemonte, Stefano

2018-04-01

Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N =1 supersymmetric Yang-Mills (SYM) theory and minimal walking technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N =1 SYM, minimal walking technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to compute the running coupling in the MiniMom scheme. We analyze several different ensembles of lattice Monte Carlo simulations for the SU(2) adjoint QCD with Nf=1 /2 ,1 ,3 /2 , and 2 Dirac fermions. We show how the running of the coupling changes as the number of interacting fermions is increased towards the conformal window.

The continuous adjoint approach to the k-ε turbulence model for shape optimization and optimal active control of turbulent flows

NASA Astrophysics Data System (ADS)

Papoutsis-Kiachagias, E. M.; Zymaris, A. S.; Kavvadias, I. S.; Papadimitriou, D. I.; Giannakoglou, K. C.

2015-03-01

The continuous adjoint to the incompressible Reynolds-averaged Navier-Stokes equations coupled with the low Reynolds number Launder-Sharma k-ε turbulence model is presented. Both shape and active flow control optimization problems in fluid mechanics are considered, aiming at minimum viscous losses. In contrast to the frequently used assumption of frozen turbulence, the adjoint to the turbulence model equations together with appropriate boundary conditions are derived, discretized and solved. This is the first time that the adjoint equations to the Launder-Sharma k-ε model have been derived. Compared to the formulation that neglects turbulence variations, the impact of additional terms and equations is evaluated. Sensitivities computed using direct differentiation and/or finite differences are used for comparative purposes. To demonstrate the need for formulating and solving the adjoint to the turbulence model equations, instead of merely relying upon the 'frozen turbulence assumption', the gain in the optimization turnaround time offered by the proposed method is quantified.

A comparison of discrete versus continuous adjoint states to invert groundwater flow in heterogeneous dual porosity systems

NASA Astrophysics Data System (ADS)

Delay, Frederick; Badri, Hamid; Fahs, Marwan; Ackerer, Philippe

2017-12-01

Dual porosity models become increasingly used for simulating groundwater flow at the large scale in fractured porous media. In this context, model inversions with the aim of retrieving the system heterogeneity are frequently faced with huge parameterizations for which descent methods of inversion with the assistance of adjoint state calculations are well suited. We compare the performance of discrete and continuous forms of adjoint states associated with the flow equations in a dual porosity system. The discrete form inherits from previous works by some of the authors, as the continuous form is completely new and here fully differentiated for handling all types of model parameters. Adjoint states assist descent methods by calculating the gradient components of the objective function, these being a key to good convergence of inverse solutions. Our comparison on the basis of synthetic exercises show that both discrete and continuous adjoint states can provide very similar solutions close to reference. For highly heterogeneous systems, the calculation grid of the continuous form cannot be too coarse, otherwise the method may show lack of convergence. This notwithstanding, the continuous adjoint state is the most versatile form as its non-intrusive character allows for plugging an inversion toolbox quasi-independent from the code employed for solving the forward problem.

Optimization of wind plant layouts using an adjoint approach

DOE PAGES

King, Ryan N.; Dykes, Katherine; Graf, Peter; ...

2017-03-10

Using adjoint optimization and three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations, we present a new gradient-based approach for optimally siting wind turbines within utility-scale wind plants. By solving the adjoint equations of the flow model, the gradients needed for optimization are found at a cost that is independent of the number of control variables, thereby permitting optimization of large wind plants with many turbine locations. Moreover, compared to the common approach of superimposing prescribed wake deficits onto linearized flow models, the computational efficiency of the adjoint approach allows the use of higher-fidelity RANS flow models which can capture nonlinear turbulent flowmore » physics within a wind plant. The steady-state RANS flow model is implemented in the Python finite-element package FEniCS and the derivation and solution of the discrete adjoint equations are automated within the dolfin-adjoint framework. Gradient-based optimization of wind turbine locations is demonstrated for idealized test cases that reveal new optimization heuristics such as rotational symmetry, local speedups, and nonlinear wake curvature effects. Layout optimization is also demonstrated on more complex wind rose shapes, including a full annual energy production (AEP) layout optimization over 36 inflow directions and 5 wind speed bins.« less

Optimization of wind plant layouts using an adjoint approach

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

King, Ryan N.; Dykes, Katherine; Graf, Peter

Using adjoint optimization and three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations, we present a new gradient-based approach for optimally siting wind turbines within utility-scale wind plants. By solving the adjoint equations of the flow model, the gradients needed for optimization are found at a cost that is independent of the number of control variables, thereby permitting optimization of large wind plants with many turbine locations. Moreover, compared to the common approach of superimposing prescribed wake deficits onto linearized flow models, the computational efficiency of the adjoint approach allows the use of higher-fidelity RANS flow models which can capture nonlinear turbulent flowmore » physics within a wind plant. The steady-state RANS flow model is implemented in the Python finite-element package FEniCS and the derivation and solution of the discrete adjoint equations are automated within the dolfin-adjoint framework. Gradient-based optimization of wind turbine locations is demonstrated for idealized test cases that reveal new optimization heuristics such as rotational symmetry, local speedups, and nonlinear wake curvature effects. Layout optimization is also demonstrated on more complex wind rose shapes, including a full annual energy production (AEP) layout optimization over 36 inflow directions and 5 wind speed bins.« less

A 2-D/1-D transverse leakage approximation based on azimuthal, Fourier moments

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

Stimpson, Shane G.; Collins, Benjamin S.; Downar, Thomas

Here, the MPACT code being developed collaboratively by Oak Ridge National Laboratory and the University of Michigan is the primary deterministic neutron transport solver within the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). In MPACT, the two-dimensional (2-D)/one-dimensional (1-D) scheme is the most commonly used method for solving neutron transport-based three-dimensional nuclear reactor core physics problems. Several axial solvers in this scheme assume isotropic transverse leakages, but work with the axial S N solver has extended these leakages to include both polar and azimuthal dependence. However, explicit angular representation can be burdensome for run-time and memory requirements. The workmore » here alleviates this burden by assuming that the azimuthal dependence of the angular flux and transverse leakages are represented by a Fourier series expansion. At the heart of this is a new axial SN solver that takes in a Fourier expanded radial transverse leakage and generates the angular fluxes used to construct the axial transverse leakages used in the 2-D-Method of Characteristics calculations.« less

A 2-D/1-D transverse leakage approximation based on azimuthal, Fourier moments

DOE PAGES

Stimpson, Shane G.; Collins, Benjamin S.; Downar, Thomas

2017-01-12

Here, the MPACT code being developed collaboratively by Oak Ridge National Laboratory and the University of Michigan is the primary deterministic neutron transport solver within the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). In MPACT, the two-dimensional (2-D)/one-dimensional (1-D) scheme is the most commonly used method for solving neutron transport-based three-dimensional nuclear reactor core physics problems. Several axial solvers in this scheme assume isotropic transverse leakages, but work with the axial S N solver has extended these leakages to include both polar and azimuthal dependence. However, explicit angular representation can be burdensome for run-time and memory requirements. The workmore » here alleviates this burden by assuming that the azimuthal dependence of the angular flux and transverse leakages are represented by a Fourier series expansion. At the heart of this is a new axial SN solver that takes in a Fourier expanded radial transverse leakage and generates the angular fluxes used to construct the axial transverse leakages used in the 2-D-Method of Characteristics calculations.« less

Fisheye camera method for spatial non-uniformity corrections in luminous flux measurements with integrating spheres

NASA Astrophysics Data System (ADS)

Kokka, Alexander; Pulli, Tomi; Poikonen, Tuomas; Askola, Janne; Ikonen, Erkki

2017-08-01

This paper presents a fisheye camera method for determining spatial non-uniformity corrections in luminous flux measurements with integrating spheres. Using a fisheye camera installed into a port of an integrating sphere, the relative angular intensity distribution of the lamp under test is determined. This angular distribution is used for calculating the spatial non-uniformity correction for the lamp when combined with the spatial responsivity data of the sphere. The method was validated by comparing it to a traditional goniophotometric approach when determining spatial correction factors for 13 LED lamps with different angular spreads. The deviations between the spatial correction factors obtained using the two methods ranged from -0.15 % to 0.15%. The mean magnitude of the deviations was 0.06%. For a typical LED lamp, the expanded uncertainty (k = 2 ) for the spatial non-uniformity correction factor was evaluated to be 0.28%. The fisheye camera method removes the need for goniophotometric measurements in determining spatial non-uniformity corrections, thus resulting in considerable system simplification. Generally, no permanent modifications to existing integrating spheres are required.

Preliminary Results from the Application of Automated Adjoint Code Generation to CFL3D

NASA Technical Reports Server (NTRS)

Carle, Alan; Fagan, Mike; Green, Lawrence L.

1998-01-01

This report describes preliminary results obtained using an automated adjoint code generator for Fortran to augment a widely-used computational fluid dynamics flow solver to compute derivatives. These preliminary results with this augmented code suggest that, even in its infancy, the automated adjoint code generator can accurately and efficiently deliver derivatives for use in transonic Euler-based aerodynamic shape optimization problems with hundreds to thousands of independent design variables.

Global Modeling and Data Assimilation. Volume 11; Documentation of the Tangent Linear and Adjoint Models of the Relaxed Arakawa-Schubert Moisture Parameterization of the NASA GEOS-1 GCM; 5.2

NASA Technical Reports Server (NTRS)

Suarez, Max J. (Editor); Yang, Wei-Yu; Todling, Ricardo; Navon, I. Michael

1997-01-01

A detailed description of the development of the tangent linear model (TLM) and its adjoint model of the Relaxed Arakawa-Schubert moisture parameterization package used in the NASA GEOS-1 C-Grid GCM (Version 5.2) is presented. The notational conventions used in the TLM and its adjoint codes are described in detail.

Carbon Monitoring System Flux Estimation and Attribution: Impact of ACOS-GOSAT X(CO2) Sampling on the Inference of Terrestrial Biospheric Sources and Sinks

NASA Technical Reports Server (NTRS)

Liu, Junjie; Bowman, Kevin W.; Lee, Memong; Henze, David K.; Bousserez, Nicolas; Brix, Holger; Collatz, G. James; Menemenlis, Dimitris; Ott, Lesley; Pawson, Steven;

On the physical Hilbert space of loop quantum cosmology

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

Noui, Karim; Perez, Alejandro; Vandersloot, Kevin

2005-02-15

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable, consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.

Iterative spectral methods and spectral solutions to compressible flows

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Zang, T. A.

1982-01-01

A spectral multigrid scheme is described which can solve pseudospectral discretizations of self-adjoint elliptic problems in O(N log N) operations. An iterative technique for efficiently implementing semi-implicit time-stepping for pseudospectral discretizations of Navier-Stokes equations is discussed. This approach can handle variable coefficient terms in an effective manner. Pseudospectral solutions of compressible flow problems are presented. These include one dimensional problems and two dimensional Euler solutions. Results are given both for shock-capturing approaches and for shock-fitting ones.

Development of WRF-CO2 4DVAR Data Assimilation System

NASA Astrophysics Data System (ADS)

Zheng, T.; French, N. H. F.

2016-12-01

Four dimensional variational (4DVar) assimilation systems have been widely used for CO2 inverse modeling at global scale. At regional scale, however, 4DVar assimilation systems have been lacking. At present, most regional CO2 inverse models use Lagrangian particle backward trajectory tools to compute influence function in an analytical/synthesis framework. To provide a 4DVar based alternative, we developed WRF-CO2 4DVAR based on Weather Research and Forecasting (WRF), its chemistry extension (WRF-Chem), and its data assimilation system (WRFDA/WRFPLUS). Different from WRFDA, WRF-CO2 4DVAR does not optimize meteorology initial condition, instead it solves for the optimized CO2 surface fluxes (sources/sink) constrained by atmospheric CO2 observations. Based on WRFPLUS, we developed tangent linear and adjoint code for CO2 emission, advection, vertical mixing in boundary layer, and convective transport. Furthermore, we implemented an incremental algorithm to solve for optimized CO2 emission scaling factors by iteratively minimizing the cost function in a Bayes framework. The model sensitivity (of atmospheric CO2 with respect to emission scaling factor) calculated by tangent linear and adjoint model agrees well with that calculated by finite difference, indicating the validity of the newly developed code. The effectiveness of WRF-CO2 4DVar for inverse modeling is tested using forward-model generated pseudo-observation data in two experiments: first-guess CO2 fluxes has a 50% overestimation in the first case and 50% underestimation in the second. In both cases, WRF-CO2 4DVar reduces cost function to less than 10-4 of its initial values in less than 20 iterations and successfully recovers the true values of emission scaling factors. We expect future applications of WRF-CO2 4DVar with satellite observations will provide insights for CO2 regional inverse modeling, including the impacts of model transport error in vertical mixing.

Estimation of Regional Carbon Balance from Atmospheric Observations

NASA Astrophysics Data System (ADS)

Denning, S.; Uliasz, M.; Skidmore, J.

2002-12-01

Variations in the concentration of CO2 and other trace gases in time and space contain information about sources and sinks at regional scales. Several methods have been developed to quantitatively extract this information from atmospheric measurements. Mass-balance techniques depend on the ability to repeatedly sample the same mass of air, which involves careful attention to airmass trajectories. Inverse and adjoint techniques rely on decomposition of the source field into quasi-independent "basis functions" that are propagated through transport models and then used to synthesize optimal linear combinations that best match observations. A recently proposed method for regional flux estimation from continuous measurements at tall towers relies on time-mean vertical gradients, and requires careful trajectory analysis to map the estimates onto regional ecosystems. Each of these techniques is likely to be applied to measurements made during the North American Carbon Program. We have also explored the use of Bayesian synthesis inversion at regional scales, using a Lagrangian particle dispersion model driven by mesoscale transport fields. Influence functions were calculated for each hypothetical observation in a realistic diurnally-varying flow. These influence functions were then treated as basis functions for the purpose of separate inversions for daytime photosynthesis and 24-hour mean ecosystem respiration. Our results highlight the importance of estimating CO2 fluxes through the lateral boundaries of the model. Respiration fluxes were well constrained by one or two hypothetical towers, regardless of inflow fluxes. Time-varying assimilation fluxes were less well constrained, and much more dependent on knowledge of inflow fluxes. The small net difference between respiration and photosynthesis was the most difficult to determine, being extremely sensitive to knowledge of inflow fluxes. Finally, we explored the feasibility of directly incorporating mid-day concentration values measured at surface-layer flux towers in global inversions for regional surface fluxes. We found that such data would substantially improve the observational constraint on current carbon cycle models, especially if applied selectively to a well-designed subset of the current network of flux towers.

A POD reduced order model for resolving angular direction in neutron/photon transport problems

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

Buchan, A.G., E-mail: andrew.buchan@imperial.ac.uk; Calloo, A.A.; Goffin, M.G.

2015-09-01

This article presents the first Reduced Order Model (ROM) that efficiently resolves the angular dimension of the time independent, mono-energetic Boltzmann Transport Equation (BTE). It is based on Proper Orthogonal Decomposition (POD) and uses the method of snapshots to form optimal basis functions for resolving the direction of particle travel in neutron/photon transport problems. A unique element of this work is that the snapshots are formed from the vector of angular coefficients relating to a high resolution expansion of the BTE's angular dimension. In addition, the individual snapshots are not recorded through time, as in standard POD, but instead theymore » are recorded through space. In essence this work swaps the roles of the dimensions space and time in standard POD methods, with angle and space respectively. It is shown here how the POD model can be formed from the POD basis functions in a highly efficient manner. The model is then applied to two radiation problems; one involving the transport of radiation through a shield and the other through an infinite array of pins. Both problems are selected for their complex angular flux solutions in order to provide an appropriate demonstration of the model's capabilities. It is shown that the POD model can resolve these fluxes efficiently and accurately. In comparison to high resolution models this POD model can reduce the size of a problem by up to two orders of magnitude without compromising accuracy. Solving times are also reduced by similar factors.« less

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

Raoult, Nina M.; Jupp, Tim E.; Cox, Peter M.

Land-surface models (LSMs) are crucial components of the Earth system models (ESMs) that are used to make coupled climate–carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. JULES is also extensively used offline as a land-surface impacts tool, forced with climatologies into the future. In this study, JULES is automatically differentiated with respect to JULES parameters using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimationmore » system has been developed to search for locally optimum parameters by calibrating against observations. This paper describes adJULES in a data assimilation framework and demonstrates its ability to improve the model–data fit using eddy-covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the five plant functional types (PFTs) in JULES. The optimised PFT-specific parameters improve the performance of JULES at over 85 % of the sites used in the study, at both the calibration and evaluation stages. Furthermore, the new improved parameters for JULES are presented along with the associated uncertainties for each parameter.« less

Atmospheric Ammonia Over China: Emission Estimates And Impact On Air Quality

NASA Astrophysics Data System (ADS)

Zhang, L.; Chen, Y.; Zhao, Y.; Henze, D. K.

2016-12-01

Ammonia (NH3) in the atmosphere is an important precursor of aerosols, and its deposition through wet and dry processes can cause adverse effects on ecosystems. The ammonia emissions over China are particularly large due to intensive agricultural activities, yet our current estimates of Chinese ammonia emissions and associated consequences on air quality are subject to large errors. We use the GEOS-Chem chemical transport model and its adjoint model to better quantify this issue. The TES satellite observations of ammonia concentrations and surface measurements of wet deposition fluxes are assimilated into the model to constrain the ammonia emissions over China. Optimized emissions show a strong seasonal variability with emissions in summer a factor of 3 higher than winter. This is consistent with an improved bottom-up estimate of Chinese ammonia emissions from fertilizer use by using more practical fertilizer application rates for different crop types. We further use the GEOS-Chem adjoint at 0.25x0.3125 degree resolution to examine the sources contributing to the PM2.5 air pollution over North China. We show that wintertime PM2.5 over Beijing is largely contributed by residential and industrial sources, and ammonia emissions from agriculture activities. PM2.5 concentrations over North China are particularly sensitive to emissions of ammonia and nitrogen oxides, reflecting strong formation of aerosol nitrate in the cold seasons.

Land-surface parameter optimisation using data assimilation techniques: the adJULES system V1.0

NASA Astrophysics Data System (ADS)

Raoult, Nina M.; Jupp, Tim E.; Cox, Peter M.; Luke, Catherine M.

2016-08-01

Land-surface models (LSMs) are crucial components of the Earth system models (ESMs) that are used to make coupled climate-carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. JULES is also extensively used offline as a land-surface impacts tool, forced with climatologies into the future. In this study, JULES is automatically differentiated with respect to JULES parameters using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimation system has been developed to search for locally optimum parameters by calibrating against observations. This paper describes adJULES in a data assimilation framework and demonstrates its ability to improve the model-data fit using eddy-covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the five plant functional types (PFTs) in JULES. The optimised PFT-specific parameters improve the performance of JULES at over 85 % of the sites used in the study, at both the calibration and evaluation stages. The new improved parameters for JULES are presented along with the associated uncertainties for each parameter.

Inverse Regional Modeling with Adjoint-Free Technique

NASA Astrophysics Data System (ADS)

Yaremchuk, M.; Martin, P.; Panteleev, G.; Beattie, C.

2016-02-01

The ongoing parallelization trend in computer technologies facilitates the use ensemble methods in geophysical data assimilation. Of particular interest are ensemble techniques which do not require the development of tangent linear numerical models and their adjoints for optimization. These ``adjoint-free'' methods minimize the cost function within the sequence of subspaces spanned by a carefully chosen sets perturbations of the control variables. In this presentation, an adjoint-free variational technique (a4dVar) is demonstrated in an application estimating initial conditions of two numerical models: the Navy Coastal Ocean Model (NCOM), and the surface wave model (WAM). With the NCOM, performance of both adjoint and adjoint-free 4dVar data assimilation techniques is compared in application to the hydrographic surveys and velocity observations collected in the Adriatic Sea in 2006. Numerical experiments have shown that a4dVar is capable of providing forecast skill similar to that of conventional 4dVar at comparable computational expense while being less susceptible to excitation of ageostrophic modes that are not supported by observations. Adjoint-free technique constrained by the WAM model is tested in a series of data assimilation experiments with synthetic observations in the southern Chukchi Sea. The types of considered observations are directional spectra estimated from point measurements by stationary buoys, significant wave height (SWH) observations by coastal high-frequency radars and along-track SWH observations by satellite altimeters. The a4dVar forecast skill is shown to be 30-40% better than the skill of the sequential assimilaiton method based on optimal interpolation which is currently used in operations. Prospects of further development of the a4dVar methods in regional applications are discussed.

Transient sensitivities of sea ice export through the Canadian Arctic Archipelago inferred from a coupled ocean/sea-ice adjoint model

NASA Astrophysics Data System (ADS)

Heimbach, P.; Losch, M.; Menemenlis, D.; Campin, J.; Hill, C.

2008-12-01

The sensitivity of sea-ice export through the Canadian Arctic Archipelago (CAA), measured in terms of its solid freshwater export through Lancaster Sound, to changes in various elements of the ocean and sea-ice state, and to elements of the atmospheric forcing fields through time and space is assessed by means of a coupled ocean/sea-ice adjoint model. The adjoint model furnishes full spatial sensitivity maps (also known as Lagrange multipliers) of the export metric to a variety of model variables at any chosen point in time, providing the unique capability to quantify major drivers of sea-ice export variability. The underlying model is the MIT ocean general circulation model (MITgcm), which is coupled to a Hibler-type dynamic/thermodynamic sea-ice model. The configuration is based on the Arctic face of the ECCO3 high-resolution cubed-sphere model, but coarsened to 36-km horizontal grid spacing. The adjoint of the coupled system has been derived by means of automatic differentiation using the software tool TAF. Finite perturbation simulations are performed to check the information provided by the adjoint. The sea-ice model's performance in the presence of narrow straits is assessed with different sea-ice lateral boundary conditions. The adjoint sensitivity clearly exposes the role of the model trajectory and the transient nature of the problem. The complex interplay between forcing, dynamics, and boundary condition is demonstrated in the comparison between the different calculations. The study is a step towards fully coupled adjoint-based ocean/sea-ice state estimation at basin to global scales as part of the ECCO efforts.

Global Seismic Imaging Based on Adjoint Tomography

NASA Astrophysics Data System (ADS)

Bozdag, E.; Lefebvre, M.; Lei, W.; Peter, D. B.; Smith, J. A.; Zhu, H.; Komatitsch, D.; Tromp, J.

2013-12-01

Our aim is to perform adjoint tomography at the scale of globe to image the entire planet. We have started elastic inversions with a global data set of 253 CMT earthquakes with moment magnitudes in the range 5.8 ≤ Mw ≤ 7 and used GSN stations as well as some local networks such as USArray, European stations, etc. Using an iterative pre-conditioned conjugate gradient scheme, we initially set the aim to obtain a global crustal and mantle model with confined transverse isotropy in the upper mantle. Global adjoint tomography has so far remained a challenge mainly due to computational limitations. Recent improvements in our 3D solvers (e.g., a GPU version) and access to high-performance computational centers (e.g., ORNL's Cray XK7 "Titan" system) now enable us to perform iterations with higher-resolution (T > 9 s) and longer-duration (200 min) simulations to accommodate high-frequency body waves and major-arc surface waves, respectively, which help improve data coverage. The remaining challenge is the heavy I/O traffic caused by the numerous files generated during the forward/adjoint simulations and the pre- and post-processing stages of our workflow. We improve the global adjoint tomography workflow by adopting the ADIOS file format for our seismic data as well as models, kernels, etc., to improve efficiency on high-performance clusters. Our ultimate aim is to use data from all available networks and earthquakes within the magnitude range of our interest (5.5 ≤ Mw ≤ 7) which requires a solid framework to manage big data in our global adjoint tomography workflow. We discuss the current status and future of global adjoint tomography based on our initial results as well as practical issues such as handling big data in inversions and on high-performance computing systems.

A string realisation of Ω-deformed Abelian N =2* theory

NASA Astrophysics Data System (ADS)

Angelantonj, Carlo; Antoniadis, Ignatios; Samsonyan, Marine

2017-10-01

The N =2* supersymmetric gauge theory is a massive deformation of N = 4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian N =2* theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N = 2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω-background, in agreement with a recent proposal.

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

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

Finn, John M., E-mail: finn@lanl.gov

2015-03-15

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint.more » We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012)], appears to work very well.« less

Analytic approach to photoelectron transport.

NASA Technical Reports Server (NTRS)

Stolarski, R. S.

1972-01-01

The equation governing the transport of photoelectrons in the ionosphere is shown to be equivalent to the equation of radiative transfer. In the single-energy approximation this equation is solved in closed form by the method of discrete ordinates for isotropic scattering and for a single-constituent atmosphere. The results include prediction of the angular distribution of photoelectrons at all altitudes and, in particular, the angular distribution of the escape flux. The implications of these solutions in real atmosphere calculations are discussed.

Spectral-element simulations of wave propagation in complex exploration-industry models: Imaging and adjoint tomography

NASA Astrophysics Data System (ADS)

Luo, Y.; Nissen-Meyer, T.; Morency, C.; Tromp, J.

2008-12-01

Seismic imaging in the exploration industry is often based upon ray-theoretical migration techniques (e.g., Kirchhoff) or other ideas which neglect some fraction of the seismic wavefield (e.g., wavefield continuation for acoustic-wave first arrivals) in the inversion process. In a companion paper we discuss the possibility of solving the full physical forward problem (i.e., including visco- and poroelastic, anisotropic media) using the spectral-element method. With such a tool at hand, we can readily apply the adjoint method to tomographic inversions, i.e., iteratively improving an initial 3D background model to fit the data. In the context of this inversion process, we draw connections between kernels in adjoint tomography and basic imaging principles in migration. We show that the images obtained by migration are nothing but particular kinds of adjoint kernels (mainly density kernels). Migration is basically a first step in the iterative inversion process of adjoint tomography. We apply the approach to basic 2D problems involving layered structures, overthrusting faults, topography, salt domes, and poroelastic regions.

The Flare/CME Connection

NASA Technical Reports Server (NTRS)

Moore, Ron; Falconer, David; Sterling, Alphonse

2008-01-01

We present evidence supporting the view that, while many flares are produced by a confined magnetic explosion that does not produce a CME, every CME is produced by an ejective magnetic explosion that also produces a flare. The evidence is that the observed heliocentric angular width of the full-blown CME plasmoid in the outer corona (at 3 to 20 solar radii) is about that predicted by the standard model for CME production, from the amount of magnetic flux covered by the co-produced flare arcade. In the standard model, sheared and twisted sigmoidal field in the core of an initially closed magnetic arcade erupts. As it erupts, tether-cutting reconnection, starting between the legs of the erupting sigmoid and continuing between the merging stretched legs of the enveloping arcade, simultaneously produces a growing flare arcade and unleashes the erupting sigmoid and arcade to become the low-beta plasmoid (magnetic bubble) that becomes the CME. The flare arcade is the downward product of the reconnection and the CME plasmoid is the upward product. The unleashed, expanding CME plasmoid is propelled into the outer corona and solar wind by its own magnetic field pushing on the surrounding field in the inner and outer corona. This tether-cutting scenario predicts that the amount of magnetic flux in the full-blown CME plasmoid nearly equals that covered by the full-grown flare arcade. This equality predicts (1) the field strength in the flare region from the ratio of the angular width of the CME in the outer corona to angular width of the full-grown flare arcade, and (2) an upper bound on the angular width of the CME in the outer corona from the total magnetic flux in the active region from which the CME explodes. We show that these predictions are fulfilled by observed CMEs. This agreement validates the standard model. The model explains (1) why most CMEs have much greater angular widths than their co-produced flares, and (2) why the radial path of a CME in the outer corona can be laterally far offset from the co-produced flare.

Reynolds stress and heat flux in spherical shell convection

NASA Astrophysics Data System (ADS)

Käpylä, P. J.; Mantere, M. J.; Guerrero, G.; Brandenburg, A.; Chatterjee, P.

2011-07-01

Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate. Aims: Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry. Methods: We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results: For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong "banana cells". Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance. Movies and Appendix A are available in electronic form at http://www.aanda.org

Model atmospheres and radiation of magnetic neutron stars: Anisotropic thermal emission

NASA Technical Reports Server (NTRS)

Pavlov, G. G.; Shibanov, Yu. A.; Ventura, J.; Zavlin, V. E.

1994-01-01

We investigate the anisotropy of the thermal radiation emitted by a surface element of a neutron star atmosphere (e.g., by a polar cap of a radio pulsar). Angular dependences of the partial fluxes at various photon energies, and spectra at various angles are obtained for different values of the effective temperature T(sub eff) and magnetic field strength B, and for different directions of the magnetic field. It is shown that the local radiation of the magnetized neutron star atmospheres is highly anisotropic, with the maximum flux emitted in the magnetic field direction. At high B the angular dependences in the soft X-ray range have two maxima, a high narrow peak along B and a lower and broader maximum at intermediate angles. The radiation is strongly polarized, the modulation of the degree of polarization due to the rotation of the neurtron star may be much higher than that for the radiative flux. The results obtained are compared with recent ROSAT observations of the thermal-like radiation from the radio pulsars PSR 1929+10 and PSR J0437-4715.

Drag reduction at a plane wall

NASA Technical Reports Server (NTRS)

Hill, D. C.

1993-01-01

The objective is to determine by analytical means how drag on a plane wall may be modified favorably using a minimal amount of flow information - preferably only information at the wall. What quantities should be measured? How should that information be assimilated in order to arrive at effective control? As a prototypical problem, incompressible, viscous flow, governed by the Navier-Stokes equations, past a plane wall at which the no-slip condition was modified was considered. The streamwise and spanwise velocity components are required to be zero, but the normal component is to be specified according to some control law. The challenge is to choose the wall-normal velocity component based on flow conditions at the wall so that the mean drag is as small as possible. There can be no net mass flux through the wall, and the total available control energy is constrained. A turbulent flow is highly unsteady and has detailed spatial structure. The mean drag on the wall is the integral over the wall of the local shear forces exerted by the fluid, which is then averaged in time; it is a 'macroscopic' property of the flow. It is not obvious how unsteady boundary control is to be applied in order to modify the mean flow most effectively, especially in view of the non- self-adjoint nature of the governing equations. An approximate analytical solution to the suboptimal scheme is pursued.

Relativistic Dynamos in Magnetospheres of Rotating Compact Objects

NASA Astrophysics Data System (ADS)

Tomimatsu, Akira

2000-01-01

The kinematic evolution of axisymmetric magnetic fields in rotating magnetospheres of relativistic compact objects is analytically studied, based on relativistic Ohm's law in stationary axisymmetric geometry. By neglecting the poloidal flows of plasma in simplified magnetospheric models, we discuss a self-excited dynamo due to the frame-dragging effect (originally pointed out by Khanna & Camenzind) and propose alternative processes to generate axisymmetric magnetic fields against ohmic dissipation. The first process (which may be called ``induced excitation'') is caused by the help of a background uniform magnetic field in addition to the dragging of inertial frames. It is shown that excited multipolar components of poloidal and azimuthal fields are sustained as stationary modes, and outgoing Poynting flux converges toward the rotation axis. The second process is a self-excited dynamo through azimuthal convection current, which is found to be effective if plasma rotation becomes highly relativistic with a sharp gradient in the angular velocity. In this case, no frame-dragging effect is needed, and the coupling between charge separation and plasma rotation becomes important. We discuss briefly the results in relation to active phenomena in the relativistic magnetospheres.

Influence of ionisation zone motion in high power impulse magnetron sputtering on angular ion flux and NbO x film growth

DOE PAGES

Franz, Robert; Clavero, César; Kolbeck, Jonathan; ...

2016-01-21

Here, the ion energies and fluxes in the high power impulse magnetron sputtering plasma from a Nb target were analysed angularly resolved along the tangential direction of the racetrack. A reactive oxygen-containing atmosphere was used as such discharge conditions are typically employed for the synthesis of thin films. Asymmetries in the flux distribution of the recorded ions as well as their energies and charge states were noticed when varying the angle between mass-energy analyser and target surface. More positively charged ions with higher count rates in the medium energy range of their distributions were detected in +E x B thanmore » in -E x B direction, thus confirming the notion that ionisation zones (also known as spokes or plasma bunches) are associated with moving potential humps. The motion of the recorded negatively charged high-energy oxygen ions was unaffected. NbO x thin films at different angles and positions were synthesised and analysed as to their structure and properties in order to correlate the observed plasma properties to the film growth conditions. The chemical composition and the film thickness varied with changing deposition angle, where the latter, similar to the ion fluxes, was higher in +E x B than in -E x B direction.« less

Design, fabrication and characterization of a micro-fluxgate intended for parallel robot application

NASA Astrophysics Data System (ADS)

Kirchhoff, M. R.; Bogdanski, G.; Büttgenbach, S.

2009-05-01

This paper presents a micro-magnetometer based on the fluxgate principle. Fluxgates detect the magnitude and direction of DC and low-frequency AC magnetic fields. The detectable flux density typically ranges from several 10 nT to about 1 mT. The introduced fluxgate sensor is fabricated using MEMS-technologies, basically UV depth lithography and electroplating for manufacturing high aspect ratio structures. It consists of helical copper coils around a soft magnetic nickel-iron (NiFe) core. The core is designed in so-called racetrack geometry, whereby the directional sensitivity of the sensor is considerably higher compared to common ring-core fluxgates. The electrical operation is based on analyzing the 2nd harmonic of the AC output signal. Configuration, manufacturing and selected characteristics of the fluxgate magnetometer are discussed in this work. The fluxgate builds the basis of an innovative angular sensor system for a parallel robot with HEXA-structure. Integrated into the passive joints of the parallel robot, the fluxgates are combined with permanent magnets rotating on the joint shafts. The magnet transmits the angular information via its magnetic orientation. In this way, the angles between the kinematic elements are measured, which allows self-calibration of the robot and the fast analytical solution of direct kinematics for an advanced workspace monitoring.

State observer for synchronous motors

DOEpatents

Lang, Jeffrey H.

1994-03-22

A state observer driven by measurements of phase voltages and currents for estimating the angular orientation of a rotor of a synchronous motor such as a variable reluctance motor (VRM). Phase voltages and currents are detected and serve as inputs to a state observer. The state observer includes a mathematical model of the electromechanical operation of the synchronous motor. The characteristics of the state observer are selected so that the observer estimates converge to the actual rotor angular orientation and velocity, winding phase flux linkages or currents.

A Missile-Borne Angular Velocity Sensor Based on Triaxial Electromagnetic Induction Coils

PubMed Central

Li, Jian; Wu, Dan; Han, Yan

2016-01-01

Aiming to solve the problem of the limited measuring range for angular motion parameters of high-speed rotating projectiles in the field of guidance and control, a self-adaptive measurement method for angular motion parameters based on the electromagnetic induction principle is proposed. First, a framework with type bent “I-shape” is used to design triaxial coils in a mutually orthogonal way. Under the condition of high rotational speed of a projectile, the induction signal of the projectile moving across a geomagnetic field is acquired by using coils. Second, the frequency of the pulse signal is adjusted self-adaptively. Angular velocity and angular displacement are calculated in the form of periodic pulse counting and pulse accumulation, respectively. Finally, on the basis of that principle prototype of the sensor is researched and developed, performance of measuring angular motion parameters are tested on the sensor by semi-physical and physical simulation experiments, respectively. Experimental results demonstrate that the sensor has a wide measuring range of angular velocity from 1 rps to 100 rps with a measurement error of less than 0.3%, and the angular displacement measurement error is lower than 0.2°. The proposed method satisfies measurement requirements for high-speed rotating projectiles with an extremely high dynamic range of rotational speed and high precision, and has definite value to engineering applications in the fields of attitude determination and geomagnetic navigation. PMID:27706039

A Missile-Borne Angular Velocity Sensor Based on Triaxial Electromagnetic Induction Coils.

PubMed

Li, Jian; Wu, Dan; Han, Yan

2016-09-30

Aiming to solve the problem of the limited measuring range for angular motion parameters of high-speed rotating projectiles in the field of guidance and control, a self-adaptive measurement method for angular motion parameters based on the electromagnetic induction principle is proposed. First, a framework with type bent "I-shape" is used to design triaxial coils in a mutually orthogonal way. Under the condition of high rotational speed of a projectile, the induction signal of the projectile moving across a geomagnetic field is acquired by using coils. Second, the frequency of the pulse signal is adjusted self-adaptively. Angular velocity and angular displacement are calculated in the form of periodic pulse counting and pulse accumulation, respectively. Finally, on the basis of that principle prototype of the sensor is researched and developed, performance of measuring angular motion parameters are tested on the sensor by semi-physical and physical simulation experiments, respectively. Experimental results demonstrate that the sensor has a wide measuring range of angular velocity from 1 rps to 100 rps with a measurement error of less than 0.3%, and the angular displacement measurement error is lower than 0.2°. The proposed method satisfies measurement requirements for high-speed rotating projectiles with an extremely high dynamic range of rotational speed and high precision, and has definite value to engineering applications in the fields of attitude determination and geomagnetic navigation.

Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

NASA Technical Reports Server (NTRS)

Rallabhandi, Siriam K.; Diskin, Boris; Nielsen, Eric J.

2012-01-01

This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Park, Michael A.

2006-01-01

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Park, Michael A.

2005-01-01

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Deterministic Local Sensitivity Analysis of Augmented Systems - II: Applications to the QUENCH-04 Experiment Using the RELAP5/MOD3.2 Code System

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

Ionescu-Bujor, Mihaela; Jin Xuezhou; Cacuci, Dan G.

2005-09-15

The adjoint sensitivity analysis procedure for augmented systems for application to the RELAP5/MOD3.2 code system is illustrated. Specifically, the adjoint sensitivity model corresponding to the heat structure models in RELAP5/MOD3.2 is derived and subsequently augmented to the two-fluid adjoint sensitivity model (ASM-REL/TF). The end product, called ASM-REL/TFH, comprises the complete adjoint sensitivity model for the coupled fluid dynamics/heat structure packages of the large-scale simulation code RELAP5/MOD3.2. The ASM-REL/TFH model is validated by computing sensitivities to the initial conditions for various time-dependent temperatures in the test bundle of the Quench-04 reactor safety experiment. This experiment simulates the reflooding with water ofmore » uncovered, degraded fuel rods, clad with material (Zircaloy-4) that has the same composition and size as that used in typical pressurized water reactors. The most important response for the Quench-04 experiment is the time evolution of the cladding temperature of heated fuel rods. The ASM-REL/TFH model is subsequently used to perform an illustrative sensitivity analysis of this and other time-dependent temperatures within the bundle. The results computed by using the augmented adjoint sensitivity system, ASM-REL/TFH, highlight the reliability, efficiency, and usefulness of the adjoint sensitivity analysis procedure for computing time-dependent sensitivities.« less

Equilibrium sensitivities of the Greenland ice sheet inferred from the adjoint of the three- dimensional thermo-mechanical model SICOPOLIS

NASA Astrophysics Data System (ADS)

Heimbach, P.; Bugnion, V.

2008-12-01

We present a new and original approach to understanding the sensitivity of the Greenland ice sheet to key model parameters and environmental conditions. At the heart of this approach is the use of an adjoint ice sheet model. MacAyeal (1992) introduced adjoints in the context of applying control theory to estimate basal sliding parameters (basal shear stress, basal friction) of an ice stream model which minimize a least-squares model vs. observation misfit. Since then, this method has become widespread to fit ice stream models to the increasing number and diversity of satellite observations, and to estimate uncertain model parameters. However, no attempt has been made to extend this method to comprehensive ice sheet models. Here, we present a first step toward moving beyond limiting the use of control theory to ice stream models. We have generated an adjoint of the three-dimensional thermo-mechanical ice sheet model SICOPOLIS of Greve (1997). The adjoint was generated using the automatic differentiation (AD) tool TAF. TAF generates exact source code representing the tangent linear and adjoint model of the parent model provided. Model sensitivities are given by the partial derivatives of a scalar-valued model diagnostic or "cost function" with respect to the controls, and can be efficiently calculated via the adjoint. An effort to generate an efficient adjoint with the newly developed open-source AD tool OpenAD is also under way. To gain insight into the adjoint solutions, we explore various cost functions, such as local and domain-integrated ice temperature, total ice volume or the velocity of ice at the margins of the ice sheet. Elements of our control space include initial cold ice temperatures, surface mass balance, as well as parameters such as appear in Glen's flow law, or in the surface degree-day or basal sliding parameterizations. Sensitivity maps provide a comprehensive view, and allow a quantification of where and to which variables the ice sheet model is most sensitive to. The model used in the present study includes simplifications in the model physics, parameterizations which rely on uncertain empirical constants, and is unable to capture fast ice streams. Nevertheless, as a proof-of-concept, this method can readily be extended to incorporate higher-order physics or parameterizations (or be applied to other models). It also opens the door to ice sheet state estimation: using the model's physics jointly with field and satellite observations to estimate a best estimate of the state of the ice sheets.

The role of spatial memory and frames of reference in the precision of angular path integration.

PubMed

Arthur, Joeanna C; Philbeck, John W; Kleene, Nicholas J; Chichka, David

2012-09-01

Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatial memory is particularly likely in spatial updating tasks in which one's self-location estimate is referenced to external space. To test this idea, we administered passive, non-visual body rotations (ranging 40°-140°) about the yaw axis and asked participants to use verbal reports or open-loop manual pointing to indicate the magnitude of the rotation. Prior to some trials, previews of the surrounding environment were given. We found that when participants adopted an egocentric frame of reference, the previously-observed benefit of previews on within-subject response precision was not manifested, regardless of whether remembered spatial frameworks were derived from vision or spatial language. We conclude that the powerful effect of spatial memory is dependent on one's frame of reference during self-motion updating. Copyright © 2012 Elsevier B.V. All rights reserved.

Design optimization using adjoint of Long-time LES for the trailing edge of a transonic turbine vane

NASA Astrophysics Data System (ADS)

Talnikar, Chaitanya; Wang, Qiqi

2017-11-01

Adjoint-based design optimization methods have been applied to low-fidelity simulation methods like Reynolds Averaged Navier-Stokes (RANS) and are useful for designing fluid machinery components. But to reliably capture the complex flow phenomena involved in turbomachinery, high fidelity simulations like large eddy simulation (LES) are required. Unfortunately due to the chaotic dynamics of turbulence, the unsteady adjoint method for LES diverges and produces incorrect gradients. Using a viscosity stabilized unsteady adjoint method developed for LES, the gradient can be obtained with reasonable accuracy. In this paper, design of the trailing edge of a gas turbine inlet guide vane is performed with the objective to reduce stagnation pressure loss and heat transfer over the surface of the vane. Slight changes in the shape of trailing edge can significantly impact these quantities by altering the boundary layer development process and separation points. The trailing edge is parameterized using a linear combination of 5 convex designs. Bayesian optimization is used as a global optimizer with the objective function evaluated from the LES and gradients obtained using the viscosity adjoint method. Results from the optimization, performed on the supercomputer Mira, are presented.

Electrical Resistivity Tomography using a finite element based BFGS algorithm with algebraic multigrid preconditioning

NASA Astrophysics Data System (ADS)

Codd, A. L.; Gross, L.

2018-03-01

We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.

Angular Momentum Transport in Turbulent Flow between Independently Rotating Cylinders

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

Paoletti, M. S.; Lathrop, D. P.; Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742

2011-01-14

We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the ({Omega}{sub 1}, {Omega}{sub 2}) parameter space at high Reynolds numbers, where {Omega}{sub 1} ({Omega}{sub 2}) is the inner (outer) cylinder angular velocity. We find that the Rossby number Ro=({Omega}{sub 1}-{Omega}{sub 2})/{Omega}{sub 2} fully determines the state and torque G as compared to G(Ro={infinity}){identical_to}G{sub {infinity}.} The ratio G/G{sub {infinity}} is a linear function of Ro{sup -1} in four sections of the parameter space. For flows with radially increasing angular momentum, our measured torques greatly exceed those of previousmore » experiments [Ji et al., Nature (London), 444, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys. 347, 734 (1999)].« less

Full moment tensor and source location inversion based on full waveform adjoint method

NASA Astrophysics Data System (ADS)

Morency, C.

2012-12-01

The development of high-performance computing and numerical techniques enabled global and regional tomography to reach high levels of precision, and seismic adjoint tomography has become a state-of-the-art tomographic technique. The method was successfully used for crustal tomography of Southern California (Tape et al., 2009) and Europe (Zhu et al., 2012). Here, I will focus on the determination of source parameters (full moment tensor and location) based on the same approach (Kim et al, 2011). The method relies on full wave simulations and takes advantage of the misfit between observed and synthetic seismograms. An adjoint wavefield is calculated by back-propagating the difference between observed and synthetics from the receivers to the source. The interaction between this adjoint wavefield and the regular forward wavefield helps define Frechet derivatives of the source parameters, that is, the sensitivity of the misfit with respect to the source parameters. Source parameters are then recovered by minimizing the misfit based on a conjugate gradient algorithm using the Frechet derivatives. First, I will demonstrate the method on synthetic cases before tackling events recorded at the Geysers. The velocity model used at the Geysers is based on the USGS 3D velocity model. Waveform datasets come from the Northern California Earthquake Data Center. Finally, I will discuss strategies to ultimately use this method to characterize smaller events for microseismic and induced seismicity monitoring. References: - Tape, C., Q. Liu, A. Maggi, and J. Tromp, 2009, Adjoint tomography of the Southern California crust: Science, 325, 988992. - Zhu, H., Bozdag, E., Peter, D., and Tromp, J., 2012, Structure of the European upper mantle revealed by adjoint method: Nature Geoscience, 5, 493-498. - Kim, Y., Q. Liu, and J. Tromp, 2011, Adjoint centroid-moment tensor inversions: Geophys. J. Int., 186, 264278. Prepared by LLNL under Contract DE-AC52-07NA27344.

On the Direct Assimilation of Along-track Sea Surface Height Observations into a Free-surface Ocean Model Using a Weak Constraints Four Dimensional Variational (4dvar) Method

NASA Astrophysics Data System (ADS)

Ngodock, H.; Carrier, M.; Smith, S. R.; Souopgui, I.; Martin, P.; Jacobs, G. A.

2016-02-01

The representer method is adopted for solving a weak constraints 4dvar problem for the assimilation of ocean observations including along-track SSH, using a free surface ocean model. Direct 4dvar assimilation of SSH observations along the satellite tracks requires that the adjoint model be integrated with Dirac impulses on the right hand side of the adjoint equations for the surface elevation equation. The solution of this adjoint model will inevitably include surface gravity waves, and it constitutes the forcing for the tangent linear model (TLM) according to the representer method. This yields an analysis that is contaminated by gravity waves. A method for avoiding the generation of the surface gravity waves in the analysis is proposed in this study; it consists of removing the adjoint of the free surface from the right hand side (rhs) of the free surface mode in the TLM. The information from the SSH observations will still propagate to all other variables via the adjoint of the balance relationship between the barotropic and baroclinic modes, resulting in the correction to the surface elevation. Two assimilation experiments are carried out in the Gulf of Mexico: one with adjoint forcing included on the rhs of the TLM free surface equation, and the other without. Both analyses are evaluated against the assimilated SSH observations, SSH maps from Aviso and independent surface drifters, showing that the analysis that did not include adjoint forcing in the free surface is more accurate. This study shows that when a weak constraint 4dvar approach is considered for the assimilation of along-track SSH observations using a free surface model, with the aim of correcting the mesoscale circulation, an independent model error should not be assigned to the free surface.

A demonstration of adjoint methods for multi-dimensional remote sensing of the atmosphere and surface

NASA Astrophysics Data System (ADS)

Martin, William G. K.; Hasekamp, Otto P.

2018-01-01

In previous work, we derived the adjoint method as a computationally efficient path to three-dimensional (3D) retrievals of clouds and aerosols. In this paper we will demonstrate the use of adjoint methods for retrieving two-dimensional (2D) fields of cloud extinction. The demonstration uses a new 2D radiative transfer solver (FSDOM). This radiation code was augmented with adjoint methods to allow efficient derivative calculations needed to retrieve cloud and surface properties from multi-angle reflectance measurements. The code was then used in three synthetic retrieval studies. Our retrieval algorithm adjusts the cloud extinction field and surface albedo to minimize the measurement misfit function with a gradient-based, quasi-Newton approach. At each step we compute the value of the misfit function and its gradient with two calls to the solver FSDOM. First we solve the forward radiative transfer equation to compute the residual misfit with measurements, and second we solve the adjoint radiative transfer equation to compute the gradient of the misfit function with respect to all unknowns. The synthetic retrieval studies verify that adjoint methods are scalable to retrieval problems with many measurements and unknowns. We can retrieve the vertically-integrated optical depth of moderately thick clouds as a function of the horizontal coordinate. It is also possible to retrieve the vertical profile of clouds that are separated by clear regions. The vertical profile retrievals improve for smaller cloud fractions. This leads to the conclusion that cloud edges actually increase the amount of information that is available for retrieving the vertical profile of clouds. However, to exploit this information one must retrieve the horizontally heterogeneous cloud properties with a 2D (or 3D) model. This prototype shows that adjoint methods can efficiently compute the gradient of the misfit function. This work paves the way for the application of similar methods to 3D remote sensing problems.

Covering Resilience: A Recent Development for Binomial Checkpointing

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

Walther, Andrea; Narayanan, Sri Hari Krishna

In terms of computing time, adjoint methods offer a very attractive alternative to compute gradient information, required, e.g., for optimization purposes. However, together with this very favorable temporal complexity result comes a memory requirement that is in essence proportional with the operation count of the underlying function, e.g., if algorithmic differentiation is used to provide the adjoints. For this reason, checkpointing approaches in many variants have become popular. This paper analyzes an extension of the so-called binomial approach to cover also possible failures of the computing systems. Such a measure of precaution is of special interest for massive parallel simulationsmore » and adjoint calculations where the mean time between failure of the large scale computing system is smaller than the time needed to complete the calculation of the adjoint information. We describe the extensions of standard checkpointing approaches required for such resilience, provide a corresponding implementation and discuss first numerical results.« less

An Adjoint-Based Approach to Study a Flexible Flapping Wing in Pitching-Rolling Motion

NASA Astrophysics Data System (ADS)

Jia, Kun; Wei, Mingjun; Xu, Min; Li, Chengyu; Dong, Haibo

2017-11-01

Flapping-wing aerodynamics, with advantages in agility, efficiency, and hovering capability, has been the choice of many flyers in nature. However, the study of bio-inspired flapping-wing propulsion is often hindered by the problem's large control space with different wing kinematics and deformation. The adjoint-based approach reduces largely the computational cost to a feasible level by solving an inverse problem. Facing the complication from moving boundaries, non-cylindrical calculus provides an easy extension of traditional adjoint-based approach to handle the optimization involving moving boundaries. The improved adjoint method with non-cylindrical calculus for boundary treatment is first applied on a rigid pitching-rolling plate, then extended to a flexible one with active deformation to further increase its propulsion efficiency. The comparison of flow dynamics with the initial and optimal kinematics and deformation provides a unique opportunity to understand the flapping-wing mechanism. Supported by AFOSR and ARL.

Learning a trajectory using adjoint functions and teacher forcing

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad B.; Barhen, Jacob

1992-01-01

A new methodology for faster supervised temporal learning in nonlinear neural networks is presented which builds upon the concept of adjoint operators to allow fast computation of the gradients of an error functional with respect to all parameters of the neural architecture, and exploits the concept of teacher forcing to incorporate information on the desired output into the activation dynamics. The importance of the initial or final time conditions for the adjoint equations is discussed. A new algorithm is presented in which the adjoint equations are solved simultaneously (i.e., forward in time) with the activation dynamics of the neural network. We also indicate how teacher forcing can be modulated in time as learning proceeds. The results obtained show that the learning time is reduced by one to two orders of magnitude with respect to previously published results, while trajectory tracking is significantly improved. The proposed methodology makes hardware implementation of temporal learning attractive for real-time applications.

Hawking radiation via anomaly cancellation for the black holes of five-dimensional minimal gauged supergravity

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

Porfyriadis, Achilleas P.

2009-04-15

The anomaly cancellation method proposed by Wilczek et al. is applied to the general charged rotating black holes in five-dimensional minimal gauged supergravity. Thus Hawking temperature and fluxes are found. The Hawking temperature obtained agrees with the surface gravity formula. The black holes have charge and two unequal angular momenta, and these give rise to appropriate terms in the effective U(1) gauge field of the reduced (1+1)-dimensional theory. In particular, it is found that the terms in this U(1) gauge field correspond exactly to the correct electrostatic potential and the two angular velocities on the horizon of the black holes,more » and so the results for the Hawking fluxes derived here from the anomaly cancellation method are in complete agreement with the ones obtained from integrating the Planck distribution.« less

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

Vieira, H.S., E-mail: horacio.santana.vieira@hotmail.com; Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba, CEP 58233-000, Araruna, PB; Bezerra, V.B., E-mail: valdir@fisica.ufpb.br

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux. -- Highlights:more » •A cosmic string is introduced along the axis of symmetry of the dyonic black hole. •The covariant Klein–Gordon equation for a charged massive scalar field in this background is analyzed. •Both angular and radial parts are transformed to a confluent Heun equation. •The resulting Hawking radiation spectrum and the energy flux are obtained.« less

Expectations for high energy diffuse galactic neutrinos for different cosmic ray distributions

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

Pagliaroli, Giulia; Evoli, Carmelo; Villante, Francesco Lorenzo, E-mail: giulia.pagliaroli@gssi.infn.it, E-mail: carmelo.evoli@gssi.infn.it, E-mail: francesco.villante@lngs.infn.it

2016-11-01

The interaction of cosmic rays with the gas contained in our Galaxy is a guaranteed source of diffuse high energy neutrinos. We provide expectations for this component by considering different assumptions for the cosmic ray distribution in the Galaxy which are intended to cover the large uncertainty in cosmic ray propagation models. We calculate the angular dependence of the diffuse galactic neutrino flux and the corresponding rate of High Energy Starting Events in IceCube by including the effect of detector angular resolution. Moreover we discuss the possibility to discriminate the galactic component from an isotropic astrophysical flux. We show thatmore » a statistically significant excess of events from the galactic plane in present IceCube data would disfavour models in which the cosmic ray density is uniform , thus bringing relevant information on the cosmic ray radial distribution.« less

APPARATUS FOR CONTROLLING NEUTRONIC REACTORS

DOEpatents

Dietrich, J.R.; Harrer, J.M.

1958-09-16

A device is described for rapidly cortrolling the reactivity of an active portion of a reactor. The inveniion consists of coaxially disposed members each having circumferenital sections of material having dlfferent neutron absorbing characteristics and means fur moving the members rotatably and translatably relative to each other within the active portion to vary the neutron flux therein. The angular and translational movements of any member change the neutron flux shadowing effect of that member upon the other member.

Neutron measurements of the OGO-VI Spacecraft

NASA Technical Reports Server (NTRS)

Lockwood, J. A.

1973-01-01

The neutron measurements with the OGO-6 spacecraft are reported. Topics discussed include: the design and calibration of a neutron monitor for measuring the cosmic ray neutron leakages from the earth's atmosphere, determination of latitude dependence of cosmic ray leakage flux, determination of the angular distribution of neutron leakage flux as deduced by measurements of the altitude dependence, and verification of the solar modulation of the cosmic ray source for the neutron leakage.

Flux-Feedback Magnetic-Suspension Actuator

NASA Technical Reports Server (NTRS)

Groom, Nelson J.

1990-01-01

Flux-feedback magnetic-suspension actuator provides magnetic suspension and control forces having linear transfer characteristics between force command and force output over large range of gaps. Hall-effect devices used as sensors for electronic feedback circuit controlling currents flowing in electromagnetic windings to maintain flux linking suspended element at substantially constant value independent of changes in length of gap. Technique provides effective method for maintenance of constant flux density in gap and simpler than previous methods. Applications include magnetic actuators for control of shapes and figures of antennas and of precise segmented reflectors, magnetic suspensions in devices for storage of angular momentum and/or kinetic energy, and systems for control, pointing, and isolation of instruments.

Quantum Dynamical Applications of Salem's Theorem

NASA Astrophysics Data System (ADS)

Damanik, David; Del Rio, Rafael

2009-07-01

We consider the survival probability of a state that evolves according to the Schrödinger dynamics generated by a self-adjoint operator H. We deduce from a classical result of Salem that upper bounds for the Hausdorff dimension of a set supporting the spectral measure associated with the initial state imply lower bounds on a subsequence of time scales for the survival probability. This general phenomenon is illustrated with applications to the Fibonacci operator and the critical almost Mathieu operator. In particular, this gives the first quantitative dynamical bound for the critical almost Mathieu operator.

An abstract approach to evaporation models in rarefied gas dynamics

NASA Astrophysics Data System (ADS)

Greenberg, W.; van der Mee, C. V. M.

1984-03-01

Strong evaporation models involving 1D stationary problems with linear self-adjoint collision operators and solutions in abstract Hilbert spaces are investigated analytically. An efficient algorithm for locating the transition from existence to nonexistence of solutions is developed and applied to the 1D and 3D BGK model equations and the 3D BGK model in moment form, demonstrating the nonexistence of stationary evaporation states with supersonic drift velocities. Applications to similar models in electron and phonon transport, radiative transfer, and neutron transport are suggested.

The spectral function of a singular differential operator of order 2m

NASA Astrophysics Data System (ADS)

Kozko, Artem I.; Pechentsov, Alexander S.

2010-12-01

We study the spectral function of a self-adjoint semibounded below differential operator on a Hilbert space L_2 \\lbrack 0,\\infty) and obtain the formulae for the spectral function of the operator (-1)^{m}y^{(2m)}(x) with general boundary conditions at the zero. In particular, for the boundary conditions y(0)=y'(0)=\\dots=y^{(m-1)}(0)=0 we find the explicit form of the spectral function \\Theta_{mB'}(x,x,\\lambda) on the diagonal x=y for \\lambda \\ge 0.

Groundwater Source Identification Using Backward Fractional-Derivative Models

NASA Astrophysics Data System (ADS)

Zhang, Y.; Sun, H.; Zheng, C.

2017-12-01

The forward Fractional Advection Dispersion Equation (FADE) provides a useful model for non-Fickian transport in heterogeneous porous media. This presentation introduces the corresponding backward FADE model, to identify groundwater source location and release time. The backward method is developed from the theory of inverse problems, and the resultant backward FADE differs significantly from the traditional backward ADE because the fractional derivative is not self-adjoint and the probability density function for backward locations is highly skewed. Finally, the method is validated using tracer data from well-known field experiments.

Convergence of quantum electrodynamics in a curved modification of Minkowski space.

PubMed Central

Segal, I E; Zhou, Z

1994-01-01

The interaction and total hamiltonians for quantum electrodynamics, in the interaction representation, are entirely regular self-adjoint operators in Hilbert space, in the universal covering manifold M of the conformal compactification of Minkowski space Mo. (M is conformally equivalent to the Einstein universe E, in which Mo may be canonically imbedded.) In a fixed Lorentz frame this may be expressed as convergence in a spherical space with suitable periodic boundary conditions in time. The traditional relativistic theory is the formal limit of the present variant as the space curvature vanishes. PMID:11607455

Computing the sensitivity of drag and lift in flow past a circular cylinder: Time-stepping versus self-consistent analysis

NASA Astrophysics Data System (ADS)

Meliga, Philippe

2017-07-01

We provide in-depth scrutiny of two methods making use of adjoint-based gradients to compute the sensitivity of drag in the two-dimensional, periodic flow past a circular cylinder (Re≲189 ): first, the time-stepping analysis used in Meliga et al. [Phys. Fluids 26, 104101 (2014), 10.1063/1.4896941] that relies on classical Navier-Stokes modeling and determines the sensitivity to any generic control force from time-dependent adjoint equations marched backwards in time; and, second, a self-consistent approach building on the model of Mantič-Lugo et al. [Phys. Rev. Lett. 113, 084501 (2014), 10.1103/PhysRevLett.113.084501] to compute semilinear approximations of the sensitivity to the mean and fluctuating components of the force. Both approaches are applied to open-loop control by a small secondary cylinder and allow identifying the sensitive regions without knowledge of the controlled states. The theoretical predictions obtained by time-stepping analysis reproduce well the results obtained by direct numerical simulation of the two-cylinder system. So do the predictions obtained by self-consistent analysis, which corroborates the relevance of the approach as a guideline for efficient and systematic control design in the attempt to reduce drag, even though the Reynolds number is not close to the instability threshold and the oscillation amplitude is not small. This is because, unlike simpler approaches relying on linear stability analysis to predict the main features of the flow unsteadiness, the semilinear framework encompasses rigorously the effect of the control on the mean flow, as well as on the finite-amplitude fluctuation that feeds back nonlinearly onto the mean flow via the formation of Reynolds stresses. Such results are especially promising as the self-consistent approach determines the sensitivity from time-independent equations that can be solved iteratively, which makes it generally less computationally demanding. We ultimately discuss the extent to which relevant information can be gained from a hybrid modeling computing self-consistent sensitivities from the postprocessing of DNS data. Application to alternative control objectives such as increasing the lift and alleviating the fluctuating drag and lift is also discussed.

Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.

1988-01-01

The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.

Charge exchange in cometary coma: Discovery of H- ions in the solar wind close to comet 67P/Churyumov-Gerasimenko.

PubMed

Burch, J L; Cravens, T E; Llera, K; Goldstein, R; Mokashi, P; Tzou, C-Y; Broiles, T

2015-07-16

As Rosetta was orbiting comet 67P/Churyumov-Gerasimenko, the Ion and Electron Sensor detected negative particles with angular distributions like those of the concurrently measured solar wind protons but with fluxes of only about 10% of the proton fluxes and energies of about 90% of the proton energies. Using well-known cross sections and energy-loss data, it is determined that the fluxes and energies of the negative particles are consistent with the production of H - ions in the solar wind by double charge exchange with molecules in the coma.

Comparison of adjoint and analytical Bayesian inversion methods for constraining Asian sources of carbon monoxide using satellite (MOPITT) measurements of CO columns

NASA Astrophysics Data System (ADS)

Kopacz, Monika; Jacob, Daniel J.; Henze, Daven K.; Heald, Colette L.; Streets, David G.; Zhang, Qiang

2009-02-01

We apply the adjoint of an atmospheric chemical transport model (GEOS-Chem CTM) to constrain Asian sources of carbon monoxide (CO) with 2° × 2.5° spatial resolution using Measurement of Pollution in the Troposphere (MOPITT) satellite observations of CO columns in February-April 2001. Results are compared to the more common analytical method for solving the same Bayesian inverse problem and applied to the same data set. The analytical method is more exact but because of computational limitations it can only constrain emissions over coarse regions. We find that the correction factors to the a priori CO emission inventory from the adjoint inversion are generally consistent with those of the analytical inversion when averaged over the large regions of the latter. The adjoint solution reveals fine-scale variability (cities, political boundaries) that the analytical inversion cannot resolve, for example, in the Indian subcontinent or between Korea and Japan, and some of that variability is of opposite sign which points to large aggregation errors in the analytical solution. Upward correction factors to Chinese emissions from the prior inventory are largest in central and eastern China, consistent with a recent bottom-up revision of that inventory, although the revised inventory also sees the need for upward corrections in southern China where the adjoint and analytical inversions call for downward correction. Correction factors for biomass burning emissions derived from the adjoint and analytical inversions are consistent with a recent bottom-up inventory on the basis of MODIS satellite fire data.

The distribution of ion orbit loss fluxes of ions and energy from the plasma edge across the last closed flux surface into the scrape-off layer

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

Stacey, Weston M.; Schumann, Matthew T.

A more detailed calculation strategy for the evaluation of ion orbit loss of thermalized plasma ions in the edge of tokamaks is presented. In both this and previous papers, the direct loss of particles from internal flux surfaces is calculated from the conservation of canonical angular momentum, energy, and magnetic moment. The previous result that almost all of the ion energy and particle fluxes crossing the last closed flux surface are in the form of ion orbit fluxes is confirmed, and the new result that the distributions of these fluxes crossing the last closed flux surface into the scrape-off layermore » are very strongly peaked about the outboard midplane is demonstrated. Previous results of a preferential loss of counter current particles leading to a co-current intrinsic rotation peaking just inside of the last closed flux surface are confirmed. Various physical details are discussed.« less

Interferometric Imaging Directly with Closure Phases and Closure Amplitudes

NASA Astrophysics Data System (ADS)

Chael, Andrew A.; Johnson, Michael D.; Bouman, Katherine L.; Blackburn, Lindy L.; Akiyama, Kazunori; Narayan, Ramesh

2018-04-01

Interferometric imaging now achieves angular resolutions as fine as ∼10 μas, probing scales that are inaccessible to single telescopes. Traditional synthesis imaging methods require calibrated visibilities; however, interferometric calibration is challenging, especially at high frequencies. Nevertheless, most studies present only a single image of their data after a process of “self-calibration,” an iterative procedure where the initial image and calibration assumptions can significantly influence the final image. We present a method for efficient interferometric imaging directly using only closure amplitudes and closure phases, which are immune to station-based calibration errors. Closure-only imaging provides results that are as noncommittal as possible and allows for reconstructing an image independently from separate amplitude and phase self-calibration. While closure-only imaging eliminates some image information (e.g., the total image flux density and the image centroid), this information can be recovered through a small number of additional constraints. We demonstrate that closure-only imaging can produce high-fidelity results, even for sparse arrays such as the Event Horizon Telescope, and that the resulting images are independent of the level of systematic amplitude error. We apply closure imaging to VLBA and ALMA data and show that it is capable of matching or exceeding the performance of traditional self-calibration and CLEAN for these data sets.

Pulsar Magnetohydrodynamic Winds

NASA Astrophysics Data System (ADS)

Okamoto, Isao; Sigalo, Friday B.

2006-12-01

The acceleration and collimation/decollimation of relativistic magnetocentrifugal winds are discussed concerning a cold plasma from a strongly magnetized, rapidly rotating neutron star in a steady axisymmetric state based on ideal magnetohydrodynamics. There exist unipolar inductors associated with the field line angular frequency, α, at the magnetospheric base surface, SB, with a huge potential difference between the poles and the equator, which drive electric current through the pulsar magnetosphere. Any ``current line'' must emanate from one terminal of the unipolar inductor and return to the other, converting the Poynting flux to the kinetic flux of the wind at finite distances. In a plausible field structure satisfying the transfield force-balance equation, the fast surface, SF, must exist somewhere between the subasymptotic and asymptotic domains, i.e., at the innermost point along each field line of the asymptotic domain of \\varpaA2/\\varpi2 ≪ 1, where \\varpiA is the Alfvénic axial distance. The criticality condition at SF yields the Lorentz factor, γF = μ\\varepsilon1/3, and the angular momentum flux, β, as the eigenvalues in terms of the field line angular velocity, α, the mass flux per unit flux tube, η, and one of the Bernoulli integrals, μδ, which are assumed to be specifiable as the boundary conditions at SB. The other Bernoulli integral, μɛ, is related to μδ as μɛ = μδ[1-(α2\\varpiA2/c2)]-1, and both μɛ and \\varpiA2 are eigenvalues to be determined by the criticality condition at SF. Ongoing MHD acceleration is possible in the superfast domain. This fact may be helpful in resolving a discrepancy between the wind theory and the Crab-nebula model. It is argued that the ``anti-collimation theorem'' holds for relativistic winds, based on the curvature of field streamlines determined by the transfield force balance. The ``theorem'' combines with the ``current-closure condition'' as a global condition in the wind zone to produce a two-component ``quasi-conical'' field structure as one of the basic properties of MHD outflows of centrifugal origin in the pulsar magnetosphere.

Effects of Wall-Normal and Angular Momentum Injections in Airfoil Separation Control

NASA Astrophysics Data System (ADS)

Munday, Phillip M.; Taira, Kunihiko

2018-05-01

The objective of this computational study is to quantify the influence of wall-normal and angular momentum injections in suppressing laminar flow separation over a canonical airfoil. Open-loop control of fully separated, incompressible flow over a NACA 0012 airfoil at $\\alpha = 9^\\circ$ and $Re = 23,000$ is examined with large-eddy simulations. This study independently introduces wall-normal momentum and angular momentum into the separated flow using swirling jets through model boundary conditions. The response of the flow field and the surface vorticity fluxes to various combinations of actuation inputs are examined in detail. It is observed that the addition of angular momentum input to wall-normal momentum injection enhances the suppression of flow separation. Lift enhancement and suppression of separation with the wall-normal and angular momentum inputs are characterized by modifying the standard definition of the coefficient of momentum. The effect of angular momentum is incorporated into the modified coefficient of momentum by introducing a characteristic swirling jet velocity based on the non-dimensional swirl number. With this single modified coefficient of momentum, we are able to categorize each controlled flow into separated, transitional, and attached flows.

Land-surface parameter optimisation using data assimilation techniques: the adJULES system V1.0

DOE PAGES

Raoult, Nina M.; Jupp, Tim E.; Cox, Peter M.; ...

2016-08-25

Land-surface models (LSMs) are crucial components of the Earth system models (ESMs) that are used to make coupled climate–carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. JULES is also extensively used offline as a land-surface impacts tool, forced with climatologies into the future. In this study, JULES is automatically differentiated with respect to JULES parameters using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimationmore » system has been developed to search for locally optimum parameters by calibrating against observations. This paper describes adJULES in a data assimilation framework and demonstrates its ability to improve the model–data fit using eddy-covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the five plant functional types (PFTs) in JULES. The optimised PFT-specific parameters improve the performance of JULES at over 85 % of the sites used in the study, at both the calibration and evaluation stages. Furthermore, the new improved parameters for JULES are presented along with the associated uncertainties for each parameter.« less

Adaptive Nodal Transport Methods for Reactor Transient Analysis

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

Thomas Downar; E. Lewis

2005-08-31

Develop methods for adaptively treating the angular, spatial, and time dependence of the neutron flux in reactor transient analysis. These methods were demonstrated in the DOE transport nodal code VARIANT and the US NRC spatial kinetics code, PARCS.

Some aspects of cosmic synchrotron sources

NASA Technical Reports Server (NTRS)

Epstein, R. I.

1973-01-01

Synchrotron emission is considered from individual particles which have small pitch angles and the general properties of synchrotron sources which mainly contain such particles, as well as the emissivities and degrees of circular polarization for specific source distributions. The limitation of synchrotron source models for optical pulsars and compact extragalactic objects are discussed, and it is shown that several existing models for the pulsar NP 0532 are inconsistent with the measured time variations and polarizations of the optical emission. Discussion is made also of whether the low frequency falloffs in the extragalactic objects PKS 2134 + 004, OQ 208, and NGC 1068 is due to emission from particles with small pitch angles or absorption by a thermal plasma or synchrotron self-absorption. It is concluded that the absorption interpretations cannot account for the turnover in the spectrum of PKS 2134 + 004. Measurements of polarization, angular structure, and X-ray flux are also described.

Improvement of basal conditions knowledge in Antarctica using data assimilation methods

NASA Astrophysics Data System (ADS)

Mosbeux, C.; Gillet-Chaulet, F.; Gagliardini, O.

2017-12-01

The current global warming seems to have direct consequences on ice-sheet mass loss. Unfortunately, as highlighted in the last IPCC report, current ice-sheets models face several difficulties in assessing the future evolution of the dynamics of ice sheets for the next century. Indeed, projections are still plagued with high uncertainties partially due to the poor representation of occurring physical processes, but also due to the poor initialisation of ice flow models. More specifically, simulations are very sensitive to initial parameters such as the basal friction between ice-sheet and bedrock and the bedrock topography which are still badly known because of a lack of direct observations or large uncertainty on measurements. Improving the knowledge of these two parameters in Greenland and Antarctica is therefore a prerequisite for making reliable projections. Data assimilation methods have been developed in order to overcome this problem such as the Bayesian approach of Pralong and Gudmundsson (2009) or the adjoint method tested by Goldberg and Heimbach (2013) and Perego et al. (2014). The present work is based on two different assimilation algorithms to better constrain both basal drag and bedrock elevation parameters. The first algorithm is entirely based on the adjoint method while the second one uses an iterative method coupling inversion of basal friction based on an adjoint method and through an inversion of bedrock topography using a nudging method. Both algorithms have been implemented in the finite element ice sheet and ice flow model Elmer/Ice and have been tested in a twin experiment showing a clear improvement of both parameters knowledge (Mosbeux et al., 2016). Here, the methods are applied to a real 3D case in East Antarctica and with an ensemble method approach. The application of both algorithms reduces the uncertainty on basal conditions, for instance by providing more details to the basal geometry when compared to usual DEM. Moreover, as in the previous experiment, the reconstruction of both basal elevation and basal friction significantly decreases ice flux divergence anomalies when compared to classical methods where only the friction is inverted. Finally, we conduct prognostic simulations, allowing to assess the impact of the different initialisations obtained with the ensemble method.

Self-Consistent Sources for Integrable Equations Via Deformations of Binary Darboux Transformations

NASA Astrophysics Data System (ADS)

Chvartatskyi, Oleksandr; Dimakis, Aristophanes; Müller-Hoissen, Folkert

2016-08-01

We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation of the potential that is central in this method. As examples, we obtain in particular matrix versions of self-consistent source extensions of the KdV, Boussinesq, sine-Gordon, nonlinear Schrödinger, KP, Davey-Stewartson, two-dimensional Toda lattice and discrete KP equation. We also recover a (2+1)-dimensional version of the Yajima-Oikawa system from a deformation of the pKP hierarchy. By construction, these systems are accompanied by a hetero binary Darboux transformation, which generates solutions of such a system from a solution of the source-free system and additionally solutions of an associated linear system and its adjoint. The essence of all this is encoded in universal equations in the framework of bidifferential calculus.

Angular dependence of critical current density and magnetoresistance of sputtered high-T{sub c}-films

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

Geerkens, A.; Frenck, H.J.; Ewert, S.

1994-12-31

The angular dependence of the critical current density and the magnetoresistance of high-T{sub c}-films in high and low magnetic fields and for different temperatures were measured to investigate the flux pinning and the superconducting properties. A comparison of the results for the different superconductors shows their increasing dependence on the angle {Theta} between the magnetic field and the c-axis of the film due to the anisotropy of the chosen superconductor. Furthermore the influence of the current direction to the {Theta}-rotation plane is discussed.

Angular dependence of critical current density and magnetoresistance of sputtered high-T(sub c)-films

NASA Technical Reports Server (NTRS)

Geerkens, A.; Meven, M.; Frenck, H.-J.; Ewert, S.

1995-01-01

The angular dependence of the critical current density and the magnetoresistance of high-T(sub c)-films in high and low magnetic fields and for different temperatures were measured to investigate the flux pinning and the superconducting properties. A comparison of the results for the different superconductors shows their increasing dependence on the angle Theta between the magnetic field and the c-axis of the film due to the anisotropy of the chosen superconductor. Furthermore the influence of the current direction to the Theta-rotation plane is discussed.

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

Superposition of nonparaxial vectorial complex-source spherically focused beams: Axial Poynting singularity and reverse propagation

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2016-08-01

In this work, counterintuitive effects such as the generation of an axial (i.e., long the direction of wave motion) zero-energy flux density (i.e., axial Poynting singularity) and reverse (i.e., negative) propagation of nonparaxial quasi-Gaussian electromagnetic (EM) beams are examined. Generalized analytical expressions for the EM field's components of a coherent superposition of two high-order quasi-Gaussian vortex beams of opposite handedness and different amplitudes are derived based on the complex-source-point method, stemming from Maxwell's vector equations and the Lorenz gauge condition. The general solutions exhibiting unusual effects satisfy the Helmholtz and Maxwell's equations. The EM beam components are characterized by nonzero integer degree and order (n ,m ) , respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and a weighting (real) factor 0 ≤α ≤1 that describes the transition of the beam from a purely vortex (α =0 ) to a nonvortex (α =1 ) type. An attractive feature for this superposition is the description of strongly focused (or strongly divergent) wave fields. Computations of the EM power density as well as the linear and angular momentum density fluxes illustrate the analysis with particular emphasis on the polarization states of the vector potentials forming the beams and the weight of the coherent beam superposition causing the transition from the vortex to the nonvortex type. Should some conditions determined by the polarization state of the vector potentials and the beam parameters be met, an axial zero-energy flux density is predicted in addition to a negative retrograde propagation effect. Moreover, rotation reversal of the angular momentum flux density with respect to the beam handedness is anticipated, suggesting the possible generation of negative (left-handed) torques. The results are particularly useful in applications involving the design of strongly focused optical laser tweezers, tractor beams, optical spanners, arbitrary scattering, radiation force, angular momentum, and torque in particle manipulation, and other related topics.

Melting of the Abrikosov flux lattice in anisotropic superconductors

NASA Technical Reports Server (NTRS)

Beck, R. G.; Farrell, D. E.; Rice, J. P.; Ginsberg, D. M.; Kogan, V. G.

1992-01-01

It has been proposed that the Abrikosov flux lattice in high-Tc superconductors is melted over a significant fraction of the phase diagram. A thermodynamic argument is provided which establishes that the angular dependence of the melting temperature is controlled by the superconducting mass anisotropy. Using a low-frequency torsional-oscillator technique, this relationship has been tested in untwinned single-crystal YBa2Cu3O(7-delta). The results offer decisive support for the melting proposal.

Study of the Performance of Stainless Steel A-TIG Welds

NASA Astrophysics Data System (ADS)

Shyu, S. W.; Huang, H. Y.; Tseng, K. H.; Chou, C. P.

2008-04-01

The purpose of the present work was to investigate the effect of oxide fluxes on weld morphology, arc voltage, mechanical properties, angular distortion and hot cracking susceptibility obtained with TIG welding, which applied to the welding of 5 mm thick austenitic stainless steel plates. A novel variant of the autogenous TIG welding process, oxide powders (Al2O3, Cr2O3, TiO2, SiO2 and CaO) was applied on a type 304 stainless steel through a thin layer of the flux to produce a bead on plate welds. The experimental results indicated that the increase in the penetration is significant with the use of Cr2O3, TiO2, and SiO2. A-TIG welding can increase the weld depth to bead-width ratio, and tends to reduce the angular distortion of the weldment. It was also found that A-TIG welding can increase the retained delta-ferrite content of stainless steel 304 welds and, in consequence, the hot-cracking susceptibility of as-welded is reduced. Physically constricting the plasma column and reducing the anode spot are the possible mechanism for the effect of certain flux on A-TIG penetration.

Energy Deposition and Escape Fluxes Induced by Energetic Solar Wind Ions and ENAs Precipitating into Mars Atmosphere: Accurate Consideration of Energy Transfer Collisions

NASA Astrophysics Data System (ADS)

Kharchenko, V. A.; Lewkow, N.; Gacesa, M.

2014-12-01

Formation and evolution of neutral fluxes of atoms and molecules escaping from the Mars atmosphere have been investigated for the sputtering and photo-chemical mechanisms. Energy and momentum transfer in collisions between the atmospheric gas and fast atoms and molecules have been considered using our recently obtained angular and energy dependent cross sections[1]. We have showed that accurate angular dependent collision cross sections are critical for the description of the energy relaxation of precipitating keV energetic ions/ENAs and for computations of altitude profiles of the fast atom and molecule production rates in recoil collisions. Upward and escape fluxes of the secondary energetic He and O atoms and H2, N2, CO and CO2 molecules, induced by precipitating ENAs, have been determined and their non-thermal energy distribution functions have been computed at different altitudes for different solar conditions. Precipitation and energy deposition of the energetic H2O molecules and products of their dissociations into the Mars atmosphere in the Comet C/2013 A1 (Siding Spring) - Mars interaction have been modeled using accurate cross sections. Reflection of precipitating ENAs by the Mars atmosphere has been analyzed in detail. [1] N. Lewkow and V. Kharchenko, "Precipitation of Energetic Neutral Atoms and Escape Fluxes induced from the Mars Atmosphere, ApJ, v.790, p.98 (2014).

Precipitation of energetic neutral atoms and induced non-thermal escape fluxes from the Martian atmosphere

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

Lewkow, N. R.; Kharchenko, V.

2014-08-01

The precipitation of energetic neutral atoms, produced through charge exchange collisions between solar wind ions and thermal atmospheric gases, is investigated for the Martian atmosphere. Connections between parameters of precipitating fast ions and resulting escape fluxes, altitude-dependent energy distributions of fast atoms and their coefficients of reflection from the Mars atmosphere, are established using accurate cross sections in Monte Carlo (MC) simulations. Distributions of secondary hot (SH) atoms and molecules, induced by precipitating particles, have been obtained and applied for computations of the non-thermal escape fluxes. A new collisional database on accurate energy-angular-dependent cross sections, required for description of themore » energy-momentum transfer in collisions of precipitating particles and production of non-thermal atmospheric atoms and molecules, is reported with analytic fitting equations. Three-dimensional MC simulations with accurate energy-angular-dependent cross sections have been carried out to track large ensembles of energetic atoms in a time-dependent manner as they propagate into the Martian atmosphere and transfer their energy to the ambient atoms and molecules. Results of the MC simulations on the energy-deposition altitude profiles, reflection coefficients, and time-dependent atmospheric heating, obtained for the isotropic hard sphere and anisotropic quantum cross sections, are compared. Atmospheric heating rates, thermalization depths, altitude profiles of production rates, energy distributions of SH atoms and molecules, and induced escape fluxes have been determined.« less

An Inviscid Decoupled Method for the Roe FDS Scheme in the Reacting Gas Path of FUN3D

NASA Technical Reports Server (NTRS)

Thompson, Kyle B.; Gnoffo, Peter A.

2016-01-01

An approach is described to decouple the species continuity equations from the mixture continuity, momentum, and total energy equations for the Roe flux difference splitting scheme. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This work lays the foundation for development of an efficient adjoint solution procedure for high speed reacting flow.

Application of quasi-distributions for solving inverse problems of neutron and {gamma}-ray transport

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

Pogosbekyan, L.R.; Lysov, D.A.

The considered inverse problems deal with the calculation of the unknown values of nuclear installations by means of the known (goal) functionals of neutron/{gamma}-ray distributions. The example of these problems might be the calculation of the automatic control rods position as function of neutron sensors reading, or the calculation of experimentally-corrected values of cross-sections, isotopes concentration, fuel enrichment via the measured functional. The authors have developed the new method to solve inverse problem. It finds flux density as quasi-solution of the particles conservation linear system adjointed to equalities for functionals. The method is more effective compared to the one basedmore » on the classical perturbation theory. It is suitable for vectorization and it can be used successfully in optimization codes.« less

A New Method for Computing Three-Dimensional Capture Fraction in Heterogeneous Regional Systems using the MODFLOW Adjoint Code

NASA Astrophysics Data System (ADS)

Clemo, T. M.; Ramarao, B.; Kelly, V. A.; Lavenue, M.

2011-12-01

Capture is a measure of the impact of groundwater pumping upon groundwater and surface water systems. The computation of capture through analytical or numerical methods has been the subject of articles in the literature for several decades (Bredehoeft et al., 1982). Most recently Leake et al. (2010) described a systematic way to produce capture maps in three-dimensional systems using a numerical perturbation approach in which capture from streams was computed using unit rate pumping at many locations within a MODFLOW model. The Leake et al. (2010) method advances the current state of computing capture. A limitation stems from the computational demand required by the perturbation approach wherein days or weeks of computational time might be required to obtain a robust measure of capture. In this paper, we present an efficient method to compute capture in three-dimensional systems based upon adjoint states. The efficiency of the adjoint method will enable uncertainty analysis to be conducted on capture calculations. The USGS and INTERA have collaborated to extend the MODFLOW Adjoint code (Clemo, 2007) to include stream-aquifer interaction and have applied it to one of the examples used in Leake et al. (2010), the San Pedro Basin MODFLOW model. With five layers and 140,800 grid blocks per layer, the San Pedro Basin model, provided an ideal example data set to compare the capture computed from the perturbation and the adjoint methods. The capture fraction map produced from the perturbation method for the San Pedro Basin model required significant computational time to compute and therefore the locations for the pumping wells were limited to 1530 locations in layer 4. The 1530 direct simulations of capture require approximately 76 CPU hours. Had capture been simulated in each grid block in each layer, as is done in the adjoint method, the CPU time would have been on the order of 4 years. The MODFLOW-Adjoint produced the capture fraction map of the San Pedro Basin model at 704,000 grid blocks (140,800 grid blocks x 5 layers) in just 6 minutes. The capture fraction maps from the perturbation and adjoint methods agree closely. The results of this study indicate that the adjoint capture method and its associated computational efficiency will enable scientists and engineers facing water resource management decisions to evaluate the sensitivity and uncertainty of impacts to regional water resource systems as part of groundwater supply strategies. Bredehoeft, J.D., S.S. Papadopulos, and H.H. Cooper Jr, Groundwater: The water budget myth. In Scientific Basis of Water-Resources Management, ed. National Research Council (U.S.), Geophysical Study Committee, 51-57. Washington D.C.: National Academy Press, 1982. Clemo, Tom, MODFLOW-2005 Ground-Water Model-Users Guide to Adjoint State based Sensitivity Process (ADJ), BSU CGISS 07-01, Center for the Geophysical Investigation of the Shallow Subsurface, Boise State University, 2007. Leake, S.A., H.W. Reeves, and J.E. Dickinson, A New Capture Fraction Method to Map How Pumpage Affects Surface Water Flow, Ground Water, 48(5), 670-700, 2010.

Dynamics of low- and high-Z metal ions emitted during nanosecond laser-produced plasmas

NASA Astrophysics Data System (ADS)

Elsied, Ahmed M.; Diwakar, Prasoon K.; Polek, Mathew; Hassanein, Ahmed

2016-11-01

Dynamics of metal ions during laser-produced plasmas was studied. A 1064 nm, Nd: YAG laser pulse was used to ablate pure Al, Fe, Co, Mo, and Sn samples. Ion flux and velocity were measured using Faraday cup ion collector. Time-of-flight measurements showed decreasing ion flux and ion velocity with increasing atomic weight, and heavy metal ion flux profile exhibited multiple peaks that was not observed in lighter metals. Slow peak was found to follow shifted Maxwell Boltzmann distribution, while the fast peak was found to follow Gaussian distribution. Ion flux angular distribution that was carried out on Mo and Al using fixed laser intensity 2.5 × 1010 W/cm2 revealed that the slow ion flux peaks at small angles, that is, close to normal to the target ˜0° independent of target's atomic weight, and fast ion flux for Mo peaks at large angles ˜40° measured from the target normal, while it completely absents for Al. This difference in spatial and temporal distribution reveals that the emission mechanism of the fast and slow ions is different. From the slow ion flux angular distribution, the measured plume expansion ratio (plume forward peaking) was 1.90 and 2.10 for Al and Mo, respectively. Moreover, the effect of incident laser intensity on the ion flux emission as well as the emitted ion velocity were investigated using laser intensities varying from 2.5 × 1010 W/cm2 to 1.0 × 1011 W/cm2. Linear increase of fast ion flux and velocity, and quadratic increase of slow ion flux and velocity were observed. For further understanding of plume dynamics, laser optical emission spectroscopy was used to characterize Sn plasma by measuring the temporal and spatial evolution of plasma electron density Ne and electron temperature Te. At 3.5 mm away from the target, plasma density showed slow decrease with time, however electron temperature was observed to decrease dramatically. The maximum plasma density and temperature occurred at 0.5 mm away from target and were measured to be 8.0 × 1017 cm-3 and 1.3 eV, respectively.

Finite-frequency tomography using adjoint methods-Methodology and examples using membrane surface waves

NASA Astrophysics Data System (ADS)

Tape, Carl; Liu, Qinya; Tromp, Jeroen

2007-03-01

We employ adjoint methods in a series of synthetic seismic tomography experiments to recover surface wave phase-speed models of southern California. Our approach involves computing the Fréchet derivative for tomographic inversions via the interaction between a forward wavefield, propagating from the source to the receivers, and an `adjoint' wavefield, propagating from the receivers back to the source. The forward wavefield is computed using a 2-D spectral-element method (SEM) and a phase-speed model for southern California. A `target' phase-speed model is used to generate the `data' at the receivers. We specify an objective or misfit function that defines a measure of misfit between data and synthetics. For a given receiver, the remaining differences between data and synthetics are time-reversed and used as the source of the adjoint wavefield. For each earthquake, the interaction between the regular and adjoint wavefields is used to construct finite-frequency sensitivity kernels, which we call event kernels. An event kernel may be thought of as a weighted sum of phase-specific (e.g. P) banana-doughnut kernels, with weights determined by the measurements. The overall sensitivity is simply the sum of event kernels, which defines the misfit kernel. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, that is, the Fréchet derivative. A non-linear conjugate gradient algorithm is used to iteratively improve the model while reducing the misfit function. We illustrate the construction of the gradient and the minimization algorithm, and consider various tomographic experiments, including source inversions, structural inversions and joint source-structure inversions. Finally, we draw connections between classical Hessian-based tomography and gradient-based adjoint tomography.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Magnetic Manipulation of Massless Dirac Fermions in Graphene Quantum Dot

NASA Astrophysics Data System (ADS)

Lin, Xin; Pan, Hui; Xu, Huai-Zhe

2010-12-01

We have theoretically analyzed the quasibound states in a graphene quantum dot (GQD) with a magnetic flux Φ in the centre. It is shown that the two-fold time reversal degeneracy is broken and the quasibound states of GQD with positive/negative angular momentum shifted upwards / downwards with increasing the magnetic flux. The variation of the quasibound energy depends linearly on the magnetic flux, which is quite different from the parabolic relationship for Schrödinger electrons. The GQD's quasibound states spectrum shows an obvious Aharonov—Bohm (AB) oscillations with the magnetic flux. It is also shown that the quasibound state with energy equal to the barrier height becomes a bound state completely confined in GQD.

Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"

EPA Science Inventory

Ammonia emissions parameters in North America can be refined in order to improve the evaluation of modeled concentrations against observations. Here, we seek to do so by developing and applying the GEOS-Chem adjoint nested over North America to conductassimilation of observations...

Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide

DOE PAGES

Favorite, Jeffrey A.; Perko, Zoltan; Kiedrowski, Brian C.; ...

2017-03-01

The ability to perform sensitivity analyses using adjoint-based first-order sensitivity theory has existed for decades. This paper provides guidance on how adjoint sensitivity methods can be used to predict the effect of material density and composition uncertainties in critical experiments, including when these uncertain parameters are correlated or constrained. Two widely used Monte Carlo codes, MCNP6 (Ref. 2) and SCALE 6.2 (Ref. 3), are both capable of computing isotopic density sensitivities in continuous energy and angle. Additionally, Perkó et al. have shown how individual isotope density sensitivities, easily computed using adjoint methods, can be combined to compute constrained first-order sensitivitiesmore » that may be used in the uncertainty analysis. This paper provides details on how the codes are used to compute first-order sensitivities and how the sensitivities are used in an uncertainty analysis. Constrained first-order sensitivities are computed in a simple example problem.« less

Extending the Binomial Checkpointing Technique for Resilience

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

Walther, Andrea; Narayanan, Sri Hari Krishna

In terms of computing time, adjoint methods offer a very attractive alternative to compute gradient information, re- quired, e.g., for optimization purposes. However, together with this very favorable temporal complexity result comes a memory requirement that is in essence proportional with the operation count of the underlying function, e.g., if algo- rithmic differentiation is used to provide the adjoints. For this reason, checkpointing approaches in many variants have become popular. This paper analyzes an extension of the so-called binomial approach to cover also possible failures of the computing systems. Such a measure of precaution is of special interest for massivemore » parallel simulations and adjoint calculations where the mean time between failure of the large scale computing system is smaller than the time needed to complete the calculation of the adjoint information. We de- scribe the extensions of standard checkpointing approaches required for such resilience, provide a corresponding imple- mentation and discuss numerical results.« less

Adjoint Sensitivity Analysis for Scale-Resolving Turbulent Flow Solvers

NASA Astrophysics Data System (ADS)

Blonigan, Patrick; Garai, Anirban; Diosady, Laslo; Murman, Scott

2017-11-01

Adjoint-based sensitivity analysis methods are powerful design tools for engineers who use computational fluid dynamics. In recent years, these engineers have started to use scale-resolving simulations like large-eddy simulations (LES) and direct numerical simulations (DNS), which resolve more scales in complex flows with unsteady separation and jets than the widely-used Reynolds-averaged Navier-Stokes (RANS) methods. However, the conventional adjoint method computes large, unusable sensitivities for scale-resolving simulations, which unlike RANS simulations exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by conventional adjoint methods, but has a high computational cost even for relatively small simulations. The following talk discusses a more computationally efficient formulation of LSS, ``non-intrusive'' LSS, and its application to turbulent flows simulated with a discontinuous-Galkerin spectral-element-method LES/DNS solver. Results are presented for the minimal flow unit, a turbulent channel flow with a limited streamwise and spanwise domain.

A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport

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

Bal, Guillaume, E-mail: gb2030@columbia.edu; Davis, Anthony B., E-mail: Anthony.B.Davis@jpl.nasa.gov; Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106-4030

2011-08-20

Highlights: {yields} We introduce a variance reduction scheme for Monte Carlo (MC) transport. {yields} The primary application is atmospheric remote sensing. {yields} The technique first solves the adjoint problem using a deterministic solver. {yields} Next, the adjoint solution is used as an importance function for the MC solver. {yields} The adjoint problem is solved quickly since it ignores the volume. - Abstract: A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or amore » airplane). It uses a deterministic approximation of an adjoint transport solution to reduce variance, computed quickly by ignoring atmospheric interactions. This allows significant variance and computational cost reductions when the atmospheric scattering and absorption coefficient are small. When combined with an atmospheric photon-redirection scheme, significant variance reduction (equivalently acceleration) is achieved in the presence of atmospheric interactions.« less

Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

1999-01-01

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Neural network training by integration of adjoint systems of equations forward in time

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

1992-01-01

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically, it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved, but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. The trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Characterization of emergent leakage neutrons from multiple layers of hydrogen/water in the lunar regolith by Monte Carlo simulation

NASA Astrophysics Data System (ADS)

SU, J.; Sagdeev, R.; Usikov, D.; Chin, G.; Boyer, L.; Livengood, T. A.; McClanahan, T. P.; Murray, J.; Starr, R. D.

2013-12-01

Introduction: The leakage flux of lunar neutrons produced by precipitation of galactic cosmic ray (GCR) particles in the upper layer of the lunar regolith and measured by orbital instruments such as the Lunar Exploration Neutron Detector (LEND) is investigated by Monte Carlo simulation. Previous Monte Carlo (MC) simulations have been used to investigate neutron production and leakage from the lunar surface to assess the elemental composition of lunar soil [1-6] and its effect on the leakage neutron flux. We investigate effects on the emergent flux that depend on the physical distribution of hydrogen within the regolith. We use the software package GEANT4 [7] to calculate neutron production from spallation by GCR particles [8,9] in the lunar soil. Multiple layers of differing hydrogen/water at different depths in the lunar regolith model are introduced to examine enhancement or suppression of leakage neutron flux. We find that the majority of leakage thermal and epithermal neutrons are produced in 25 cm to 75 cm deep from the lunar surface. Neutrons produced in the shallow top layer retain more of their original energy due to fewer scattering interactions and escape from the lunar surface mostly as fast neutrons. This provides a diagnostic tool in interpreting leakage neutron flux enhancement or suppression due to hydrogen concentration distribution in lunar regolith. We also find that the emitting angular distribution of thermal and epithermal leakage neutrons can be described by cos3/2(theta) where the fast neutrons emitting angular distribution is cos(theta). The energy sensitivity and angular response of the LEND detectors SETN and CSETN are investigated using the leakage neutron spectrum from GEANT4 simulations. A simplified LRO model is used to benchmark MCNPX[10] and GEANT4 on CSETN absolute count rate corresponding to neutron flux from bombardment of 120MV solar potential GCR particles on FAN lunar soil. We are able to interpret the count rates of SETN and CSETN from the leakage neutron spectrum, emission angle, detector energy sensitivity and angular response. Reference: [1] W. C. Feldman, et al., Science 4 September 1998: Vol. 281 no. 5382 pp. 1496-1500. [2] Gasnault, O., et al., (2000) J. Geophys. Res., 105(E2), 4263-4271. [3] Little, R. C., et al. (2003), J. Geophys. Res., 108(E5), 5046. [4] McKinney et al., (2006), J. Geophys. Res., 111, E06004. [5] Lawrence et al., (2006), J. Geophys. Res., 111, E08001. [6] Looper et al, (2013), Space Weather, VOL. 11, 142-152. [7] J. Allison, et al, (2006) IEEE TRANS. ON NUCL SCI, VOL. 53, NO. 1. [8] J. Masarik and R. Reedy (1996), J. Geophys. Res., 101, 18,891-18,912. [9] P. O'Neil (2010) IEEE Trans. Nucl. Sci., 57(6), 3148-3153. [10] D. Pelowitz, (2005), Rep. LA-CP-05-0369, LANL, Los Alamos, NM.

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

NASA Technical Reports Server (NTRS)

Grossman, Bernard

1999-01-01

The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing.

Neural Correlates of Self-Reference Effect in Early Alzheimer's Disease.

PubMed

Gaubert, Malo; Villain, Nicolas; Landeau, Brigitte; Mézenge, Florence; Egret, Stéphanie; Perrotin, Audrey; Belliard, Serge; de La Sayette, Vincent; Eustache, Francis; Desgranges, Béatrice; Chételat, Gaël; Rauchs, Géraldine

2017-01-01

Information that is processed with reference to the self (i.e., self-referential processing, SRP) is generally associated with better remembering than information processed in a semantic condition. This benefit of self on memory performance is called self-reference effect (SRE). In the present study, we assessed changes in the SRE and SRP-related brain activity in patients diagnosed with mild cognitive impairment or early Alzheimer's disease (MCI/AD). Fifteen patients with confirmed amyloid-β deposits (positive florbetapir-PET scan) and 28 healthy controls (negative florbetapir-PET scan) were included. Participants either had to judge personality trait adjectives with reference to themselves (self condition) or to a celebrity (other condition), or determine whether these adjectives were positive or not (semantic condition). These adjectives were then presented with distractors in a surprise recognition task. Functional MRI data were acquired during both the judgment and recognition tasks. The SRE was observed in controls, but reduced in patients. Both controls and patients activated cortical midline structures when judging items with reference to themselves, but patients exhibited reduced activity in the angular gyrus. In patients, activity at encoding in the angular gyrus positively correlated with subsequent recognition accuracy in the self condition (self accuracy). This region also exhibited significant hypometabolism and Aβ burden, both related to self accuracy. By contrast, there were no differences in brain activity during recognition, either between the self and semantic conditions, or between groups. These results highlight SRE impairment in patients with MCI/AD, despite intact activity in cortical midline structures, and suggest that dysfunction of the angular gyrus is related to this impairment.

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

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

Yang, R; Fallone, B; Cross Cancer Institute, Edmonton, AB

Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. Themore » LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).« less

Adjoint-Based Uncertainty Quantification with MCNP

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

Seifried, Jeffrey E.

2011-09-01

This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence inmore » the simulation is acquired.« less

Adjoint shape optimization for fluid-structure interaction of ducted flows

NASA Astrophysics Data System (ADS)

Heners, J. P.; Radtke, L.; Hinze, M.; Düster, A.

2018-03-01

Based on the coupled problem of time-dependent fluid-structure interaction, equations for an appropriate adjoint problem are derived by the consequent use of the formal Lagrange calculus. Solutions of both primal and adjoint equations are computed in a partitioned fashion and enable the formulation of a surface sensitivity. This sensitivity is used in the context of a steepest descent algorithm for the computation of the required gradient of an appropriate cost functional. The efficiency of the developed optimization approach is demonstrated by minimization of the pressure drop in a simple two-dimensional channel flow and in a three-dimensional ducted flow surrounded by a thin-walled structure.

NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO

NASA Astrophysics Data System (ADS)

Vidard, A.; Bouttier, P.-A.; Vigilant, F.

2015-04-01

Tangent linear and adjoint models (TAMs) are efficient tools to analyse and to control dynamical systems such as NEMO. They can be involved in a large range of applications such as sensitivity analysis, parameter estimation or the computation of characteristic vectors. A TAM is also required by the 4D-Var algorithm, which is one of the major methods in data assimilation. This paper describes the development and the validation of the tangent linear and adjoint model for the NEMO ocean modelling platform (NEMOTAM). The diagnostic tools that are available alongside NEMOTAM are detailed and discussed, and several applications are also presented.

NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO

NASA Astrophysics Data System (ADS)

Vidard, A.; Bouttier, P.-A.; Vigilant, F.

2014-10-01

The tangent linear and adjoint model (TAM) are efficient tools to analyse and to control dynamical systems such as NEMO. They can be involved in a large range of applications such as sensitivity analysis, parameter estimation or the computation of characteristics vectors. TAM is also required by the 4-D-VAR algorithm which is one of the major method in Data Assimilation. This paper describes the development and the validation of the Tangent linear and Adjoint Model for the NEMO ocean modelling platform (NEMOTAM). The diagnostic tools that are available alongside NEMOTAM are detailed and discussed and several applications are also presented.

On universal knot polynomials

NASA Astrophysics Data System (ADS)

Mironov, A.; Mkrtchyan, R.; Morozov, A.

2016-02-01

We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

Charge exchange in cometary coma: Discovery of H− ions in the solar wind close to comet 67P/Churyumov‐Gerasimenko

PubMed Central

Cravens, T. E.; Llera, K.; Goldstein, R.; Mokashi, P.; Tzou, C.‐Y.; Broiles, T.

2015-01-01

Abstract As Rosetta was orbiting comet 67P/Churyumov‐Gerasimenko, the Ion and Electron Sensor detected negative particles with angular distributions like those of the concurrently measured solar wind protons but with fluxes of only about 10% of the proton fluxes and energies of about 90% of the proton energies. Using well‐known cross sections and energy‐loss data, it is determined that the fluxes and energies of the negative particles are consistent with the production of H− ions in the solar wind by double charge exchange with molecules in the coma. PMID:27656008

Auroral-particle precipitation and trapping caused by electrostatic double layers in the ionosphere.

PubMed

Albert, R D; Lindstrom, P J

1970-12-25

Interpretation of high-resolution angular distribution measurements of the primary auroral electron flux detected by a rocket probe launched into a visible aurora from Fort Churchill in the fall of 1966 leads to the following conclusions. The auroral electron flux is nearly monoenergetic and has a quasi-trapped as well as a precipitating component. The quasi-trapped flux appears to be limited to a region defined by magnetic-mirror points and multiple electrostatic double layers in the ionosphere. The electrostatic field of the double-layer distribution enhances the aurora by lowering the magnetic-mirror points and supplying energy to the primary auroral electrons.

Light-sheet generation in inhomogeneous media using self-reconstructing beams and the STED-principle.

PubMed

Gohn-Kreuz, Cristian; Rohrbach, Alexander

2016-03-21

Self-reconstruction of Bessel beams in inhomogeneous media is beneficial in light-sheet based microscopy. Although the beam's ring system enables propagation stability, the resulting image contrast is reduced. Here, we show that by a combination of two self-reconstructing beams with different orbital angular momenta it is possible to inhibit fluorescence from the ring system by using stimulated emission depletion (STED) even in strongly scattering media. Our theoretical study shows that the remaining fluorescence γ depends non-linearly on the beams' relative radial and orbital angular momenta. For various scattering media we demonstrate that γ remains remarkably stable over long beam propagation distances.

Adjoint Sensitivity Analysis of Radiative Transfer Equation: Temperature and Gas Mixing Ratio Weighting Functions for Remote Sensing of Scattering Atmospheres in Thermal IR

NASA Technical Reports Server (NTRS)

Ustinov, E.

1999-01-01

Sensitivity analysis based on using of the adjoint equation of radiative transfer is applied to the case of atmospheric remote sensing in the thermal spectral region with non-negligeable atmospheric scattering.

Powerful non-geoeffective interplanetary disturbance of July 2012 observed by muon hodoscope URAGAN

NASA Astrophysics Data System (ADS)

Astapov, I. I.; Barbashina, N. S.; Petrukhin, A. A.; Shutenko, V. V.; Veselovsky, I. S.

2015-12-01

The most powerful coronal mass ejection of the 24th solar cycle took place on the opposite side of the Sun on July 23, 2012 and had no geomagnetic consequences. Nevertheless, as a result of passing of the ejection through the heliosphere, variations of galactic cosmic rays flux were observed on the Earth. These variations were registered by the muon hodoscope URAGAN (MEPhI, Moscow). Muon flux angular distributions on the Earth's surface are reported and analyzed.

Suppression of the multi-azimuthal-angle instability in dense neutrino gas during supernova accretion phase

NASA Astrophysics Data System (ADS)

Chakraborty, Sovan; Mirizzi, Alessandro; Saviano, Ninetta; Seixas, David de Sousa

2014-05-01

It has been recently pointed out that by removing the axial symmetry in the "multi-angle effects" associated with the neutrino-neutrino interactions for supernova (SN) neutrinos a new multi-azimuthal-angle (MAA) instability would arise. In particular, for a flux ordering Fνe>Fν ¯e>Fνx, as expected during the SN accretion phase, this instability occurs in the normal neutrino mass hierarchy. However, during this phase, the ordinary matter density can be larger than the neutrino one, suppressing the self-induced conversions. In this regard, we investigate the matter suppression of the MAA effects, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. We compare these results with the numerical solution of the SN neutrino nonlinear evolution equations. Assuming axially symmetric distributions of neutrino momenta, we find that the large matter term strongly inhibits the MAA effects. In particular, the hindrance becomes stronger including realistic forward-peaked neutrino angular distributions. As a result, in our model for a 10.8 M⊙ iron-core SNe, MAA instability does not trigger any flavor conversion during the accretion phase. Instead, for a 8.8 M⊙ O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, flavor conversions are possible also at early times.

Toward regional-scale adjoint tomography in the deep earth

NASA Astrophysics Data System (ADS)

Masson, Y.; Romanowicz, B. A.

2013-12-01

Thanks to the development of efficient numerical computation methods, such as the Spectral Element Method (SEM) and to the increasing power of computer clusters, it is now possible to obtain regional-scale images of the Earth's interior using adjoint-tomography (e.g. Tape, C., et al., 2009). As for now, these tomographic models are limited to the upper layers of the earth, i.e., they provide us with high-resolution images of the crust and the upper part of the mantle. Given the gigantic amount of calculation it represents, obtaing similar models at the global scale (i.e. images of the entire Earth) seems out of reach at the moment. Furthermore, it's likely that the first generation of such global adjoint tomographic models will have a resolution significantly smaller than the current regional models. In order to image regions of interests in the deep Earth, such as plumes, slabs or large low shear velocity provinces (LLSVPs), while keeping the computation tractable, we are developing new tools that will allow us to perform regional-scale adjoint-tomography at arbitrary depths. In a recent study (Masson et al., 2013), we showed that a numerical equivalent of the time reversal mirrors used in experimental acoustics permits to confine the wave propagation computations (i.e. using SEM simulations) inside the region to be imaged. With this ability to limit wave propagation modeling inside a region of interest, obtaining the adjoint sensitivity kernels needed for tomographic imaging is only two steps further. First, the local wavefield modeling needs to be coupled with field extrapolation techniques in order to obtain synthetic seismograms at the surface of the earth. These seismograms will account for the 3D structure inside the region of interest in a quasi-exact manner. We will present preliminary results where the field-extrapolation is performed using Green's function computed in a 1D Earth model thanks to the Direct Solution Method (DSM). Once synthetic seismograms can be obtained, it is possible to evaluate the misfit between observed and computed seismograms. The second step will then be to extrapolate the misfit function back into the SEM region in order to compute local adjoint sensitivity kernels. When available, these kernels will allow us to perform regional-scale adjoint tomography at arbitrary locations inside the earth. Masson Y., Cupillard P., Capdeville Y., & Romanowicz B., 2013. On the numerical implementation of time-reversal mirrors for tomographic imaging, Journal of Geophysical Research (under review). Tape, C., et al. (2009). "Adjoint tomography of the southern California crust." Science 325(5943): 988-992.

Double-Difference Global Adjoint Tomography

NASA Astrophysics Data System (ADS)

Orsvuran, R.; Bozdag, E.; Lei, W.; Tromp, J.

2017-12-01

The adjoint method allows us to incorporate full waveform simulations in inverse problems. Misfit functions play an important role in extracting the relevant information from seismic waveforms. In this study, our goal is to apply the Double-Difference (DD) methodology proposed by Yuan et al. (2016) to global adjoint tomography. Dense seismic networks, such as USArray, lead to higher-resolution seismic images underneath continents. However, the imbalanced distribution of stations and sources poses challenges in global ray coverage. We adapt double-difference multitaper measurements to global adjoint tomography. We normalize each DD measurement by its number of pairs, and if a measurement has no pair, as may frequently happen for data recorded at oceanic stations, classical multitaper measurements are used. As a result, the differential measurements and pair-wise weighting strategy help balance uneven global kernel coverage. Our initial experiments with minor- and major-arc surface waves show promising results, revealing more pronounced structure near dense networks while reducing the prominence of paths towards cluster of stations. We have started using this new measurement in global adjoint inversions, addressing azimuthal anisotropy in upper mantle. Meanwhile, we are working on combining the double-difference approach with instantaneous phase measurements to emphasize contributions of scattered waves in global inversions and extending it to body waves. We will present our results and discuss challenges and future directions in the context of global tomographic inversions.

Radiation Source Mapping with Bayesian Inverse Methods

DOE PAGES

Hykes, Joshua M.; Azmy, Yousry Y.

2017-03-22

In this work, we present a method to map the spectral and spatial distributions of radioactive sources using a limited number of detectors. Locating and identifying radioactive materials is important for border monitoring, in accounting for special nuclear material in processing facilities, and in cleanup operations following a radioactive material spill. Most methods to analyze these types of problems make restrictive assumptions about the distribution of the source. In contrast, the source mapping method presented here allows an arbitrary three-dimensional distribution in space and a gamma peak distribution in energy. To apply the method, the problem is cast as anmore » inverse problem where the system’s geometry and material composition are known and fixed, while the radiation source distribution is sought. A probabilistic Bayesian approach is used to solve the resulting inverse problem since the system of equations is ill-posed. The posterior is maximized with a Newton optimization method. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint, discrete ordinates flux solutions, obtained in this work by the Denovo code, is required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes form the linear mapping from the state space to the response space. The test of the method’s success is simultaneously locating a set of 137Cs and 60Co gamma sources in a room. This test problem is solved using experimental measurements that we collected for this purpose. Because of the weak sources available for use in the experiment, some of the expected photopeaks were not distinguishable from the Compton continuum. However, by supplanting 14 flawed measurements (out of a total of 69) with synthetic responses computed by MCNP, the proof-of-principle source mapping was successful. The locations of the sources were predicted within 25 cm for two of the sources and 90 cm for the third, in a room with an ~4-x 4-m floor plan. Finally, the predicted source intensities were within a factor of ten of their true value.« less

Development and application of a hybrid transport methodology for active interrogation systems

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

Royston, K.; Walters, W.; Haghighat, A.

A hybrid Monte Carlo and deterministic methodology has been developed for application to active interrogation systems. The methodology consists of four steps: i) neutron flux distribution due to neutron source transport and subcritical multiplication; ii) generation of gamma source distribution from (n, 7) interactions; iii) determination of gamma current at a detector window; iv) detection of gammas by the detector. This paper discusses the theory and results of the first three steps for the case of a cargo container with a sphere of HEU in third-density water cargo. To complete the first step, a response-function formulation has been developed tomore » calculate the subcritical multiplication and neutron flux distribution. Response coefficients are pre-calculated using the MCNP5 Monte Carlo code. The second step uses the calculated neutron flux distribution and Bugle-96 (n, 7) cross sections to find the resulting gamma source distribution. In the third step the gamma source distribution is coupled with a pre-calculated adjoint function to determine the gamma current at a detector window. The AIMS (Active Interrogation for Monitoring Special-Nuclear-Materials) software has been written to output the gamma current for a source-detector assembly scanning across a cargo container using the pre-calculated values and taking significantly less time than a reference MCNP5 calculation. (authors)« less

SELF-CANCELLATION OF EPHEMERAL REGIONS IN THE QUIET SUN

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

Yang, Shuhong; Zhang, Jun; Li, Ting

2012-06-20

With the observations from the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory, we statistically investigate the ephemeral regions (ERs) in the quiet Sun. We find that there are two types of ERs: normal ERs (NERs) and self-canceled ERs (SERs). Each NER emerges and grows with separation of its opposite polarity patches which will cancel or coalesce with other surrounding magnetic flux. Each SER also emerges and grows and its dipolar patches separate at first, but a part of the magnetic flux of the SER will move together and cancel gradually, which is described with the term 'self-cancellation' bymore » us. We identify 2988 ERs, among which there are 190 SERs, about 6.4% of the ERs. The mean value of self-cancellation fraction of SERs is 62.5%, and the total self-canceled flux of SERs is 9.8% of the total ER flux. Our results also reveal that the higher the ER magnetic flux is, (1) the easier the performance of ER self-cancellation is, (2) the smaller the self-cancellation fraction is, and (3) the more the self-canceled flux is. We think that the self-cancellation of SERs is caused by the submergence of magnetic loops connecting the dipolar patches, without magnetic energy release.« less

Resolution of quantum singularities

NASA Astrophysics Data System (ADS)

Konkowski, Deborah; Helliwell, Thomas

2017-01-01

A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.

The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities

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

Pavlenko, V N; Potapov, D K

2015-09-30

This paper is concerned with the existence of semiregular solutions to the Dirichlet problem for an equation of elliptic type with discontinuous nonlinearity and when the differential operator is not assumed to be formally self-adjoint. Theorems on the existence of semiregular (positive and negative) solutions for the problem under consideration are given, and a principle of upper and lower solutions giving the existence of semiregular solutions is established. For positive values of the spectral parameter, elliptic spectral problems with discontinuous nonlinearities are shown to have nontrivial semiregular (positive and negative) solutions. Bibliography: 32 titles.

Feynman propagators on static spacetimes

NASA Astrophysics Data System (ADS)

Dereziński, Jan; Siemssen, Daniel

We consider the Klein-Gordon equation on a static spacetime and minimally coupled to a static electromagnetic potential. We show that it is essentially self-adjoint on Cc∞. We discuss various distinguished inverses and bisolutions of the Klein-Gordon operator, focusing on the so-called Feynman propagator. We show that the Feynman propagator can be considered the boundary value of the resolvent of the Klein-Gordon operator, in the spirit of the limiting absorption principle known from the theory of Schrödinger operators. We also show that the Feynman propagator is the limit of the inverse of the Wick rotated Klein-Gordon operator.

A New Class of Highly Accurate Differentiation Schemes Based on the Prolate Spheroidal Wave Functions

DTIC Science & Technology

2011-04-07

predictor - corrector scheme. Such an approach for the solution of time-dependent PDEs, which is some- times referred to as the “method of lines,” is studied...particular, λj = i j |λj |. We define the self -adjoint operator Qc : L 2([−1, 1]) → L2([−1, 1]) by the formula Qc(φ) = 1 π ∫ 1 −1 sin( c (x− t)) x− t φ...Gaussian quadratures for bandlimited functions is to use the Newton-type nonlinear optimization algorithm of [14]. Specifically, for bandlimit c and

Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism

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

Ramos, J. J.; White, R. L.

The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.

Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations

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

Gropp, W.D.; Keyes, D.E.

1988-03-01

The authors discuss the parallel implementation of preconditioned conjugate gradient (PCG)-based domain decomposition techniques for self-adjoint elliptic partial differential equations in two dimensions on several architectures. The complexity of these methods is described on a variety of message-passing parallel computers as a function of the size of the problem, number of processors and relative communication speeds of the processors. They show that communication startups are very important, and that even the small amount of global communication in these methods can significantly reduce the performance of many message-passing architectures.

Extremal values of the sojourn time

NASA Astrophysics Data System (ADS)

Astaburuaga, M. A.; Cortés, V. H.; Duclos, P.

2010-11-01

Consider a self-adjoint operator H on a separable Hilbert space \\ {H} with non-trivial absolutely continuous component. We study the general properties of the real-valued functional, \\tau _{H}(\\psi )=\\int _{{\\ R}}|(e^{-itH}\\psi,\\psi )|^2\\,dt, which in quantum mechanics represents the sojourn time (or life time) of an initial state \\psi \\in \\ {H}. We characterize the critical points of the sojourn time, τX, of the operator multiplication by x in L^2({\\ R}), and prove that it attains a global maximum in the unit sphere of the Sobolev space \\ {W}^{1,2}({\\ R}).

Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism

DOE PAGES

Ramos, J. J.; White, R. L.

2018-03-01

The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.

Quantum probe of Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mangut, M.

2018-04-01

Particle probe analysis of the Kehagias-Sfetsos black hole spacetime of Hořava-Lifshitz gravity is extended to wave probe analysis within the framework of quantum mechanics. The time-like naked singularity that develops when ωM2 < 1/2 is probed with quantum fields obeying Klein-Gordon and Chandrasekhar-Dirac equations. The quantum field probe of the naked singularity has revealed that both the spatial part of the wave and the Hamiltonian operators of Klein-Gordon and Chandrasekhar-Dirac equations are essentially self-adjoint, and thus, the naked singularity in the Kehagias-Sfetsos spacetime becomes quantum mechanically non-singular.

Angular dependence of multiangle dynamic light scattering for particle size distribution inversion using a self-adapting regularization algorithm

NASA Astrophysics Data System (ADS)

Li, Lei; Yu, Long; Yang, Kecheng; Li, Wei; Li, Kai; Xia, Min

2018-04-01

The multiangle dynamic light scattering (MDLS) technique can better estimate particle size distributions (PSDs) than single-angle dynamic light scattering. However, determining the inversion range, angular weighting coefficients, and scattering angle combination is difficult but fundamental to the reconstruction for both unimodal and multimodal distributions. In this paper, we propose a self-adapting regularization method called the wavelet iterative recursion nonnegative Tikhonov-Phillips-Twomey (WIRNNT-PT) algorithm. This algorithm combines a wavelet multiscale strategy with an appropriate inversion method and could self-adaptively optimize several noteworthy issues containing the choices of the weighting coefficients, the inversion range and the optimal inversion method from two regularization algorithms for estimating the PSD from MDLS measurements. In addition, the angular dependence of the MDLS for estimating the PSDs of polymeric latexes is thoroughly analyzed. The dependence of the results on the number and range of measurement angles was analyzed in depth to identify the optimal scattering angle combination. Numerical simulations and experimental results for unimodal and multimodal distributions are presented to demonstrate both the validity of the WIRNNT-PT algorithm and the angular dependence of MDLS and show that the proposed algorithm with a six-angle analysis in the 30-130° range can be satisfactorily applied to retrieve PSDs from MDLS measurements.

VizieR Online Data Catalog: 22-GHz water maser clouds (Richards+, 2012)

NASA Astrophysics Data System (ADS)

Richards, A. M. S.; Etoka, S.; Gray, M. D.; Lekht, E. E.; Mendoza-Torres, J. E.; Murakawa, K.; Rudnitskij, G.; Yates, J. A.

2012-07-01

Measurements of 22-GHz water maser clouds, made with the MERLIN radio interferometer. Obects presented (number of epochs): S Per (2); U Ori (4); U Her (3); IK Tau (3); RT Vir (7); W Hya (4). Results for VX Sgr were presented in Murakawa et al, 2003, Cat. J/MNRAS/344/1. The position and other properties of each patch of maser emission in each channel were measured by fitting 2D Gaussian components. The components form features corresponding to spatially distinct clouds and the properties of each cloud was calculated as described in the paper. For each cloud, we give the mean Vlsr, the total velocity extent DV, the full width half maximum DV1/2, the offsets of the cloud centroid from the assumed stellar position x, y and a (=sqrt(x2+y2), the feature largest angular size l and the peak flux density I. All velocities, angular distances and flux densities are in km/s, mas and Jy, respectively. (2 data files).

Observation of the shadowing of cosmic rays by the Moon using a deep underground detector

NASA Astrophysics Data System (ADS)

Ambrosio, M.; Antolini, R.; Aramo, C.; Auriemma, G.; Baldini, A.; Barbarino, G. C.; Barish, B. C.; Battistoni, G.; Bellotti, R.; Bemporad, C.; Bernardini, P.; Bilokon, H.; Bisi, V.; Bloise, C.; Bower, C.; Bussino, S.; Cafagna, F.; Calicchio, M.; Campana, D.; Carboni, M.; Castellano, M.; Cecchini, S.; Cei, F.; Chiarella, V.; Choudhary, B. C.; Coutu, S.; de Benedictis, L.; de Cataldo, G.; Dekhissi, H.; de Marzo, C.; de Mitri, I.; Derkaoui, J.; de Vincenzi, M.; di Credico, A.; Erriquez, O.; Favuzzi, C.; Forti, C.; Fusco, P.; Giacomelli, G.; Giannini, G.; Giglietto, N.; Giorgini, M.; Grassi, M.; Gray, L.; Grillo, A.; Guarino, F.; Guarnaccia, P.; Gustavino, C.; Habig, A.; Hanson, K.; Heinz, R.; Huang, Y.; Iarocci, E.; Katsavounidis, E.; Kearns, E.; Kim, H.; Kyriazopoulou, S.; Lamanna, E.; Lane, C.; Levin, D. S.; Lipari, P.; Longley, N. P.; Longo, M. J.; Maaroufi, F.; Mancarella, G.; Mandrioli, G.; Manzoor, S.; Neri, A. Margiotta; Marini, A.; Martello, D.; Marzari-Chiesa, A.; Mazziotta, M. N.; Mazzotta, C.; Michael, D. G.; Mikheyev, S.; Miller, L.; Monacelli, P.; Montaruli, T.; Monteno, M.; Mufson, S.; Musser, J.; Nicoló, D.; Orth, C.; Osteria, G.; Ouchrif, M.; Palamara, O.; Patera, V.; Patrizii, L.; Pazzi, R.; Peck, C. W.; Petrera, S.; Pistilli, P.; Popa, V.; Pugliese, V.; Rainò, A.; Reynoldson, J.; Ronga, F.; Rubizzo, U.; Satriano, C.; Satta, L.; Scapparone, E.; Scholberg, K.; Sciubba, A.; Serra-Lugaresi, P.; Severi, M.; Sioli, M.; Sitta, M.; Spinelli, P.; Spinetti, M.; Spurio, M.; Steinberg, R.; Stone, J. L.; Sulak, L. R.; Surdo, A.; Tarlè, G.; Togo, V.; Ugolotti, D.; Vakili, M.; Walter, C. W.; Webb, R.

1999-01-01

Using data collected by the MACRO experiment during the years 1989-1996, we show evidence for the shadow of the Moon in the underground cosmic ray flux with a significance of 3.6σ. This detection of the shadowing effect is the first by an underground detector. A maximum-likelihood analysis is used to determine that the angular resolution of the apparatus is 0.9°+/-0.3°. These results demonstrate MACRO's capabilities as a muon telescope by confirming its absolute pointing ability and quantifying its angular resolution.

Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas

NASA Technical Reports Server (NTRS)

Rallabhandi, Sriram K.

2013-01-01

This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent area cost functionals are discussed and further refined using ground loudness based objectives.

Parameter Optimization for Turbulent Reacting Flows Using Adjoints

NASA Astrophysics Data System (ADS)

Lapointe, Caelan; Hamlington, Peter E.

2017-11-01

The formulation of a new adjoint solver for topology optimization of turbulent reacting flows is presented. This solver provides novel configurations (e.g., geometries and operating conditions) based on desired system outcomes (i.e., objective functions) for complex reacting flow problems of practical interest. For many such problems, it would be desirable to know optimal values of design parameters (e.g., physical dimensions, fuel-oxidizer ratios, and inflow-outflow conditions) prior to real-world manufacture and testing, which can be expensive, time-consuming, and dangerous. However, computational optimization of these problems is made difficult by the complexity of most reacting flows, necessitating the use of gradient-based optimization techniques in order to explore a wide design space at manageable computational cost. The adjoint method is an attractive way to obtain the required gradients, because the cost of the method is determined by the dimension of the objective function rather than the size of the design space. Here, the formulation of a novel solver is outlined that enables gradient-based parameter optimization of turbulent reacting flows using the discrete adjoint method. Initial results and an outlook for future research directions are provided.

Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils

NASA Technical Reports Server (NTRS)

Lee, Byung Joon; Liou, Meng-Sing

2012-01-01

This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.

[Purifying process of gynostemma pentaphyllum saponins based on "adjoint marker" online control technology and identification of their compositions by UPLC-QTOF-MS].

PubMed

Fan, Dong-Dong; Kuang, Yan-Hui; Dong, Li-Hua; Ye, Xiao; Chen, Liang-Mian; Zhang, Dong; Ma, Zhen-Shan; Wang, Jin-Yu; Zhu, Jing-Jing; Wang, Zhi-Min; Wang, De-Qin; Li, Chu-Yuan

2017-04-01

To optimize the purification process of gynostemma pentaphyllum saponins (GPS) based on "adjoint marker" online control technology with GPS as the testing index. UPLC-QTOF-MS technology was used for qualitative analysis. "Adjoint marker" online control results showed that the end point of load sample was that the UV absorbance of effluent liquid was equal to half of that of load sample solution, and the absorbance was basically stable when the end point was stable. In UPLC-QTOF-MS qualitative analysis, 16 saponins were identified from GPS, including 13 known gynostemma saponins and 3 new saponins. This optimized method was proved to be simple, scientific, reasonable, easy for online determination, real-time record, and can be better applied to the mass production and automation of production. The results of qualitative analysis indicated that the "adjoint marker" online control technology can well retain main efficacy components of medicinal materials, and provide analysis tools for the process control and quality traceability. Copyright© by the Chinese Pharmaceutical Association.

An adjoint-based simultaneous estimation method of the asthenosphere's viscosity and afterslip using a fast and scalable finite-element adjoint solver

NASA Astrophysics Data System (ADS)

Agata, Ryoichiro; Ichimura, Tsuyoshi; Hori, Takane; Hirahara, Kazuro; Hashimoto, Chihiro; Hori, Muneo

2018-04-01

The simultaneous estimation of the asthenosphere's viscosity and coseismic slip/afterslip is expected to improve largely the consistency of the estimation results to observation data of crustal deformation collected in widely spread observation points, compared to estimations of slips only. Such an estimate can be formulated as a non-linear inverse problem of material properties of viscosity and input force that is equivalent to fault slips based on large-scale finite-element (FE) modeling of crustal deformation, in which the degree of freedom is in the order of 109. We formulated and developed a computationally efficient adjoint-based estimation method for this inverse problem, together with a fast and scalable FE solver for the associated forward and adjoint problems. In a numerical experiment that imitates the 2011 Tohoku-Oki earthquake, the advantage of the proposed method is confirmed by comparing the estimated results with those obtained using simplified estimation methods. The computational cost required for the optimization shows that the proposed method enabled the targeted estimation to be completed with moderate amount of computational resources.

An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

DOE PAGES

Goldberg, Daniel N.; Narayanan, Sri Hari Krishna; Hascoet, Laurent; ...

2016-05-20

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enablingmore » larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.« less

Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach

NASA Astrophysics Data System (ADS)

Aguilar, José G.; Magri, Luca; Juniper, Matthew P.

2017-07-01

Strict pollutant emission regulations are pushing gas turbine manufacturers to develop devices that operate in lean conditions, with the downside that combustion instabilities are more likely to occur. Methods to predict and control unstable modes inside combustion chambers have been developed in the last decades but, in some cases, they are computationally expensive. Sensitivity analysis aided by adjoint methods provides valuable sensitivity information at a low computational cost. This paper introduces adjoint methods and their application in wave-based low order network models, which are used as industrial tools, to predict and control thermoacoustic oscillations. Two thermoacoustic models of interest are analyzed. First, in the zero Mach number limit, a nonlinear eigenvalue problem is derived, and continuous and discrete adjoint methods are used to obtain the sensitivities of the system to small modifications. Sensitivities to base-state modification and feedback devices are presented. Second, a more general case with non-zero Mach number, a moving flame front and choked outlet, is presented. The influence of the entropy waves on the computed sensitivities is shown.

First status report on regional ground-water flow modeling for the Paradox Basin, Utah

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

Andrews, R.W.

1984-05-01

Regional ground-water flow within the principal hydrogeologic units of the Paradox Basin is evaluated by developing a conceptual model of the flow regime in the shallow aquifers and the deep-basin brine aquifers and testing these models using a three-dimensional, finite-difference flow code. Semiquantitative sensitivity analysis (a limited parametric study) is conducted to define the system response to changes in hydrologic properties or boundary conditions. A direct method for sensitivity analysis using an adjoint form of the flow equation is applied to the conceptualized flow regime in the Leadville limestone aquifer. All steps leading to the final results and conclusions aremore » incorporated in this report. The available data utilized in this study is summarized. The specific conceptual models, defining the areal and vertical averaging of litho-logic units, aquifer properties, fluid properties, and hydrologic boundary conditions, are described in detail. Two models were evaluated in this study: a regional model encompassing the hydrogeologic units above and below the Paradox Formation/Hermosa Group and a refined scale model which incorporated only the post Paradox strata. The results are delineated by the simulated potentiometric surfaces and tables summarizing areal and vertical boundary fluxes, Darcy velocities at specific points, and ground-water travel paths. Results from the adjoint sensitivity analysis include importance functions and sensitivity coefficients, using heads or the average Darcy velocities to represent system response. The reported work is the first stage of an ongoing evaluation of the Gibson Dome area within the Paradox Basin as a potential repository for high-level radioactive wastes.« less

SCALE 6.2 Continuous-Energy TSUNAMI-3D Capabilities

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

Perfetti, Christopher M; Rearden, Bradley T

2015-01-01

The TSUNAMI (Tools for Sensitivity and UNcertainty Analysis Methodology Implementation) capabilities within the SCALE code system make use of sensitivity coefficients for an extensive number of criticality safety applications, such as quantifying the data-induced uncertainty in the eigenvalue of critical systems, assessing the neutronic similarity between different systems, quantifying computational biases, and guiding nuclear data adjustment studies. The need to model geometrically complex systems with improved ease of use and fidelity and the desire to extend TSUNAMI analysis to advanced applications have motivated the development of a SCALE 6.2 module for calculating sensitivity coefficients using three-dimensional (3D) continuous-energy (CE) Montemore » Carlo methods: CE TSUNAMI-3D. This paper provides an overview of the theory, implementation, and capabilities of the CE TSUNAMI-3D sensitivity analysis methods. CE TSUNAMI contains two methods for calculating sensitivity coefficients in eigenvalue sensitivity applications: (1) the Iterated Fission Probability (IFP) method and (2) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization (CLUTCH) method. This work also presents the GEneralized Adjoint Response in Monte Carlo method (GEAR-MC), a first-of-its-kind approach for calculating adjoint-weighted, generalized response sensitivity coefficients—such as flux responses or reaction rate ratios—in CE Monte Carlo applications. The accuracy and efficiency of the CE TSUNAMI-3D eigenvalue sensitivity methods are assessed from a user perspective in a companion publication, and the accuracy and features of the CE TSUNAMI-3D GEAR-MC methods are detailed in this paper.« less

Analytical Model for Estimating the Zenith Angle Dependence of Terrestrial Cosmic Ray Fluxes

PubMed Central

Sato, Tatsuhiko

2016-01-01

A new model called “PHITS-based Analytical Radiation Model in the Atmosphere (PARMA) version 4.0” was developed to facilitate instantaneous estimation of not only omnidirectional but also angular differential energy spectra of cosmic ray fluxes anywhere in Earth’s atmosphere at nearly any given time. It consists of its previous version, PARMA3.0, for calculating the omnidirectional fluxes and several mathematical functions proposed in this study for expressing their zenith-angle dependences. The numerical values of the parameters used in these functions were fitted to reproduce the results of the extensive air shower simulation performed by Particle and Heavy Ion Transport code System (PHITS). The angular distributions of ground-level muons at large zenith angles were specially determined by introducing an optional function developed on the basis of experimental data. The accuracy of PARMA4.0 was closely verified using multiple sets of experimental data obtained under various global conditions. This extension enlarges the model’s applicability to more areas of research, including design of cosmic-ray detectors, muon radiography, soil moisture monitoring, and cosmic-ray shielding calculation. PARMA4.0 is available freely and is easy to use, as implemented in the open-access EXcel-based Program for Calculating Atmospheric Cosmic-ray Spectrum (EXPACS). PMID:27490175

Analytical Model for Estimating the Zenith Angle Dependence of Terrestrial Cosmic Ray Fluxes.

PubMed

Sato, Tatsuhiko

2016-01-01

A new model called "PHITS-based Analytical Radiation Model in the Atmosphere (PARMA) version 4.0" was developed to facilitate instantaneous estimation of not only omnidirectional but also angular differential energy spectra of cosmic ray fluxes anywhere in Earth's atmosphere at nearly any given time. It consists of its previous version, PARMA3.0, for calculating the omnidirectional fluxes and several mathematical functions proposed in this study for expressing their zenith-angle dependences. The numerical values of the parameters used in these functions were fitted to reproduce the results of the extensive air shower simulation performed by Particle and Heavy Ion Transport code System (PHITS). The angular distributions of ground-level muons at large zenith angles were specially determined by introducing an optional function developed on the basis of experimental data. The accuracy of PARMA4.0 was closely verified using multiple sets of experimental data obtained under various global conditions. This extension enlarges the model's applicability to more areas of research, including design of cosmic-ray detectors, muon radiography, soil moisture monitoring, and cosmic-ray shielding calculation. PARMA4.0 is available freely and is easy to use, as implemented in the open-access EXcel-based Program for Calculating Atmospheric Cosmic-ray Spectrum (EXPACS).

FIRST, a fibered aperture masking instrument: Results of the Lick observing campaign

NASA Astrophysics Data System (ADS)

Bordwell, Baylee; Duchene, Gaspard; Huby, Elsa; Goebel, Sean; Marchis, Franck; Perrin, Guy; Lacour, Sylvestre; Kotani, Takayuki; Gates, Elinor L.; Choquet, Elodie

2015-01-01

FIRST is a prototype instrument aimed at achieving high dynamic range and angular resolution in ground-based images at visible wavelengths near the diffraction limit. FIRST utilizes an aperture masking-like technique that makes use of single-mode fibers and pupil remapping to maximize the area of the telescope mirror in use. While located at Lick observatory in 2011 and 2012, FIRST observed 25 binary systems with the Shane 3m telescope, with separations ranging from 20 to 200 mas, comparable to the 50 mas diffraction limit for our central wavelength. Huby et al. (2013) has reported results for the Capella system that established the utility of FIRST for characterizing stellar binaries using the directly measured spectral flux ratio. Using an improved data analysis pipeline, we obtained closure phase measurements for a majority of the targets observed at Lick, and derived angular separations and spectral flux ratios. From the spectral flux ratios we obtained spectra for the companions over at least 600-850 nm with R~300. Finally, by obtaining results for many binary systems we have better constrained the current performance of FIRST, which has an exciting future ahead at its current location behind SCExAO at the Subaru 8.2 m telescope, where it will eventually become available for general use by the astronomical community.

Influence of M-TIG and A-TIG Welding Process on Microstructure and Mechanical Behavior of 409 Ferritic Stainless Steel

NASA Astrophysics Data System (ADS)

Vidyarthy, R. S.; Dwivedi, D. K.; Vasudevan, M.

2017-03-01

The current study investigates the effects of activating flux tungsten inert gas welding (A-TIG) and multipass tungsten inert gas welding (M-TIG) on the weld morphology, angular distortion, microstructures and mechanical properties when welding 8-mm-thick 409 ferritic stainless steel (FSS). SiO2 was used as activating flux for A-TIG welding, while SUPERTIG ER309L was used as filler for M-TIG welding. Bead-on-plate weld trials were carried out to obtain the full penetration by using different combinations of flux coating density, welding speed and welding current. An optical microscope, field emission scanning microscope (FESEM), and x-ray diffractometer were used for the metallurgical characterizations. Vickers hardness, tensile test, Charpy toughness test, and creep behavior test were carried out to evaluate the mechanical properties of the base and weld metals. Experimental results indicate that the A-TIG process can increase the joint penetration and tends to reduce the angular distortion of the 409 FSS weldment. The A-TIG welded joint also exhibited greater mechanical strength. However, a critically low Charpy toughness was measured for the A-TIG weld fusion zone, which was later sufficiently improved after post weld heat treatment (PWHT). It was concluded that PWHT is mandatory for A-TIG welded 409 FSS.

Line-of-sight magnetic flux imbalances caused by electric currents

NASA Technical Reports Server (NTRS)

Gary, G. Allen; Rabin, Douglas

1995-01-01

Several physical and observational effects contribute to the significant imbalances of magnetic flux that are often observed in active regions. We consider an effect not previously treated: the influence of electric currents in the photosphere. Electric currents can cause a line-of-sight flux imbalance because of the directionality of the magnetic field they produce. Currents associated with magnetic flux tubes produce larger imbalances than do smoothly-varying distributions of flux and current. We estimate the magnitude of this effect for current densities, total currents, and magnetic geometry consistent with observations. The expected imbalances lie approximately in the range 0-15%, depending on the character of the current-carying fields and the angle from which they are viewed. Observationally, current-induced flux imbalances could be indicated by a statistical dependence of the imbalance on angular distance from disk center. A general study of magnetic flux balance in active regions is needed to determine the relative importance of other- probably larger- effects such as dilute flux (too weak to measure or rendered invisible by radiative transfer effects), merging with weak background fields, and long-range connections between active regions.

High-resolution CO2 and CH4 flux inverse modeling combining GOSAT, OCO-2 and ground-based observations

NASA Astrophysics Data System (ADS)

Maksyutov, S. S.; Oda, T.; Saito, M.; Ito, A.; Janardanan Achari, R.; Sasakawa, M.; Machida, T.; Kaiser, J. W.; Belikov, D.; Valsala, V.; O'Dell, C.; Yoshida, Y.; Matsunaga, T.

2017-12-01

We develop a high-resolution CO2 and CH4 flux inversion system that is based on the Lagrangian-Eulerian coupled tracer transport model, and is designed to estimate surface fluxes from atmospheric CO2 and CH4 data observed by the GOSAT and OCO-2 satellites and by global in-situ networks, including observation in Siberia. We use the Lagrangian particle dispersion model (LPDM) FLEXPART to estimate the surface flux footprints for each observation at 0.1-degree spatial resolution for three days of transport. The LPDM is coupled to a global atmospheric tracer transport model (NIES-TM). The adjoint of the coupled transport model is used in an iterative optimization procedure based on either quasi-Newtonian algorithm or singular value decomposition. Combining surface and satellite data for use in inversion requires correcting for biases present in satellite observation data, that is done in a two-step procedure. As a first step, bi-weekly corrections to prior flux fields are estimated for the period of 2009 to 2015 from in-situ CO2 and CH4 data from global observation network, included in Obspack-GVP (for CO2), WDCGG (CH4) and JR-STATION datasets. High-resolution prior fluxes were prepared for anthropogenic emissions (ODIAC and EDGAR), biomass burning (GFAS), and the terrestrial biosphere. The terrestrial biosphere flux was constructed using a vegetation mosaic map and separate simulations of CO2 fluxes by the VISIT model for each vegetation type present in a grid. The prior flux uncertainty for land is scaled proportionally to monthly mean GPP by the MODIS product for CO2 and EDGAR emissions for CH4. Use of the high-resolution transport leads to improved representation of the anthropogenic plumes, often observed at continental continuous observation sites. OCO-2 observations are aggregated to 1 second averages, to match the 0.1 degree resolution of the transport model. Before including satellite observations in the inversion, the monthly varying latitude-dependent bias is estimated by comparing satellite observations with column abundance simulated with surface fluxes optimized by surface inversion. The bias-corrected GOSAT and OCO-2 data are then used in the inversion together with ground-based observations. Application of the bias correction to satellite data reduces the difference between the flux estimates based on ground-based and satellite observations.

Leonardo-BRDF: A New Generation Satellite Constellation

NASA Technical Reports Server (NTRS)

Esper, Jaime; Neeck, Steven; Wiscombe, Warren; Ryschkewitsch, Michael; Andary, J. (Technical Monitor)

2000-01-01

Instantaneous net radiation flux at the top of the atmosphere is one of the primary drivers of climate and global change. Since the dawn of the satellite era, great efforts and expense have gone into measuring this flux from single satellites and even (for a several-year period) from a constellation of three satellites called ERBE. However, the reflected solar flux is an angular and spectral integral over the so-called "BRDF" or Bidirectional Reflectance Distribution Function, which is the angular distribution of reflected solar radiation for each solar zenith angle and each wavelength. Previous radiation flux satellites could not measure instantaneous BRDF, so scientists have had to fall back on models or composites. Because their range of observed solar zenith angles was very limited due to sunsynchronous orbits, the resultant flux maps are too inaccurate to see the dynamics of radiation flux or to reliably correlate it with specific phenomena (hurricanes, biomass fires, urban pollution, dust outbreaks, etc.). Accuracy only becomes acceptable after monthly averaging, but this washes out almost all cause-and-effect information, further exacerbated by the lack of spectral resolution. Leonardo-BRDF is a satellite system designed to measure the instantaneous spectral BRDF using a formation of highly coordinated satellites, all pointing at the same Earth targets at the same time. It will allow scientists for the first time to assess the radiative forcing of climate due to specific phenomena, which is bound to be important in the ongoing debate about global warming and what is causing it. The formation is composed of two satellite types having, as instrument payloads, single highly-integrated miniature imaging spectrometers or radiometers. Two nearby "keystone" satellites anchor the formation and fly in static orbits. They employ wide field of view imaging spectrometers that are extremely light and compact. The keystone satellites are identical and can operate in alongtrack or cross-track mode, or anything in between, at ground command. This provides inherent system redundancy and cross-calibration capability. Several "wing-man" satellites in non-static orbits fly in formation up to 1000 km out from the keystone satellites to provide additional along- and cross-track angular sampling. They view the target(s) observed by the keystone satellites from different zenith and azimuth angles and are maneuverable within a limited range of zenith angle using thrusters, and within a large range of azimuth angle using clever orbit design. The wing-man satellites carry single miniature imaging radiometers with just a few wavelength bands in order to be lighter and more agile.

Next-Generation Angular Distribution Models for Top-of-Atmosphere Radiative Flux Calculation from CERES Instruments: Validation

NASA Technical Reports Server (NTRS)

Su, W.; Corbett, J.; Eitzen, Z.; Liang, L.

2015-01-01

Radiative fluxes at the top of the atmosphere (TOA) from the Clouds and the Earth's Radiant Energy System (CERES) instrument are fundamental variables for understanding the Earth's energy balance and how it changes with time. TOA radiative fluxes are derived from the CERES radiance measurements using empirical angular distribution models (ADMs). This paper evaluates the accuracy of CERES TOA fluxes using direct integration and flux consistency tests. Direct integration tests show that the overall bias in regional monthly mean TOA shortwave (SW) flux is less than 0.2Wm(exp -2) and the RMSE is less than 1.1Wm(exp -2). The bias and RMSE are very similar between Terra and Aqua. The bias in regional monthly mean TOA LW fluxes is less than 0.5Wm(exp -2) and the RMSE is less than 0.8Wm(exp -)2 for both Terra and Aqua. The accuracy of the TOA instantaneous flux is assessed by performing tests using fluxes inverted from nadir- and oblique-viewing angles using CERES along-track observations and temporally and spatially matched MODIS observations, and using fluxes inverted from multi-angle MISR observations. The averaged TOA instantaneous SW flux uncertainties from these two tests are about 2.3% (1.9Wm(exp -2) over clear ocean, 1.6% (4.5Wm(exp -2) over clear land, and 2.0% (6.0Wm(exp -) over clear snow/ice; and are about 3.3% (9.0Wm(exp -2), 2.7% (8.4Wm(exp -2), and 3.7% (9.9Wm(exp -2) over ocean, land, and snow/ice under all-sky conditions. The TOA SW flux uncertainties are generally larger for thin broken clouds than for moderate and thick overcast clouds. The TOA instantaneous daytime LW flux uncertainties derived from the CERESMODIS test are 0.5% (1.5Wm(exp -2), 0.8% (2.4Wm(exp -2), and 0.7% (1.3Wm(exp -2) over clear ocean, land, and snow/ice; and are about 1.5% (3.5Wm(exp -2), 1.0% (2.9Wm(exp -2), and 1.1% (2.1Wm(exp -2) over ocean, land, and snow/ice under all-sky conditions. The TOA instantaneous nighttime LW flux uncertainties are about 0.5-1% (<2.0Wm(exp -2) for all surface types. Flux uncertainties caused by errors in scene identification are also assessed by using the collocated CALIPSO, CloudSat, CERES and MODIS data product. Errors in scene identification tend to underestimate TOA SW flux by about 0.6Wm(exp -2) and overestimate TOA daytime (nighttime) LW flux by 0.4 (0.2)Wm(exp -2) when all CERES viewing angles are considered.

Variational data assimilation for the initial-value dynamo problem.

PubMed

Li, Kuan; Jackson, Andrew; Livermore, Philip W

2011-11-01

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries.

Can a Wind Model Mimic a Convection-Dominated Accretion Flow Model?

NASA Astrophysics Data System (ADS)

Chang, Heon-Young

2001-06-01

In this paper we investigate the properties of advection-dominated accretion flows(ADAFs) in case that outflows carry away infalling matter with its angular momentum and energy. Positive Bernoulli numbers in ADAFs allow a fraction of the gas to be ex-pelled in a form of outflows. The ADAFs are also unstable to convection. We present self-similar solutions for advection-dominated accretion flows in the presence of out-flows from the accretion flows (ADIOS). The axisymmetric flow is treated in variables integrated over polar sections and the effects of outflows on the accretion rlow are parameterized for possible configurations compatible with the one dimensional self-similar ADAF solution. We explicitly derive self-similar solutions of ADAFs in the presence of outflows and show that the strong outflows in the accretion flows result in a flatter density profile, which is similar to that of the convection-dominated accretion flows (CDAFs) in which convection transports the a! ngular momentum inward and the energy outward. These two different versions of the ADAF model should show similar behaviors in X-ray spectrum to some extent. Even though the two models may show similar behaviors, they should be distinguishable due to different physical properties. We suggest that for a central object of which mass is known these two different accretion flows should have different X-ray flux value due to deficient matter in the wind model.

A Bayesian Framework for Coupled Estimation of Key Unknown Parameters of Land Water and Energy Balance Equations

NASA Astrophysics Data System (ADS)

Farhadi, L.; Abdolghafoorian, A.

2015-12-01

The land surface is a key component of climate system. It controls the partitioning of available energy at the surface between sensible and latent heat, and partitioning of available water between evaporation and runoff. Water and energy cycle are intrinsically coupled through evaporation, which represents a heat exchange as latent heat flux. Accurate estimation of fluxes of heat and moisture are of significant importance in many fields such as hydrology, climatology and meteorology. In this study we develop and apply a Bayesian framework for estimating the key unknown parameters of terrestrial water and energy balance equations (i.e. moisture and heat diffusion) and their uncertainty in land surface models. These equations are coupled through flux of evaporation. The estimation system is based on the adjoint method for solving a least-squares optimization problem. The cost function consists of aggregated errors on state (i.e. moisture and temperature) with respect to observation and parameters estimation with respect to prior values over the entire assimilation period. This cost function is minimized with respect to parameters to identify models of sensible heat, latent heat/evaporation and drainage and runoff. Inverse of Hessian of the cost function is an approximation of the posterior uncertainty of parameter estimates. Uncertainty of estimated fluxes is estimated by propagating the uncertainty for linear and nonlinear function of key parameters through the method of First Order Second Moment (FOSM). Uncertainty analysis is used in this method to guide the formulation of a well-posed estimation problem. Accuracy of the method is assessed at point scale using surface energy and water fluxes generated by the Simultaneous Heat and Water (SHAW) model at the selected AmeriFlux stations. This method can be applied to diverse climates and land surface conditions with different spatial scales, using remotely sensed measurements of surface moisture and temperature states

Modeling Finite Faults Using the Adjoint Wave Field

NASA Astrophysics Data System (ADS)

Hjörleifsdóttir, V.; Liu, Q.; Tromp, J.

2004-12-01

Time-reversal acoustics, a technique in which an acoustic signal is recorded by an array of transducers, time-reversed, and retransmitted, is used, e.g., in medical therapy to locate and destroy gallstones (for a review see Fink, 1997). As discussed by Tromp et al. (2004), time-reversal techniques for locating sources are closely linked to so-called `adjoint methods' (Talagrand and Courtier, 1987), which may be used to evaluate the gradient of a misfit function. Tromp et al. (2004) illustrate how a (finite) source inversion may be implemented based upon the adjoint wave field by writing the change in the misfit function, δ χ, due to a change in the moment-density tensor, δ m, as an integral of the adjoint strain field ɛ x,t) over the fault plane Σ : δ χ = ∫ 0T∫_Σ ɛ x,T-t) :δ m(x,t) d2xdt. We find that if the real fault plane is located at a distance δ h in the direction of the fault normal hat n, then to first order an additional factor of ∫ 0T∫_Σ δ h (x) ∂ n ɛ x,T-t):m(x,t) d2xdt is added to the change in the misfit function. The adjoint strain is computed by using the time-reversed difference between data and synthetics recorded at all receivers as simultaneous sources and recording the resulting strain on the fault plane. In accordance with time-reversal acoustics, all the resulting waves will constructively interfere at the position of the original source in space and time. The level of convergence will be deterimined by factors such as the source-receiver geometry, the frequency of the recorded data and synthetics, and the accuracy of the velocity structure used when back propagating the wave field. The terms ɛ x,T-t) and ∂ n ɛ x,T-t):m(x,t) can be viewed as sensitivity kernels for the moment density and the faultplane location respectively. By looking at these quantities we can make an educated choice of fault parametrization given the data in hand. The process can then be repeated to invert for the best source model, as demonstrated by Tromp et al. (2004) for the magnitude of a point force. In this presentation we explore the applicability of adjoint methods to estimating finite source parameters. Fink, M. (1997), Time reversed acoustics, Physics Today, 50(3), 34--40. Talagrand, O., and P.~Courtier (1987), Variational assimilation of meteorological observations with the adjoint vorticity equatuation. I: Theory, Q. J. R. Meteorol. Soc., 113, 1311--1328. Tromp, J., C.~Tape, and Q.~Liu (2004), Waveform tomography, adjoint methods, time reversal, and banana-doughnut kernels, Geophys. Jour. Int., in press

Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2006-01-01

A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design.

Point-particle effective field theory I: classical renormalization and the inverse-square potential

NASA Astrophysics Data System (ADS)

Burgess, C. P.; Hayman, Peter; Williams, M.; Zalavári, László

2017-04-01

Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original prob-lem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective point-particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction catalysis, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.

Self-focusing skyrmion racetracks in ferrimagnets

NASA Astrophysics Data System (ADS)

Kim, Se Kwon; Lee, Kyung-Jin; Tserkovnyak, Yaroslav

2017-04-01

We theoretically study the dynamics of ferrimagnetic skyrmions in inhomogeneous metallic films close to the angular momentum compensation point. In particular, it is shown that the line of the vanishing angular momentum can be utilized as a self-focusing racetrack for skyrmions. To that end, we begin by deriving the equations of motion for the dynamics of collinear ferrimagnets in the presence of a charge current. The obtained equations of motion reduce to those of ferromagnets and antiferromagnets at two special limits. In the collective coordinate approach, a skyrmion behaves as a massive charged particle moving in a viscous medium subjected to a magnetic field. Analogous to the snake orbits of electrons in a nonuniform magnetic field, we show that a ferrimagnet with nonuniform angular momentum density can exhibit the snake trajectories of skyrmions, which can be utilized as racetracks for skyrmions.

Microbial community dynamics in soil aggregates shape biogeochemical gas fluxes from soil profiles - upscaling an aggregate biophysical model.

PubMed

Ebrahimi, Ali; Or, Dani

2016-09-01

Microbial communities inhabiting soil aggregates dynamically adjust their activity and composition in response to variations in hydration and other external conditions. These rapid dynamics shape signatures of biogeochemical activity and gas fluxes emitted from soil profiles. Recent mechanistic models of microbial processes in unsaturated aggregate-like pore networks revealed a highly dynamic interplay between oxic and anoxic microsites jointly shaped by hydration conditions and by aerobic and anaerobic microbial community abundance and self-organization. The spatial extent of anoxic niches (hotspots) flicker in time (hot moments) and support substantial anaerobic microbial activity even in aerated soil profiles. We employed an individual-based model for microbial community life in soil aggregate assemblies represented by 3D angular pore networks. Model aggregates of different sizes were subjected to variable water, carbon and oxygen contents that varied with soil depth as boundary conditions. The study integrates microbial activity within aggregates of different sizes and soil depth to obtain estimates of biogeochemical fluxes from the soil profile. The results quantify impacts of dynamic shifts in microbial community composition on CO2 and N2 O production rates in soil profiles in good agreement with experimental data. Aggregate size distribution and the shape of resource profiles in a soil determine how hydration dynamics shape denitrification and carbon utilization rates. Results from the mechanistic model for microbial activity in aggregates of different sizes were used to derive parameters for analytical representation of soil biogeochemical processes across large scales of practical interest for hydrological and climate models. © 2016 John Wiley & Sons Ltd.

Video Meteor Fluxes

NASA Technical Reports Server (NTRS)

Campbell-Brown, M. D.; Braid, D.

2011-01-01

The flux of meteoroids, or number of meteoroids per unit area per unit time, is critical for calibrating models of meteoroid stream formation and for estimating the hazard to spacecraft from shower and sporadic meteors. Although observations of meteors in the millimetre to centimetre size range are common, flux measurements (particularly for sporadic meteors, which make up the majority of meteoroid flux) are less so. It is necessary to know the collecting area and collection time for a given set of observations, and to correct for observing biases and the sensitivity of the system. Previous measurements of sporadic fluxes are summarized in Figure 1; the values are given as a total number of meteoroids striking the earth in one year to a given limiting mass. The Gr n et al. (1985) flux model is included in the figure for reference. Fluxes for sporadic meteoroids impacting the Earth have been calculated for objects in the centimeter size range using Super-Schmidt observations (Hawkins & Upton, 1958); this study used about 300 meteors, and used only the physical area of overlap of the cameras at 90 km to calculate the flux, corrected for angular speed of meteors, since a large angular speed reduces the maximum brightness of the meteor on the film, and radiant elevation, which takes into account the geometric reduction in flux when the meteors are not perpendicular to the horizontal. They bring up corrections for both partial trails (which tends to increase the collecting area) and incomplete overlap at heights other than 90 km (which tends to decrease it) as effects that will affect the flux, but estimated that the two effects cancelled one another. Halliday et al. (1984) calculated the flux of meteorite-dropping fireballs with fragment masses greater than 50 g, over the physical area of sky accessible to the MORP fireball cameras, counting only observations in clear weather. In the micron size range, LDEF measurements of small craters on spacecraft have been used to estimate the flux (Love & Brownlee, 1993); here the physical area of the detector is well known, but the masses depend strongly on the unknown velocity distribution. In the same size range, Thomas & Netherway (1989) used the narrow-beam radar at Jindalee to calculate the flux of sporadics. In between these very large and very small sizes, a number of video and photographic observations were reduced by Ceplecha (2001). These fluxes were calculated (details are given in Ceplecha, 1988) taking the Halliday et al. (1984) MORP fireball fluxes, slightly corrected in mass, as a calibration, and adjusting the flux of small cameras to overlap with the number/mass relation from that work.

Forces in magnetospheric launching of micro-ejections

NASA Astrophysics Data System (ADS)

Cemeljic, Miljenko

2013-07-01

In 2D-axisymmetric simulations with our resistive MHD code Zeus-347 we show that micro-ejections, a quasi-stationary fast ejecta of matter of small mass and angular momentum fluxes, can be launched from a purely resistive magnetosphere above the disk gap. They are produced by a combination of pressure gradient and magnetic forces, in presence of ongoing magnetic reconnection along the boundary layer between the star and the disk, where a current sheet is formed. Mass flux of micro-ejections increases with increasing magnetic field strength and stellar rotation rate.

Results from the HARP Experiment

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

Borghi, Silvia

2006-07-11

The HARP experiment at CERN performed extensive measurements of hadronic cross-sections and secondary particle yields in the momentum range 1.5-15 GeV/c aiming at full angular coverage and full particle identification. We report about the double-differential production cross-section for positive pions, for incident protons of 12.9 GeV/c momentum hitting an aluminum target of 5% nuclear interaction length. The measurement of this cross-section has direct application to the prediction of the neutrino flux of K2K experiment and in particular on the far-near neutrino flux ratio.

Mitigation of Engine Inlet Distortion Through Adjoint-Based Design

NASA Technical Reports Server (NTRS)

Ordaz, Irian; Rallabhandi, Sriram; Nielsen, Eric J.; Diskin, Boris

2017-01-01

The adjoint-based design capability in FUN3D is extended to allow efficient gradient- based optimization and design of concepts with highly integrated aero-propulsive systems. A circumferential distortion calculation, along with the derivatives needed to perform adjoint-based design, have been implemented in FUN3D. This newly implemented distortion calculation can be used not only for design but also to drive the existing mesh adaptation process and reduce the error associated with the fan distortion calculation. The design capability is demonstrated by the shape optimization of an in-house aircraft concept equipped with an aft fuselage propulsor. The optimization objective is the minimization of flow distortion at the aerodynamic interface plane of this aft fuselage propulsor.

The validity of an assessment of maximum angular velocity of knee extension (KE) using a gyroscope.

PubMed

Arai, Takeshi; Obuchi, Shuichi; Shiba, Yoshitaka; Omuro, Kazuya; Inaba, Yasuko; Kojima, Motonaga

2012-01-01

Although it is more important to assess the muscular power of the lower extremities than the strength, no simplified method for doing so has been found. The aim of this study was to assess the validity of the assessment of the angular velocity of KE using a gyroscope. Participants included 105 community-dwelling older people (55 women, 50 men, age ± standard deviation (SD) 75±5.3). Pearson correlation coefficients and Spearman rank-correlation coefficients were used to examine the relationships between the angular velocity of KE and functional performance measurements, a self-efficacy scale and health-related quality of life (HRQOL). The data from the gyroscope were significantly correlated with some physical functions such as muscle strength (r=0.304, p<0.01), and walking velocity (r=0.543, p<0.001). In addition, the joint angular velocity was significantly correlated with self-efficacy (r=0.219-0.329, p<0.01-0.05) and HRQOL (r=0.207-0.359, p<0.01-0.05). The absolute value of the correlation coefficient of angular velocity tended to be greater than that of the muscle strength for mobility functions such as walking velocity and the timed-up-and-go (TUG) test. In conclusion, it was found that the assessment of the angular velocity of the knee joint using a gyroscope could be a feasible and meaningful measurement in the geriatrics field. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Dynamics of magnetic flux tubes in an advective flow around a black hole

NASA Astrophysics Data System (ADS)

Deb, Arnab; Giri, Kinsuk; Chakrabarti, Sandip K.

2017-12-01

Entangled magnetic fields entering into an accretion flow would very soon be stretched into a dominant toroidal component due to strong differentially rotating motion inside the accretion disc. This is particularly true for weakly viscous, low angular momentum transonic or advective discs. We study the trajectories of toroidal flux tubes inside a geometrically thick flow that undergoes a centrifugal force supported shock. We also study effects of these flux tubes on the dynamics of the inflow and the outflow. We use a finite difference method (total variation diminishing) for this purpose and specifically focused on whether these flux tubes significantly affect the properties of the outflows such as its collimation and the rate. It is seen that depending upon the cross-sectional radius of the flux tubes that control the drag force, these field lines may move towards the central object or oscillate vertically before eventually escaping out of the funnel wall (pressure zero surfaces) along the vertical direction. A comparison of results obtained with and without flux tubes show these flux tubes could play a pivotal role in collimation and acceleration of jets and outflows.

Extra-tropical QBO signals in angular momentum and wave forcing

NASA Technical Reports Server (NTRS)

Baldwin, Mark P.; Tung, Ka Kit

1994-01-01

Although the period of the equatorial stratospheric quasi-biennal oscillation (QBO) is approximately 30 months, quasi-biennial modulation of the extratropical annual cycle may be expected to produce additional spectral peaks at approximately to produce additional spectral peaks at approximately 8.6 and 20 months in the extratropics. Using Northern Hemisphere data for 1964-78 and global data for 1978-93 it is shown that these spectral peaks are robust in both angular momentum and Eliassen-Palm flux divergence. This spectral signature represents a circulation anomaly in both hemispheres, and implies a dynamical origin to the previously observed similar spectral peaks in column ozone in the extratropics.

Electrostatic twisted modes in multi-component dusty plasmas

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

Ayub, M. K.; National Centre for Physics, Shahdra Valley Road, Quaid-i-Azam University Campus, Islamabad 44000; Pohang University of Sciences and Technology, Pohang, Gyeongbuk 790-784

Various electrostatic twisted modes are re-investigated with finite orbital angular momentum in an unmagnetized collisionless multi-component dusty plasma, consisting of positive/negative charged dust particles, ions, and electrons. For this purpose, hydrodynamical equations are employed to obtain paraxial equations in terms of density perturbations, while assuming the Gaussian and Laguerre-Gaussian (LG) beam solutions. Specifically, approximated solutions for potential problem are studied by using the paraxial approximation and expressed the electric field components in terms of LG functions. The energy fluxes associated with these modes are computed and corresponding expressions for orbital angular momenta are derived. Numerical analyses reveal that radial/angular modemore » numbers as well as dust number density and dust charging states strongly modify the LG potential profiles attributed to different electrostatic modes. Our results are important for understanding particle transport and energy transfer due to wave excitations in multi-component dusty plasmas.« less

Linear Array Ambient Noise Adjoint Tomography Reveals Intense Crust-Mantle Interactions in North China Craton

NASA Astrophysics Data System (ADS)

Zhang, Chao; Yao, Huajian; Liu, Qinya; Zhang, Ping; Yuan, Yanhua O.; Feng, Jikun; Fang, Lihua

2018-01-01

We present a 2-D ambient noise adjoint tomography technique for a linear array with a significant reduction in computational cost and show its application to an array in North China. We first convert the observed data for 3-D media, i.e., surface-wave empirical Green's functions (EGFs) to the reconstructed EGFs (REGFs) for 2-D media using a 3-D/2-D transformation scheme. Different from the conventional steps of measuring phase dispersion, this technology refines 2-D shear wave speeds along the profile directly from REGFs. With an initial model based on traditional ambient noise tomography, adjoint tomography updates the model by minimizing the frequency-dependent Rayleigh wave traveltime delays between the REGFs and synthetic Green functions calculated by the spectral-element method. The multitaper traveltime difference measurement is applied in four-period bands: 20-35 s, 15-30 s, 10-20 s, and 6-15 s. The recovered model shows detailed crustal structures including pronounced low-velocity anomalies in the lower crust and a gradual crust-mantle transition zone beneath the northern Trans-North China Orogen, which suggest the possible intense thermo-chemical interactions between mantle-derived upwelling melts and the lower crust, probably associated with the magmatic underplating during the Mesozoic to Cenozoic evolution of this region. To our knowledge, it is the first time that ambient noise adjoint tomography is implemented for a 2-D medium. Compared with the intensive computational cost and storage requirement of 3-D adjoint tomography, this method offers a computationally efficient and inexpensive alternative to imaging fine-scale crustal structures beneath linear arrays.

Angular momentum exchange in white dwarf binaries accreting through direct impact

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

Sepinsky, J. F.; Kalogera, V., E-mail: jeremy.sepinsky@scranton.edu, E-mail: vicky@northwestern.edu

We examine the exchange of angular momentum between the component spins and the orbit in semi-detached double white dwarf binaries undergoing mass transfer through direct impact of the transfer stream. We approximate the stream as a series of discrete massive particles ejected in the ballistic limit at the inner Lagrangian point of the donor toward the accretor. This work improves upon similar earlier studies in a number of ways. First, we self-consistently calculate the total angular momentum of the orbit at all times. This includes changes in the orbital angular momentum during the ballistic trajectory of the ejected mass, asmore » well as changes during the ejection/accretion due to the radial component of the particle's velocity. Second, we calculate the particle's ballistic trajectory for each system, which allows us to determine the precise position and velocity of the particle upon accretion. We can then include specific information about the radius of the accretor as well as the angle of impact. Finally, we ensure that the total angular momentum is conserved, which requires the donor star spin to vary self-consistently. With these improvements, we calculate the angular momentum change of the orbit and each binary component across the entire parameter space of direct impact double white dwarf binary systems. We find a significant decrease in the amount of angular momentum removed from the orbit during mass transfer, as well as cases where this process increases the angular momentum of the orbit at the expense of the spin angular momentum of the donor. We conclude that, unlike earlier claims in the literature, mass transfer through direct impact need not destabilize the binary and that the quantity and sign of the orbital angular momentum transfer depends on the binary properties, particularly the masses of the double white dwarf binary component stars. This stabilization may significantly impact the population synthesis calculations of the expected numbers of events/systems for which double white dwarfs may be a progenitor, e.g., Type Ia supernovae, Type.Ia supernovae, and AM CVn.« less

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny-Lin equation

NASA Astrophysics Data System (ADS)

Rashidi, Saeede; Hejazi, S. Reza

This paper investigates the invariance properties of the time fractional Benny-Lin equation with Riemann-Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto-Sivashinsky equation and Navier-Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny-Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

Rotation in vibration, optimization, and aeroelastic stability problems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.

1974-01-01

The effects of rotation in the areas of vibrations, dynamic stability, optimization, and aeroelasticity were studied. The governing equations of motion for the study of vibration and dynamic stability of a rapidly rotating deformable body were developed starting from the nonlinear theory of elasticity. Some common features such as the limitations of the classical theory of elasticity, the choice of axis system, the property of self-adjointness, the phenomenon of frequency splitting, shortcomings of stability methods as applied to gyroscopic systems, and the effect of internal and external damping on stability in gyroscopic systems are identified and discussed, and are then applied to three specific problems.

Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation

NASA Astrophysics Data System (ADS)

de la Rosa, R.; Gandarias, M. L.; Bruzón, M. S.

2016-11-01

In this paper we study the generalized variable-coefficient Gardner equations of the form ut + A(t) unux + C(t) u2nux + B(t) uxxx + Q(t) u = 0 . This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva et al. (2015). The use of the equivalence group of this class allows us to perform an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations by using a general theorem on conservation laws. We also construct conservation laws by applying the multipliers method.

Additive schemes for certain operator-differential equations

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2010-12-01

Unconditionally stable finite difference schemes for the time approximation of first-order operator-differential systems with self-adjoint operators are constructed. Such systems arise in many applied problems, for example, in connection with nonstationary problems for the system of Stokes (Navier-Stokes) equations. Stability conditions in the corresponding Hilbert spaces for two-level weighted operator-difference schemes are obtained. Additive (splitting) schemes are proposed that involve the solution of simple problems at each time step. The results are used to construct splitting schemes with respect to spatial variables for nonstationary Navier-Stokes equations for incompressible fluid. The capabilities of additive schemes are illustrated using a two-dimensional model problem as an example.

Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle

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

Peplow, Douglas E.; Mosher, Scott W; Evans, Thomas M

2012-08-01

For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADISmore » also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.« less

One-shot synthetic aperture digital holographic microscopy with non-coplanar angular-multiplexing and coherence gating.

PubMed

Lin, Yu-Chih; Tu, Han-Yen; Wu, Xin-Ru; Lai, Xin-Ji; Cheng, Chau-Jern

2018-05-14

This paper proposes one-shot synthetic aperture digital holographic microscopy using a combination of angular-multiplexing and coherence gating. The proposed angular-multiplexing technique uses multiple noncoplanar incident beams into the synthetic aperture to create tight packed passbands so as to extend spatial frequency spectrum. Coherence gating is performed to prevent the self-interference among the multiple beams. Based on the design guideline proposed herein, a phase-only spatial light modulator is employed as an adjustable blazed grating to split multiple noncoplanar beams and perform angular-multiplexing, and then using coherence gating based on low-coherence-light, superresolution imaging is achieved after one-shot acquisition.

Angular Distribution of the X-ray Reflection in Accretion Disks

NASA Astrophysics Data System (ADS)

Garcia, Javier; Dauser, T.; Lohfink, A. M.; Kallman, T. R.; McClintock, J. E.; Steiner, J. F.; Brenneman, L.; Wilms, J.; Reynolds, C. S.; Tombesi, F.

2014-01-01

For the study of black holes, it is essential to have an accurate disk-reflection model with a proper treatment of the relativistic effects that occur near strong gravitational fields. These models are used to constrain the properties of the disk, including its inner radius, the degree of ionization of the gas, and the elemental abundances. Importantly, reflection models are the key to measuring black hole spin via the Fe-line method. However, most current reflection models only provide an angle-averaged solution for the flux reflected at the surface of the disk, which can systematically affect the inferred disk emission. We overcome this limitation by exploiting the full capabilities of our reflection code XILLVER. The solution of the reflected intensity of the radiation field is calculated for each photon energy, position in the slab, and viewing angle. We use this information to construct a grid of reflection models in which the inclination of the system is included as a free fitting parameter. Additionally, we directly connect the angle-resolved XILLVER model with the relativistic blurring code RELLINE to produce a self-consistent numerical model for to angular distribution of the reflected X-ray spectra from ionized accretion disks around black holes. The new model, RELCONV_XILL, is provided in the appropriate format to be used in combination with the commonly used fitting packages. An additional version of the new model, RELCONV_LP_XILL, which simulates the reflected spectra in a lampost scenario, is also supplied.

Adjoint Airfoil Optimization of Darrieus-Type Vertical Axis Wind Turbine

NASA Astrophysics Data System (ADS)

Fuchs, Roman; Nordborg, Henrik

2012-11-01

We present the feasibility of using an adjoint solver to optimize the torque of a Darrieus-type vertical axis wind turbine (VAWT). We start with a 2D cross section of a symmetrical airfoil and restrict us to low solidity ratios to minimize blade vortex interactions. The adjoint solver of the ANSYS FLUENT software package computes the sensitivities of airfoil surface forces based on a steady flow field. Hence, we find the torque of a full revolution using a weighted average of the sensitivities at different wind speeds and angles of attack. The weights are computed analytically, and the range of angles of attack is given by the tip speed ratio. Then the airfoil geometry is evolved, and the proposed methodology is evaluated by transient simulations.

Examination of Observation Impacts derived from OSEs and Adjoint Models

NASA Technical Reports Server (NTRS)

Gelaro, Ronald

2008-01-01

With the adjoint of a data assimilation system, the impact of any or all assimilated observations on measures of forecast skill can be estimated accurately and efficiently. The approach allows aggregation of results in terms of individual data types, channels or locations, all computed simultaneously. In this study, adjoint-based estimates of observation impact are compared with results from standard observing system experiments (OSEs) in the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) GEOS-5 system. The two approaches are shown to provide unique, but complimentary, information. Used together, they reveal both redundancies and dependencies between observing system impacts as observations are added or removed. Understanding these dependencies poses a major challenge for optimizing the use of the current observational network and defining requirements for future observing systems.

Experimental and raytrace results for throat-to-throat compound parabolic concentrators

NASA Technical Reports Server (NTRS)

Leviton, D. B.; Leitch, J. W.

1986-01-01

Compound parabolic concentrators are nonimaging cone-shaped optics with useful angular transmission characteristics. Two cones used throat-to-throat accept radiant flux within one well-defined acceptance angle and redistribute it into another. If the entrance cone is fed with Lambertian flux, the exit cone produces a beam whose half-angle is the exit cone's acceptance angle and whose cross section shows uniform irradiance from near the exit mouth to infinity. (The pair is a beam angle transformer). The design of one pair of cones is discussed, also an experiment to map the irradiance of the emergent beam, and a raytracing program which models the cones fed by Lambertian flux. Experimental results compare favorably with raytrace results.

Post-filamentation high-intensive light channels formation upon ultrashort laser pulses self-focusing in air

NASA Astrophysics Data System (ADS)

Geints, Yu. E.; Ionin, A. A.; Mokrousova, D. V.; Seleznev, L. V.; Sinitsyn, D. V.; Sunchugasheva, E. S.; Zemlyanov, A. A.

2017-01-01

Experimental and theoretical study of the post-filamentation stage of focused high-power Ti:Sa laser pulses in air is presented. Angular divergence of the laser beam, as well as angular and spatial characteristics of specific spatially localized light structures, the post-filament channels (PFCs), under different initial focusing conditions and laser beam energy are investigated. We show that PFC angular divergence is always less than that of the whole laser beam and tends to decrease with laser pulse energy increase and beam focal length elongation.

Edge momentum transport by neutrals: an interpretive numerical framework

NASA Astrophysics Data System (ADS)

Omotani, J. T.; Newton, S. L.; Pusztai, I.; Viezzer, E.; Fülöp, T.; The ASDEX Upgrade Team

2017-06-01

Due to their high cross-field mobility, neutrals can contribute to momentum transport even at the low relative densities found inside the separatrix and they can generate intrinsic rotation. We use a charge-exchange dominated solution to the neutral kinetic equation, coupled to neoclassical ions, to evaluate the momentum transport due to neutrals. Numerical solutions to the drift-kinetic equation allow us to cover the full range of collisionality, including the intermediate levels typical of the tokamak edge. In the edge there are several processes likely to contribute to momentum transport in addition to neutrals. Therefore, we present here an interpretive framework that can evaluate the momentum transport through neutrals based on radial plasma profiles. We demonstrate its application by analysing the neutral angular momentum flux for an L-mode discharge in the ASDEX Upgrade tokamak. The magnitudes of the angular momentum fluxes we find here due to neutrals of 0.6-2 \\text{N} \\text{m} are comparable to the net torque on the plasma from neutral beam injection, indicating the importance of neutrals for rotation in the edge.

Spectra and angular distributions of atmospheric gamma rays from 0.3 to 10 MeV at lambda = 40 deg

NASA Technical Reports Server (NTRS)

Ling, J. C.; Gruber, D. E.

1977-01-01

Measurements of the spectral and angular distributions of atmospheric gamma sq cm rays in the energy range 0.3-10 MeV over Palestine, Texas, at residual depths of 2.5 and 70 g/sq cm are reported. In confirmation of the general features of a model prediction, the measurements show at 2.5 g/sq cm upward moving fluxes greater than the downward moving fluxes, the effect increasing with energy, and approximate isotropy at 70 g/sq cm. Numerous characteristic gamma-ray lines were observed, most prominently at 0.511, 1.6, 2.3, 4.4, and 6.1 MeV. Their intensities were also compared with model predictions. Observations were made with an actively shielded scintillator counter with two detectors, one of aperture 50 deg FWHM and the other of 120 deg FWHM. Above 1 MeV, contributions to the counting rate from photons penetrating the shield annulus and from neutron interactions were large; they were studied by means of a Monte Carlo code and are extensively discussed.

TORT/MCNP coupling method for the calculation of neutron flux around a core of BWR.

PubMed

Kurosawa, Masahiko

2005-01-01

For the analysis of BWR neutronics performance, accurate data are required for neutron flux distribution over the In-Reactor Pressure Vessel equipments taking into account the detailed geometrical arrangement. The TORT code can calculate neutron flux around a core of BWR in a three-dimensional geometry model, but has difficulties in fine geometrical modelling and lacks huge computer resource. On the other hand, the MCNP code enables the calculation of the neutron flux with a detailed geometry model, but requires very long sampling time to give enough number of particles. Therefore, a TORT/MCNP coupling method has been developed to eliminate the two problems mentioned above in each code. In this method, the TORT code calculates angular flux distribution on the core surface and the MCNP code calculates neutron spectrum at the points of interest using the flux distribution. The coupling method will be used as the DOT-DOMINO-MORSE code system. This TORT/MCNP coupling method was applied to calculate the neutron flux at points where induced radioactivity data were measured for 54Mn and 60Co and the radioactivity calculations based on the neutron flux obtained from the above method were compared with the measured data.

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

NASA Technical Reports Server (NTRS)

Grossman, Bernard

1999-01-01

Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing. In order for large scale optimization to become routine, the benefits of parallel architectures should be exploited. Although the flow solver has been parallelized using compiler directives. The parallel efficiency is under 50 percent. Clearly, parallel versions of the codes will have an immediate impact on the ability to design realistic configurations on fine meshes, and this effort is currently underway.

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

NASA Technical Reports Server (NTRS)

Green, Lawrence; Carle, Alan; Fagan, Mike

1999-01-01

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

MAGNETIC GAMES BETWEEN A PLANET AND ITS HOST STAR: THE KEY ROLE OF TOPOLOGY

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

Strugarek, A.; Brun, A. S.; Réville, V.

Magnetic interactions between a star and a close-in planet are postulated to be a source of enhanced emissions and to play a role in the secular evolution of the orbital system. Close-in planets generally orbit in the sub-alfvénic region of the stellar wind, which leads to efficient transfers of energy and angular momentum between the star and the planet. We model the magnetic interactions occurring in close-in star–planet systems with three-dimensional, global, compressible magnetohydrodynamic numerical simulations of a planet orbiting in a self-consistent stellar wind. We focus on the cases of magnetized planets and explore three representative magnetic configurations. Themore » Poynting flux originating from the magnetic interactions is an energy source for enhanced emissions in star–planet systems. Our results suggest a simple geometrical explanation for ubiquitous on/off enhanced emissions associated with close-in planets, and confirm that the Poynting fluxes can reach powers of the order of 10{sup 19} W. Close-in planets are also shown to migrate due to magnetic torques for sufficiently strong stellar wind magnetic fields. The topology of the interaction significantly modifies the shape of the magnetic obstacle that leads to magnetic torques. As a consequence, the torques can vary by at least an order of magnitude as the magnetic topology of the interaction varies.« less

A cosmic and solar X-ray and gamma-ray instrument for a scout launch

NASA Technical Reports Server (NTRS)

Forrest, D. J.; Vestrand, W. T.; Chupp, E. L.

1988-01-01

An overview is presented for a set of simple and robust X-ray and gamma ray instruments which have both cosmic and solar objectives. The primary solar scientific objective is the study of the beaming of energetic electrons and ions in solar flares. The instrument will measure spectra and polarization of flare emissions up to 10 MeV. At X-ray energies both the directly emitted flux and the reflected albedo flux will be measured with a complement of six X-ray sensors. Each of these detectors will have a different high Z filter selected to optimize both the energy resolution and high rate capabilities in the energy band 10 to 300 keV. At energies greater than 100 keV seven 7.6 x 7.6 cm NaI and a set of 30 concentric plastic scattering detectors will record the spectra and polarization of electron bremsstrahlung and nuclear gamma rays. All of the components of the instrument are in existence and have passed flight tests for earlier space missions. The instrument will use a spinning solar oriented Scout spacecraft. The NaI detectors will act as a self-modulating gamma ray detector for cosmic sources in a broad angular band which lies at 90 degrees to the Sun-Earth vector and hence will scan the entire sky in 6 months.

Magnetic Games between a Planet and Its Host Star: The Key Role of Topology

NASA Astrophysics Data System (ADS)

Strugarek, A.; Brun, A. S.; Matt, S. P.; Réville, V.

2015-12-01

Magnetic interactions between a star and a close-in planet are postulated to be a source of enhanced emissions and to play a role in the secular evolution of the orbital system. Close-in planets generally orbit in the sub-alfvénic region of the stellar wind, which leads to efficient transfers of energy and angular momentum between the star and the planet. We model the magnetic interactions occurring in close-in star-planet systems with three-dimensional, global, compressible magnetohydrodynamic numerical simulations of a planet orbiting in a self-consistent stellar wind. We focus on the cases of magnetized planets and explore three representative magnetic configurations. The Poynting flux originating from the magnetic interactions is an energy source for enhanced emissions in star-planet systems. Our results suggest a simple geometrical explanation for ubiquitous on/off enhanced emissions associated with close-in planets, and confirm that the Poynting fluxes can reach powers of the order of 1019 W. Close-in planets are also shown to migrate due to magnetic torques for sufficiently strong stellar wind magnetic fields. The topology of the interaction significantly modifies the shape of the magnetic obstacle that leads to magnetic torques. As a consequence, the torques can vary by at least an order of magnitude as the magnetic topology of the interaction varies.

Consequences of an Immense Hadean-Archean Heat Flux that Results from Virial Theorem Constraints on the Earth's Initial Axial Spin

NASA Astrophysics Data System (ADS)

Hofmeister, A. M.; Criss, R. E.

2016-12-01

Early Earth conditions were largely erased, but the powerful Virial Theorem (VT) constrains Earth's post-accretion state, which largely dictates subsequent thermal and dynamical evolution. Proposals of huge initial inventories of primordial heat are based on Kelvin's disproven theory of starlight. Rather, the VT requires that gravitational potential of the Solar nebula was converted to rotational energy in a conservative, bound accretionary system, which is confirmed by planetary orbit characteristics. In addition, the VT relates axial spin to gravitational self-potential (Ug,self) of each body [2016 Can. J. Phys. p. 380]. From the VT, ½Ug,self binds the body and is unavailable, but spin energy (SE), also equal to ½Ug,self, degrades while gradually evolving heat via friction. The VT likewise restricts primordial heat of core formation, and is consistent with entropy reduction due to ordering and volume restriction [2015 J. Earth Sci., p. 124]. High initial Virial spin is confirmed by (1) data on young stars, (2) independent projections of Earth's initial spin as 2-17 hrs (from fossils and the current rate of spin loss: Lathe 2006), and (3) current SE for all planets defining a power-law trend with Ug,self, which further requires a universal cause for spin loss [2012 Planet. Space Sci. p. 111]. Spin loss is caused by tidal friction and differential rotation of layers. Dissipation is concentrated in the upper layers and especially in the brittle zone, which are much weaker than the highly compressed, essentially hydrostatic interior. With friction, neither mechanical energy nor angular momentum are conserved. Earth's frictional dissipation is immense. Uniform release over time would provide 300-700 TW. This source dominated heat generation for 2 Ga, whereas radiogenic heat dominates today. Exponential spin down suggests 100x more heat production during the Hadean than now, which obliterated early rocks while promoting outgassing and differentiation. Reduction to 10x present levels in the Archean permitted formation of a thin lithosphere and stabilized an ocean and atmosphere. Frictional heat from spin loss helps explain why oceanic heat flux today resembles that of continents which store all the chondritic U and Th. Topside frictional and radiogenic heat production prohibits lower mantle convection.

Investigating Sensitivity to Saharan Dust in Tropical Cyclone Formation Using Nasa's Adjoint Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel

2015-01-01

As tropical cyclones develop from easterly waves coming of the coast of Africa they interact with dust from the Sahara desert. There is a long standing debate over whether this dust inhibits or advances the developing storm and how much influence it has. Dust can surround the storm and absorb incoming solar radiation, cooling the air below. As a result an energy source for the system is potentially diminished, inhibiting growth of the storm. Alternatively dust may interact with clouds through micro-physical processes, for example by causing more moisture to condense, potentially increasing the strength. As a result of climate change, concentrations and amount of dust in the atmosphere will likely change. It it is important to properly understand its effect on tropical storm formation. The adjoint of an atmospheric general circulation model provides a very powerful tool for investigating sensitivity to initial conditions. The National Aeronautics and Space Administration (NASA) has recently developed an adjoint version of the Goddard Earth Observing System version 5 (GEOS-5) dynamical core, convection scheme, cloud model and radiation schemes. This is extended so that the interaction between dust and radiation is also accounted for in the adjoint model. This provides a framework for examining the sensitivity to dust in the initial conditions. Specifically the set up allows for an investigation into the extent to which dust affects cyclone strength through absorption of radiation. In this work we investigate the validity of using an adjoint model for examining sensitivity to dust in hurricane formation. We present sensitivity results for a number of systems that developed during the Atlantic hurricane season of 2006. During this period there was a significant outbreak of Saharan dust and it is has been argued that this outbreak was responsible for the relatively calm season. This period was also covered by an extensive observation campaign. It is shown that the adjoint can provide insight into the sensitivity and reveals a relatively low sensitivity to dust compared to, for example, the thermodynamic variables. However a secondary sensitivity though moisture is seen. If dust dries the air it can significantly reduce the cyclone intensity through the moisture.

Investigating sensitivity to Saharan dust in tropical cyclone formation using NASA's adjoint model

NASA Astrophysics Data System (ADS)

Holdaway, Daniel

2015-04-01

As tropical cyclones develop from easterly waves coming off the coast of Africa they interact with dust from the Sahara desert. There is a long standing debate over whether this dust inhibits or advances the developing storm and how much influence it has. Dust can surround the storm and absorb incoming solar radiation, cooling the air below. As a result an energy source for the system is potentially diminished, inhibiting growth of the storm. Alternatively dust may interact with clouds through micro-physical processes, for example by causing more moisture to condense, potentially increasing the strength. As a result of climate change, concentrations and amount of dust in the atmosphere will likely change. It it is important to properly understand its effect on tropical storm formation. The adjoint of an atmospheric general circulation model provides a very powerful tool for investigating sensitivity to initial conditions. The National Aeronautics and Space Administration (NASA) has recently developed an adjoint version of the Goddard Earth Observing System version 5 (GEOS-5) dynamical core, convection scheme, cloud model and radiation schemes. This is extended so that the interaction between dust and radiation is also accounted for in the adjoint model. This provides a framework for examining the sensitivity to dust in the initial conditions. Specifically the set up allows for an investigation into the extent to which dust affects cyclone strength through absorption of radiation. In this work we investigate the validity of using an adjoint model for examining sensitivity to dust in hurricane formation. We present sensitivity results for a number of systems that developed during the Atlantic hurricane season of 2006. During this period there was a significant outbreak of Saharan dust and it is has been argued that this outbreak was responsible for the relatively calm season. This period was also covered by an extensive observation campaign. It is shown that the adjoint can provide insight into the sensitivity and reveals a relatively low sensitivity to dust compared to, for example, the thermodynamic variables. However a secondary sensitivity though moisture is seen. If dust dries the air it can significantly reduce the cyclone intensity through the moisture.

Adjoint assimilation of altimetric, surface drifter, and hydrographic data in a quasi-geostrophic model of the Azores Current

NASA Astrophysics Data System (ADS)

Morrow, Rosemary; de Mey, Pierre

1995-12-01

The flow characteristics in the region of the Azores Current are investigated by assimilating TOPEX/POSEIDON and ERS 1 altimeter data into the multilevel Harvard quasigeostrophic (QG) model with open boundaries (Miller et al., 1983) using an adjoint variational scheme (Moore, 1991). The study site lies in the path of the Azores Current, where a branch retroflects to the south in the vicinity of the Madeira Rise. The region was the site of an intensive field program in 1993, SEMAPHORE. We had two main aims in this adjoint assimilation project. The first was to see whether the adjoint method could be applied locally to optimize an initial guess field, derived from the continous assimilation of altimetry data using optimal interpolation (OI). The second aim was to assimilate a variety of different data sets and evaluate their importance in constraining our QG model. The adjoint assimilation of surface data was effective in optimizing the initial conditions from OI. After 20 iterations the cost function was generally reduced by 50-80%, depending on the chosen data constraints. The primary adjustment process was via the barotropic mode. Altimetry proved to be a good constraint on the variable flow field, in particular, for constraining the barotropic field. The excellent data quality of the TOPEX/POSEIDON (T/P) altimeter data provided smooth and reliable forcing; but for our mesoscale study in a region of long decorrelation times O(30 days), the spatial coverage from the combined T/P and ERS 1 data sets was more important for constraining the solution and providing stable flow at all levels. Surface drifters provided an excellent constraint on both the barotropic and baroclinic model fields. More importantly, the drifters provided a reliable measure of the mean field. Hydrographic data were also applied as a constraint; in general, hydrography provided a weak but effective constraint on the vertical Rossby modes in the model. Finally, forecasts run over a 2-month period indicate that the initial conditions optimized by the 20-day adjoint assimilation provide more stable, longer-term forecasts.

Stellar Diameters and Temperatures. III. Main-sequence A, F, G, and K Stars: Additional High-precision Measurements and Empirical Relations

NASA Astrophysics Data System (ADS)

Boyajian, Tabetha S.; von Braun, Kaspar; van Belle, Gerard; Farrington, Chris; Schaefer, Gail; Jones, Jeremy; White, Russel; McAlister, Harold A.; ten Brummelaar, Theo A.; Ridgway, Stephen; Gies, Douglas; Sturmann, Laszlo; Sturmann, Judit; Turner, Nils H.; Goldfinger, P. J.; Vargas, Norm

2013-07-01

Based on CHARA Array measurements, we present the angular diameters of 23 nearby, main-sequence stars, ranging from spectral types A7 to K0, 5 of which are exoplanet host stars. We derive linear radii, effective temperatures, and absolute luminosities of the stars using Hipparcos parallaxes and measured bolometric fluxes. The new data are combined with previously published values to create an Angular Diameter Anthology of measured angular diameters to main-sequence stars (luminosity classes V and IV). This compilation consists of 125 stars with diameter uncertainties of less than 5%, ranging in spectral types from A to M. The large quantity of empirical data is used to derive color-temperature relations to an assortment of color indices in the Johnson (BVR J I J JHK), Cousins (R C I C), Kron (R K I K), Sloan (griz), and WISE (W 3 W 4) photometric systems. These relations have an average standard deviation of ~3% and are valid for stars with spectral types A0-M4. To derive even more accurate relations for Sun-like stars, we also determined these temperature relations omitting early-type stars (T eff > 6750 K) that may have biased luminosity estimates because of rapid rotation; for this subset the dispersion is only ~2.5%. We find effective temperatures in agreement within a couple of percent for the interferometrically characterized sample of main-sequence stars compared to those derived via the infrared flux method and spectroscopic analysis.

Results of investigation of muon fluxes of superhigh energy cosmic rays with X-ray emulsion chambers

NASA Technical Reports Server (NTRS)

Ivanenko, I. P.; Ivanova, M. A.; Kuzmichev, L. A.; Ilyina, N. P.; Mandritskaya, K. V.; Osipova, E. A.; Rakobolskaya, I. V.; Zatsepin, G. T.

1985-01-01

The overall data from the investigation of the cosmic ray muon flux in the range of zenith angles (0-90) deg within the energy range (3.5 to 5.0) TeV is presented. The exposure of large X-ray emulsion chambers underground was 1200 tons. year. The data were processe using the method which was applied in the experiment Pamir and differred from the earlier applied one. The obtained value of a slope power index of the differential energy spectrum of the global muon flux is =3.7 that corresponds to the slope of the pion generation differential spectrum, gamma sub PI = 2.75 + or - .04. The analysis of the muon zenith-angular distribution showed that the contribution of rapid generation muons in the total muon flux agree the best with the value .2% and less with .7% at a 90% reliability level.

Time behavior of solar flare particles to 5 AU

NASA Technical Reports Server (NTRS)

Haffner, J. W.

1972-01-01

A simple model of solar flare radiation event particle transport is developed to permit the calculation of fluxes and related quantities as a function of distance from the sun (R). This model assumes the particles spiral around the solar magnetic field lines with a constant pitch angle. The particle angular distributions and onset plus arrival times as functions of energy at 1 AU agree with observations if the pitch angle distribution peaks near 90 deg. As a consequence the time dependence factor is essentially proportional to R/1.7, (R in AU), and the event flux is proportional to R/2.

Ultraviolet spectrophotometer for measuring columnar atmospheric ozone from aircraft

NASA Technical Reports Server (NTRS)

Hanser, F. A.; Sellers, B.; Briehl, D. C.

1978-01-01

An ultraviolet spectrophotometer (UVS) to measure downward solar fluxes from an aircraft or other high altitude platform is described. The UVS uses an ultraviolet diffuser to obtain large angular response with no aiming requirement, a twelve-position filter wheel with narrow (2-nm) and broad (20-nm) bandpass filters, and an ultraviolet photodiode. The columnar atmospheric ozone above the UVS (aircraft) is calculated from the ratios of the measured ultraviolet fluxes. Comparison with some Dobson station measurements gives agreement to 2%. Some UVS measured ozone profiles over the Pacific Ocean for November 1976 are shown to illustrate the instrument's performance.

Seismic Window Selection and Misfit Measurements for Global Adjoint Tomography

NASA Astrophysics Data System (ADS)

Lei, W.; Bozdag, E.; Lefebvre, M.; Podhorszki, N.; Smith, J. A.; Tromp, J.

2013-12-01

Global Adjoint Tomography requires fast parallel processing of large datasets. After obtaing the preprocessed observed and synthetic seismograms, we use the open source software packages FLEXWIN (Maggi et al. 2007) to select time windows and MEASURE_ADJ to make measurements. These measurements define adjoint sources for data assimilation. Previous versions of these tools work on a pair of SAC files---observed and synthetic seismic data for the same component and station, and loop over all seismic records associated with one earthquake. Given the large number of stations and earthquakes, the frequent read and write operations create severe I/O bottlenecks on modern computing platforms. We present new versions of these tools utilizing a new seismic data format, namely the Adaptive Seismic Data Format(ASDF). This new format shows superior scalability for applications on high-performance computers and accommodates various types of data, including earthquake, industry and seismic interferometry datasets. ASDF also provides user-friendly APIs, which can be easily integrated into the adjoint tomography workflow and combined with other data processing tools. In addition to solving the I/O bottleneck, we are making several improvements to these tools. For example, FLEXWIN is tuned to select windows for different types of earthquakes. To capture their distinct features, we categorize earthquakes by their depths and frequency bands. Moreover, instead of only picking phases between the first P arrival and the surface-wave arrivals, our aim is to select and assimilate many other later prominent phases in adjoint tomography. For example, in the body-wave band (17 s - 60 s), we include SKS, sSKS and their multiple, while in the surface-wave band (60 s - 120 s) we incorporate major-arc surface waves.

An approach to computing discrete adjoints for MPI-parallelized models applied to Ice Sheet System Model 4.11

NASA Astrophysics Data System (ADS)

Larour, Eric; Utke, Jean; Bovin, Anton; Morlighem, Mathieu; Perez, Gilberto

2016-11-01

Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar, gravity, and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model (ISSM), written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written, but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of the ISSM. We present a comprehensive approach to (1) carry out type changing through the ISSM, hence facilitating operator overloading, (2) bind to external solvers such as MUMPS and GSL-LU, and (3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the northeastern Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential to enable a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected, in Greenland and Antarctica.

An Approach to Computing Discrete Adjoints for MPI-Parallelized Models Applied to the Ice Sheet System Model}

NASA Astrophysics Data System (ADS)

Perez, G. L.; Larour, E. Y.; Morlighem, M.

2016-12-01

Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model, written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of ISSM. We present a comprehensive approach to 1) carry out type changing through ISSM, hence facilitating operator overloading, 2) bind to external solvers such as MUMPS and GSL-LU and 3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the North-East Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, Central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential of enabling a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or alreay collected in Greenland and Antarctica, such as surface altimetry, surface velocities, and/or gravity measurements.

Mode-Division-Multiplexing of Multiple Bessel-Gaussian Beams Carrying Orbital-Angular-Momentum for Obstruction-Tolerant Free-Space Optical and Millimetre-Wave Communication Links.

PubMed

Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P J; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J; Ashrafi, Solyman; Molisch, Andreas F; Tur, Moshe; Willner, Alan E

2016-03-01

We experimentally investigate the potential of using 'self-healing' Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.

Mode-Division-Multiplexing of Multiple Bessel-Gaussian Beams Carrying Orbital-Angular-Momentum for Obstruction-Tolerant Free-Space Optical and Millimetre-Wave Communication Links

PubMed Central

Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P. J.; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J.; Ashrafi, Solyman; Molisch, Andreas F.; Tur, Moshe; Willner, Alan E.

2016-01-01

We experimentally investigate the potential of using ‘self-healing’ Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively. PMID:26926068

Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

2010-01-01

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

2009-01-01

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

NASA Technical Reports Server (NTRS)

Ustino, Eugene A.

2006-01-01

This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

Recent Improvements in Aerodynamic Design Optimization on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

2000-01-01

Recent improvements in an unstructured-grid method for large-scale aerodynamic design are presented. Previous work had shown such computations to be prohibitively long in a sequential processing environment. Also, robust adjoint solutions and mesh movement procedures were difficult to realize, particularly for viscous flows. To overcome these limiting factors, a set of design codes based on a discrete adjoint method is extended to a multiprocessor environment using a shared memory approach. A nearly linear speedup is demonstrated, and the consistency of the linearizations is shown to remain valid. The full linearization of the residual is used to precondition the adjoint system, and a significantly improved convergence rate is obtained. A new mesh movement algorithm is implemented and several advantages over an existing technique are presented. Several design cases are shown for turbulent flows in two and three dimensions.

Adjoint equations and analysis of complex systems: Application to virus infection modelling

NASA Astrophysics Data System (ADS)

Marchuk, G. I.; Shutyaev, V.; Bocharov, G.

2005-12-01

Recent development of applied mathematics is characterized by ever increasing attempts to apply the modelling and computational approaches across various areas of the life sciences. The need for a rigorous analysis of the complex system dynamics in immunology has been recognized since more than three decades ago. The aim of the present paper is to draw attention to the method of adjoint equations. The methodology enables to obtain information about physical processes and examine the sensitivity of complex dynamical systems. This provides a basis for a better understanding of the causal relationships between the immune system's performance and its parameters and helps to improve the experimental design in the solution of applied problems. We show how the adjoint equations can be used to explain the changes in hepatitis B virus infection dynamics between individual patients.

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

Baines, Ellyn K.; Armstrong, J. Thomas; Schmitt, Henrique R.

Using the Navy Precision Optical Interferometer, we measured the angular diameters of 10 stars that have previously measured solar-like oscillations. Our sample covered a range of evolutionary stages but focused on evolved subgiant and giant stars. We combined our angular diameters with Hipparcos parallaxes to determine the stars' physical radii, and used photometry from the literature to calculate their bolometric fluxes, luminosities, and effective temperatures. We then used our results to test the scaling relations used by asteroseismology groups to calculate radii and found good agreement between the radii measured here and the radii predicted by stellar oscillation studies. Themore » precision of the relations is not as well constrained for giant stars as it is for less evolved stars.« less

Study on photonic angular momentum states in coaxial magneto-optical waveguides

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

Yang, Mu; Wu, Li-Ting; Guo, Tian-Jing

2014-10-21

By rigorously solving Maxwell's equations, we develop a full-wave electromagnetic theory for the study of photonic angular momentum states (PAMSs) in coaxial magneto-optical (MO) waveguides. Paying attention to a metal-MO-metal coaxial configuration, we show that the dispersion curves of the originally degenerated PAMSs experience a splitting, which are determined by the off-diagonal permittivity tensor element of the MO medium. We emphasize that this broken degeneracy in dispersion relation is accompanied by modified distributions of field component and transverse energy flux. A qualitative analysis about the connection between the split dispersion behavior and the field distribution is provided. Potential applications aremore » discussed.« less

The INCAS Project: An Innovative Contact-Less Angular Sensor

NASA Astrophysics Data System (ADS)

Ghislanzoni, L.; Di Cintio, A.; Solimando, M.; Parzianello, G.

2013-09-01

Angular Positions sensors are widely used in all spacecrafts, including re-entry vehicles and launchers, where mechanisms and pointing-scanning devices are required. The main applications are on mechanisms for TeleMeasure (TM) related to the release and deployment of devices, or on rotary mechanisms such as Solar Array Drive Mechanism (SADM) and Antenna Pointing Mechanism (APM). Longer lifetime (up to 7- 10 years) is becoming a new driver for the coming missions and contact technology sensors often incur in limitations due to the wear of the contacting parts [1].A Self-Compensating Absolute Angular Encoder was developed and tested in the frame of an ESA's ARTES 5.2 project, named INCAS (INnovative Contact-less Angular Sensor). More in particular, the INCAS sensor addresses a market need for contactless angular sensors aimed at replacing the more conventional rotary potentiometers, while featuring the same level of accuracy performances and extending the expected lifetime.

Ability of the current global observing network to constrain N2O sources and sinks

NASA Astrophysics Data System (ADS)

Millet, D. B.; Wells, K. C.; Chaliyakunnel, S.; Griffis, T. J.; Henze, D. K.; Bousserez, N.

2014-12-01

The global observing network for atmospheric N2O combines flask and in-situ measurements at ground stations with sustained and campaign-based aircraft observations. In this talk we apply a new global model of N2O (based on GEOS-Chem) and its adjoint to assess the strengths and weaknesses of this network for quantifying N2O emissions. We employ an ensemble of pseudo-observation analyses to evaluate the relative constraints provided by ground-based (surface, tall tower) and airborne (HIPPO, CARIBIC) observations, and the extent to which variability (e.g. associated with pulsing or seasonality of emissions) not captured by the a priori inventory can bias the inferred fluxes. We find that the ground-based and HIPPO datasets each provide a stronger constraint on the distribution of global emissions than does the CARIBIC dataset on its own. Given appropriate initial conditions, we find that our inferred surface fluxes are insensitive to model errors in the stratospheric loss rate of N2O over the timescale of our analysis (2 years); however, the same is not necessarily true for model errors in stratosphere-troposphere exchange. Finally, we examine the a posteriori error reduction distribution to identify priority locations for future N2O measurements.

Analysis of dpa rates in the HFIR reactor vessel using a hybrid Monte Carlo/deterministic method

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

Blakeman, Edward

2016-01-01

The Oak Ridge High Flux Isotope Reactor (HFIR), which began full-power operation in 1966, provides one of the highest steady-state neutron flux levels of any research reactor in the world. An ongoing vessel integrity analysis program to assess radiation-induced embrittlement of the HFIR reactor vessel requires the calculation of neutron and gamma displacements per atom (dpa), particularly at locations near the beam tube nozzles, where radiation streaming effects are most pronounced. In this study we apply the Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) technique in the ADVANTG code to develop variance reduction parameters for use in the MCNP radiationmore » transport code. We initially evaluated dpa rates for dosimetry capsule locations, regions in the vicinity of the HB-2 beamline, and the vessel beltline region. We then extended the study to provide dpa rate maps using three-dimensional cylindrical mesh tallies that extend from approximately 12 below to approximately 12 above the axial extent of the core. The mesh tally structures contain over 15,000 mesh cells, providing a detailed spatial map of neutron and photon dpa rates at all locations of interest. Relative errors in the mesh tally cells are typically less than 1%.« less

Characterization of high order spatial discretizations and lumping techniques for discontinuous finite element SN transport

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

Maginot, P. G.; Ragusa, J. C.; Morel, J. E.

2013-07-01

We examine several possible methods of mass matrix lumping for discontinuous finite element discrete ordinates transport using a Lagrange interpolatory polynomial trial space. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping in a purely absorbing 1-D slab cell for the linear discontinuous approximation, we show that when used with higher degree interpolatory polynomial trial spaces, traditional lumping does yield strictly positive outflows and does not increase in accuracy with an increase in trial space polynomial degree. As an alternative, we examine methods which are 'self-lumping'. Self-lumping methods yield diagonal mass matrices by using numerical quadrature restrictedmore » to the Lagrange interpolatory points. Using equally-spaced interpolatory points, self-lumping is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows in pure absorbers for odd power polynomials in 1-D slab geometry. By changing interpolatory points from the traditional equally-spaced points to the quadrature points of the Gauss-Legendre or Lobatto-Gauss-Legendre quadratures, it is possible to generate solution representations with a diagonal mass matrix and a strictly positive outflow for any degree polynomial solution representation in a pure absorber medium in 1-D slab geometry. Further, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to the quadrature points of high order accuracy numerical quadrature schemes. (authors)« less

Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching [Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems

DOE PAGES

Zhang, Hong; Abhyankar, Shrirang; Constantinescu, Emil; ...

2017-01-24

Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whosemore » sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields.« less

Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching [Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems

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

Zhang, Hong; Abhyankar, Shrirang; Constantinescu, Emil

Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whosemore » sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields.« less

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

PubMed

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields.

PubMed

Yang, R; Zelyak, O; Fallone, B G; St-Aubin, J

2018-01-30

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields

NASA Astrophysics Data System (ADS)

Yang, R.; Zelyak, O.; Fallone, B. G.; St-Aubin, J.

2018-02-01

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

Two-Way Atmospheric and Oceanic Coupling of the Adriatic Bora

DTIC Science & Technology

2010-01-15

v.,^-- 15 Februaiy 2003 Hourly Latent and Sensible Heat Fluxes for Vellrat (February 2003) M 200 * v,_ A. J^A~~^ ’V-V/ VST COAMPS5 OBS •"V-v...using techniques used by Kuzmic et al. (2007). These include calculations of the magnitude of the complex correlation coefficient and the angular

Tango

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

Parker, Jeffrey

Tango enables the accelerated numerical solution of the multiscale problem of self-consistent transport and turbulence. Fast turbulence results in fluxes of heat and particles that slowly change the mean profiles of temperature and density. The fluxes are computed by separate turbulence simulation codes; Tang solves for the self-consistent change in mean temperature or density given those fluxes.

Respective contribution of orientation contrast and illusion of self-tilt to the rod-and-frame effect.

PubMed

Cian, C; Esquivié, D; Barraud, P A; Raphel, C

1995-01-01

The visual angle subtended by the frame seems to be an important determinant of the contribution of orientation contrast and illusion of self-tilt (ie vection) to the rod-and-frame effect. Indeed, the visuovestibular factor (which produces vection) seems to be predominant in large displays and the contrast effect in small displays. To determine how these two phenomena are combined to account for the rod-and-frame effect, independent estimates of the magnitude of each component in relation to the angular size subtended by the display were examined. Thirty-five observers were exposed to three sets of experimental situations: body-adjustment test (illusion of self-tilt only), the tilt illusion (contrast only) and the rod-and-frame test, each display subtending 7, 12, 28, and 45 deg of visual angle. Results showed that errors recorded in the three situations increased linearly with the angular size. Whatever the size of the frame, both mechanisms, contrast effect (tilt illusion) and illusory effect on self-orientation (body-adjustment test), are always present. However, rod-and-frame errors became greater at a faster rate than the other two effects as the size of teh stimuli became larger. Neither one nor the other independent phenomenen, nor the combined effect could fully account for the rod-and-frame effect whatever the angular size of the apparatus.

Muon Simulation at the Daya Bay SIte

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

Mengyun, Guan; Jun, Cao; Changgen, Yang

2006-05-23

With a pretty good-resolution mountain profile, we simulated the underground muon background at the Daya Bay site. To get the sea-level muon flux parameterization, a modification to the standard Gaisser's formula was introduced according to the world muon data. MUSIC code was used to transport muon through the mountain rock. To deploy the simulation, first we generate a statistic sample of sea-level muon events according to the sea-level muon flux distribution formula; then calculate the slant depth of muon passing through the mountain using an interpolation method based on the digitized data of the mountain; finally transport muons through rockmore » to get underground muon sample, from which we can get results of muon flux, mean energy, energy distribution and angular distribution.« less

Towards Seismic Tomography Based Upon Adjoint Methods

NASA Astrophysics Data System (ADS)

Tromp, J.; Liu, Q.; Tape, C.; Maggi, A.

2006-12-01

We outline the theory behind tomographic inversions based on 3D reference models, fully numerical 3D wave propagation, and adjoint methods. Our approach involves computing the Fréchet derivatives for tomographic inversions via the interaction between a forward wavefield, propagating from the source to the receivers, and an `adjoint' wavefield, propagating from the receivers back to the source. The forward wavefield is computed using a spectral-element method (SEM) and a heterogeneous wave-speed model, and stored as synthetic seismograms at particular receivers for which there is data. We specify an objective or misfit function that defines a measure of misfit between data and synthetics. For a given receiver, the differences between the data and the synthetics are time reversed and used as the source of the adjoint wavefield. For each earthquake, the interaction between the regular and adjoint wavefields is used to construct finite-frequency sensitivity kernels, which we call event kernel. These kernels may be thought of as weighted sums of measurement-specific banana-donut kernels, with weights determined by the measurements. The overall sensitivity is simply the sum of event kernels, which defines the misfit kernel. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, i.e., the Fréchet derivatives. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, i.e., the Fréchet derivatives. A conjugate gradient algorithm is used to iteratively improve the model while reducing the misfit function. Using 2D examples for Rayleigh wave phase-speed maps of southern California, we illustrate the construction of the gradient and the minimization algorithm, and consider various tomographic experiments, including source inversions, structural inversions, and joint source-structure inversions. We also illustrate the characteristics of these 3D finite-frequency kernels based upon adjoint simulations for a variety of global arrivals, e.g., Pdiff, P'P', and SKS, and we illustrate how the approach may be used to investigate body- and surface-wave anisotropy. In adjoint tomography any time segment in which the data and synthetics match reasonably well is suitable for measurement, and this implies a much greater number of phases per seismogram can be used compared to classical tomography in which the sensitivity of the measurements is determined analytically for specific arrivals, e.g., P. We use an automated picking algorithm based upon short-term/long-term averages and strict phase and amplitude anomaly criteria to determine arrivals and time windows suitable for measurement. For shallow global events the algorithm typically identifies of the order of 1000~windows suitable for measurement, whereas for a deep event the number can reach 4000. For southern California earthquakes the number of phases is of the order of 100 for a magnitude 4.0 event and up to 450 for a magnitude 5.0 event. We will show examples of event kernels for both global and regional earthquakes. These event kernels form the basis of adjoint tomography.

Design of a transportable high efficiency fast neutron spectrometer

DOE PAGES

Roecker, C.; Bernstein, A.; Bowden, N. S.; ...

2016-04-12

A transportable fast neutron detection system has been designed and constructed for measuring neutron energy spectra and flux ranging from tens to hundreds of MeV. The transportability of the spectrometer reduces the detector-related systematic bias between different neutron spectra and flux measurements, which allows for the comparison of measurements above or below ground. The spectrometer will measure neutron fluxes that are of prohibitively low intensity compared to the site-specific background rates targeted by other transportable fast neutron detection systems. To measure low intensity high-energy neutron fluxes, a conventional capture-gating technique is used for measuring neutron energies above 20 MeV andmore » a novel multiplicity technique is used for measuring neutron energies above 100 MeV. The spectrometer is composed of two Gd containing plastic scintillator detectors arranged around a lead spallation target. To calibrate and characterize the position dependent response of the spectrometer, a Monte Carlo model was developed and used in conjunction with experimental data from gamma ray sources. Multiplicity event identification algorithms were developed and used with a Cf-252 neutron multiplicity source to validate the Monte Carlo model Gd concentration and secondary neutron capture efficiency. The validated Monte Carlo model was used to predict an effective area for the multiplicity and capture gating analyses. For incident neutron energies between 100 MeV and 1000 MeV with an isotropic angular distribution, the multiplicity analysis predicted an effective area of 500 cm 2 rising to 5000 cm 2. For neutron energies above 20 MeV, the capture-gating analysis predicted an effective area between 1800 cm 2 and 2500 cm 2. As a result, the multiplicity mode was found to be sensitive to the incident neutron angular distribution.« less

M-dwarf stellar winds: the effects of realistic magnetic geometry on rotational evolution and planets

NASA Astrophysics Data System (ADS)

Vidotto, A. A.; Jardine, M.; Morin, J.; Donati, J. F.; Opher, M.; Gombosi, T. I.

2014-02-01

We perform three-dimensional numerical simulations of stellar winds of early-M-dwarf stars. Our simulations incorporate observationally reconstructed large-scale surface magnetic maps, suggesting that the complexity of the magnetic field can play an important role in the angular momentum evolution of the star, possibly explaining the large distribution of periods in field dM stars, as reported in recent works. In spite of the diversity of the magnetic field topologies among the stars in our sample, we find that stellar wind flowing near the (rotational) equatorial plane carries most of the stellar angular momentum, but there is no preferred colatitude contributing to mass-loss, as the mass flux is maximum at different colatitudes for different stars. We find that more non-axisymmetric magnetic fields result in more asymmetric mass fluxes and wind total pressures ptot (defined as the sum of thermal, magnetic and ram pressures). Because planetary magnetospheric sizes are set by pressure equilibrium between the planet's magnetic field and ptot, variations of up to a factor of 3 in ptot (as found in the case of a planet orbiting at several stellar radii away from the star) lead to variations in magnetospheric radii of about 20 per cent along the planetary orbital path. In analogy to the flux of cosmic rays that impact the Earth, which is inversely modulated with the non-axisymmetric component of the total open solar magnetic flux, we conclude that planets orbiting M-dwarf stars like DT Vir, DS Leo and GJ 182, which have significant non-axisymmetric field components, should be the more efficiently shielded from galactic cosmic rays, even if the planets lack a protective thick atmosphere/large magnetosphere of their own.

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

Roecker, C.; Bernstein, A.; Bowden, N. S.

A transportable fast neutron detection system has been designed and constructed for measuring neutron energy spectra and flux ranging from tens to hundreds of MeV. The transportability of the spectrometer reduces the detector-related systematic bias between different neutron spectra and flux measurements, which allows for the comparison of measurements above or below ground. The spectrometer will measure neutron fluxes that are of prohibitively low intensity compared to the site-specific background rates targeted by other transportable fast neutron detection systems. To measure low intensity high-energy neutron fluxes, a conventional capture-gating technique is used for measuring neutron energies above 20 MeV andmore » a novel multiplicity technique is used for measuring neutron energies above 100 MeV. The spectrometer is composed of two Gd containing plastic scintillator detectors arranged around a lead spallation target. To calibrate and characterize the position dependent response of the spectrometer, a Monte Carlo model was developed and used in conjunction with experimental data from gamma ray sources. Multiplicity event identification algorithms were developed and used with a Cf-252 neutron multiplicity source to validate the Monte Carlo model Gd concentration and secondary neutron capture efficiency. The validated Monte Carlo model was used to predict an effective area for the multiplicity and capture gating analyses. For incident neutron energies between 100 MeV and 1000 MeV with an isotropic angular distribution, the multiplicity analysis predicted an effective area of 500 cm 2 rising to 5000 cm 2. For neutron energies above 20 MeV, the capture-gating analysis predicted an effective area between 1800 cm 2 and 2500 cm 2. As a result, the multiplicity mode was found to be sensitive to the incident neutron angular distribution.« less

Impact of convection and resistivity on angular momentum transport in dwarf novae

NASA Astrophysics Data System (ADS)

Scepi, N.; Lesur, G.; Dubus, G.; Flock, M.

2018-01-01

The eruptive cycles of dwarf novae are thought to be due to a thermal-viscous instability in the accretion disk surrounding the white dwarf. This model has long been known to imply enhanced angular momentum transport in the accretion disk during outburst. This is measured by the stress to pressure ratio α, with α ≈ 0.1 required in outburst compared to α ≈ 0.01 in quiescence. Such an enhancement in α has recently been observed in simulations of turbulent transport driven by the magneto-rotational instability (MRI) when convection is present, without requiring a net magnetic flux. We independently recover this result by carrying out PLUTO magnetohydrodynamic (MHD) simulations of vertically stratified, radiative, shearing boxes with the thermodynamics and opacities appropriate to dwarf novae. The results are robust against the choice of vertical boundary conditions. The thermal equilibrium solutions found by the simulations trace the well-known S-curve in the density-temperature plane that constitutes the core of the disk thermal-viscous instability model. We confirm that the high values of α ≈ 0.1 occur near the tip of the hot branch of the S-curve, where convection is active. However, we also present thermally stable simulations at lower temperatures that have standard values of α ≈ 0.03 despite the presence of vigorous convection. We find no simple relationship between α and the strength of the convection, as measured by the ratio of convective to radiative flux. The cold branch is only very weakly ionized so, in the second part of this work, we studied the impact of non-ideal MHD effects on transport. Ohmic dissipation is the dominant effect in the conditions of quiescent dwarf novae. We include resistivity in the simulations and find that the MRI-driven transport is quenched (α ≈ 0) below the critical density at which the magnetic Reynolds number Rm ≤ 104. This is problematic because the X-ray emission observed in quiescent systems requires ongoing accretion onto the white dwarf. We verify that these X-rays cannot self-sustain MRI-driven turbulence by photo-ionizing the disk and discuss possible solutions to the issue of accretion in quiescence.

Self-force on an electric dipole in the spacetime of a cosmic string

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

Muniz, C.R., E-mail: celiomuniz@yahoo.com; Bezerra, V.B., E-mail: valdir@ufpb.br

2014-01-15

We calculate the electrostatic self-force on an electric dipole in the spacetime generated by a static, thin, infinite and straight cosmic string. The electric dipole is held fixed in different configurations, namely, parallel, perpendicular to the cosmic string and oriented along the azimuthal direction around this topological defect, which is stretched along the z axis. We show that the self-force is equivalent to an interaction of the electric dipole with an effective dipole moment which depends on the linear mass density of the cosmic string and on the configuration. The plots of the self-forces as functions of the parameter whichmore » determines the angular deficit of the cosmic string are shown for those different configurations. -- Highlights: •Review of regularized Green’s function applied to the problem. •Self-force on an electric dipole in the string spacetime for some orientations. •Representation via graphs of the self-forces versus angular parameter of the cosmic string. •Self-force induced by the string seen as an interaction between two dipoles. •Discussion about the superposition principle in this non-trivial background.« less

Quantum gravitational collapse as a Dirac particle on the half line

NASA Astrophysics Data System (ADS)

Hassan, Syed Moeez; Husain, Viqar; Ziprick, Jonathan

2018-05-01

We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy spectrum |E |m , where m is the rest mass of the shell and E is the Arnowitt-Deser-Misner mass. For sufficiently large m , the ground state energy level is negative. This suggests that classical positivity of energy does not survive quantization. The scattering states provide a realization of singularity avoidance. We speculate on the consequences of these results for black hole radiation.

Linear transformation and oscillation criteria for Hamiltonian systems

NASA Astrophysics Data System (ADS)

Zheng, Zhaowen

2007-08-01

Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.

On the problem of time in quantum mechanics

NASA Astrophysics Data System (ADS)

Bauer, M.

2017-05-01

The problem of time in quantum mechanics (QM) concerns the fact that in the Schrödinger equation time is a parameter, not an operator. Pauli's objection to a time-energy uncertainty relation analogue to the position-momentum one, conjectured by Heisenberg early on, seemed to exclude the existence of such an operator. However Dirac's formulation of an electron's relativistic QM does allow the introduction of a dynamical time operator that is self-adjoint. Consequently, it can be considered as the generator of a unitary transformation of the system, as well as an additional system observable subject to uncertainty. In the present paper these aspects are examined within the standard framework of relativistic QM.

Generalized Birkhoffian representation of nonholonomic systems and its discrete variational algorithm

NASA Astrophysics Data System (ADS)

Liu, Shixing; Liu, Chang; Hua, Wei; Guo, Yongxin

2016-11-01

By using the discrete variational method, we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework, and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm. Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework. Project supported by the National Natural Science Foundation of China (Grant Nos. 11472124, 11572145, 11202090, and 11301350), the Doctor Research Start-up Fund of Liaoning Province, China (Grant No. 20141050), the China Postdoctoral Science Foundation (Grant No. 2014M560203), and the General Science and Technology Research Plans of Liaoning Educational Bureau, China (Grant No. L2013005).

FAST TRACK COMMUNICATION: \\ {P}\\ {T}-symmetry, Cartan decompositions, Lie triple systems and Krein space-related Clifford algebras

NASA Astrophysics Data System (ADS)

Günther, Uwe; Kuzhel, Sergii

2010-10-01

Gauged \\ {P}\\ {T} quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie-triple structure is found and an interpretation as \\ {P}\\ {T}-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space-related J-self-adjoint extensions for PTQM setups with ultra-localized potentials.

Shape determination and control for large space structures

NASA Technical Reports Server (NTRS)

Weeks, C. J.

1981-01-01

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and performance criteria for the comparison of estimates or control forms. Results are illustrated by simulations in the one dimensional case with a flexible beam model, and in the multidimensional case with a finite model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic mode. These expansions provide approximated solutions in the event that a used form analytical solution to the system boundary value problem is not available.

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

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

Sackett, S.J.

JASON solves general electrostatics problems having either slab or cylindrical symmetry. More specifically, it solves the self-adjoint elliptic equation, div . (KgradV) - ..gamma..V + rho = 0 in an aritrary two-dimensional domain. For electrostatics, V is the electrostatic potential, K is the dielectric tensor, and rho is the free-charge density. The parameter ..gamma.. is identically zero for electrostatics but may have a positive nonzero value in other cases (e.g., capillary surface problems with gravity loading). The system of algebraic equations used in JASON is generated by the finite element method. Four-node quadrilateral elements are used for most of themore » mesh. Triangular elements, however, are occasionally used on boundaries to avoid severe mesh distortions. 15 figures. (RWR)« less

Self-Organized Criticality Properties of the Turbulence-Induced Particle Flux at the Plasma Edge of the HT-6M Tokamak

NASA Astrophysics Data System (ADS)

Wang, Wen-Hao; Yu, Chang-Xuan; Wen, Yi-Zhi; Xu, Yu-Hong; Ling, Bi-Li; Gong, Xian-Zu; Liu, Bao-Hua; Wan, Bao-Nian

2001-06-01

The power spectrum and the probability distribution function (PDF) of the turbulence-induced particle flux Γ in the velocity shear layer of the HT-6M edge region have been measured and analysed. Three regions of frequency dependence (f 0, f-1, f-4) have been observed in the spectrum of the flux. The PDF of the flux displays a Γ-1 scaling over one decade in Γ. Using the rescaled-range statistical technique, we find that the degree of the self-similarity (Hurst exponent) of the particle flux in the measured region ranges from 0.64 to 0.83. All of these results may mean that the plasma transport is in a state characterized by self-organized criticality.

Biologically inspired artificial compound eyes.

PubMed

Jeong, Ki-Hun; Kim, Jaeyoun; Lee, Luke P

2006-04-28

This work presents the fabrication of biologically inspired artificial compound eyes. The artificial ommatidium, like that of an insect's compound eyes, consists of a refractive polymer microlens, a light-guiding polymer cone, and a self-aligned waveguide to collect light with a small angular acceptance. The ommatidia are omnidirectionally arranged along a hemispherical polymer dome such that they provide a wide field of view similar to that of a natural compound eye. The spherical configuration of the microlenses is accomplished by reconfigurable microtemplating, that is, polymer replication using the deformed elastomer membrane with microlens patterns. The formation of polymer waveguides self-aligned with microlenses is also realized by a self-writing process in a photosensitive polymer resin. The angular acceptance is directly measured by three-dimensional optical sectioning with a confocal microscope, and the detailed optical characteristics are studied in comparison with a natural compound eye.

Determination of solar flare accelerated ion angular distributions from SMM gamma ray and neutron measurements and determination of the He-3/H ratio in the solar photosphere from SMM gamma ray measurements

NASA Technical Reports Server (NTRS)

Lingenfelter, Richard E.

1989-01-01

Comparisons of Solar Maximum Mission (SMM) observations of gamma-ray line and neutron emission with theoretical calculation of their expected production by flare accelerated ion interactions in the solar atmosphere have led to significant advances in the understanding of solar flare particle acceleration and interaction, as well as the flare process itself. These comparisons have enabled the determination of, not only the total number and energy spectrum of accelerated ions trapped at the sun, but also the ion angular distribution as they interact in the solar atmosphere. The Monte Carlo program was modified to include in the calculations of ion trajectories the effects of both mirroring in converging magnetic fields and of pitch angle scattering. Comparing the results of these calculations with the SMM observations, not only the angular distribution of the interacting ions can be determined, but also the initial angular distribution of the ions at acceleration. The reliable determination of the solar photospheric He-3 abundance is of great importance for understanding nucleosynthesis in the early universe and its implications for cosmology, as well as for the study of the evolution of the sun. It is also essential for the determinations of the spectrum and total number of flare accelerated ions from the SMM/GRS gamma-ray line measurements. Systematic Monte Carlo calculations of the time dependence were made as a function of the He-3 abundance and other variables. A new series of calculations were compared for the time-dependent flux of 2.223 MeV neutron capture line emission and the ratio of the time-integrated flux in the 2.223 MeV line to that in the 4.1 to 6.4 MeV nuclear deexcitation band.

Naval Research Laboratory Multiscale Targeting Guidance for T-PARC and TCS-08

DTIC Science & Technology

2010-01-01

Naval Research Laboratory Multiscale Targeting Guidance for T- PARC and TCS-08 CAROLYN A. REYNOLDS AND JAMES D. DOYLE Marine Meteorology Division...of The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign (T- PARC ) and the Office of Naval Research’s...These products were produced with 24-, 36-, and 48-h lead times. The nonhydrostatic adjoint system used during T- PARC /TCS-08 contains an exact adjoint to

A POSTERIORI ERROR ANALYSIS OF TWO STAGE COMPUTATION METHODS WITH APPLICATION TO EFFICIENT DISCRETIZATION AND THE PARAREAL ALGORITHM.

PubMed

Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff

2016-01-01

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute "dual-weighted" a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.

2003-01-01

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Generalized Ince Gaussian beams

NASA Astrophysics Data System (ADS)

Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

2006-08-01

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Data-based adjoint and H2 optimal control of the Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Banks, Michael; Bodony, Daniel

2017-11-01

Equation-free, reduced-order methods of control are desirable when the governing system of interest is of very high dimension or the control is to be applied to a physical experiment. Two-phase flow optimal control problems, our target application, fit these criteria. Dynamic Mode Decomposition (DMD) is a data-driven method for model reduction that can be used to resolve the dynamics of very high dimensional systems and project the dynamics onto a smaller, more manageable basis. We evaluate the effectiveness of DMD-based forward and adjoint operator estimation when applied to H2 optimal control approaches applied to the linear and nonlinear Ginzburg-Landau equation. Perspectives on applying the data-driven adjoint to two phase flow control will be given. Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program, under Grant Number N00014-16-1-2617.

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids by Using Complex Variables

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Kleb, William L.

2005-01-01

A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Kleb, William L.

2005-01-01

A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

Adjoint Fokker-Planck equation and runaway electron dynamics

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

Liu, Chang; Brennan, Dylan P.; Bhattacharjee, Amitava

2016-01-15

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay timemore » in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.« less

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.