Humbird, Kelli D
2016-01-01
Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a mathematically related set of adjoint equations. The information contained in the equations can be combined to produce sensitivity information in a computationally efficient manner. In this work, sensitivity analyses are performed on systems described by flux-limited radiative diffusion using the adjoint approach. The sensitivities computed are shown to agree with standard perturbation theory, and can be obtained in significantly less computational time.
Humbird, Kelli D.; McClarren, Ryan G.
2016-01-01
Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a mathematically related set of adjoint equations. The information contained in the equations can be combined to produce sensitivity information in a computationally efficient manner. In this work, sensitivity analyses are performed on systems described by flux-limited ...
Laboure, Vincent M.; McClarren, Ryan G.; Wang, Yaqi
2016-01-01
In this paper, we derive a method for the second-order form of the transport equation that is both globally conservative and compatible with voids, using Continuous Finite Element Methods (CFEM). The main idea is to use the Least-Squares (LS) form of the transport equation in the void regions and the Self-Adjoint Angular Flux (SAAF) form elsewhere. While the SAAF formulation is globally conservative, the LS formulation need a correction in void. The price to pay for this fix is the loss of sy...
Humbird, Kelli D.; McClarren, Ryan G.
2017-03-01
Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a mathematically related set of adjoint equations. The information contained in the equations can be combined to produce sensitivity information in a computationally efficient manner. In this work, sensitivity analyses are performed on systems described by flux-limited radiative diffusion using the adjoint approach. The sensitivities computed are shown to agree with standard perturbation theory and require significantly less computational time. The adjoint approach saves the computational cost of one forward solve per sensitivity, making the method attractive when multiple sensitivities are of interest.
Directory of Open Access Journals (Sweden)
T. Ziehn
2011-11-01
Full Text Available Accurate modelling of the carbon cycle strongly depends on the parametrization of its underlying processes. The Carbon Cycle Data Assimilation System (CCDAS can be used as an estimator algorithm to derive posterior parameter values and uncertainties for the Biosphere Energy Transfer and Hydrology scheme (BETHY. However, the simultaneous optimization of all process parameters can be challenging, due to the complexity and non-linearity of the BETHY model. Therefore, we propose a new concept that uses ensemble runs and the adjoint optimization approach of CCDAS to derive the full probability density function (PDF for posterior soil carbon parameters and the net carbon flux at the global scale. This method allows us to optimize only those parameters that can be constrained best by atmospheric carbon dioxide (CO_{2} data. The prior uncertainties of the remaining parameters are included in a consistent way through ensemble runs, but are not constrained by data. The final PDF for the optimized parameters and the net carbon flux are then derived by superimposing the individual PDFs for each ensemble member. We find that the optimization with CCDAS converges much faster, due to the smaller number of processes involved. Faster convergence also gives us much increased confidence that we find the global minimum in the reduced parameter space.
Laboure, Vincent M; Wang, Yaqi
2016-01-01
In this paper, we derive a method for the second-order form of the transport equation that is both globally conservative and compatible with voids, using Continuous Finite Element Methods (CFEM). The main idea is to use the Least-Squares (LS) form of the transport equation in the void regions and the Self-Adjoint Angular Flux (SAAF) form elsewhere. While the SAAF formulation is globally conservative, the LS formulation need a correction in void. The price to pay for this fix is the loss of symmetry of the bilinear form. We first derive this Conservative LS (CLS) formulation in void. Second we combine the SAAF and CLS forms and end up with an hybrid SAAF-CLS method, having the desired properties. We show that extending the theory to near-void regions is a minor complication and can be done without affecting the global conservation of the scheme. Being angular discretization agnostic, this method can be applied to both discrete ordinates (SN) and spherical harmonics (PN) methods. However, since a globally conse...
A general nonlinear inverse transport algorithm using forward and adjoint flux computations
Energy Technology Data Exchange (ETDEWEB)
Norton, S.J. [Oak Ridge National Lab., TN (United States)
1997-04-01
Iterative approaches to the nonlinear inverse transport problem are described, which give rise to the structure that best predicts a set of transport observations. Such methods are based on minimizing a global error functional measuring the discrepancy between predicted and observed transport data. Required for this minimization is the functional gradient (Frechet derivative) of the global error evaluated with respect to a set of unknown material parameters (specifying boundary locations, scattering cross sections, etc.) which are to be determined. It is shown how this functional gradient is obtained from numerical solutions to the forward and adjoint transport problems computed once per iteration. This approach is not only far more efficient, but also more accurate, than a finite-difference method for computing the gradient of the global error. The general technique can be applied to inverse-transport problems of all descriptions, provided only that solutions to the forward and adjoint problems can be found numerically. As an illustration, two inverse problems are treated: the reconstruction of an anisotropic scattering function in a one-dimensional homogeneous slab and the two-dimensional imaging of a spatially-varying scattering cross section.
Energy Technology Data Exchange (ETDEWEB)
Vincent M. Laboure; Yaqi Wang; Mark D. DeHart
2016-05-01
In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment, in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutions (MMS) and find the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.
Energy Technology Data Exchange (ETDEWEB)
Zheng, Weixiong [Texas A & M Univ., College Station, TX (United States); Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); DeHart, Mark D. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2016-09-01
In this report, we present a new upwinding scheme for the multiscale capability in Rattlesnake, the MOOSE based radiation transport application. Comparing with the initial implementation of multiscale utilizing Lagrange multipliers to impose strong continuity of angular flux on interface of in-between subdomains, this scheme does not require the particular domain partitioning. This upwinding scheme introduces discontinuity of angular flux and resembles the classic upwinding technique developed for solving first order transport equation using discontinuous finite element method (DFEM) on the subdomain interfaces. Because this scheme restores the causality of radiation streaming on the interfaces, significant accuracy improvement can be observed with moderate increase of the degrees of freedom comparing with the continuous method over the entire solution domain. Hybrid SN-PN is implemented and tested with this upwinding scheme. Numerical results show that the angular smoothing required by Lagrange multiplier method is not necessary for the upwinding scheme.
Truchet, G.; Leconte, P.; Peneliau, Y.; Santamarina, A.; Malvagi, F.
2014-06-01
Pile-oscillation experiments are performed in the MINERVE reactor at the CEA Cadarache to improve nuclear data accuracy. In order to precisely calculate small reactivity variations (experiments, a reference calculation need to be achieved. This calculation may be accomplished using the continuous-energy Monte Carlo code TRIPOLI-4® by using the eigenvalue difference method. This "direct" method has shown limitations in the evaluation of very small reactivity effects because it needs to reach a very small variance associated to the reactivity in both states. To answer this problem, it has been decided to implement the exact perturbation theory in TRIPOLI-4® and, consequently, to calculate a continuous-energy adjoint flux. The Iterated Fission Probability (IFP) method was chosen because it has shown great results in some other Monte Carlo codes. The IFP method uses a forward calculation to compute the adjoint flux, and consequently, it does not rely on complex code modifications but on the physical definition of the adjoint flux as a phase-space neutron importance. In the first part of this paper, the IFP method implemented in TRIPOLI-4® is described. To illustrate the effciency of the method, several adjoint fluxes are calculated and compared with their equivalent obtained by the deterministic code APOLLO-2. The new implementation can calculate angular adjoint flux. In the second part, a procedure to carry out an exact perturbation calculation is described. A single cell benchmark has been used to test the accuracy of the method, compared with the "direct" estimation of the perturbation. Once again the method based on the IFP shows good agreement for a calculation time far more inferior to the "direct" method. The main advantage of the method is that the relative accuracy of the reactivity variation does not depend on the magnitude of the variation itself, which allows us to calculate very small reactivity perturbations with high precision. Other applications of
Serakos, Demetrios
2015-01-01
This book defines and develops the generalized adjoint of an input-output system. It is the result of a theoretical development and examination of the generalized adjoint concept and the conditions under which systems analysis using adjoints is valid. Results developed in this book are useful aids for the analysis and modeling of physical systems, including the development of guidance and control algorithms and in developing simulations. The generalized adjoint system is defined and is patterned similarly to adjoints of bounded linear transformations. Next the elementary properties of the generalized adjoint system are derived. For a space of input-output systems, a generalized adjoint map from this space of systems to the space of generalized adjoints is defined. Then properties of the generalized adjoint map are derived. Afterward the author demonstrates that the inverse of an input-output system may be represented in terms of the generalized adjoint. The use of generalized adjoints to determine bounds for ...
Introduction to Adjoint Models
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.
Energy Technology Data Exchange (ETDEWEB)
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2000-07-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)
Adjoint affine fusion and tadpoles
Urichuk, Andrew; Walton, Mark A.
2016-06-01
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 written 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.
Adjoint affine fusion and tadpoles
Urichuk, Andrew
2016-01-01
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 written 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.
Adjoint affine fusion and tadpoles
Energy Technology Data Exchange (ETDEWEB)
Urichuk, Andrew, E-mail: andrew.urichuk@uleth.ca [Physics and Astronomy Department, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); Walton, Mark A., E-mail: walton@uleth.ca [Physics and Astronomy Department, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste (Italy)
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 written 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.
Institute of Scientific and Technical Information of China (English)
CHENG Qiang; CAO JianWen; WANG Bin; ZHANG HaiBin
2009-01-01
The adjoint code generator (ADG) is developed to produce the adjoint codes, which are used to analytically calculate gradients and the Hessian-vector products with the costs independent of the number of the independent variables. Different from other automatic differentiation tools, the implementation of ADG has advantages of using the least program behavior decomposition method and several static dependence analysis techniques. In this paper we first address the concerned concepts and fundamentals, and then introduce the functionality and the features of ADG. In particular, we also discuss the design architecture of ADG and implementation details including the recomputation and storing strategy and several techniques for code optimization. Some experimental results in several applications are presented at the end.
MCNP: Multigroup/adjoint capabilities
Energy Technology Data Exchange (ETDEWEB)
Wagner, J.C.; Redmond, E.L. II; Palmtag, S.P.; Hendricks, J.S.
1994-04-01
This report discusses various aspects related to the use and validity of the general purpose Monte Carlo code MCNP for multigroup/adjoint calculations. The increased desire to perform comparisons between Monte Carlo and deterministic codes, along with the ever-present desire to increase the efficiency of large MCNP calculations has produced a greater user demand for the multigroup/adjoint capabilities. To more fully utilize these capabilities, we review the applications of the Monte Carlo multigroup/adjoint method, describe how to generate multigroup cross sections for MCNP with the auxiliary CRSRD code, describe how to use the multigroup/adjoint capability in MCNP, and provide examples and results indicating the effectiveness and validity of the MCNP multigroup/adjoint treatment. This information should assist users in taking advantage of the MCNP multigroup/adjoint capabilities.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Tracking down the ENSO delayed oscillator with an adjoint OGCM
Van Oldenborgh, G J; Venzke, S; Eckert, C; Giering, R; Oldenborgh, Geert Jan van; Burgers, Gerrit; Venzke, Stephan; Eckert, Christian; Giering, Ralf
1997-01-01
The adjoint of an ocean general circulation model is used as a tool for investigating the causes of changes in ENSO SST indices. We identify adjoint Kelvin and Rossby waves in the sensitivities to sea level and wind stress at earlier times, which can be traced back for more than a year through western and weak eastern boundary reflections. Depending on the thermocline depth the first and second baroclinic modes are excited. The sensitivities to the heat flux and SST are local and decay in about a month. The sensitivities to the fluxes are converted into the influence of SST using the adjoint of a statistical atmosphere model. Focusing on SST perturbations in the index region itself, we recover, up to a scale factor, the delayed oscillator concept.
Nonlinear self-adjointness and conservation laws
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H, E-mail: nib@bth.se [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)
2011-10-28
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation u{sub t} - {Delta}u = 0 becomes strictly self-adjoint after multiplying by u{sup -1}. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems. (fast track communication)
Towards Global Adjoint Tomography
Bozdag, E.; Zhu, H.; Peter, D.; Tromp, J.
2012-04-01
Adjoint tomography based on 3D wave simulations provides new opportunities to improve tomographic images for the following reasons: 1) the full non-linearity of wave propagation may be taken into account in the forward problem, 2) 3D background models may be used to compute Fréchet kernels and, 3) seismic models may be updated in an iterative scheme. Our aim is to use this technique based on a spectral element method (Komatitsch & Tromp 2002) to obtain a global Earth model, which is becoming feasible with current computational facilities. To this end, we select 255 global CMT events distributed worldwide having moment magnitudes between 5.8 and 7. As a reference earth model, we use 3D transversely isotropic mantle model S362ANI (Kustowski et al. 2008) with 3D crustal model Crust2.0 (Bassin et al. 2000). In numerical simulations, Moho variations in Crust2.0 are honored if crustal thickness is less than 15 km or greater than 35 km to have a better sampling of the crustal model, particularly very thin oceanic crust. Using the advantages of numerical simulations, our strategy is to invert crustal and mantle structure together to avoid any bias introduced into upper-mantle images due to "crustal corrections", which are commonly used in classical tomography. Prior to the structure inversion, we reinvert global CMT solutions by computing Green functions in the 3D reference model to take into account effects of crustal variations on source parameters. Changes in source parameters are modest, but consistent with reported global CMT errors. In general, inversion results of selected earthquakes indicate a decrease in depth, particularly for ridge events, which can be up to 12 km, and a change in scalar moment of less than 30%. Event locations mostly change by less than 5 km. We use the updated CMT solutions to run forward simulations for adjoint tomography and plan to reinvert source parameters whenever we see a significant improvement in our tomographic model. 3D
Chen, Han
2016-01-01
Many control applications can be formulated as optimization constrained by conservation laws. Such optimization can be efficiently solved by gradient-based methods, where the gradient is obtained through the adjoint method. Traditionally, the adjoint method has not been able to be implemented in "gray-box" conservation law simulations. In gray-box simulations, the analytical and numerical form of the conservation law is unknown, but the space-time solution of relevant flow quantities is available. Without the adjoint gradient, optimization can be challenging for problems with many control variables. However, much information about the gray-box simulation is contained in its space-time solution, which motivates us to estimate the adjoint gradient by leveraging the space-time solution. This article considers a type of gray-box simulations where the flux function is partially unknown. A method is introduced to estimate the adjoint gradient at a cost independent of the number of control variables. The method firs...
Double-Difference Adjoint Tomography
Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen
2016-04-01
We introduce a double-difference method for the inversion of seismic wavespeed structure by adjoint tomography. Differences between seismic observations and model-based predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby largely canceling out the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher-resolution) structural variations in areas close to the stations. Whereas in conventional tomography, a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography, one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Quasi self-adjoint nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.s, E-mail: torrisi@dmi.unict.i, E-mail: tracina@dmi.unict.i [Dipartimento di Matematica e Informatica, University of Catania (Italy)
2010-11-05
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)
Adjoint Functors and Representation Dimensions
Institute of Scientific and Technical Information of China (English)
Chang Chang XI
2006-01-01
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
Aerospace Applications of Adjoint Theory
2010-01-01
program. Peterson [12], and later Howe [13] and Tarrant [14), illustrated how the method could be easily applied to the performance analysis of generic...Hill Book Company, New York, NY, 1965. [14] Tarrant , G.A., " The Method of Adjoint Systems and its Application to Guided Missile Noise Studies
Model adjointization and its cost
Institute of Scientific and Technical Information of China (English)
CHENG Qiang; ZHANG Linbo; WANG Bin
2004-01-01
In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) and in tools design, and does not require programs to be evenly separable but the cost in terms of operations count and memory is similar to methods using checkpointing. This article starts by summarizing the rules of adjointization and then presents the implementation of LPBD. Next, the definition of the separable program space, based on the fundamental assumptions (FA) of automatic differentiation, is given and the differentiation cost functions are derived. Also,two constants of fundamental importance in AD, σ and μ, are derived under FA. Under the assumption of even separability, the adjoint cost of simple and deep decomposition is subsequently discussed quantitatively using checkpointing. Finally, the adjoint costs in terms of operations count and memory through the LPBD method are shown to be uniformly dependent on the depth of structure or decomposition.
Self-adjointness of deformed unbounded operators
Energy Technology Data Exchange (ETDEWEB)
Much, Albert [Instituto de Ciencias Nucleares, UNAM, México D.F. 04510 (Mexico)
2015-09-15
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
The adjoint neutron transport equation and the statistical approach for its solution
Saracco, Paolo; Ravetto, Piero
2016-01-01
The adjoint equation was introduced in the early days of neutron transport and its solution, the neutron importance, has ben used for several applications in neutronics. The work presents at first a critical review of the adjoint neutron transport equation. Afterwards, the adjont model is constructed for a reference physical situation, for which an analytical approach is viable, i.e. an infinite homogeneous scattering medium. This problem leads to an equation that is the adjoint of the slowing-down equation that is well-known in nuclear reactor physics. A general closed-form analytical solution to such adjoint equation is obtained by a procedure that can be used also to derive the classical Placzek functions. This solution constitutes a benchmark for any statistical or numerical approach to the adjoint equation. A sampling technique to evaluate the adjoint flux for the transport equation is then proposed and physically interpreted as a transport model for pseudo-particles. This can be done by introducing appr...
Directory of Open Access Journals (Sweden)
Yaodeng Chen
2014-01-01
Full Text Available There are two different approaches on how to formulate adjoint numerical model (ANM. Aiming at the disputes arising from the construction methods of ANM, the differences between nonlinear shallow water equation and its adjoint equation are analyzed; the hyperbolicity and homogeneity of the adjoint equation are discussed. Then, based on unstructured meshes and finite volume method, a new adjoint model was advanced by getting numerical model of the adjoint equations directly. Using a gradient check, the correctness of the adjoint model was verified. The results of twin experiments to invert the bottom friction coefficient (Manning’s roughness coefficient indicate that the adjoint model can extract the observation information and produce good quality inversion. The reason of disputes about construction methods of ANM is also discussed in the paper.
Adjoint Error Estimation for Linear Advection
Energy Technology Data Exchange (ETDEWEB)
Connors, J M; Banks, J W; Hittinger, J A; Woodward, C S
2011-03-30
An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.
Energy Technology Data Exchange (ETDEWEB)
Curbelo, Jesus P.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: jperez@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-Graduacao em Modelagem Computacional; Hernandez, Carlos R.G., E-mail: cgh@instec.cu [Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2015-07-01
The spectral Green's function (SGF) method is a numerical method that is free of spatial truncation errors for slab-geometry fixed-source discrete ordinates (S{sub N}) adjoint problems. The method is based on the standard spatially discretized adjoint S{sub N} balance equations and a nonstandard adjoint auxiliary equation expressing the node-average adjoint angular flux, in each discretization node, as a weighted combination of the node-edge outgoing adjoint fluxes. The auxiliary equation contains parameters which act as Green's functions for the cell-average adjoint angular flux. These parameters are determined by means of a spectral analysis which yields the local general solution of the S{sub N} equations within each node of the discretization grid. In this work a number of advances in the SGF adjoint method are presented: the method is extended to adjoint S{sub N} problems considering linearly anisotropic scattering and non-zero prescribed boundary conditions for the forward source-detector problem. Numerical results to typical model problems are considered to illustrate the efficiency and accuracy of the o offered method. (author)
Hekmat, Mohamad Hamed; Mirzaei, Masoud
2015-01-01
In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced.
Adjoint method and runaway electron avalanche
Liu, Chang; Brennan, Dylan P.; Boozer, Allen H.; Bhattacharjee, Amitava
2017-02-01
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. 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.
Local fibred right adjoints are polynomial
DEFF Research Database (Denmark)
Kock, Anders; Kock, Joachim
2013-01-01
For any locally cartesian closed category E, we prove that a local fibred right adjoint between slices of E is given by a polynomial. The slices in question are taken in a well known fibred sense......For any locally cartesian closed category E, we prove that a local fibred right adjoint between slices of E is given by a polynomial. The slices in question are taken in a well known fibred sense...
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
On the adjoint operator in photoacoustic tomography
Arridge, Simon R.; Betcke, Marta M.; Cox, Ben T.; Lucka, Felix; Treeby, Brad E.
2016-11-01
Photoacoustic tomography (PAT) is an emerging biomedical imaging from coupled physics technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.
Double-difference adjoint seismic tomography
Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen
2016-09-01
We introduce a `double-difference' method for the inversion for seismic wave speed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings and systematic uncertainties. To alleviate the corresponding non-uniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and practically. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher resolution) structural variations in areas close to the stations. Whereas in conventional tomography a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.
ADGEN: ADjoint GENerator for computer models
Energy Technology Data Exchange (ETDEWEB)
Worley, B.A.; Pin, F.G.; Horwedel, J.E.; Oblow, E.M.
1989-05-01
This paper presents the development of a FORTRAN compiler and an associated supporting software library called ADGEN. ADGEN reads FORTRAN models as input and produces and enhanced version of the input model. The enhanced version reproduces the original model calculations but also has the capability to calculate derivatives of model results of interest with respect to any and all of the model data and input parameters. The method for calculating the derivatives and sensitivities is the adjoint method. Partial derivatives are calculated analytically using computer calculus and saved as elements of an adjoint matrix on direct assess storage. The total derivatives are calculated by solving an appropriate adjoint equation. ADGEN is applied to a major computer model of interest to the Low-Level Waste Community, the PRESTO-II model. PRESTO-II sample problem results reveal that ADGEN correctly calculates derivatives of response of interest with respect to 300 parameters. The execution time to create the adjoint matrix is a factor of 45 times the execution time of the reference sample problem. Once this matrix is determined, the derivatives with respect to 3000 parameters are calculated in a factor of 6.8 that of the reference model for each response of interest. For a single 3000 for determining these derivatives by parameter perturbations. The automation of the implementation of the adjoint technique for calculating derivatives and sensitivities eliminates the costly and manpower-intensive task of direct hand-implementation by reprogramming and thus makes the powerful adjoint technique more amenable for use in sensitivity analysis of existing models. 20 refs., 1 fig., 5 tabs.
Adjoint-Based Uncertainty Quantification with MCNP
Energy Technology Data Exchange (ETDEWEB)
Seifried, Jeffrey E. [Univ. of California, Berkeley, CA (United States)
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 in the simulation is acquired.
The Roots of Adjoint Polynomial of the Graphs Contain Triangles
Institute of Scientific and Technical Information of China (English)
YECheng-fu
2004-01-01
We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.
Dual of QCD with One Adjoint Fermion
DEFF Research Database (Denmark)
Mojaza, Matin; Nardecchia, Marco; Pica, Claudio;
2011-01-01
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the...
Development of CO2 inversion system based on the adjoint of the global coupled transport model
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
Chiral transition of fundamental and adjoint quarks
Energy Technology Data Exchange (ETDEWEB)
Capdevilla, R.M. [Instituto de Física Teórica, UNESP – Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070 São Paulo, SP (Brazil); Doff, A., E-mail: agomes@utfpr.edu.br [Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR (Brazil); Natale, A.A., E-mail: natale@ift.unesp.br [Instituto de Física Teórica, UNESP – Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070 São Paulo, SP (Brazil); Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil)
2014-01-20
The chiral symmetry breaking transition of quarks in the fundamental and adjoint representation is studied in a model where the gap equation contains two contributions, one containing a confining propagator and another corresponding to the exchange of one-dressed dynamically massive gluons. When quarks are in the fundamental representation the confinement effect dominates the chiral symmetry breaking while the gluon exchange is suppressed due to the dynamical gluon mass effect in the propagator and in the coupling constant. In this case the chiral and deconfinement transition temperatures are approximately the same. For quarks in the adjoint representation, due to the larger Casimir eigenvalue, the gluon exchange is operative and the chiral transition happens at a larger temperature than the deconfinement one.
Double-difference adjoint seismic tomography
Yuan, Yanhua O; Tromp, Jeroen
2016-01-01
We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relat...
Optimal Multistage Algorithm for Adjoint Computation
Energy Technology Data Exchange (ETDEWEB)
Aupy, Guillaume; Herrmann, Julien; Hovland, Paul; Robert, Yves
2016-01-01
We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.
Dual of QCD with One Adjoint Fermion
Mojaza, Matin; Pica, Claudio; Sannino, Francesco
2011-01-01
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the anomalous dimension of the Dirac fermion mass operator to be less than one in the conformal window.
Chiral phases of fundamental and adjoint quarks
Energy Technology Data Exchange (ETDEWEB)
Natale, A. A. [Centro de Ciências Naturais e Humanas, Universidade Federal do ABC 09210-170, Santo André, SP (Brazil); Instituto de Física Teórica - UNESP Rua Dr. Bento T. Ferraz, 271, Bl.II - 01140-070, São Paulo, SP (Brazil)
2016-01-22
We consider a QCD chiral symmetry breaking model where the gap equation contains an effective confining propagator and a dressed gluon propagator with a dynamically generated mass. This model is able to explain the ratios between the chiral transition and deconfinement temperatures in the case of fundamental and adjoint quarks. It also predicts the recovery of the chiral symmetry for a large number of quarks (n{sub f} ≈ 11 – 13) in agreement with lattice data.
Adjoint string breaking in the pseudoparticle approach
Szasz, Christian
2008-01-01
We apply the pseudoparticle approach to SU(2) Yang-Mills theory and perform a detailed study of the potential between two static charges for various representations. Whereas for charges in the fundamental representation we find a linearly rising confining potential, we clearly observe string breaking, when considering charges in the adjoint representation. We also demonstrate Casimir scaling and compute gluelump masses for different spin and parity. Numerical results are in qualitative agreement with lattice results.
Directory of Open Access Journals (Sweden)
D. A. Belikov
2015-07-01
Full Text Available We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA model that consists of the National Institute for Environmental Studies (NIES model as an Eulerian three-dimensional transport model (TM, and FLEXPART (FLEXible PARTicle dispersion model as the Lagrangian plume diffusion model (LPDM. The tangent and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving the performance of the computing, including MPI (Message Passing Interface. As results, the adjoint of Eulerian model is discrete. Construction of the adjoint of the Lagrangian component did not require any code modification, as LPDMs are able to track a significant number of particles back in time and thereby calculate the sensitivity of observations to the neighboring emissions areas. Eulerian and Lagrangian adjoint components were coupled at the time boundary in the global domain.The results are verified using a series of test experiments. The forward simulation shown the coupled model is effective in reproducing the seasonal cycle and short-term variability of CO2 even in the case of multiple limiting factors, such as high uncertainty of fluxes and the low resolution of the Eulerian model. The adjoint model demonstrates the high accuracy compared to direct forward sensitivity calculations and fast performance. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation.
Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander
2016-02-01
We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated
Supersymmetric Descendants of Self-Adjointly Extended Quantum Mechanical Hamiltonians
Al-Hashimi, M H; Shalaby, A; Wiese, U -J
2013-01-01
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.
Energy Technology Data Exchange (ETDEWEB)
Yoo, S.; Henderson, D.L. [Dept. of Medical Physics, Madison, WI (United States); Thomadsen, B.R. [Dept. of Medical Physics and Dept. of Human Oncology, Madison (United States)
2001-07-01
Interstitial brachytherapy is a type of radiation in which radioactive sources are implanted directly into cancerous tissue. Determination of dose delivered to tissue by photons emitted from implanted seeds is an important step in the treatment plan process. In this paper we will investigate the use of the discrete ordinates method and the adjoint method to calculate absorbed dose in the regions of interest. MIP (mixed-integer programming) is used to determine the optimal seed distribution that conforms the prescribed dose to the tumor and delivers minimal dose to the sensitive structures. The patient treatment procedure consists of three steps: (1) image acquisition with the transrectal ultrasound (TRUS) and assessing the region of interest, (2) adjoint flux computation with discrete ordinate code for inverse dose calculation, and (3) optimization with the MIP branch-and-bound method.
Generalized Uncertainty Principle and Self-Adjoint Operators
Balasubramanian, Venkat; Vagenas, Elias C
2014-01-01
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Generalized uncertainty principle and self-adjoint operators
Energy Technology Data Exchange (ETDEWEB)
Balasubramanian, Venkat, E-mail: vbalasu8@uwo.ca [Department of Applied Mathematics, University of Western Ontario London, Ontario N6A 5B7 (Canada); Das, Saurya, E-mail: saurya.das@uleth.ca [Theoretical Physics Group, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4 (Canada); Vagenas, Elias C., E-mail: elias.vagenas@ku.edu.kw [Theoretical Physics Group, Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)
2015-09-15
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Elementary operators on self-adjoint operators
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, .
Local Volatility Calibration Using An Adjoint Proxy
Directory of Open Access Journals (Sweden)
Gabriel TURINICI
2008-11-01
Full Text Available We document the calibration of the local volatility in a framework similar to Coleman, Li and Verma. The quality of a surface is assessed through a functional to be optimized; the specificity of the approach is to separate the optimization (performed with any suitable optimization algorithm from the computation of the functional where we use an adjoint (as in L. Jiang et. al. to obtain an approximation; moreover our main calibration variable is the implied volatility (the procedure can also accommodate the Greeks. The procedure performs well on benchmarks from the literature and on FOREX data.
Radiation source reconstruction with known geometry and materials using the adjoint
Energy Technology Data Exchange (ETDEWEB)
Hykes, Joshua M.; Azmy, Yousry Y., E-mail: jmhykes@ncsu.edu, E-mail: yyazmy@ncsu.gov [Department of Nuclear Engineering, North Carolina State University, Raleigh, NC (United States)
2011-07-01
We present a method to estimate an unknown isotropic source distribution, in space and energy, using detector measurements when the geometry and material composition are known. The estimated source distribution minimizes the difference between the measured and computed responses of detectors located at a selected number of points within the domain. In typical methods, a forward flux calculation is performed for each source guess in an iterative process. In contrast, we use the adjoint flux to compute the responses. Potential applications of the proposed method include determining the distribution of radio-contaminants following a nuclear event, monitoring the flow of radioactive fluids in pipes to determine hold-up locations, and retroactive reconstruction of radiation fields using workers' detectors' readings. After presenting the method, we describe a numerical test problem to demonstrate the preliminary viability of the method. As expected, using the adjoint flux reduces the number of transport solves to be proportional to the number of detector measurements, in contrast to methods using the forward flux that require a typically larger number proportional to the number of spatial mesh cells. (author)
Self-adjointness of the Gaffney Laplacian on Vector Bundles
Energy Technology Data Exchange (ETDEWEB)
Bandara, Lashi, E-mail: lashi.bandara@chalmers.se [Chalmers University of Technology and University of Gothenburg, Mathematical Sciences (Sweden); Milatovic, Ognjen, E-mail: omilatov@unf.edu [University of North Florida, Department of Mathematics and Statistics (United States)
2015-12-15
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Al-Hashimi, M.H., E-mail: hashimi@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Salman, M., E-mail: msalman@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Shalaby, A., E-mail: amshalab@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Physics Department, Faculty of Science, Mansoura University (Egypt); Wiese, U.-J., E-mail: wiese@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA (United States)
2013-10-15
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
On the product of the self-adjoint operators
Directory of Open Access Journals (Sweden)
Wulf Rehder
1982-01-01
Full Text Available A proof is given for the fact that the product of two self-adjoint operators, one of which is also positive, is again self-adjoint if and only if the product is normal. This theorem applies, in particular, if one operator is an orthogonal projection. In general, the positivity requirement cannot be dropped.
A reduced adjoint approach to variational data assimilation
Altaf, Muhammad
2013-02-01
The adjoint method has been used very often for variational data assimilation. The computational cost to run the adjoint model often exceeds several original model runs and the method needs significant programming efforts to implement the adjoint model code. The work proposed here is variational data assimilation based on proper orthogonal decomposition (POD) which avoids the implementation of the adjoint of the tangent linear approximation of the original nonlinear model. An ensemble of the forward model simulations is used to determine the approximation of the covariance matrix and only the dominant eigenvectors of this matrix are used to define a model subspace. The adjoint of the tangent linear model is replaced by the reduced adjoint based on this reduced space. Thus the adjoint model is run in reduced space with negligible computational cost. Once the gradient is obtained in reduced space it is projected back in full space and the minimization process is carried in full space. In the paper the reduced adjoint approach to variational data assimilation is introduced. The characteristics and performance of the method are illustrated with a number of data assimilation experiments in a ground water subsurface contaminant model. © 2012 Elsevier B.V.
Adjoint method for hybrid guidance loop state-space models
Weiss, M.; Bucco, D.
2015-01-01
A framework is introduced to develop the theory of the adjoint method for models including both continuous and discrete dynamics. The basis of this framework consists of the class of impulsive linear dynamic systems. It allows extension of the adjoint method to more general models that include multi
The compressible adjoint equations in geodynamics: equations and numerical assessment
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
Tsunami waveform inversion by adjoint methods
Pires, Carlos; Miranda, Pedro M. A.
2001-09-01
An adjoint method for tsunami waveform inversion is proposed, as an alternative to the technique based on Green's functions of the linear long wave model. The method has the advantage of being able to use the nonlinear shallow water equations, or other appropriate equation sets, and to optimize an initial state given as a linear or nonlinear function of any set of free parameters. This last facility is used to perform explicit optimization of the focal fault parameters, characterizing the initial sea surface displacement of tsunamigenic earthquakes. The proposed methodology is validated with experiments using synthetic data, showing the possibility of recovering all relevant details of a tsunami source from tide gauge observations, providing that the adjoint method is constrained in an appropriate manner. It is found, as in other methods, that the inversion skill of tsunami sources increases with the azimuthal and temporal coverage of assimilated tide gauge stations; furthermore, it is shown that the eigenvalue analysis of the Hessian matrix of the cost function provides a consistent and useful methodology to choose the subset of independent parameters that can be inverted with a given dataset of observations and to evaluate the error of the inversion process. The method is also applied to real tide gauge series, from the tsunami of the February 28, 1969, Gorringe Bank earthquake, suggesting some reasonable changes to the assumed focal parameters of that event. It is suggested that the method proposed may be able to deal with transient tsunami sources such as those generated by submarine landslides.
Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator
Weir, John
2008-01-01
We prove that the eigenvalues of a certain highly non-self-adjoint operator correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many eigenvalues which accumulate only at infinity.
Adjoint-based uncertainty quantification and sensitivity analysis for reactor depletion calculations
Stripling, Hayes Franklin
Depletion calculations for nuclear reactors model the dynamic coupling between the material composition and neutron flux and help predict reactor performance and safety characteristics. In order to be trusted as reliable predictive tools and inputs to licensing and operational decisions, the simulations must include an accurate and holistic quantification of errors and uncertainties in its outputs. Uncertainty quantification is a formidable challenge in large, realistic reactor models because of the large number of unknowns and myriad sources of uncertainty and error. We present a framework for performing efficient uncertainty quantification in depletion problems using an adjoint approach, with emphasis on high-fidelity calculations using advanced massively parallel computing architectures. This approach calls for a solution to two systems of equations: (a) the forward, engineering system that models the reactor, and (b) the adjoint system, which is mathematically related to but different from the forward system. We use the solutions of these systems to produce sensitivity and error estimates at a cost that does not grow rapidly with the number of uncertain inputs. We present the framework in a general fashion and apply it to both the source-driven and k-eigenvalue forms of the depletion equations. We describe the implementation and verification of solvers for the forward and ad- joint equations in the PDT code, and we test the algorithms on realistic reactor analysis problems. We demonstrate a new approach for reducing the memory and I/O demands on the host machine, which can be overwhelming for typical adjoint algorithms. Our conclusion is that adjoint depletion calculations using full transport solutions are not only computationally tractable, they are the most attractive option for performing uncertainty quantification on high-fidelity reactor analysis problems.
Gauge Mediation Models with Adjoint Messengers
Gogoladze, Ilia; Shafi, Qaisar; Un, Cem Salih
2016-01-01
We present a class of models in the framework of gauge mediation supersymmetry breaking where the messenger fields transform in the adjoint representation of the Standard Model gauge symmetry. To avoid unacceptably light right-handed sleptons in the spectrum we introduce a non-zero U(1)_B-L D-term. This leads to an additional contribution to the soft supersymmetry breaking mass terms which makes the right-handed slepton masses compatible with the current experimental bounds. We show that in this framework the observed 125 GeV Higgs boson mass can be accommodated with the sleptons accessible at the LHC, while the squarks and gluinos lie in the multi-TeV range. We also discuss the issue of the fine-tuning and show that the desired relic dark matter abundance can also be accommodated.
GPU-accelerated adjoint algorithmic differentiation
Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe
2016-03-01
Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the ;tape;. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.
Adjoint Networks with Inverting and Noninverting Current Conveyors
J. Cajka; T. Dostal; Vrba, K.
2000-01-01
Four types of second-generation current conveyors are shown. The realisation of the above conveyors using differential voltage current conveyors (VDCC) is presented. Two examples illustrate the building of adjoint networks containing second-generation current conveyors.
Adjoint method for the optimum planning of industrial pollutant sources
Institute of Scientific and Technical Information of China (English)
LIU Feng; HU Fei; ZHU Jiang
2005-01-01
The optimum planning of industrial pollutant sources, which optimizes the economic object without violating environmental constraints, is an important and hard task to be conquered. In this paper, an adjoint method is developed to solve the problem. The penalty function is introduced to deal with the environmental inequality constraints, and Lagrange function is constructed to derive the adjoint equation and the gradient of the object function. In this means, the gradient of the object function can be calculated by solving the adjoint equation, and the information from the gradient is used to make the object function descend and approach to an optimal solution after some iterations. A two-dimensional, simplified model is used for numerical experiments. The theoretical derivations are verified by the results of the experiments. Furthermore, the adjoint method is shown to be of excellent convergence and efficiency, which is adaptive to the fast development of air quality numerical models and super computers.
Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method
Directory of Open Access Journals (Sweden)
Khaled Gamal Eltohamy
2015-12-01
Full Text Available In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.
Self-Adjointness Criterion for Operators in Fock Spaces
Energy Technology Data Exchange (ETDEWEB)
Falconi, Marco, E-mail: marco.falconi@univ-rennes1.fr [Université de Rennes I, IRMAR and Centre Henri Lebesgue (France)
2015-12-15
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.
Optimizing Spectral Wave Estimates with Adjoint-Based Sensitivity Maps
2014-02-18
forecasts of nearshore wave conditions are important to a diverse constituency, including vacation destinations such as Miami Beach or San Diego, coastal...a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 18 FEB 2014 2. REPORT TYPE 3. DATES...Sensitivity maps for wave spectra For any type of adjoint, sensitivity maps may be constructed from adjoint output to track the response of system properties
Universal Racah matrices and adjoint knot polynomials: Arborescent knots
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.
Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
Mironov, A
2015-01-01
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 (SU_N) and Kauffman (SO_N) polynomials. For E_8 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 6x6 case. The adjoint polynomials do not distinguish between mutant...
Global adjoint tomography: first-generation model
Bozdağ, Ebru; Peter, Daniel; Lefebvre, Matthieu; Komatitsch, Dimitri; Tromp, Jeroen; Hill, Judith; Podhorszki, Norbert; Pugmire, David
2016-12-01
We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named `Titan', a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematically reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used `crustal corrections'. We used data from 253 earthquakes in the magnitude range 5.8 ≤ Mw ≤ 7.0. We started inversions by combining ˜30 s body-wave data with ˜60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ˜17 s body waves with ˜45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the resolution
Global adjoint tomography: first-generation model
Bozdağ, Ebru
2016-09-23
We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named \\'Titan\\', a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematically reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used \\'crustal corrections\\'. We used data from 253 earthquakes in the magnitude range 5.8 ≤ M ≤ 7.0. We started inversions by combining ~30 s body-wave data with ~60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ~17 s body waves with ~45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the
Flux tubes at Finite Temperature
Bicudo, Pedro; Cardoso, Marco
2016-01-01
We show the flux tubes produced by static quark-antiquark, quark-quark and quark-gluon charges at finite temperature. The sources are placed in the lattice with fundamental and adjoint Polyakov loops. We compute the square densities of the chromomagnetic and chromoelectric fields above and below the phase transition. Our results are gauge invariant and produced in pure gauge SU(3). The codes are written in CUDA and the computations are performed with GPUs.
Adjoint methods for aerodynamic wing design
Grossman, Bernard
1993-01-01
A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.
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.
Adjoint-based Optimal Flow Control for Compressible DNS
Otero, J Javier; Sandberg, Richard D
2016-01-01
A novel adjoint-based framework oriented to optimal flow control in compressible direct numerical simulations is presented. Also, a new formulation of the adjoint characteristic boundary conditions is introduced, which enhances the stability of the adjoint simulations. The flow configuration chosen as a case study consists of a two dimensional open cavity flow with aspect ratio $L/H=3$ and Reynolds number $Re=5000$. This flow configuration is of particular interest, as the turbulent and chaotic nature of separated flows pushes the adjoint approach to its limit. The target of the flow actuation, defined as cost, is the reduction of the pressure fluctuations at the sensor location. To exploit the advantages of the adjoint method, a large number of control parameters is used. The control consists of an actuating sub-domain where a two-dimensional body force is applied at every point within the sub-volume. This results in a total of $2.256 \\cdot 10^6$ control parameters. The final actuation achieved a successful ...
Adjoint inversion modeling of Asian dust emission using lidar observations
Directory of Open Access Journals (Sweden)
K. Yumimoto
2008-06-01
Full Text Available A four-dimensional variational (4D-Var data assimilation system for a regional dust model (RAMS/CFORS-4DVAR; RC4 is applied to an adjoint inversion of a heavy dust event over eastern Asia during 20 March–4 April 2007. The vertical profiles of the dust extinction coefficients derived from NIES Lidar network are directly assimilated, with validation using observation data. Two experiments assess impacts of observation site selection: Experiment A uses five Japanese observation sites located downwind of dust source regions; Experiment B uses these and two other sites near source regions. Assimilation improves the modeled dust extinction coefficients. Experiment A and Experiment B assimilation results are mutually consistent, indicating that observations of Experiment A distributed over Japan can provide comprehensive information related to dust emission inversion. Time series data of dust AOT calculated using modeled and Lidar dust extinction coefficients improve the model results. At Seoul, Matsue, and Toyama, assimilation reduces the root mean square differences of dust AOT by 35–40%. However, at Beijing and Tsukuba, the RMS differences degrade because of fewer observations during the heavy dust event. Vertical profiles of the dust layer observed by CALIPSO are compared with assimilation results. The dense dust layer was trapped at potential temperatures (θ of 280–300 K and was higher toward the north; the model reproduces those characteristics well. Latitudinal distributions of modeled dust AOT along the CALIPSO orbit paths agree well with those of CALIPSO dust AOT, OMI AI, and MODIS coarse-mode AOT, capturing the latitude at which AOTs and AI have high values. Assimilation results show increased dust emissions over the Gobi Desert and Mongolia; especially for 29–30 March, emission flux is about 10 times greater. Strong dust uplift fluxes over the Gobi Desert and Mongolia cause the heavy dust event. Total optimized dust emissions are 57
Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems
Garg, Vikram V
2014-09-27
Background Models based on the Helmholtz `slip\\' approximation are often used for the simulation of electroosmotic flows. The objectives of this paper are to construct adjoint-consistent formulations of such models, and to develop adjoint-based numerical tools for adaptive mesh refinement and parameter sensitivity analysis. Methods We show that the direct formulation of the `slip\\' model is adjoint inconsistent, and leads to an ill-posed adjoint problem. We propose a modified formulation of the coupled `slip\\' model, which is shown to be well-posed, and therefore automatically adjoint-consistent. Results Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional microfluidics problems. Conclusions An adjoint-consistent formulation for Helmholtz `slip\\' models of electroosmotic flows has been proposed. This formulation provides adjoint solutions that can be reliably used for mesh refinement and sensitivity analysis.
Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations
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Júlio Cesar Santos Sampaio
2014-01-01
Full Text Available The concepts of strictly, quasi, weak, and nonlinearly self-adjoint differential equations are revisited. A nonlinear self-adjoint classification of a class of equations with second and third order is carried out.
Approximation of weak adjoints by reverse automatic differentiation of BDF methods
Beigel, Dörte; Wirsching, Leonard; Bock, Hans Georg
2011-01-01
With this contribution, we shed light on the relation between the discrete adjoints of multistep backward differentiation formula (BDF) methods and the solution of the adjoint differential equation. To this end, we develop a functional-analytic framework based on a constrained variational problem and introduce the notion of weak adjoint solutions. We devise a finite element Petrov-Galerkin interpretation of the BDF method together with its discrete adjoint scheme obtained by reverse internal numerical differentiation. We show how the finite element approximation of the weak adjoint is computed by the discrete adjoint scheme and prove its asymptotic convergence in the space of normalized functions of bounded variation. We also obtain asymptotic convergence of the discrete adjoints to the classical adjoints on the inner time interval. Finally, we give numerical results for non-adaptive and fully adaptive BDF schemes. The presented framework opens the way to carry over the existing theory on global error estimat...
Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology
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.
Improving the Fit of a Land-Surface Model to Data Using its Adjoint
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.
Double-Difference Measurements in Global Adjoint Tomography
Orsvuran, Ridvan; Yuan, Yanhua; Lei, Wenjie; Bozdag, Ebru; Simons, Frederik J.; Tromp, Jeroen
2017-04-01
The adjoint method efficiently incorporates 3D seismic wave simulations and Fréchet kernels in seismic tomography, and has been successfully applied to exploration and global-scale imaging problems. It is well known that the success of inversions is closely tied to the chosen misfit function. The recently proposed double-difference (DD) method for adjoint inversions (Yuan et al. 2016) minimizes systematic errors in structural inversions related to source parameters, such as origin times, source time functions, etc. Moreover, since the DD method is based on differential measurements between station pairs, bias in structural inversions due to an uneven distribution of stations is also reduced. In this study, our aim is to take advantages of the DD method in real full-waveform inversion problems based on earthquake data. Our main focus is to demonstrate it at the global-scale adjoint tomography. To this end, we closely follow the global adjoint tomography strategies presented in Bozdag et al. (2016) and first consider extending phase misfits, such as multitaper cross-correlation measurements, to the DD approach. The major challenges are to reduce the computational cost of making differential measurements on every station pair and assimilating misfits of all phases in DD measurements. We have initiated the first tests with surface-wave data only. We explore how to incorporate body waves in double-difference adjoint tomography and implement various other misfits, such as instantaneous phase measurements, in the context of global inversions. We discuss how we can implement DD measurements into global adjoint tomography studies in a feasible way and present our initial results.
Searching for Standard Model Adjoint Scalars with Diboson Resonance Signatures
Carpenter, Linda M
2015-01-01
We explore the phenomenology of scalar fields in the adjoint representation of SM gauge groups. We write a general set of dimension 5 effective operators in which SM adjoint scalars couple to pairs of standard model bosons. Using these effective operators, we explore new possible decay channels of a scalar color octet into a gluon and a Z boson/ gluon and a photon. We recast several analyses from Run I of the LHC to find constraints on an a scalar octet decaying into these channels, and we project the discovery potential of color octets in our gluon+photon channel for the 14 TeV run of LHC.
On the Adjoint of a Strongly Continuous Semigroup
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Diómedes Bárcenas
2008-01-01
Full Text Available Using some techniques from vector integration, we prove the weak measurability of the adjoint of strongly continuous semigroups which factor through Banach spaces without isomorphic copy of l1; we also prove the strong continuity away from zero of the adjoint if the semigroup factors through Grothendieck spaces. These results are used, in particular, to characterize the space of strong continuity of {T**(t}t≥0, which, in addition, is also characterized for abstract L- and M-spaces. As a corollary, it is proven that abstract L-spaces with no copy of l1 are finite-dimensional.
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids
Christ, Michael
2010-01-01
It was proved independently by Foschi and Hundertmark, Zharnitsky that Gaussians extremize the adjoint Fourier restriction inequality for L^2 functions on the paraboloid in the two lowest-dimesional cases. Here we prove that Gaussians are critical points for the L^p to L^q adjoint Fourier restriction inequalities if and only if p=2. Also, Gaussians are critial points for the L^2 to L^r_t L^q_x Strichartz inequalities for all admissible pairs (r,q) in (1,infinity)^2.
High Order Adjoint Derivatives using ESDIRK Methods for Oil Reservoir Production Optimization
DEFF Research Database (Denmark)
Capolei, Andrea; Stenby, Erling Halfdan; Jørgensen, John Bagterp
2012-01-01
and continuous adjoints . The high order integration scheme allows larger time steps and therefore faster solution times. We compare gradient computation by the continuous adjoint method to the discrete adjoint method and the finite-difference method. The methods are implemented for a two phase flow reservoir...
Compressions of maximal dissipative and self-adjoint linear relations and of dilations
Azizov, T.Ya.; Dijksma, A.; Wanjala, G.
2013-01-01
In this paper we generalize results from Stenger (1968) [30], Nudelman (2011) [28] and Azizov and Dijksma (2012) [7] to maximal dissipative and self-adjoint linear relations and discuss related results for nonnegative self-adjoint extensions of nonnegative symmetric linear relations and self-adjoint
Hoteit, Ibrahim
2010-03-02
An eddy-permitting adjoint-based assimilation system has been implemented to estimate the state of the tropical Pacific Ocean. The system uses the Massachusetts Institute of Technology\\'s general circulation model and its adjoint. The adjoint method is used to adjust the model to observations by controlling the initial temperature and salinity; temperature, salinity, and horizontal velocities at the open boundaries; and surface fluxes of momentum, heat, and freshwater. The model is constrained with most of the available data sets in the tropical Pacific, including Tropical Atmosphere and Ocean, ARGO, expendable bathythermograph, and satellite SST and sea surface height data, and climatologies. Results of hindcast experiments in 2000 suggest that the iterated adjoint-based descent is able to significantly improve the model consistency with the multivariate data sets, providing a dynamically consistent realization of the tropical Pacific circulation that generally matches the observations to within specified errors. The estimated model state is evaluated both by comparisons with observations and by checking the controls, the momentum balances, and the representation of small-scale features that were not well sampled by the observations used in the assimilation. As part of these checks, the estimated controls are smoothed and applied in independent model runs to check that small changes in the controls do not greatly change the model hindcast. This is a simple ensemble-based uncertainty analysis. In addition, the original and smoothed controls are applied to a version of the model with doubled horizontal resolution resulting in a broadly similar “downscaled” hindcast, showing that the adjustments are not tuned to a single configuration (meaning resolution, topography, and parameter settings). The time-evolving model state and the adjusted controls should be useful for analysis or to supply the forcing, initial, and boundary conditions for runs of other models.
Äkäslompolo, S.; Bonheure, G.; Tardini, G.; Kurki-Suonio, T.; The ASDEX Upgrade Team
2015-10-01
The activation probe is a robust tool to measure flux of fusion products from a magnetically confined plasma. A carefully chosen solid sample is exposed to the flux, and the impinging ions transmute the material making it radioactive. Ultra-low level gamma-ray spectroscopy is used post mortem to measure the activity and, thus, the number of fusion products. This contribution presents the numerical analysis of the first measurement in the ASDEX Upgrade tokamak, which was also the first experiment to measure a single discharge. The ASCOT suite of codes was used to perform adjoint/reverse Monte Carlo calculations of the fusion products. The analysis facilitates, for the first time, a comparison of numerical and experimental values for absolutely calibrated flux. The results agree to within a factor of about two, which can be considered a quite good result considering the fact that all features of the plasma cannot be accounted in the simulations.Also an alternative to the present probe orientation was studied. The results suggest that a better optimized orientation could measure the flux from a significantly larger part of the plasma. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
Adjoint-based optimization of a foam EOR process
Namdar Zanganeh, M.; Kraaijevanger, J.F.B.M.; Buurman, H.W.; Jansen, J.D.; Rossen, W.R.
2012-01-01
We apply adjoint-based optimization to a Surfactant-Alternating-Gas foam process using a linear foam model introducing gradual changes in gas mobility and a nonlinear foam model giving abrupt changes in gas mobility as function of oil and water saturations and surfactant concentration. For the
Non-self-adjoint hamiltonians defined by Riesz bases
Energy Technology Data Exchange (ETDEWEB)
Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)
2014-03-15
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
Adjoint analysis of mixed continuous/discrete systems in simulink
Bucco, D.; Weiss, M.
2010-01-01
The adjoint simulation method is a well established and efficient tool for gaining insight and understanding of key parameters affecting the behaviour and performance of a guided missile homing system. Traditionally, the method has been employed by various missile companies during the preliminary an
Nefness of adjoint bundles for ample vector bundles
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Hidetoshi Maeda
1995-11-01
Full Text Available Let E be an ample vector bundle of rank >1 on a smooth complex projective variety X of dimension n. This paper gives a classification of pairs (X,E whose adjoint bundles K_X+det E are not nef in the case when r=n-2.
Adjoint analysis of mixed continuous/discrete systems in simulink
Bucco, D.; Weiss, M.
2010-01-01
The adjoint simulation method is a well established and efficient tool for gaining insight and understanding of key parameters affecting the behaviour and performance of a guided missile homing system. Traditionally, the method has been employed by various missile companies during the preliminary
Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling
Davis, B. N.; LeVeque, R. J.
2016-12-01
One difficulty in developing numerical methods for tsunami modeling is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain, particularly when tracking a tsunami propagating across the ocean. The open source GeoClaw software deals with this issue by using block-structured adaptive mesh refinement to selectively refine around propagating waves. For problems where only a target area of the total solution is of interest (e.g., one coastal community), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. In this work, we show that solving the time-dependent adjoint equation and using a suitable inner product with the forward solution allows more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and potentially for other tsunami applications beyond adaptive refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source GeoClaw software and present tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement.
On self-adjointness of singular Floquet Hamiltonians
DEFF Research Database (Denmark)
Duclos, Pierre; Jensen, Arne
2010-01-01
Schrödinger equations with time-dependent interactions are studied. We investigate how to define the Floquet Hamiltonian as a self-adjoint operator, when the interaction is singular in time or space. Using these results we establish the existence of a bounded propagator, by applying a result given...
Large-volume results in SU(2) with adjoint fermions
Del Debbio, Luigi; Pica, Claudio; Patella, Agostino; Rago, Antonio; Roman, Sabin
2014-01-01
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, and extrapolate to thermodynamic limit when possible.
Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"
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 sensitivity analysis of high frequency structures with Matlab
Bakr, Mohamed; Demir, Veysel
2017-01-01
This book covers the theory of adjoint sensitivity analysis and uses the popular FDTD (finite-difference time-domain) method to show how wideband sensitivities can be efficiently estimated for different types of materials and structures. It includes a variety of MATLAB® examples to help readers absorb the content more easily.
Large-volume results in SU(2) with adjoint fermions
DEFF Research Database (Denmark)
Del Debbio, Luigi; Lucini, Biagio; Pica, Claudio;
2013-01-01
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, an...
Finite volume effects in SU(2) with two adjoint fermions
DEFF Research Database (Denmark)
Del Debbio, Luigi; Lucini, Biagio; Patella, Agostino;
2011-01-01
Many evidences from lattice simulations support the idea that SU(2) with two Dirac flavors in the adjoint representation (also called Minimal Walking Technicolor) is IR conformal. A possible way to see this is through the behavior of the spectrum of the mass-deformed theory. When fermions are mas...
Toward regional-scale adjoint tomography in the deep earth
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
Energy Technology Data Exchange (ETDEWEB)
Hep, J.; Konecna, A.; Krysl, V.; Smutny, V. [Calculation Dept., Skoda JS plc, Orlik 266, 31606 Plzen (Czech Republic)
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 weighting 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
Äkäslompolo, Simppa; Tardini, Giovanni; Kurki-Suonio, Taina
2015-01-01
The activation probe is a robust tool to measure flux of fusion products from a magnetically confined plasma. A carefully chosen solid sample is exposed to the flux, and the impinging ions transmute the material makig it radioactive. Ultra-low level gamma-ray spectroscopy is used post mortem to measure the activity and, thus, the number of fusion products. This contribution presents the numerical analysis of the first measurement in the ASDEX Upgrade tokamak, which was also the first experiment to measure a single discharge. The ASCOT suite of codes was used to perform adjoint/reverse Monte-Carlo calculations of the fusion products. The analysis facilitated, for the first time, a comparison of numerical and experimental values for absolutely calibrated flux. The results agree to within 40%, which can be considered remarkable considering the fact that all features of the plasma cannot be accounted in the simulations. Also an alternative probe orientation was studied. The results suggest that a better optimized...
Adjoint optimal control problems for the RANS system
Attavino, A.; Cerroni, D.; Da Vià, R.; Manservisi, S.; Menghini, F.
2017-01-01
Adjoint optimal control in computational fluid dynamics has become increasingly popular recently because of its use in several engineering and research studies. However the optimal control of turbulent flows without the use of Direct Numerical Simulation is still an open problem and various methods have been proposed based on different approaches. In this work we study optimal control problems for a turbulent flow modeled with a Reynolds-Averaged Navier-Stokes system. The adjoint system is obtained through the use of a Lagrangian multiplier method by setting as objective of the control a velocity matching profile or an increase or decrease in the turbulent kinetic energy. The optimality system is solved with an in-house finite element code and numerical results are reported in order to show the validity of this approach.
Mitigation of Engine Inlet Distortion Through Adjoint-Based Design
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.
Three-Dimensional Turbulent RANS Adjoint-Based Error Correction
Park, Michael A.
2003-01-01
Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.
Nonself-adjoint semicrossed products by abelian semigroups
Fuller, Adam Hanley
2011-01-01
Let $\\mathcal{S}$ be the semigroup $\\mathcal{S}=\\sum^{\\oplus k}_{i=1}\\Sc{S}_i$, where for each $i\\in I$, $\\mathcal{S}_i$ is a countable subsemigroup of the additive semigroup $\\B{R}_+$ containing 0. We consider representations of $\\mathcal{S}$ as contractions $\\{T_s\\}_{s\\in\\mathcal{S}}$ on a Hilbert space with the Nica-covariance property: $T_s^*T_t=T_tT_s^*$ whenever $t\\wedge s=0$. We show that all such representations have a unique minimal isometric Nica-covariant dilation. This result is used to help analyse the nonself-adjoint semicrossed product algebras formed from Nica-covariant representations of the action of $\\mathcal{S}$ on an operator algebra $\\mathcal{A}$ by completely contractive endomorphisms. We conclude by calculating the $C^*$-envelope of the isometric nonself-adjoint semicrossed product algebra (in the sense of Kakariadis and Katsoulis).
Higher order self-adjoint operators with polynomial coefficients
Directory of Open Access Journals (Sweden)
Hassan Azad
2017-01-01
Full Text Available We study algebraic and analytic aspects of self-adjoint operators of order four or higher with polynomial coefficients. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain many examples up to order 8; similar examples can be constructed for all even order operators. In particular, a complete classification of all order 4 operators is given.
Arrangements, multiderivations, and adjoint quotient map of type ADE
Yoshinaga, Masahiko
2010-01-01
The first part of this paper is a survey on algebro-geometric aspects of sheaves of logarithmic vector fields of hyperplane arrangements. In the second part we prove that the relative de Rham cohomology (of degree two) of ADE-type adjoint quotient map is naturally isomorphic to the module of certain multiderivations. The isomorphism is obtained by the Gauss-Manin derivative of the Kostant-Kirillov form.
Monopole condensation in two-flavour Adjoint QCD
Cossu, G; Di Giacomo, A; Lacagnina, G; Pica, C
2008-01-01
In QCD with adjoint fermions (aQCD) the deconfining transition takes place at a lower temperature than the chiral transition. We study the two transitions by use of the Polyakov Loop, the monopole order parameter and the chiral condensate. The deconfining transition is first order, the chiral is a crossover. The order parameters for confinement are not affected by the chiral transition. We conclude that the degrees of freedom relevant to confinement are different from those describing chiral symmetry.
Hybrid Active Noise Control using Adjoint LMS Algorithms
Energy Technology Data Exchange (ETDEWEB)
Nam, Hyun Do; Hong, Sik Ki [Dankook University (Korea, Republic of)
1998-07-01
A multi-channel hybrid active noise control(MCHANC) is derived by combining hybrid active noise control techniques and adjoint LMS algorithms, and this algorithm is applied to an active noise control system in a three dimensional enclosure. A MCHANC system uses feed forward and feedback filters simultaneously to cancel noises in an enclosure. The adjoint LMs algorithm, in which the error is filtered through an adjoint filter of the secondary channel, is also used to reduce the computational burden of adaptive filters. The overall attenuation performance and convergence characteristics of MCHANC algorithm is better than both multiple-channel feed forward algorithms and multiple-channel feedback algorithms. In a large enclosure, the acoustic reverberation can be very long, which means a very high order feed forward filter must be used to cancel the reverberation noises. Strong reverberation noises are generally narrow band and low frequency, which can be effectively predicted and canceled by a feedback adaptive filters. So lower order feed forward filter taps can be used in MCHANC algorithm which combines advantages of fast convergence and small excess mean square error. In this paper, computer simulations and real time implementations is carried out on a TMS320C31 processor to evaluate the performance of the MCHANC systems. (author). 11 refs., 11 figs., 1 tab.
Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle
Energy Technology Data Exchange (ETDEWEB)
Peplow, Douglas E. [ORNL; Mosher, Scott W [ORNL; Evans, Thomas M [ORNL
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. CADIS 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.
Adjoint based sensitivity analysis of a reacting jet in crossflow
Sashittal, Palash; Sayadi, Taraneh; Schmid, Peter
2016-11-01
With current advances in computational resources, high fidelity simulations of reactive flows are increasingly being used as predictive tools in various industrial applications. In order to capture the combustion process accurately, detailed/reduced chemical mechanisms are employed, which in turn rely on various model parameters. Therefore, it would be of great interest to quantify the sensitivities of the predictions with respect to the introduced models. Due to the high dimensionality of the parameter space, methods such as finite differences which rely on multiple forward simulations prove to be very costly and adjoint based techniques are a suitable alternative. The complex nature of the governing equations, however, renders an efficient strategy in finding the adjoint equations a challenging task. In this study, we employ the modular approach of Fosas de Pando et al. (2012), to build a discrete adjoint framework applied to a reacting jet in crossflow. The developed framework is then used to extract the sensitivity of the integrated heat release with respect to the existing combustion parameters. Analyzing the sensitivities in the three-dimensional domain provides insight towards the specific regions of the flow that are more susceptible to the choice of the model.
Unsteady adjoint of pressure loss for a fundamental transonic turbine vane
Talnikar, Chaitanya; Laskowski, Gregory M
2015-01-01
High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design optimization in these aerodynamic applications. In this paper we present unsteady adjoint solutions using a large eddy simulation model for a vane from VKI using aerothermal objectives. The unsteady adjoint method is effective in capturing the gradient for a short time interval aerothermal objective, whereas the method provides diverging gradients for long time-averaged thermal objectives. As the boundary layer on the suction side near the trailing edge of the vane is turbulent, it poses a challenge for the adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially from the trailing edge region when solved backwards in time. This results in the corruption of the sensitivities obtained from the adjoint solutions. An energy analysis of the unstea...
Mehdi Delkhosh; Mohammad Delkhosh
2012-01-01
Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011). In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefited from the solution of numerical Self-adjoint equations (Mohynl-Din, 2009; Allame and Azal, 2011;...
Nasser, Mohamed M. S.; Murid, Ali H. M.; Sangawi, Ali W. K.
2013-01-01
This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a boundary integral equation with the adjoint generalized Neumann kernel for the derivative of the boundary...
Development and Applications of the FV3 GEOS-5 Adjoint Modeling System
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.
Adjoint complement to viscous finite-volume pressure-correction methods
Stück, Arthur; Rung, Thomas
2013-09-01
A hybrid-adjoint Navier-Stokes method for the pressure-based computation of hydrodynamic objective functional derivatives with respect to the shape is systematically derived in three steps: The underlying adjoint partial differential equations and boundary conditions for the frozen-turbulence Reynolds-averaged Navier-Stokes equations are considered in the first step. In step two, the adjoint discretisation is developed from the primal, unstructured finite-volume discretisation, such that adjoint-consistent approximations to the adjoint partial differential equations are obtained following a so-called hybrid-adjoint approach. A unified, discrete boundary description is outlined that supports high- and low-Reynolds number turbulent wall-boundary treatments for both the adjoint boundary condition and the boundary-based gradient formula. The third component focused in the development of the industrial adjoint CFD method is the adjoint counterpart to the primal pressure-correction algorithm. The approach is verified against the direct-differentiation method and an application to internal flow problems is presented.
Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver
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.
On adjoint symmetry equations, integrating factors and solutions of nonlinear ODEs
Energy Technology Data Exchange (ETDEWEB)
Guha, Partha [Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig (Germany); Choudhury, A Ghose [Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta-700 009 (India); Khanra, Barun [Sailendra Sircar Vidyalaya, 62A Shyampukur Street, Calcutta-700 004 (India)], E-mail: partha.guha@mis.mpg.de, E-mail: a_ghosechoudhury@rediffmail.com, E-mail: barunkhanra@rediffmail.com
2009-03-20
We consider the role of the adjoint equation in determining explicit integrating factors and first integrals of nonlinear ODEs. In Chandrasekar et al (2006 J. Math. Phys. 47 023508), the authors have used an extended version of the Prelle-Singer method for a class of nonlinear ODEs of the oscillator type. In particular, we show that their method actually involves finding a solution of the adjoint symmetry equation. Next, we consider a coupled second-order nonlinear ODE system and derive the corresponding coupled adjoint equations. We illustrate how the coupled adjoint equations can be solved to arrive at a first integral.
Hot QCD, k-strings and the adjoint monopole gas model
Altes, C P K; Altes, Chris P. Korthals; Meyer, Harvey B.
2005-01-01
When the magnetic sector of hot QCD, 3D SU(N) Yang-Mills theory, is described as a dilute gas of non-Abelian monopoles in the adjoint representation of the magnetic group, Wilson loops of N-ality k are known to obey a periodic k(N-k) law. Lattice simulations have confirmed this prediction to a few percent for N=4 and 6. We describe in detail how the magnetic flux of the monopoles produces different area laws for spatial Wilson k-loops. A simple physical argument is presented, why the predicted and observed Casimir scaling is allowed in the large-N limit by usual power-counting arguments. The same scaling is also known to hold in two-loop perturbation theory for the spatial 't Hooft loop, which measures the electric flux. We then present new lattice data for 3D N=8 k-strings as long as 3`fm' that provide further confirmation. Finally we suggest new tests in theories with spontaneous breaking and in SO(4n+2) gauge groups.
Adjoint optimization of natural convection problems: differentially heated cavity
Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.
2016-06-01
Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here
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.
On the Norm Convergence of the Self-Adjoint Trotter–Kato Product Formula with Error Bound
Indian Academy of Sciences (India)
Takashi Ichinose; Hideo Tamura
2002-02-01
The norm convergence of the Trotter–Kato product formula with error bound is shown for the semigroup generated by that operator sum of two nonnegative self-adjoint operators and which is self-adjoint.
Self-adjoint Extensions for the Neumann Laplacian and Applications
Institute of Scientific and Technical Information of China (English)
S. A. NAZAROV; J. SOKO(L)OWSKI
2006-01-01
A new technique is proposed for the analysis of shape optimization problems. The technique uses the asymptotic analysis of boundary value problems in singularly perturbed geometrical domains. The asymptotics of solutions are derived in the framework of compound and matched asymptotics expansions. The analysis involves the so-called interior topology variations. The asymptotic expansions are derived for a model problem, however the technique applies to general elliptic boundary value problems. The self-adjoint extensions of elliptic operators and the weighted spaces with detached asymptotics are exploited for the modelling of problems with small defects in geometrical domains. The error estimates for proposed approximations of shape functionals are provided.
Earthquake Source Modeling using Time-Reversal or Adjoint Methods
Hjorleifsdottir, V.; Liu, Q.; Tromp, J.
2007-12-01
In recent years there have been great advances in earthquake source modeling. Despite the effort, many questions about earthquake source physics remain unanswered. In order to address some of these questions, it is useful to reconstruct what happens on the fault during an event. In this study we focus on determining the slip distribution on a fault plane, or a moment-rate density, as a function of time and space. This is a difficult process involving many trade offs between model parameters. The difficulty lies in the fact that earthquakes are not a controlled experiment, we don't know when and where they will occur, and therefore we have only limited control over what data will be acquired for each event. As a result, much of the advance that can be made, is by extracting more information out of the data that is routinely collected. Here we use a technique that uses 3D waveforms to invert for the slip on a fault plane during rupture. By including 3D wave-forms we can use parts of the wave-forms that are often discarded, as they are altered by structural effects in ways that cannot be accurately predicted using 1D Earth models. However, generating 3D synthetic is computationally expensive. Therefore we turn to an `adjoint' method (Tarantola Geoph.~1984, Tromp et al.~GJI 2005), that reduces the computational cost relative to methods that use Green's function libraries. In it's simplest form an adjoint method for inverting for source parameters can be viewed as a time-reversal experiment performed with a wave-propagation code (McMechan GJRAS 1982). The recorded seismograms are inserted as simultaneous sources at the location of the receiver and the computed wave field (which we call the adjoint wavefield) is recorded on an array around the earthquake location. Here we show, mathematically, that for source inversions for a moment tensor (distributed) source, the time integral of the adjoint strain is the quantity to monitor. We present the results of time
Bimetric Gravity From Adjoint Frame Field In Four Dimensions
Guo, Zhi-Qiang
2015-01-01
We provide a novel model of gravity by using adjoint frame fields in four dimensions. It has a natural interpretation as a gravitational theory of a complex metric field, which describes interactions between two real metrics. The classical solutions establish three appealing features. The spherical symmetric black hole solution has an additional hair, which includes the Schwarzschild solution as a special case. The de Sitter solution is realized without introducing a cosmological constant. The constant flat background breaks the Lorentz invariance spontaneously, although the Lorentz breaking effect can be localized to the second metric while the first metric still respects the Lorentz invariance.
Advances in Global Adjoint Tomography -- Massive Data Assimilation
Ruan, Y.; Lei, W.; Bozdag, E.; Lefebvre, M. P.; Smith, J. A.; Krischer, L.; Tromp, J.
2015-12-01
Azimuthal anisotropy and anelasticity are key to understanding a myriad of processes in Earth's interior. Resolving these properties requires accurate simulations of seismic wave propagation in complex 3-D Earth models and an iterative inversion strategy. In the wake of successes in regional studies(e.g., Chen et al., 2007; Tape et al., 2009, 2010; Fichtner et al., 2009, 2010; Chen et al.,2010; Zhu et al., 2012, 2013; Chen et al., 2015), we are employing adjoint tomography based on a spectral-element method (Komatitsch & Tromp 1999, 2002) on a global scale using the supercomputer ''Titan'' at Oak Ridge National Laboratory. After 15 iterations, we have obtained a high-resolution transversely isotropic Earth model (M15) using traveltime data from 253 earthquakes. To obtain higher resolution images of the emerging new features and to prepare the inversion for azimuthal anisotropy and anelasticity, we expanded the original dataset with approximately 4,220 additional global earthquakes (Mw5.5-7.0) --occurring between 1995 and 2014-- and downloaded 300-minute-long time series for all available data archived at the IRIS Data Management Center, ORFEUS, and F-net. Ocean Bottom Seismograph data from the last decade are also included to maximize data coverage. In order to handle the huge dataset and solve the I/O bottleneck in global adjoint tomography, we implemented a python-based parallel data processing workflow based on the newly developed Adaptable Seismic Data Format (ASDF). With the help of the data selection tool MUSTANG developed by IRIS, we cleaned our dataset and assembled event-based ASDF files for parallel processing. We have started Centroid Moment Tensors (CMT) inversions for all 4,220 earthquakes with the latest model M15, and selected high-quality data for measurement. We will statistically investigate each channel using synthetic seismograms calculated in M15 for updated CMTs and identify problematic channels. In addition to data screening, we also modified
Large-N reduction with adjoint Wilson fermions
Bringoltz, Barak; Sharpe, Stephen R
2012-01-01
We analyze the large-N behavior of SU(N) lattice gauge theories with adjoint fermions by studying volume-reduced models, as pioneered by Eguchi and Kawai. We perform simulations on a single-site lattice for Nf = 1 and Nf = 2 Wilson Dirac fermions with values of N up to 53. We show for both values of Nf that in the large-N limit there is a finite region, containing both light and heavy fermions, of unbroken center symmetry where the theory exhibits volume independence. Using large-N reduction we attempt to calculate physical quantities such as the string tension and meson masses.
Mass anomalous dimension in SU(2) with two adjoint fermions
Bursa, Francis; Keegan, Liam; Pica, Claudio; Pickup, Thomas
2009-01-01
We study SU(2) lattice gauge theory with two flavours of Dirac fermions in the adjoint representation. We measure the running of the coupling in the Schroedinger Functional (SF) scheme and find it is consistent with the existence of an infrared fixed point (IRFP). We discuss how systematic errors affect the evidence for an IRFP. We present the first measurement of the running of the mass in the SF scheme. Assuming the existence of a fixed point, we can deduce the anomalous dimension at the fixed point. At the current level of accuracy, we can estimate 0.05 < gamma < 0.56 at the IRFP.
Monopole condensation in two-flavour Adjoint QCD
Cossu, G; Di Giacomo, Adriano; Lacagnina, G; Pica, C
2006-01-01
Two distinct phase transitions occur at different temperatures in QCD with adjoint fermions (aQCD): deconfinement and chiral symmetry restoration. In this model, quarks do no explicitely break the center Z(3) symmetry and therefore the Polyakov loop is a good order parameter for the deconfinement transition. We study monopole condensation by inspecting the expectation value of an operator which creates a monopole. Such a quantity is expected to be an order parameter for the deconfinement transition as in the case of fundamental fermions.
QCD thermodynamics from 3d adjoint Higgs model
Karsch, Frithjof; Patkós, András; Petreczky, P; Szép, Z; Szep, Zs.
1998-01-01
The screening masses of hot SU(N) gauge theory, defined as poles of the corresponding propagators are studied in 3d adjoint Higgs model, considered as an effective theory of QCD, using coupled gap equations and lattice Monte-Carlo simulations (for N=2). Using so-called lambda gauges non-perturbative evidence for gauge independence of the pole masses within this class of gauges is given. A possible application of the screening masses for the resummation of the free energy is discussed.
Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions
Akgun, Mehmet A.; Haftka, Raphael T.
2000-01-01
The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local
Challenges in adjoint-based well location optimization when using well models
Ashoori, E.; Jansen, J.D.
2015-01-01
There is a general consensus that the most efficient method for large-scale well location optimization is gradient-based with gradients computed with an adjoint formulation. Handels et al. (2007) (later published in journal form as Zandvliet et al., 2008), were the first to use the adjoint method fo
Comparison of the Monte Carlo adjoint-weighted and differential operator perturbation methods
Energy Technology Data Exchange (ETDEWEB)
Kiedrowski, Brian C [Los Alamos National Laboratory; Brown, Forrest B [Los Alamos National Laboratory
2010-01-01
Two perturbation theory methodologies are implemented for k-eigenvalue calculations in the continuous-energy Monte Carlo code, MCNP6. A comparison of the accuracy of these techniques, the differential operator and adjoint-weighted methods, is performed numerically and analytically. Typically, the adjoint-weighted method shows better performance over a larger range; however, there are exceptions.
The state-space approach to the method of adjoints for hybrid guidance loop models
Weiss, M.; Bucco, D.
2009-01-01
A framework is introduced to develop the theory of the Adjoint Method for models including both continuous and discrete dynamics. The basis of this framework consists of the class of impulsive linear dynamical systems. It allows extension of the Adjoint Method to more general models that include mul
Adjoint-based approach to Enhancing Mixing in Rayleigh-Taylor Turbulence
Kord, Ali; Capecelatro, Jesse
2016-11-01
A recently developed adjoint method for multi-component compressible flow is used to measure sensitivity of the mixing rate to initial perturbations in Rayleigh-Taylor (RT) turbulence. Direct numerical simulations (DNS) of RT instabilities are performed at moderate Reynolds numbers. The DNS are used to provide an initial prediction, and the corresponding space-time discrete-exact adjoint provides a sensitivity gradient for a specific quantity of interest (QoI). In this work, a QoI is defined based on the time-integrated scalar field to quantify the mixing rate. Therefore, the adjoint solution is used to measure sensitivity of this QoI to a set of initial perturbations, and inform a gradient-based line search to optimize mixing. We first demonstrate the adjoint approach in the linear regime and compare the optimized initial conditions to the expected values from linear stability analysis. The adjoint method is then used in the high Reynolds number limit where theory is no longer valid. Finally, chaos is known to contaminate the accuracy of the adjoint gradient in turbulent flows when integrated over long time horizons. We assess the influence of chaos on the accuracy of the adjoint gradient to guide the work of future studies on adjoint-based sensitivity of turbulent mixing. PhD Student, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI.
On rational R-matrices with adjoint SU(n) symmetry
Stronks, Laurens; Schuricht, Dirk
2016-01-01
Using the representation theory of Yangians we construct the rational R-matrix which takes values in the adjoint representation of SU(n). From this we derive an integrable SU(n) spin chain with lattice spins transforming under the adjoint representation. However, the resulting Hamiltonian is found to be non-Hermitian.
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
Directory of Open Access Journals (Sweden)
Tamás Fülöp
2007-11-01
Full Text Available For a class of singular potentials, including the Coulomb potential (in three and less dimensions and $V(x = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the self-adjoint version chosen. The article discusses how the self-adjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different self-adjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations.
On the Self-adjointness of the Product Operators of Two mth-Order Differential Operators on [0, +∞)
Institute of Scientific and Technical Information of China (English)
Jian Ye AN; Jiong SUN
2004-01-01
In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, +∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.
Self-adjoint oscillator operator from a modified factorization
Energy Technology Data Exchange (ETDEWEB)
Reyes, Marco A. [Departamento de Fisica, DCI Campus Leon, Universidad de Guanajuato, Apdo. Postal E143, 37150 Leon, Gto. (Mexico); Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Gutierrez, M. Ranferi [Departamento de Fisica, DCI Campus Leon, Universidad de Guanajuato, Apdo. Postal E143, 37150 Leon, Gto. (Mexico)
2011-05-30
By using an alternative factorization, we obtain a self-adjoint oscillator operator of the form L{sub δ}=d/(dx) (p{sub δ}(x)d/(dx) )-((x{sup 2})/(p{sub δ}(x)) +p{sub δ}(x)-1), where p{sub δ}(x)=1+δe{sup -x{sup 2}}, with δ element of (-1,∞) an arbitrary real factorization parameter. At positive values of δ, this operator interpolates between the quantum harmonic oscillator Hamiltonian for δ=0 and a scaled Hermite operator at high values of δ. For the negative values of δ, the eigenfunctions look like deformed quantum mechanical Hermite functions. Possible applications are mentioned. -- Highlights: → We present a generalization of the Mielnik factorization. → We study the case of linear relationship between the factorization coefficients. → We introduce a new one-parameter self-adjoint oscillator operator. → We show its properties depending on the values of the parameter.
Adjoint $SU(5)$ GUT model with $T_{7}$ flavor symmetry
Arbeláez, Carolina; Kovalenko, Sergey; Schmidt, Iván
2015-01-01
We propose an adjoint $SU(5)$ GUT model with a $T_{7}$ family symmetry and an extra $Z_{2}\\otimes Z_{2}^{\\prime }\\otimes Z_{3}\\otimes Z_{4}\\otimes Z_{12}$ discrete group, that successfully describes the prevailing Standard Model (SM) fermion mass and mixing pattern. The observed hierarchy of the charged fermion masses and the quark mixing angles arises from the $Z_{3}\\otimes Z_{4}\\otimes Z_{12}$ symmetry breaking, which occurs near the GUT scale. The light active neutrino masses are generated by type I and type III seesaw mechanisms mediated by the fermionic $SU(5)$ singlet and the adjoint $\\mathbf{24}$-plet. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be $m_{\\beta \\beta }=$ 4 and 50 meV for the normal and the inverted neutrino spectrum, respectively. We construct several benchmark scenarios, which lead to $SU(5)$ gauge coupling unification and are compatible with the known phenomenological constraints originating from the lightness of neutrinos, prot...
Adjoint-Based Forecast Error Sensitivity Diagnostics in Data Assimilation
Langland, R.; Daescu, D.
2016-12-01
We present an up-to-date review of the adjoint-data assimilation system (DAS) approach to evaluate the forecast sensitivity to error covariance parameters and provide guidance to flow-dependent adaptive covariance tuning (ACT) procedures. New applications of the forecast sensitivity to observation error covariance (FSR) are investigated including the sensitivity to observation error correlations and a priori first-order assessment to the error correlation impact on the forecasts. Issues related to ambiguities in the a posteriori estimation to the observation error covariance (R) and background error covariance (B) are discussed. A synergistic framework to adaptive covariance tuning is considered that combines R-estimates derived from a posteriori covariance diagnosis and FSR derivative information. The evaluation of the forecast sensitivity to the innovation-weight coefficients is introduced as a computationally-feasible approach to account for the characteristics of both R- and B-parameters and perform direct tuning of the DAS gain operator (K). Theoretical aspects are discussed and recent results are provided with the adjoint versions of the Naval Research Laboratory Atmospheric Variational Data Assimilation System-Accelerated Representer (NAVDAS-AR).
Haydock's recursive solution of self-adjoint problems. Discrete spectrum
Moroz, Alexander
2014-12-01
Haydock's recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber's quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock's recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials {pn(E) } in energy variable E. The polynomials {pn(E) } are orthonormal with respect to the density of states n0(E) and energy eigenstate | E > is the generating function of {pn(E) } . The generality of Haydock's recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.
Adjoint operators and perturbation theory of black holes
Cartas-Fuentevilla, R
2000-01-01
We present a new approach for finding conservation laws in the perturbation theory of black holes which applies for the more general cases of non-Hermitian equations governing the perturbations. The approach is based on a general result which establishes that a covariantly conserved current can be obtained from a solution of any system of homogeneous linear differential equations and a solution of the adjoint system. It is shown that the results obtained from the present approach become essentially the same (with some diferences) to those obtained by means of the traditional methods in the simplest black hole geometry corresponding to the Schwarzschild space-time. The future applications of our approach for studying the perturbations of black hole space-time in string theory is discussed.
Adjoint Fokker-Planck equation and runaway electron dynamics
Liu, Chang; Boozer, Allen H; Bhattacharjee, Amitava
2016-01-01
A new method to obtain the runaway probability and the expected slowing-down time for runaway electrons is developed, by solving the adjoint Fokker-Planck equation in momentum space. The runaway probability function has a smooth transition at the runaway separatrix, which can be attributed to the effect of the pitch angle scattering term in the kinetic equation. The expected slowing-down time gives a new way to estimate the runaway current decay time in experiments. The result shows that the decay rate of high energy electron is very slow when E is close to the critical electric field, which helps elucidate the hysteresis effect seen in the runaway electron population. Given the same numerical accuracy, the new method is more efficient than the Monte Carlo simulation.
Self-adjoint integral operator for bounded nonlocal transport
Maggs, J. E.; Morales, G. J.
2016-11-01
An integral operator is developed to describe nonlocal transport in a one-dimensional system bounded on both ends by material walls. The "jump" distributions associated with nonlocal transport are taken to be Lévy α -stable distributions, which become naturally truncated by the bounding walls. The truncation process results in the operator containing a self-consistent, convective inward transport term (pinch). The properties of the integral operator as functions of the Lévy distribution parameter set [α ,γ ] and the wall conductivity are presented. The integral operator continuously recovers the features of local transport when α =2 . The self-adjoint formulation allows for an accurate description of spatial variation in the Lévy parameters in the nonlocal system. Spatial variation in the Lévy parameters is shown to result in internally generated flows. Examples of cold-pulse propagation in nonlocal systems illustrate the capabilities of the methodology.
Finite volume effects in SU(2) with two adjoint fermions
Patella, Agostino; Lucini, Biagio; Pica, Claudio; Rago, Antonio
2011-01-01
Many evidences from lattice simulations support the idea that SU(2) with two Dirac flavors in the adjoint representation (also called Minimal Walking Technicolor) is IR conformal. A possible way to see this is through the behavior of the spectrum of the mass-deformed theory. When fermions are massive, a mass-gap is generated and the theory is confined. IR-conformality is recovered in the chiral limit: masses of particles vanish in the chiral limit, while their ratios stay finite. In order to trust this analysis one has to relay on the infinite volume extrapolation. We will discuss the finite volume effects on the mesonic spectrum, investigated by varying the size of the lattice and by changing the boundary conditions for the fields.
Adjoint Assimilation in Marine Ecosystem Models and an Example of Application
Institute of Scientific and Technical Information of China (English)
XU Qing; LIU Yuguang; L(U) Xianqing
2005-01-01
This paper aims at a review of the work carried out to date on the adjoint assimilation of data in marine ecosystem models since 1995. The structure and feature of the adjoint assimilation in marine ecosystem models are also introduced.To illustrate the application of the adjoint technique and its merits, a 4-variable ecosystem model coupled with a 3-D physical model is established for the Bohai Sea and the Yellow Sea. The chlorophyll concentration data derived from the SeaWiFS ocean colour data are assimilated in the model with the technique. Some results are briefly presented.
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.
Directory of Open Access Journals (Sweden)
Mehdi Delkhosh
2012-01-01
Full Text Available Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011. In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefited from the solution of numerical Self-adjoint equations (Mohynl-Din, 2009; Allame and Azal, 2011; Borhanifar et al. 2011; Sweilam and Nagy, 2011; Gülsu et al. 2011; Mohyud-Din et al. 2010; and Li et al. 1996.
Quantum cosmology of scalar-tensor theories and self-adjointness
Almeida, C R; Fabris, J C; Moniz, P V
2016-01-01
In this paper, the problem of the self-adjointness for the case of a quantum minisuperspace Hamiltonian retrieved from a Brans-Dicke (BD) action is investigated. Our matter content is presented in terms of a perfect fluid, onto which the Schutz's formalism will be applied. We use the von Neumann theorem and the similarity with the Laplacian operator in one of the variables to determine the cases where the Hamiltonian is self-adjoint and if it admits self-adjoint extensions. For the latter, we study which extension is physically more suitable.
An Adjoint-Based Adaptive Ensemble Kalman Filter
Song, Hajoon
2013-10-01
A new hybrid ensemble Kalman filter/four-dimensional variational data assimilation (EnKF/4D-VAR) approach is introduced to mitigate background covariance limitations in the EnKF. The work is based on the adaptive EnKF (AEnKF) method, which bears a strong resemblance to the hybrid EnKF/three-dimensional variational data assimilation (3D-VAR) method. In the AEnKF, the representativeness of the EnKF ensemble is regularly enhanced with new members generated after back projection of the EnKF analysis residuals to state space using a 3D-VAR [or optimal interpolation (OI)] scheme with a preselected background covariance matrix. The idea here is to reformulate the transformation of the residuals as a 4D-VAR problem, constraining the new member with model dynamics and the previous observations. This should provide more information for the estimation of the new member and reduce dependence of the AEnKF on the assumed stationary background covariance matrix. This is done by integrating the analysis residuals backward in time with the adjoint model. Numerical experiments are performed with the Lorenz-96 model under different scenarios to test the new approach and to evaluate its performance with respect to the EnKF and the hybrid EnKF/3D-VAR. The new method leads to the least root-mean-square estimation errors as long as the linear assumption guaranteeing the stability of the adjoint model holds. It is also found to be less sensitive to choices of the assimilation system inputs and parameters.
Imaging the Italian Lithosphere based on Adjoint Tomography
Magnoni, F.; Casarotti, E.; Komatitsch, D.; Melini, D.; Michelini, A.; Piersanti, A.; Tape, C.; Tromp, J.
2016-12-01
We exploit the powerful European computational resources awarded to our PRACE project IMAGINE_IT ("3D full-wave tomographic IMAGINg of the Entire ITalian lithosphere") to develop a reference, high-resolution 3D seismic wavespeed model for the Italian lithosphere. The inversion procedure consists of iterative improvements of an initial 3D traveltime tomographic model of the region constrained by a large number of full, high-quality observed seismic waveforms. The final model images the regional structure at unprecedented resolution ( 10 s) minimizing the misfit between recorded and synthetic data. Numerical wavefield simulations at high frequency are performed using a spectral-element method (code SPECFEM3D) that allows us to implement all complexities that characterize the studied region (lateral heterogeneity, topography, attenuation). This method is then efficiently combined with an adjoint technique to perform the 3D full-wave tomographic inversion. The Italian peninsula is characterized by very heterogeneous features resulting from complex tectonic evolution of the region mainly dominated by the interaction of Tyrrhenian, Adria and European plates. Our inversion includes 163 earthquakes that occurred in Italy and neighboring areas between 2005 and 2014, and a dense seismological network of 400 seismic recording stations. We perform 25 iterations of our iterative tomographic inversion process, as well as moment tensor inversions for the considered events. The resolution capabilities of our model are also explored based on point spread function analyses and calculation of the approximate Hessian. Thanks to our project IMAGINE_IT, at present the first application of adjoint tomography for the whole Italian region, we are able to constrain Vp as well as Vs at unprecedented resolution; the complex plate relationships start to be accurately modeled, and other inferences on the Italian geodynamical evolution or on fluid (such as CO2) distribution become possible.
Revisit boundary conditions for the self-adjoint angular flux formulation
Energy Technology Data Exchange (ETDEWEB)
Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.
Self-adjoint extensions of the Pauli equation in the presence of a magnetic monopole
Karat, E R; Karat, Edwin R; Schulz, Michael B
1996-01-01
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of a magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation.
Self-adjointness and conservation laws of a generalized Burgers equation
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.se, E-mail: torrisi@dmi.unict.it, E-mail: tracina@dmi.unict.it [Dipartimento di Matematica e Informatica, University of Catania, Catania (Italy)
2011-04-08
A (2 + 1)-dimensional generalized Burgers equation is considered. Having written this equation as a system of two dependent variables, we show that it is quasi self-adjoint and find a nontrivial additional conservation law.
Almost commuting self-adjoint matrices: The real and self-dual cases
Loring, Terry A.; Sørensen, Adam P. W.
2016-08-01
We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover, we prove that the same holds with self-dual in place of symmetric and also for paths of self-adjoint matrices. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin’s famous theorem on almost commuting matrices. Similarly, the self-dual case gives a version for matrices over the quaternions. To prove these results, we develop a theory of semiprojectivity for real C*-algebras and also examine various definitions of low-rank for real C*-algebras.
Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential
Directory of Open Access Journals (Sweden)
Aleksandr Mikhailovich Kholkin
2016-01-01
Full Text Available A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained.
MS S4.03.002 - Adjoint-Based Design for Configuration Shaping
Nemec, Marian; Aftosmis, Michael J.
2009-01-01
This slide presentation discusses a method of inverse design for low sonic boom using adjoint-based gradient computations. It outlines a method for shaping a configuration in order to match a prescribed near-field signature.
The adjoint sensitivity method of global electromagnetic induction for CHAMP magnetic data
Z. Martinec; J. Velimsky
2017-01-01
An existing time-domain spectral-finite element approach for the forward modelling of electromagnetic induction vector data as measured by the CHAMP satellite is, in this paper, supplemented by a new method of computing the sensitivity of the CHAMP electromagnetic induction data to the Earth's mantle electrical conductivity, which we term the adjoint sensitivity method. The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the speci...
Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians
Galapon, E A
2002-01-01
We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each characteristic time operator generates an uncountable class of self- adjoint operators canonically conjugate with the same Hamiltonian.
Adjoint-Free Variational Data Assimilation into a Regional Wave Model
2015-07-01
linearized model is localized both in space and time. Holthuijsen et al. (1997) explored a similar technique using a limited number of nonlocal ...Adjoint-Free Variational Data Assimilation into a Regional Wave Model GLEB PANTELEEV University of Alaska Fairbanks, Fairbanks, Alaska, and National...wave prediction model [Wave Model (WAM)]. The algorithm employs the adjoint-free technique and was tested in a series of data assimilation experiments
Big Data Challenges in Global Seismic 'Adjoint Tomography' (Invited)
Tromp, J.; Bozdag, E.; Krischer, L.; Lefebvre, M.; Lei, W.; Smith, J.
2013-12-01
The challenge of imaging Earth's interior on a global scale is closely linked to the challenge of handling large data sets. The related iterative workflow involves five distinct phases, namely, 1) data gathering and culling, 2) synthetic seismogram calculations, 3) pre-processing (time-series analysis and time-window selection), 4) data assimilation and adjoint calculations, 5) post-processing (pre-conditioning, regularization, model update). In order to implement this workflow on modern high-performance computing systems, a new seismic data format is being developed. The Adaptable Seismic Data Format (ASDF) is designed to replace currently used data formats with a more flexible format that allows for fast parallel I/O. The metadata is divided into abstract categories, such as "source" and "receiver", along with provenance information for complete reproducibility. The structure of ASDF is designed keeping in mind three distinct applications: earthquake seismology, seismic interferometry, and exploration seismology. Existing time-series analysis tool kits, such as SAC and ObsPy, can be easily interfaced with ASDF so that seismologists can use robust, previously developed software packages. ASDF accommodates an automated, efficient workflow for global adjoint tomography. Manually managing the large number of simulations associated with the workflow can rapidly become a burden, especially with increasing numbers of earthquakes and stations. Therefore, it is of importance to investigate the possibility of automating the entire workflow. Scientific Workflow Management Software (SWfMS) allows users to execute workflows almost routinely. SWfMS provides additional advantages. In particular, it is possible to group independent simulations in a single job to fit the available computational resources. They also give a basic level of fault resilience as the workflow can be resumed at the correct state preceding a failure. Some of the best candidates for our particular workflow
Gopalakrishnan, Ganesh
2013-07-01
An ocean state estimate has been developed for the Gulf of Mexico (GoM) using the MIT general circulation model and its adjoint. The estimate has been tested by forecasting loop current (LC) evolution and eddy shedding in the GoM. The adjoint (or four-dimensional variational) method was used to match the model evolution to observations by adjusting model temperature and salinity initial conditions, open boundary conditions, and atmospheric forcing fields. The model was fit to satellite-derived along-track sea surface height, separated into temporal mean and anomalies, and gridded sea surface temperature for 2 month periods. The optimized state at the end of the assimilation period was used to initialize the forecast for 2 months. Forecasts explore practical LC predictability and provide a cross-validation test of the state estimate by comparing it to independent future observations. The model forecast was tested for several LC eddy separation events, including Eddy Franklin in May 2010 during the deepwater horizon oil spill disaster in the GoM. The forecast used monthly climatological open boundary conditions, atmospheric forcing, and run-off fluxes. The model performance was evaluated by computing model-observation root-mean-square difference (rmsd) during both the hindcast and forecast periods. The rmsd metrics for the forecast generally outperformed persistence (keeping the initial state fixed) and reference (forecast initialized using assimilated Hybrid Coordinate Ocean Model 1/12° global analysis) model simulations during LC eddy separation events for a period of 1̃2 months.
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
Energy Technology Data Exchange (ETDEWEB)
Vishnampet, Ramanathan [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Bodony, Daniel J. [Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Freund, Jonathan B., E-mail: jbfreund@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States)
2015-03-15
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that
Determining scaling laws from geodynamic simulations using adjoint gradients.
Reuber, Georg; Kaus, Boris; Popov, Anton
2016-04-01
Whereas significant progress has been made in modelling of lithospheric and crustal scale processes in recent years, it often remains a challenge to understand which of the many model parameters is of key importance for a particular simulation. Determining this is usually done by manually changing the model input parameters and performing new simulations. For a few cases, such as for crustal-scale folding instabilities (with viscous rheologies, e.g. [1]) or for Rayleigh-Taylor instabilities, one can use existing scaling laws to obtain such insights. Yet, for a more general case, it is not straightforward to do this (apart from running many simulations). Here, we test a different approach which computes gradients of the model parameters using adjoint based methods, which has the advantage that we can test the influence of an independent number of parameters on the system by computing and analysing the covariance matrix and the gradient of the parameter space. This method might give us the chance to get insights on which parameters affect for example subduction processes and how strong the system depends on their influence. [1] Fernandez, N., & Kaus, B. J. (2014). Fold interaction and wavelength selection in 3D models of multilayer detachment folding. Tectonophysics, 632, 199-217.
Conformal vs confining scenario in SU(2) with adjoint fermions
Del Debbio, L; Patella, A; Pica, C; Rago, A
2009-01-01
The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling $\\beta = 4/g_0^2 = 2.25$ for values of the bare fermion mass $m_0$ that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near-)conformal and the confining scenario is outlined.
An adjoint-based scheme for eigenvalue error improvement
Energy Technology Data Exchange (ETDEWEB)
Merton, S.R.; Smedley-Stevenson, R.P., E-mail: Simon.Merton@awe.co.uk, E-mail: Richard.Smedley-Stevenson@awe.co.uk [AWE plc, Berkshire (United Kingdom); Pain, C.C.; El-Sheikh, A.H.; Buchan, A.G., E-mail: c.pain@imperial.ac.uk, E-mail: a.el-sheikh@imperial.ac.uk, E-mail: andrew.buchan@imperial.ac.uk [Department of Earth Science and Engineering, Imperial College, London (United Kingdom)
2011-07-01
A scheme for improving the accuracy and reducing the error in eigenvalue calculations is presented. Using a rst order Taylor series expansion of both the eigenvalue solution and the residual of the governing equation, an approximation to the error in the eigenvalue is derived. This is done using a convolution of the equation residual and adjoint solution, which is calculated in-line with the primal solution. A defect correction on the solution is then performed in which the approximation to the error is used to apply a correction to the eigenvalue. The method is shown to dramatically improve convergence of the eigenvalue. The equation for the eigenvalue is shown to simplify when certain normalizations are applied to the eigenvector. Two such normalizations are considered; the rst of these is a fission-source type of normalisation and the second is an eigenvector normalisation. Results are demonstrated on a number of demanding elliptic problems using continuous Galerkin weighted nite elements. Moreover, the correction scheme may also be applied to hyperbolic problems and arbitrary discretization. This is not limited to spatial corrections and may be used throughout the phase space of the discrete equation. The applied correction not only improves fidelity of the calculation, it allows assessment of the reliability of numerical schemes to be made and could be used to guide mesh adaption algorithms or to automate mesh generation schemes. (author)
The drag-adjoint field of a circular cylinder wake at Reynolds numbers 20, 100 and 500
Wang, Qiqi
2012-01-01
This paper analyzes the adjoint solution of the Navier-Stokes equation. We focus on flow across a circular cylinder at three Reynolds numbers, ReD = 20, 100 and 500. The objective function in the adjoint formulation is the drag on the cylinder. We use classical fluid mechanics approaches to analyze the adjoint solution, which is a vector field similar to a flow field. Production and dissipation of kinetic energy of the adjoint field is discussed. We also derive the evolution of circulation of the adjoint field along a closed material contour. These analytical results are used to explain three numerical solutions of the adjoint equations presented in this paper: The adjoint solution at ReD = 20, a viscous steady state flow, exhibits a downstream suction and an upstream jet, opposite of expected behavior of a flow field. The adjoint solution at ReD = 100, a periodic 2D unsteady flow, exhibits periodic, bean shaped circulation the near wake region. The adjoint solution at ReD = 500, a turbulent 3D unsteady flow,...
Assessing the Impact of Observations on Numerical Weather Forecasts Using the Adjoint Method
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
Light adjoint quarks in the instanton-dyon liquid model. IV.
Liu, Yizhuang; Shuryak, Edward; Zahed, Ismail
2016-11-01
We discuss the instanton-dyon liquid model with Nf Majorana quark flavors in the adjoint representation of color S Uc(2 ) at finite temperature. We briefly recall the index theorem on S1×R3 for twisted adjoint fermions in a Bogomolny-Prasad-Sommerfeld (BPS) dyon background of arbitrary holonomy and use the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction to derive the adjoint antiperiodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with Nf light and antiperiodic adjoint quarks. We develop the model in details by mapping the theory on a three-dimensional quantum effective theory with adjoint quarks with manifest S U (Nf)×Z4 Nf symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for Nf=1 . For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through S U (Nf)×Z4 Nf→O (Nf). As the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.
Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
Liu, Yizhuang; Zahed, Ismail
2016-01-01
We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $SU_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective theory with adjoint quarks with manifest $SU(N_f)\\times Z_{4N_f}$ symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for $N_f=1$. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through $SU(N_f)\\times Z_{4N...
STUDY ON THE ADJOINT METHOD IN DATA ASSIMILATION AND THE RELATED PROBLEMS
Institute of Scientific and Technical Information of China (English)
吕咸青; 吴自库; 谷艺; 田纪伟
2004-01-01
It is not reasonable that one can only use the adjoint of model in data assimilation.The simulated numerical experiment shows that for the tidal model,the result of the adjoint of equation is almost the same as that of the adjoint of model:the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°.The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea.For comparison,the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea.The initial guess values of the boundary conditions are given first,and then are adjusted to acquire the simulated results that are as close as possible to the observations.As the boundary conditions contain 72 values,which should be adjusted and how to adjust them can only be partially solved by adjusting them many times.The satisfied results are hard to acquire even gigantic efforts are done.Here,the automation of the treatment of the open boundary conditions is realized.The method is unique and superior to the traditional methods.It is emphasized that if the adjoint of equation is used,tedious and complicated mathematical deduction can be avoided.Therefore the adjoint of equation should attract much attention.
Heat Flux estimation in WEST divertor with embedded thermocouples
Gaspar, J.; Corre, Y.; Firdaouss, M.; Gardarein, J.-L.; Guilhem, D.; Houry, M.; Le Niliot, C.; Missirlian, M.; Pocheau, C.; Rigollet, F.
2016-09-01
The present paper deals with the surface heat flux estimation with embedded thermocouples (TC) in a Plasma Facing Component (PFC) of the WEST Tokamak. A 2D nonlinear unsteady calculation combined with the Conjugate Gradient Method (CGM) and the adjoint state is achieved in order to estimate the time evolution of the heat flux amplitude and decay length λq . The method is applied on different synthetic measurements in order to evaluate the accuracy of the method. The synthetic measurements are generated with realistic values of λq and magnitudes as those expected for ITER.
An adjoint-based approach for finding invariant solutions of Navier-Stokes equations
Farazmand, Mohammad
2015-01-01
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and traveling wave solutions of the Navier--Stokes equations. Using the adjoint equations, arbitrary initial conditions evolve to the vicinity of a (relative) equilibrium at which point a few Newton-type iterations yield the desired (relative) equilibrium solution. We apply this adjoint-based method to a chaotic two-dimensional Kolmogorov flow. A convergence rate of 100% is observed, leading to the discovery of 21 new steady state and traveling wave solutions at Reynolds number Re=40. Some of the new invariant solutions have spatially localized structures that were previously believed to only exist on domains with large aspect ratios. We show that one of the newly found steady state solutions underpins the temporal intermittencies, i.e., high energy dissipation episodes of the flo...
Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics
Tavener, Simon
2013-01-01
In this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjoint problems within each subdomain. The primal subdomains are discretized using either an interior penalty discontinuous Galerkin method or a continuous Galerkin method with weakly imposed Dirichlet conditions. The mixed subdomains are discretized using Raviart- Thomas mixed finite elements. The a posteriori error estimate also accounts for the errors due to adjoint-inconsistent subdomain discretizations. The coupling between the subdomain discretizations is achieved via a mortar space. We show that the numerical discretization error can be broken down into subdomain and mortar components which may be used to drive adaptive refinement.Copyright © by SIAM.
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.
Bucco, D.; Weiss, M.
2007-01-01
The COVariance and ADjoint Analysis Tool (COVAD) is a specially designed software tool, written for the Matlab/Simulink environment, which allows the user the capability to carry out system analysis and simulation using the adjoint, covariance or Monte Carlo methods. This paper describes phase one o
Bucco, D.; Weiss, M.
2007-01-01
The COVariance and ADjoint Analysis Tool (COVAD) is a specially designed software tool, written for the Matlab/Simulink environment, which allows the user the capability to carry out system analysis and simulation using the adjoint, covariance or Monte Carlo methods. This paper describes phase one
Tracking influential haze source areas in North China using an adjoint model, GRAPES-CUACE
An, X. Q.; Zhai, S. X.; Jin, M.; Gong, S. L.; Wang, Y.
2015-08-01
Based upon the adjoint theory, the adjoint of the aerosol module in the atmospheric chemical modeling system GRAPES-CUACE (Global/Regional Assimilation and PrEdiction System coupled with the CMA Unified Atmospheric Chemistry Environment) was developed and tested for its correctness. Through statistic comparison, BC (black carbon aerosol) concentrations simulated by GRAPES-CUACE were generally consistent with observations from Nanjiao (one urban observation station) and Shangdianzi (one rural observation station) stations. To track the most influential emission-sources regions and the most influential time intervals for the high BC concentration during the simulation period, the adjoint model was adopted to simulate the sensitivity of average BC concentration over Beijing at the highest concentration time point (referred to as the Objective Function) with respect to BC emission amount over Beijing-Tianjin-Hebei region. Four types of regions were selected based on administrative division and sensitivity coefficient distribution. The adjoint model was used to quantify the effects of emission-sources reduction in different time intervals over different regions by one independent simulation. Effects of different emission reduction strategies based on adjoint sensitivity information show that the more influential regions (regions with relatively larger sensitivity coefficients) do not necessarily correspond to the administrative regions, and the influence effectiveness of sensitivity-oriented regions was greater than the administrative divisions. The influence of emissions on the objective function decreases sharply approximately for the pollutants emitted 17-18 h ago in this episode. Therefore, controlling critical emission regions during critical time intervals on the basis of adjoint sensitivity analysis is much more efficient than controlling administrative specified regions during an experiential time period.
Institute of Scientific and Technical Information of China (English)
YANG YiDu; CHEN Zhen
2008-01-01
This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T. Under the condition that the approximate operator Th converges to T in norm, it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems, and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.
Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico
Gopalakrishnan, Ganesh
2013-07-01
Adjoint model sensitivity analyses were applied for the loop current (LC) and its eddy shedding in the Gulf of Mexico (GoM) using the MIT general circulation model (MITgcm). The circulation in the GoM is mainly driven by the energetic LC and subsequent LC eddy separation. In order to understand which ocean regions and features control the evolution of the LC, including anticyclonic warm-core eddy shedding in the GoM, forward and adjoint sensitivities with respect to previous model state and atmospheric forcing were computed using the MITgcm and its adjoint. Since the validity of the adjoint model sensitivities depends on the capability of the forward model to simulate the real LC system and the eddy shedding processes, a 5 year (2004–2008) forward model simulation was performed for the GoM using realistic atmospheric forcing, initial, and boundary conditions. This forward model simulation was compared to satellite measurements of sea-surface height (SSH) and sea-surface temperature (SST), and observed transport variability. Despite realistic mean state, standard deviations, and LC eddy shedding period, the simulated LC extension shows less variability and more regularity than the observations. However, the model is suitable for studying the LC system and can be utilized for examining the ocean influences leading to a simple, and hopefully generic LC eddy separation in the GoM. The adjoint sensitivities of the LC show influences from the Yucatan Channel (YC) flow and Loop Current Frontal Eddy (LCFE) on both LC extension and eddy separation, as suggested by earlier work. Some of the processes that control LC extension after eddy separation differ from those controlling eddy shedding, but include YC through-flow. The sensitivity remains stable for more than 30 days and moves generally upstream, entering the Caribbean Sea. The sensitivities of the LC for SST generally remain closer to the surface and move at speeds consistent with advection by the high-speed core of
Mass anomalous dimension of Adjoint QCD at large N from twisted volume reduction
Pérez, Margarita García; Keegan, Liam; Okawa, Masanori
2015-01-01
In this work we consider the $SU(N)$ gauge theory with two Dirac fermions in the adjoint representation, in the limit of large $N$. In this limit the infinite-volume physics of this model can be studied by means of the corresponding twisted reduced model defined on a single site lattice. Making use of this strategy we study the reduced model for various values of $N$ up to 289. By analyzing the eigenvalue distribution of the adjoint Dirac operator we test the conformality of the theory and extract the corresponding mass anomalous dimension.
The Roots of Adjoint Polynomial of the Graphs Contain Triangles%一类含三角形图的伴随多项式的根
Institute of Scientific and Technical Information of China (English)
冶成福
2004-01-01
We denote h(G, x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles.By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.
Global Adjoint Tomography: Combining Big Data with HPC Simulations
Bozdag, E.; Lefebvre, M. P.; Lei, W.; Peter, D. B.; Smith, J. A.; Komatitsch, D.; Tromp, J.
2014-12-01
The steady increase in data quality and the number of global seismographic stations have substantially grown the amount of data available for construction of Earth models. Meanwhile, developments in the theory of wave propagation, numerical methods and HPC systems have enabled unprecedented simulations of seismic wave propagation in realistic 3D Earth models which lead the extraction of more information from data, ultimately culminating in the use of entire three-component seismograms.Our aim is to take adjoint tomography further to image the entire planet which is one of the extreme cases in seismology due to its intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. We have started low resolution (T > 27 s, soon will be > 17 s) global inversions with 253 earthquakes for a transversely isotropic crust and mantle model on Oak Ridge National Laboratory's Cray XK7 "Titan" system. Recent improvements in our 3D solvers, such as the GPU version of the SPECFEM3D_GLOBE package, will allow us perform higher-resolution (T > 9 s) and longer-duration (~180 m) simulations to take the advantage of high-frequency body waves and major-arc surface waves to improve imbalanced ray coverage as a result of uneven distribution of sources and receivers on the globe. Our initial results after 10 iterations already indicate several prominent features reported in high-resolution continental studies, such as major slabs (Hellenic, Japan, Bismarck, Sandwich, etc.) and enhancement in plume structures (the Pacific superplume, the Hawaii hot spot, etc.). Our ultimate goal is to assimilate seismic data from more than 6,000 earthquakes within the magnitude range 5.5 ≤ Mw ≤ 7.0. To take full advantage of this data set on ORNL's computational resources, we need a solid framework for managing big data sets during pre-processing (e.g., data requests and quality checks), gradient calculations, and post-processing (e
Wells, K. C.; Millet, D. B.; Bousserez, N.; Henze, D. K.; Chaliyakunnel, S.; Griffis, T. J.; Dlugokencky, E. J.; Prinn, R. G.; O'Doherty, S.; Weiss, R. F.; Dutton, G. S.; Elkins, J. W.; Krummel, P. B.; Langenfelds, R. L.; Steele, P.
2015-12-01
Nitrous oxide (N2O) is a long-lived greenhouse gas with a global warming potential approximately 300 times that of CO2, and plays a key role in stratospheric ozone depletion. Human perturbation of the nitrogen cycle has led to a rise in atmospheric N2O, but large uncertainties exist in the spatial and temporal distribution of its emissions. Here we employ a 4D-Var inversion framework for N2O based on the GEOS-Chem chemical transport model and its adjoint to derive new constraints on the space-time distribution of global land and ocean N2O fluxes. Based on an ensemble of global surface measurements, we find that emissions are overestimated over Northern Hemisphere land areas and underestimated in the Southern Hemisphere. Assigning these biases to particular land or ocean regions is more difficult given the long lifetime of N2O. To quantitatively evaluate where the current N2O observing network provides local and regional emission constraints, we apply a new, efficient information content analysis technique involving radial basis functions. The technique yields optimal state vector dimensions for N2O source inversions, with model grid cells grouped in space and time according to the resolution that can actually be provided by the network of global observations. We then use these optimal state vectors in an analytical inversion to refine current top-down emission estimates.
Institute of Scientific and Technical Information of China (English)
WANG Caixia; Paola Malanotte-Rizzoli
2014-01-01
The linkage between physical and biological processes, particularly the effect of the circulation field on the distribution of phytoplankton, is studied by applying a two-dimensional model and an adjoint data assimilation approach to the Gulf of Maine-Georges Bank region. The model results, comparing well with observation data, reveal seasonal and geographic variations of phytoplankton concentration and verify that the seasonal cycles of phytoplankton are controlled by both biological sources and ad-vection processes which are functions of space and time and counterbalance each other. Although advective flux divergences have greater magnitudes on Georges Bank than in the coastal region of the western Gulf of Maine, advection control over phytoplankton concentration is more significant in the coastal region of the western Gulf of Maine. The model results also suggest that the two separated populations in the coastal regions of the western Gulf of Maine and on Georges Bank are self-sustaining.
Adjoint sensitivity in PDE constrained least squares problems as a multiphysics problem
Lahaye, D.; Mulckhuyse, W.F.W.
2012-01-01
Purpose - The purpose of this paper is to provide a framework for the implementation of an adjoint sensitivity formulation for least-squares partial differential equations constrained optimization problems exploiting a multiphysics finite elements package. The estimation of the diffusion coefficient
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E. [Department of Physics, University of San Francisco, San Francisco, CA 94117-1080 (United States)]. E-mail: camblong@usfca.edu; Epele, Luis N. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Fanchiotti, Huner [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Garcia Canal, Carlos A. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Ordonez, Carlos R. [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States); World Laboratory Center for Pan-American Collaboration in Science and Technology, University of Houston Center, Houston, TX 77204-5506 (United States)
2007-05-14
A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian.
DEFF Research Database (Denmark)
Pingen, Georg; Evgrafov, Anton; Maute, Kurt
2009-01-01
We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion...
Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir
DEFF Research Database (Denmark)
2012-01-01
are large-scale problems and require specialized numerical algorithms. In this paper, we combine a single shooting optimization algorithm based on sequential quadratic programming (SQP) with explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods and a continuous adjoint method...
Self-adjoint extensions of Coulomb systems in 1,2 and 3 dimensions
de Oliveira, Cesar R
2008-01-01
We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in $R^n$, n = 1, 2, 3. We characterize their self-adjoint extensions and, in the unidimensional case, present a discussion of controversies in the literature, particularly the question of the permeability of the origin. Potentials given by fundamental solutions of Laplace equation are also briefly considered.
Blind range influence on guidance loop performance: An adjoint-based analysis
Bucco, D.; Weiss, M.
2013-01-01
In this paper, we investigate the use of adjoint simulation for assessing the miss distance performance of a generic guidance system under the influence of a blind range condition. The term "blind range" refers to that final portion of the missile trajectory for which sensor data are not available.
Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Shondin, Yuri
2007-01-01
The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization of a generalized Nevanlinna function.
Parameter and state estimation with a time-dependent adjoint marine ice sheet model
Directory of Open Access Journals (Sweden)
D. N. Goldberg
2013-06-01
Full Text Available To date, assimilation of observations into large-scale ice models has consisted predominantly of time-independent inversions of surface velocities for basal traction, bed elevation, or ice stiffness, and has relied primarily on analytically-derived adjoints of diagnostic ice velocity models. To overcome limitations of such "snapshot" inversions, i.e. their inability to assimilate time-dependent data, or to produce initial states with minimum artificial drift and suitable for time-dependent simulations, we have developed an adjoint of a time-dependent parallel glaciological flow model. The model implements a hybrid shallow shelf-shallow ice stress balance, involves a prognostic equation for ice thickness evolution, and can represent the floating, fast-sliding, and frozen bed regimes of a marine ice sheet. The adjoint is generated by a combination of analytic methods and the use of algorithmic differentiation (AD software. Several experiments are carried out with idealized geometries and synthetic observations, including inversion of time-dependent surface elevations for past thicknesses, and simultaneous retrieval of basal traction and topography from surface data. Flexible generation of the adjoint for a range of independent uncertain variables is exemplified through sensitivity calculations of grounded ice volume to changes in basal melting of floating and basal sliding of grounded ice. The results are encouraging and suggest the feasibility, using real observations, of improved ice sheet state estimation and comprehensive transient sensitivity assessments.
THE EXISTENCE OF PERIODIC SOLUTIONS TO SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.
Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Shondin, Yuri
2007-01-01
The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization of a generalized Nevanlinna function.
Liu, Yaning; Niu, Fenglin; Chen, Min; Yang, Wencai
2017-03-01
We construct a new 3-D shear wave speed model of the crust and the uppermost mantle beneath Northeast China using the ambient noise adjoint tomography method. Without intermediate steps of measuring phase dispersion, the adjoint tomography inverts for shear wave speeds of the crust and uppermost mantle directly from 6-40 s waveforms of Empirical Green's functions (EGFs) of Rayleigh waves, which are derived from interferometry of two years of ambient noise data recorded by the 127 Northeast China Extended Seismic Array stations. With an initial 3-D model derived from traditional asymptotic surface wave tomography method, adjoint tomography refines the 3-D model by iteratively minimizing the frequency-dependent traveltime misfits between EGFs and synthetic Green's functions measured in four period bands: 6-15 s, 10-20 s, 15-30 s, and 20-40 s. Our new model shows shear wave speed anomalies that are spatially correlated with known tectonic units such as the Great Xing'an range and the Changbaishan mountain range. The new model also reveals low wave speed conduits in the mid-lower crust and the uppermost mantle with a wave speed reduction indicative of partial melting beneath the Halaha, Xilinhot-Abaga, and Jingpohu volcanic complexes, suggesting that the Cenozoic volcanism in the area has a deep origin. Overall, the adjoint tomographic images show more vertically continuous velocity anomalies with larger amplitudes due to the consideration of the finite frequency and 3-D effects.
Confining vs. conformal scenario for SU(2) with 2 adjoint fermions. Mesonic spectrum
DEFF Research Database (Denmark)
Pica, Claudio; Del Debbio, Luigi; Lucini, Biagio;
2010-01-01
The Minimal Walking Technicolor (MWT) model, based on the SU(2) gauge group with two Dirac adjoint fermions, is expected to lie close to the lower boundary of the conformal window. As such, it is believed to possess a dynamics different enough from QCD to be a viable candidate for a Technicolor t...
The adjoint sensitivity method of global electromagnetic induction for CHAMP magnetic data
Martinec, Zdeněk; Velímský, Jakub
2009-12-01
An existing time-domain spectral-finite element approach for the forward modelling of electromagnetic induction vector data as measured by the CHAMP satellite is, in this paper, supplemented by a new method of computing the sensitivity of the CHAMP electromagnetic induction data to the Earth's mantle electrical conductivity, which we term the adjoint sensitivity method. The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the specification of prescribed boundary conditions. The respective boundary-value data at the satellite's altitude are the X magnetic component measured by the CHAMP vector magnetometer along the satellite track for the forward method and the difference between the measured and predicted Z magnetic component for the adjoint method. The squares of these differences summed up over all CHAMP tracks determine the misfit. The sensitivities of the CHAMP data, that is the partial derivatives of the misfit with respect to mantle conductivity parameters, are then obtained by the scalar product of the forward and adjoint solutions, multiplied by the gradient of the conductivity and integrated over all CHAMP tracks. Such exactly determined sensitivities are checked against numerical differentiation of the misfit, and good agreement is obtained. The attractiveness of the adjoint method lies in the fact that the adjoint sensitivities are calculated for the price of only an additional forward calculation, regardless of the number of conductivity parameters. However, since the adjoint solution proceeds backwards in time, the forward solution must be stored at each time step, leading to memory requirements that are linear with respect to the number of steps undertaken. Having determined the sensitivities, we apply the conjugate gradient method to infer 1-D and 2-D conductivity structures of the Earth based on the CHAMP residual time series (after the subtraction of static field and secular variations
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.
Inversion of CO and NOx emissions using the adjoint of the IMAGES model
Directory of Open Access Journals (Sweden)
T. Stavrakou
2004-12-01
Full Text Available We use ground-based observations of CO mixing ratios and vertical column abundances together with tropospheric NO2 columns from the GOME satellite instrument as constraints for improving the global annual emission estimates of CO and NOx for the year 1997. The agreement between concentrations calculated by the global 3-dimensional CTM IMAGES and the observations is optimized using the adjoint modelling technique, which allows to invert for CO and NOx fluxes simultaneously, taking their chemical interactions into account. Our analysis quantifies a total of 39 flux parameters, comprising anthropogenic and biomass burning sources over large continental regions, soil and lightning emissions of NOx, biogenic emissions of CO and non-methane hydrocarbons, as well as the deposition velocities of both CO and NOx. Comparison between observed, prior and optimized CO mixing ratios at NOAA/CMDL sites shows that the inversion performs well at the northern mid- and high latitudes, and that it is less efficient in the Southern Hemisphere, as expected due to the scarsity of measurements over this part of the globe. The inversion, moreover, brings the model much closer to the measured NO2 columns over all regions. Sensitivity tests show that anthropogenic sources exhibit weak sensitivity to changes of the a priori errors associated to the bottom-up inventory, whereas biomass burning sources are subject to a strong variability. Our best estimate for the 1997 global top-down CO source amounts to 2760 Tg CO. Anthropogenic emissions increase by 28%, in agreement with previous inverse modelling studies, suggesting that the present bottom-up inventories underestimate the anthropogenic CO emissions in the Northern Hemisphere. The magnitude of the optimized NOx global source decreases by 14% with respect to the prior, and amounts to 42.1 Tg N, out of which 22.8 Tg N are due to anthropogenic sources. The NOx emissions increase over Tropical regions, whereas they
Institute of Scientific and Technical Information of China (English)
张慧; 刘兴祥; 冯学利
2011-01-01
We study the weak adjoint matrix and m- weak adjoint matrix＇s eigenvalues,eigenvectors and their corresponding eigenvalues eigenvector＇relationship.%研究了弱伴随矩阵、m重弱伴随矩阵的特征值、特征向量与其对应矩阵的特征值、特征向量的关系。
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
Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Dimitrakopoulos, G.; Giannakoglou, K. C.
2015-11-01
In this article, the gradient of aerodynamic objective functions with respect to design variables, in problems governed by the incompressible Navier-Stokes equations coupled with the k-ω SST turbulence model, is computed using the continuous adjoint method, for the first time. Shape optimization problems for minimizing drag, in external aerodynamics (flows around isolated airfoils), or viscous losses in internal aerodynamics (duct flows) are considered. Sensitivity derivatives computed with the proposed adjoint method are compared to those computed with finite differences or a continuous adjoint variant based on the frequently used assumption of frozen turbulence; the latter proves the need for differentiating the turbulence model. Geometries produced by optimization runs performed with sensitivities computed by the proposed method and the 'frozen turbulence' assumption are also compared to quantify the gain from formulating and solving the adjoint to the turbulence model equations.
Brezillon, Joël; Dwight, Richard P.
2009-01-01
Within the next few years, numerical shape optimization based on high fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimization problems, and the adjoint approach - which allows fast and accurate evaluations of the gradients with respect to the design parameters - is seen as a promising strategy. After describing the theory of the viscous discrete adjoint method and its impleme...
Brezillon, J.; Dwight, R.P.
2009-01-01
Within the next few years, numerical shape optimization based on high fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimization problems, and the adjoint approach - which allows fast and accurate evaluations of the gradients with respect to the design parameters - is seen as a promising strategy. After describing the theory of the viscous discrete adjoint method and its impleme...
U.S. Geological Survey, Department of the Interior — Methane (CH4) flux is the net rate of methane exchange between an ecosystem and the atmosphere. Data of this variable were generated by the USGS LandCarbon project...
Wilson flux breaking and coset space dimensional reduction
Energy Technology Data Exchange (ETDEWEB)
Zoupanos, G.
1988-02-11
Higher dimensional gauge theories lead, after dimensional reduction on coset spaces, to four-dimensional gauge theories usually with the natural emergence of a Higgs sector which is completely determined. However, the Higgs fields never appear in the adjoint representation which in many GUTs could lead to a successful spontaneous symmetry breaking towards the low energy gauge group. As an alternative we suggest that the breaking of the four-dimensional GUTs obtained from CSDR could be provided by the Wilson flux breaking and we discuss some semirealistic examples. We also speculate on the possibility that the breaking of the electroweak sector has dynamical origin.
Kraft, S.; Puel, G.; Aubry, D.; Funfschilling, C.
2016-12-01
For the calibration of multi-body models of railway vehicles, the identification of the model parameters from on-track measurement is required. This involves the solution of an inverse problem by minimising the misfit function which describes the distance between model and measurement using optimisation methods. The application of gradient-based optimisation methods is advantageous but necessitates an efficient approach for the computation of the gradients considering the large number of model parameters and the costly evaluation of the forward model. This work shows that the application of the adjoint state approach to the nonlinear vehicle-track multi-body system is suitable, reducing on the one hand the computational cost and increasing on the other hand the precision of the gradients. Gradients from the adjoint state method are computed for vehicle models and validated taking into account measurement noise.
A new method for computing the eigenfunctions and their adjoints of the dynamo operator
Schrinner, M; Jiang, J; Hoyng, P
2009-01-01
We present a new method to determine the eigensolutions of the induction and the dynamo equation in a fluid embedded in vacuum. The magnetic field is expanded in a complete set of functions. The new method is based on the biorthogonality of the adjoint electric current and the vector potential with an inner product defined by a volume integral over the fluid domain. The advantage of this method is that the velocity and the dynamo coefficients of the induction and the dynamo equation do not have to be differentiated and thus even numerically determined tabulated values of the coefficients produce reasonable results. We provide test calculations and compare with published results obtained by the classical treatment based on the biorthogonality of the magnetic field and its adjoint. We especially consider dynamos with mean-field coefficients determined from direct numerical simulations of the geodynamo and compare with initial value calculations and the full MHD simulations.
Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance
Hochuli, Roman; Arridge, Simon; Cox, Ben
2016-01-01
Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A 2D radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance in heterogeneous media. A gradient-based optimisation scheme is then used to recover 2D absorption and scattering coefficients distributions from simulated photoacoustic measurements. It is shown that the functional gradients, which are a challenge to compute efficiently using MC models, can be calculated directly from the coefficients of the harmonic angular basis used in the forward and adjoint models. This work establishes a framework for transport-based quantitative photoacoustic tomography that can fully exploit emerging highly parallel computing architectures.
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.
Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables
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.
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-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems
Asner, Liya
2012-01-01
We consider time-dependent parabolic problem s coupled across a common interface which we formulate using a Lagrange multiplier construction and solve by applying a monolithic solution technique. We derive an adjoint-based a posteriori error representation for a quantity of interest given by a linear functional of the solution. We establish the accuracy of our error representation formula through numerical experimentation and investigate the effect of error in the adjoint solution. Crucially, the error representation affords a distinction between temporal and spatial errors and can be used as a basis for a blockwise time-space refinement strategy. Numerical tests illustrate the efficacy of the refinement strategy by capturing the distinctive behavior of a localized traveling wave solution. The saddle point systems considered here are equivalent to those arising in the mortar finite element technique for parabolic problems. © 2012 Society for Industrial and Applied Mathematics.
Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas
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.
Topology Optimization of Turbulent Fluid Flow with a Sensitive Porosity Adjoint Method (SPAM)
Philippi, B
2015-01-01
A sensitive porosity adjoint method (SPAM) for optimizing the topology of fluid machines has been proposed. A sensitivity function with respect to the porosity has been developed. In the first step of the optimization process, porous media are introduced into the flow regime according to the sensitivity function. Then the optimized porous media are transformed to solid walls. The turbulent flow in porous media is accounted for by a modified eddy-viscosity based turbulence model. Its influence on the adjoint equations is nevertheless neglected, which refers to the so called frozen turbulence assumption. A test case of application in terms of the turbulent rough wall channel flow shows that a considerable reduction of the objective function can be obtained by this method. The transformation from porous media to solid walls may have important effect on the optimization results.
Essential self-adjointness of n-dimensional Dirac operators with a variable mass term
Kalf, Hubert; Yamada, Osanobu
2001-06-01
We give some results about the essential self-adjointness of the Dirac operator H=∑j=1nαj pj+m(x) αn+1+V(x) IN (N=2 [(n+1)/2]), on [C0∞(Rn{0})]N, where the αj (j=1,2,…,n) are Dirac matrices and m(x) and V(x) are real-valued functions. We are mainly interested in a singularity of V(x) and m(x) near the origin which preserves the essential self-adjointness of H. As a result, if m=m(r) is spherically symmetric or m(x)≡V(x), then we can permit a singularity of m and V which is stronger than that of the Coulomb potential.
Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; /Syracuse U.; Galvez, Richard; /Syracuse U.; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2010-08-26
We report on the results of numerical simulations of SU(N) lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with {Lambda} sites in each direction in the large-N limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of {Lambda}, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume 2{sup 4}. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit N {yields} {infinity}, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.
Weyl theorems for the polluted set of self-adjoint operators in Galerkin approximations
Boulton, Lyonell; Lewin, Mathieu
2010-01-01
Let A be a self-adjoint operator on a separable Hilbert space H and let (L_n) be a sequence of finite dimensional subspaces of the domain of A, approximating H in the large n limit. Denote by A_n the compression of A to L_n. In general the spectrum of A is only a subset of the limit of the spectra of A_n and the latter might differ from the former in a non-trivial "polluted set". In this paper we show that this polluted set is determined by the existence of particular Weyl sequences of singular type. This characterization allows us to identify verifiable conditions on self-adjoint perturbations B, ensuring that the polluted set of B is identical to that of A. The results reported are illustrated by means of several canonical examples and they reveal the many subtleties involved in the systematic study of spectral pollution.
Neutrino masses in SU(5) x U(1){sub F} with adjoint flavons
Energy Technology Data Exchange (ETDEWEB)
Nardi, Enrico [INFN, Laboratori Nazionali di Frascati, C.P. 13, Frascati (Italy); IFT-UAM/CSIC, Madrid (Spain); Universidad Autonoma de Madrid, Departamento de Fisica Teorica, Madrid (Spain); Restrepo, Diego; Velasquez, Mauricio [Universidad de Antioquia, Instituto de Fisica, Medellin (Colombia)
2012-03-15
We present a SU(5) x U(1){sub F} supersymmetric model for neutrino masses and mixings that implements the seesaw mechanism by means of the heavy SU(2) singlets and triplets states contained in three adjoints of SU(5). We discuss how Abelian U(1){sub F} symmetries can naturally yield non-hierarchical light neutrinos even when the heavy states are strongly hierarchical, and how it can also ensure that R-parity arises as an exact accidental symmetry. By assigning two flavons that break U(1){sub F} to the adjoint representation of SU(5) and assuming universality for all the fundamental couplings, the coefficients of the effective Yukawa and Majorana mass operators become calculable in terms of group theoretical quantities. There is a single free parameter in the model, however, at leading order the structure of the light neutrinos mass matrix is determined in a parameter independent way. (orig.)
Adjoint representation of the graded Lie algebra osp(2/1; C) and its exponentiation
Ilyenko, K
2003-01-01
We construct explicitly the grade star Hermitian adjoint representation of osp(2/1; C) graded Lie algebra. Its proper Lie subalgebra, the even part of the graded Lie algebra osp(2/1; C), is given by su(2) compact Lie algebra. The Baker-Campbell-Hausdorff formula is considered and reality conditions for the Grassman-odd transformation parameters, which multiply the pair of odd generators of the graded Lie algebra, are clarified.
Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation
Yaşar, Emrullah; San, Sait; Özkan, Yeşim Sağlam
2016-01-01
In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2016-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet is demonstrated.
On Lipschitz Perturbations of a Self-Adjoint Strongly Positive Operator
Directory of Open Access Journals (Sweden)
Dinu Teodorescu
2013-01-01
Full Text Available In this paper we study semilinear equations of the form Au+λF(u=f, where A is a linear self-adjoint operator, satisfying a strong positivity condition, and F is a nonlinear Lipschitz operator. As applications we develop Krasnoselskii and Ky Fan type approximation results for certain pair of maps and to illustrate the usability of the obtained results, the existence of solution of an integral equation is provided.
CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine
Directory of Open Access Journals (Sweden)
Lasse Mueller
2017-09-01
Full Text Available The adjoint method is considered as the most efficient approach to compute gradients with respect to an arbitrary number of design parameters. However, one major challenge of adjoint-based shape optimization methods is the integration into a computer-aided design (CAD workflow for practical industrial cases. This paper presents an adjoint-based framework that uses a tailored shape parameterization to satisfy geometric constraints due to mechanical and manufacturing requirements while maintaining the shape in a CAD representation. The system employs a sequential quadratic programming (SQP algorithm and in-house developed libraries for the CAD and grid generation as well as a 3D Navier–Stokes flow and adjoint solver. The developed method is applied to a multipoint optimization of a turbocharger radial turbine aiming at maximizing the total-to-static efficiency at multiple operating points while constraining the output power and the choking mass flow of the machine. The optimization converged in a few design cycles in which the total-to-static efficiency could be significantly improved over a wide operating range. Additionally, the imposed aerodynamic constraints with strict convergence tolerances are satisfied and several geometric constraints are inherently respected due to the parameterization of the turbine. In particular, radial fibered blades are used to avoid bending stresses in the turbine blades due to centrifugal forces. The methodology is a step forward towards robustness and consistency of gradient-based optimization for practical industrial cases, as it maintains the optimal shape in CAD representation. As shown in this paper, this avoids shape approximations and allows manufacturing constraints to be included.
Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics
Strauss, Y; Machnes, S; Horwitz, L P
2011-01-01
In [J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its expectation value decreases monotonically for any initial state. In this paper we study some of this operator's properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.
Adjoint gradient-based approach for aerodynamic optimization of transport aircraft
Ilic, Caslav
2013-01-01
Aerodynamic design of transport aircraft has been steadily improved over past several decades, to the point where today highly-detailed shape control is needed to achieve further improvements. Aircraft manufacturers are therefore increasingly looking into formal optimization methods, driving high-fidelity CFD analysis of finely-parametrized candidate designs. We present an adjoint gradient-based approach for maximizing the aerodynamic performance index relevant to cruise-climb mission segment...
Ibragimov, Nail H
2011-01-01
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.
On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces
Directory of Open Access Journals (Sweden)
Sobhy El-Sayed Ibrahim
2003-01-01
order, with complex coefficients and its formal adjoint Mp+ on any finite number of intervals Ip=(ap,bp, p=1,…, N, are considered in the setting of the direct sums of Lwp2(ap,bp-spaces of functions defined on each of the separate intervals. And a number of results concerning the location of the point spectra and regularity fields of general differential operators generated by such expressions are obtained.
First results for SU(2) Yang-Mills with one adjoint Dirac Fermion
Athenodorou, Andreas; Bergner, Georg; Lucini, Biagio; Patella, Agostino
2013-01-01
We present a first exploratory study of SU(2) gauge theory with one Dirac flavour in the adjoint representation. We provide initial results for the spectroscopy and the anomalous dimension for the chiral condensate. Our investigation indicates that the theory is conformal or near-conformal, with an anomalous dimension of order one. A discussion of the relevance of these findings in relation to walking technicolor scenarios is also presented.
Running of the coupling and quark mass in SU(2) with two adjoint fermions
Bursa, Francis; Keegan, Liam; Pica, Claudio; Pickup, Thomas
2009-01-01
We simulate SU(2) gauge theory with two massless Dirac fermions in the adjoint representation. We calculate the running of the Schroedinger Functional coupling and the renormalised quark mass over a wide range of length scales. The running of the coupling is consistent with the existence of an infrared fixed point (IRFP), and we find 0.07 < gamma < 0.56 at the IRFP, depending on the value of the critical coupling.
Non-variational approximation of discrete eigenvalues of self-adjoint operators
Boulton, Lyonell
2005-01-01
We establish sufficiency conditions in order to achieve approximation to discrete eigenvalues of self-adjoint operators in the second-order projection method suggested recently by Levitin and Shargorodsky, [math.SP/0212087]. We find explicit estimates for the eigenvalue error and study in detail two concrete model examples. Our results show that, unlike the majority of the standard methods, second-order projection strategies combine non-pollution and approximation at a very high level of gene...
Aerodynamic Optimization Based on Continuous Adjoint Method for a Flexible Wing
Directory of Open Access Journals (Sweden)
Zhaoke Xu
2016-01-01
Full Text Available Aerodynamic optimization based on continuous adjoint method for a flexible wing is developed using FORTRAN 90 in the present work. Aerostructural analysis is performed on the basis of high-fidelity models with Euler equations on the aerodynamic side and a linear quadrilateral shell element model on the structure side. This shell element can deal with both thin and thick shell problems with intersections, so this shell element is suitable for the wing structural model which consists of two spars, 20 ribs, and skin. The continuous adjoint formulations based on Euler equations and unstructured mesh are derived and used in the work. Sequential quadratic programming method is adopted to search for the optimal solution using the gradients from continuous adjoint method. The flow charts of rigid and flexible optimization are presented and compared. The objective is to minimize drag coefficient meanwhile maintaining lift coefficient for a rigid and flexible wing. A comparison between the results from aerostructural analysis of rigid optimization and flexible optimization is shown here to demonstrate that it is necessary to include the effect of aeroelasticity in the optimization design of a wing.
Jacobs, Christian T; Kramer, Stephan C; Funke, Simon W
2016-01-01
Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation of high-resolution and ideally 3D transient models is generally a very computationally expensive problem. As a result, existing work on the adjoint optimisation of tidal turbine placement has been mostly limited to steady-state simulations in which very high, non-physical values of the background viscosity are required to ensure that a steady-state solution exists. However, such compromises may affect the reliability of the modelled turbines, their wakes and interactions, and thus bring into question the validity of the co...
SUSY SU(5) with singlet plus adjoint matter and A{sub 4} family symmetry
Energy Technology Data Exchange (ETDEWEB)
Cooper, Iain K., E-mail: ikc1g08@soton.ac.u [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); King, Stephen F., E-mail: sfk@hep.phys.soton.ac.u [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Luhn, Christoph, E-mail: christoph.luhn@soton.ac.u [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom)
2010-06-28
We propose a supersymmetric (SUSY) SU(5) Grand Unified Theory (GUT) including a single right-handed neutrino singlet and an adjoint matter representation below the GUT scale and extend this model to include an A{sub 4} family symmetry and a gauged anomaly-free Abelian group. In our approach hierarchical neutrino masses result from a combined type I and type III seesaw mechanism, and the A{sub 4} symmetry leads to tri-bimaximal mixing which arises indirectly. The mixing between the single right-handed neutrino and the matter in the adjoint is forbidden by excluding an adjoint Higgs, leading to a diagonal heavy Majorana sector as required by constrained sequential dominance. The model also reproduces a realistic description of quark and charged lepton masses and quark mixings, including the Georgi-Jarlskog relations and the leptonic mixing sum rules s=rcos{delta} and a=-r{sup 2}/4 with r={theta}{sub C}/3.
Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time
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.
First-arrival traveltime tomography for anisotropic media using the adjoint-state method
Waheed, Umair bin
2016-05-27
Traveltime tomography using transmission data has been widely used for static corrections and for obtaining near-surface models for seismic depth imaging. More recently, it is also being used to build initial models for full-waveform inversion. The classic traveltime tomography approach based on ray tracing has difficulties in handling large data sets arising from current seismic acquisition surveys. Some of these difficulties can be addressed using the adjoint-state method, due to its low memory requirement and numerical efficiency. By coupling the gradient computation to nonlinear optimization, it avoids the need for explicit computation of the Fréchet derivative matrix. Furthermore, its cost is equivalent to twice the solution of the forward-modeling problem, irrespective of the size of the input data. The presence of anisotropy in the subsurface has been well established during the past few decades. The improved seismic images obtained by incorporating anisotropy into the seismic processing workflow justify the effort. However, previous literature on the adjoint-state method has only addressed the isotropic approximation of the subsurface. We have extended the adjoint-state technique for first-arrival traveltime tomography to vertical transversely isotropic (VTI) media. Because δ is weakly resolvable from surface seismic alone, we have developed the mathematical framework and procedure to invert for vNMO and η. Our numerical tests on the VTI SEAM model demonstrate the ability of the algorithm to invert for near-surface model parameters and reveal the accuracy achievable by the algorithm.
Nabert, Christian; Othmer, Carsten; Glassmeier, Karl-Heinz
2017-05-01
The interaction of the solar wind with a planetary magnetic field causes electrical currents that modify the magnetic field distribution around the planet. We present an approach to estimating the planetary magnetic field from in situ spacecraft data using a magnetohydrodynamic (MHD) simulation approach. The method is developed with respect to the upcoming BepiColombo mission to planet Mercury aimed at determining the planet's magnetic field and its interior electrical conductivity distribution. In contrast to the widely used empirical models, global MHD simulations allow the calculation of the strongly time-dependent interaction process of the solar wind with the planet. As a first approach, we use a simple MHD simulation code that includes time-dependent solar wind and magnetic field parameters. The planetary parameters are estimated by minimizing the misfit of spacecraft data and simulation results with a gradient-based optimization. As the calculation of gradients with respect to many parameters is usually very time-consuming, we investigate the application of an adjoint MHD model. This adjoint MHD model is generated by an automatic differentiation tool to compute the gradients efficiently. The computational cost for determining the gradient with an adjoint approach is nearly independent of the number of parameters. Our method is validated by application to THEMIS (Time History of Events and Macroscale Interactions during Substorms) magnetosheath data to estimate Earth's dipole moment.
Probing Seesaw in an Adjoint SUSY SU(5) Model at LHC
Awasthi, Ram Lal; Mitra, Manimala
2010-01-01
The SU(5) GUT model extended with fermions in the adjoint $24_F$ representation predicts triplet fermions in the 100 GeV mass range, opening up the possibility of testing seesaw at LHC. However, once the model is supersymmerized, the triplet fermion mass is constrained to be close to the GUT scale for the gauge couplings to unify. We propose an extension of the SUSY SU(5) model where type II seesaw can be tested at LHC. In this model we add a matter chiral field in the adjoint $\\hat{24}_F$ representation and Higgs chiral superfields in the symmetric $\\hat{15}_H$ and $\\hat{\\bar{15}}_H$ representations. We call this the symmetric adjoint SUSY SU(5) model. The triplet scalar and triplet fermion masses in this model are predicted to be in the 100 GeV and $10^{13}$ GeV range respectively, while the mass of the singlet fermion remains unconstrained. This gives a type I plus type II plus type III seesaw mass term for the neutrinos. The triplet scalars with masses $\\sim 100$ GeV range can be produced at the LHC. We b...
Analysis on observing optimization for the wind-driven circulation by an adjoint approach
Institute of Scientific and Technical Information of China (English)
王东晓; 吴国雄; 朱江; 兰健
2000-01-01
The adjoint approach is a variational method which is often applied to data assimilation widely in meteorology and oceanography. It is used for analyses on observing optimization for the wind-driven Sverdrup circulation. The adjoint system developed by Thacker and Long (1992), which is based on the GFDL Byran-Cox model, includes three components, i. e. the forward model, the adjoint model and the optimal algorithm. The GFDL Byran-Cox model was integrated for a long time driven by a batch of ideal wind stresses whose meridional component is set to null and zonal component is a sine function of latitudes in a rectangle box with six vertical levels and 2 by 2 degree horizontal resolution. The results are regarded as a "real" representative of the wind-driven Sverdrup circulation, from which the four dimensional fields are allowed to be sampled in several ways, such as sampling at the different levels or along the different vertical sections. To set the different samples, the fields of temperature, salinity
Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
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
Dirac fields in the background of a magnetic flux string and spectral boundary conditions
Beneventano, C G; Santangelo, E M
1999-01-01
We study the problem of a Dirac field in the background of an Aharonov-Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behaviour of eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and evaluate its vacuum fermionic number and Casimir energy.
Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey
2015-04-01
The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each
Adjoint sensitivity of global cloud droplet number to aerosol and dynamical parameters
Directory of Open Access Journals (Sweden)
V. A. Karydis
2012-10-01
Full Text Available We present the development of the adjoint of a comprehensive cloud droplet formation parameterization for use in aerosol-cloud-climate interaction studies. The adjoint efficiently and accurately calculates the sensitivity of cloud droplet number concentration (CDNC to all parameterization inputs (e.g., updraft velocity, water uptake coefficient, aerosol number and hygroscopicity with a single execution. The adjoint is then integrated within three dimensional (3-D aerosol modeling frameworks to quantify the sensitivity of CDNC formation globally to each parameter. Sensitivities are computed for year-long executions of the NASA Global Modeling Initiative (GMI Chemical Transport Model (CTM, using wind fields computed with the Goddard Institute for Space Studies (GISS Global Circulation Model (GCM II', and the GEOS-Chem CTM, driven by meteorological input from the Goddard Earth Observing System (GEOS of the NASA Global Modeling and Assimilation Office (GMAO. We find that over polluted (pristine areas, CDNC is more sensitive to updraft velocity and uptake coefficient (aerosol number and hygroscopicity. Over the oceans of the Northern Hemisphere, addition of anthropogenic or biomass burning aerosol is predicted to increase CDNC in contrast to coarse-mode sea salt which tends to decrease CDNC. Over the Southern Oceans, CDNC is most sensitive to sea salt, which is the main aerosol component of the region. Globally, CDNC is predicted to be less sensitive to changes in the hygroscopicity of the aerosols than in their concentration with the exception of dust where CDNC is very sensitive to particle hydrophilicity over arid areas. Regionally, the sensitivities differ considerably between the two frameworks and quantitatively reveal why the models differ considerably in their indirect forcing estimates.
Directory of Open Access Journals (Sweden)
Yonghan Choi
2014-01-01
Full Text Available An adjoint sensitivity-based data assimilation (ASDA method is proposed and applied to a heavy rainfall case over the Korean Peninsula. The heavy rainfall case, which occurred on 26 July 2006, caused torrential rainfall over the central part of the Korean Peninsula. The mesoscale convective system (MCS related to the heavy rainfall was classified as training line/adjoining stratiform (TL/AS-type for the earlier period, and back building (BB-type for the later period. In the ASDA method, an adjoint model is run backwards with forecast-error gradient as input, and the adjoint sensitivity of the forecast error to the initial condition is scaled by an optimal scaling factor. The optimal scaling factor is determined by minimising the observational cost function of the four-dimensional variational (4D-Var method, and the scaled sensitivity is added to the original first guess. Finally, the observations at the analysis time are assimilated using a 3D-Var method with the improved first guess. The simulated rainfall distribution is shifted northeastward compared to the observations when no radar data are assimilated or when radar data are assimilated using the 3D-Var method. The rainfall forecasts are improved when radar data are assimilated using the 4D-Var or ASDA method. Simulated atmospheric fields such as horizontal winds, temperature, and water vapour mixing ratio are also improved via the 4D-Var or ASDA method. Due to the improvement in the analysis, subsequent forecasts appropriately simulate the observed features of the TL/AS- and BB-type MCSs and the corresponding heavy rainfall. The computational cost associated with the ASDA method is significantly lower than that of the 4D-Var method.
Automation of Global Adjoint Tomography Based on ASDF and Workflow Management Tools
Lei, W.; Ruan, Y.; Bozdag, E.; Smith, J. A.; Modrak, R. T.; Krischer, L.; Chen, Y.; Lefebvre, M. P.; Tromp, J.
2016-12-01
Global adjoint tomography is computationally expensive, requiring thousands of wavefield simulations and massive data processing. Though a collaboration with the Oak Ridge National Laboratory computing group and an allocation on the `Titan' GPU-accelerated supercomputer, we have begun to assimilate waveform data from more than 4,000 earthquakes, from 1995 to 2015, in our inversions. However, since conventional file formats and signal processing tools were not designed for parallel processing of massive data volumes, use of such tools in high-resolution global inversions leads to major bottlenecks. To overcome such problems and allow for continued scientific progress, we designed the Adaptive Seismic Data Format (ASDF) and developed a set of processing tools based on ASDF, covering from signal processing (pytomo3d), time window selection (pyflex) to adjoint source (pyadjoint). These new tools greatly enhance the reproducibility and accountability of our research while taking full advantage of parallel computing, showing superior scaling on modern computational platforms. The entire inversion workflow, intrinsically complex and sensitive to human errors, is carefully handled and automated by modern workflow management tools, preventing data contamination and saving a huge amount of time. Our starting model GLAD-M15 (Bozdag et al., 2016), an elastic model with transversely isotropic upper mantle, is based on 253 earthquakes and 15 nonlinear conjugate gradient iterations. We have now completed source inversions for more than 1,000 earthquakes and have started structural inversions using a quasi-Newton optimization algorithm. We will discuss the challenges of large-scale workflows on HPC systems, the solutions offered by our new adjoint tomography tools, and the initial tomographic results obtained using the new expanded dataset.
Reuther, James; Jameson, Antony; Alonso, Juan Jose; Rimlinger, Mark J.; Saunders, David
1997-01-01
An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat
Mapping Emissions that Contribute to Air Pollution Using Adjoint Sensitivity Analysis
Bastien, L. A. J.; Mcdonald, B. C.; Brown, N. J.; Harley, R.
2014-12-01
The adjoint of the Community Multiscale Air Quality model (CMAQ) is used to map emissions that contribute to air pollution at receptors of interest. Adjoint tools provide an efficient way to calculate the sensitivity of a model response to a large number of model inputs, a task that would require thousands of simulations using a more traditional forward sensitivity approach. Initial applications of this technique, demonstrated here, are to benzene and directly-emitted diesel particulate matter, for which atmospheric reactions are neglected. Emissions of these pollutants are strongly influenced by light-duty gasoline vehicles and heavy-duty diesel trucks, respectively. We study air quality responses in three receptor areas where populations have been identified as especially susceptible to, and adversely affected by air pollution. Population-weighted air basin-wide responses for each pollutant are also evaluated for the entire San Francisco Bay area. High-resolution (1 km horizontal grid) emission inventories have been developed for on-road motor vehicle emission sources, based on observed traffic count data. Emission estimates represent diurnal, day of week, and seasonal variations of on-road vehicle activity, with separate descriptions for gasoline and diesel sources. Emissions that contribute to air pollution at each receptor have been mapped in space and time using the adjoint method. Effects on air quality of both relative (multiplicative) and absolute (additive) perturbations to underlying emission inventories are analyzed. The contributions of local versus upwind sources to air quality in each receptor area are quantified, and weekday/weekend and seasonal variations in the influence of emissions from upwind areas are investigated. The contribution of local sources to the total air pollution burden within the receptor areas increases from about 40% in the summer to about 50% in the winter due to increased atmospheric stagnation. The effectiveness of control
Self-adjointness and the Casimir effect with confined quantized spinor matter
Sitenko, Yurii A
2015-01-01
A generalization of the MIT bag boundary condition for spinor matter is proposed basing on the requirement that the Dirac hamiltonian operator be self-adjoint. An influence of a background magnetic field on the vacuum of charged spinor matter confined between two parallel material plates is studied. Employing the most general set of boundary conditions at the plates in the case of the uniform magnetic field directed orthogonally to the plates, we find the pressure from the vacuum onto the plates. In physically plausible situations, the Casimir effect is shown to be repulsive, independently of a choice of boundary conditions and of a distance between the plates.
Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds
Directory of Open Access Journals (Sweden)
T. Mine
2010-01-01
Full Text Available We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in terms of the boundary conditions. The result is an extension of the former results by Dabrowski-Šťoviček and Exner-Šťoviček-Vytřas.
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2017-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated.
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2017-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851
Kovtun, Pavel; Ünsal, Mithat; Yaffe, Laurence G.
2003-12-01
We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; hence the demonstrated non-perturbative equivalence applies to the large N limits of both string tensions and particle spectra.
Intertwining operators for non-self-adjoint Hamiltonians and bicoherent states
Bagarello, F.
2016-10-01
This paper is devoted to the construction of what we will call exactly solvable models, i.e., of quantum mechanical systems described by an Hamiltonian H whose eigenvalues and eigenvectors can be explicitly constructed out of some minimal ingredients. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed.
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Nakshatrala, Praveen B.; Tortorelli, Daniel A.
2014-01-01
Gradient-based topology optimization typically involves thousands or millions of design variables. This makes efficient sensitivity analysis essential and for this the adjoint variable method (AVM) is indispensable. For transient problems it has been observed that the traditional AVM, based...... on a differentiate-then-discretize approach, may lead to inconsistent sensitivities. Herein this effect is explicitly demonstrated for a single dof system and the source of inconsistency is identified. Additionally, we outline an alternative discretize-then-differentiate AVM that inherently produces consistent...
Diagonalization of a self-adjoint operator acting on a Hilbert module
Directory of Open Access Journals (Sweden)
Parfeny P. Saworotnow
1985-01-01
Full Text Available For each bounded self-adjoint operator T on a Hilbert module H over an H*-algebra A there exists a locally compact space m and a certain A-valued measure μ such that H is isomorphic to L2(μ⊗A and T corresponds to a multiplication with a continuous function. There is a similar result for a commuting family of normal operators. A consequence for this result is a representation theorem for generalized stationary processes.
An update in monopole condensation in two-flavour Adjoint QCD
Lacagnina, G; D'Elia, M; Di Giacomo, A; Pica, C
2007-01-01
QCD with fermions in the adjoint representation (aQCD) is a model for which a deconfinement and a chiral phase transition take place at different temperatures. In this work, we present a study of the deconfinement transition in the dual superconductor picture based on the evaluation of an operator which carries magnetic charge. The expectation value of this operator signals monopole condensation and is an order parameter for deconfinement as in the case of fermions in the fundamental representation. We find a sharp first order deconfinement transition. We also study the effects of the chiral transition on the monopole order parameter and find them negligible.
Propagators of hot SU(2) gauge theory from 3d adjoint Higgs model
Karsch, Frithjof
2000-01-01
We study propagators of the lattice 3d adjoint Higgs model, considered as an effective theory of 4d SU(2) gauge theory at high temperature. The propagators are calculated in so-called lambda-gauges. From the long distance behaviour of the propagators we extract the screening masses. It is shown that the pole masses extracted from the propagators agree well with the screening masses obtained recently in finite temperature SU(2) theory. The gauge dependence of the screening masses is also discussed.
Screening Masses of Hot SU(2) Gauge Theory from the 3D Adjoint Higgs Model
Karsch, Frithjof; Petreczky, P
1999-01-01
We study the Landau gauge propagators of the lattice SU(2) 3d adjoint Higgs model, considered as an effective theory of high temperature 4d SU(2) gauge theory. From the long distance behaviour of the propagators we extract the screening masses. It is shown that the pole masses extracted from the propagators agree well with the screening masses obtained recently in finite temperature SU(2) theory. The relation of the propagator masses to the masses extracted from gauge invariant correlators is also discussed. In so-called lambda gauges non-perturbative evidence is given for the gauge independence of pole masses within this class of gauges.
On Maximal Abelian Self-adjoint Subalgebras of Factors of Type Ⅱ1
Institute of Scientific and Technical Information of China (English)
Li Guang WANG
2005-01-01
In this note, we show that if (N) is a proper subfactor of a factor (M) of type Ⅱ1 with finite Jones index, then there is a maximal abelian self-adjoint subalgebra (masa) (A) of (N) that is not a masa in (M). Popa showed that there is a proper subfactor (R)O of the hyperfinite type Ⅱ1 factor (R) such that each masa in (R)O is also a masa in (R). We shall give a detailed proof of Popa's result.
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Mani, Karthik
Adjoint methods have found applications in several key areas of computational fluid dynamics (CFD), namely, shape optimization and goal based adaptive solutions. CFD has become an essential tool in the design process by enabling the rapid testing of multiple designs, and currently it is normal practice to use CFD in conjunction with optimization algorithms for design improvement. In the context of shape optimization problems based on CFD, adjoint methods offer the significant advantage of computing sensitivity derivatives of the optimization cost function with respect to the set of design parameters, at a cost that is essentially independent of the number of design parameters. Adjoint methods reduce the cost of obtaining the complete gradient vector at any point in the design space equivalent to that of a single flow solution at the same point in the design space. This immediately enables the use of all gradient based optimization algorithms and lifts any restrictions on the number of design parameters required for the adequate definition of the optimization problem. Adaptive techniques in CFD constitute the other aspect where adjoint methods have have made great inroads. Typical adaptive solutions of the governing flow equations rely on estimating the local error in an evolving solution to target regions of the computational mesh for increased discrete resolution. The main goal of any adaptive solution method is the overall increase in solution accuracy with minimal increase in computational cost. However, targeting local error in the solution does not translate into efficient use of computational resources, since ultimately it is the accurate estimation of boundary integrated functional quantities such as load coefficients that are of importance to the user. Contrary to local error-based methods, adjoint methods allow the adaptation of the computational mesh specifically for the improvement of functionals such as load coefficients. This is achieved by
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
Martin, Nathan
2014-01-01
This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability to identify the friction coefficient for such methods with a non-linear friction law. The exact adjoint problem is solved, based on second order numerical schemes, and a comparison with the so called "self-adjoint" approximation, neglecting the viscosity dependency to the velocity (leading to an incorrect gradient), common in glaciology, is carried out. For data with a noise of $1\\%$, a lower bound of identifiable wavelengths of $10$ ice thicknesses in the friction coefficient is established, when using the exact adjoint method, while the "self-adjoint" method is limited, even for lower noise, to a minimum of $20$ ice thicknesses wavelengths. The second order exact gradient method therefore provides robustness and reliability for the parameter identification process. In othe...
Ibort, A
2012-01-01
In these three lectures we will discuss some fundamental aspects of the theory of self-adjoint extensions of the covariant Laplace-Beltrami and Dirac operators on compact Riemannian manifolds with smooth boundary emphasizing the relation with the theory of global boundary conditions. Self-adjoint extensions of symmetric operators, specially of the Laplace-Beltrami and Dirac operators, are fundamental in Quantum Physics as they determine either the energy of quantum systems and/or their unitary evolution. The well-known von Neumann's theory of self-adjoint extensions of symmetric operators is not always easily applicable to differential operators, while the description of extensions in terms of boundary conditions constitutes a more natural approach. Thus an effort is done in offering a description of self-adjoint extensions in terms of global boundary conditions showing how an important family of self-adjoint extensions for the Laplace-Beltrami and Dirac operators are easily describable in this way. Moreover ...
Critical flux determination by flux-stepping
DEFF Research Database (Denmark)
Beier, Søren; Jonsson, Gunnar Eigil
2010-01-01
In membrane filtration related scientific literature, often step-by-step determined critical fluxes are reported. Using a dynamic microfiltration device, it is shown that critical fluxes determined from two different flux-stepping methods are dependent upon operational parameters such as step......, such values are more or less useless in itself as critical flux predictors, and constant flux verification experiments have to be conducted to check if the determined critical fluxes call predict sustainable flux regimes. However, it is shown that using the step-by-step predicted critical fluxes as start...
Magnetic Field Separation Around Planets Using an Adjoint-Method Approach
Nabert, Christian; Glassmeier, Karl-Heinz; Heyner, Daniel; Othmer, Carsten
The two spacecraft of the BepiColombo mission will reach planet Mercury in 2022. The magnetometers on-board these polar orbiting spacecraft will provide a detailed map of the magnetic field in Mercury's environment. Unfortunately, a separation of the magnetic field into internal and external parts using the classical Gauss-algorithm is not possible due to strong electric currents in the orbit region of the spacecraft. These currents are due to the interaction of the solar wind with Mercury's planetary magnetic field. We use an MHD code to simulate this interaction process. This requires a first choice of Mercury's planetary field which is used and modified until the simulation results fit to the actual measurements. This optimization process is carried out most efficiently using an adjoint-method. The adjoint-method is well known for its low computational cost in order to determine sensitivities required for the minimization. In a first step, the validity of our approach to separate magnetic field contributions into internal and external parts is demonstrated using synthetic generated data. Furthermore, we apply our approach to satellite measurements of the Earth's magnetic field. We can compare the results with the well known planetary field of the Earth to prove practical suitability.
Optimization of computations for adjoint field and Jacobian needed in 3D CSEM inversion
Dehiya, Rahul; Singh, Arun; Gupta, Pravin K.; Israil, M.
2017-01-01
We present the features and results of a newly developed code, based on Gauss-Newton optimization technique, for solving three-dimensional Controlled-Source Electromagnetic inverse problem. In this code a special emphasis has been put on representing the operations by block matrices for conjugate gradient iteration. We show how in the computation of Jacobian, the matrix formed by differentiation of system matrix can be made independent of frequency to optimize the operations at conjugate gradient step. The coarse level parallel computing, using OpenMP framework, is used primarily due to its simplicity in implementation and accessibility of shared memory multi-core computing machine to almost anyone. We demonstrate how the coarseness of modeling grid in comparison to source (comp`utational receivers) spacing can be exploited for efficient computing, without compromising the quality of the inverted model, by reducing the number of adjoint calls. It is also demonstrated that the adjoint field can even be computed on a grid coarser than the modeling grid without affecting the inversion outcome. These observations were reconfirmed using an experiment design where the deviation of source from straight tow line is considered. Finally, a real field data inversion experiment is presented to demonstrate robustness of the code.
Ocean acoustic tomography from different receiver geometries using the adjoint method.
Zhao, Xiaofeng; Wang, Dongxiao
2015-12-01
In this paper, an ocean acoustic tomography inversion using the adjoint method in a shallow water environment is presented. The propagation model used is an implicit Crank-Nicolson finite difference parabolic equation solver with a non-local boundary condition. Unlike previous matched-field processing works using the complex pressure fields as the observations, here, the observed signals are the transmission losses. Based on the code tests of the tangent linear model, the adjoint model, and the gradient, the optimization problem is solved by a gradient-based minimization algorithm. The inversions are performed in numerical simulations for two geometries: one in which hydrophones are sparsely distributed in the horizontal direction, and another in which the hydrophones are distributed vertically. The spacing in both cases is well beyond the half-wavelength threshold at which beamforming could be used. To deal with the ill-posedness of the inverse problem, a linear differential regularization operator of the sound-speed profile is used to smooth the inversion results. The L-curve criterion is adopted to select the regularization parameter, and the optimal value can be easily determined at the elbow of the logarithms of the residual norm of the measured-predicted fields and the norm of the penalty function.
Tide-surge adjoint modeling: A new technique to understand forecast uncertainty
Wilson, Chris; Horsburgh, Kevin J.; Williams, Jane; Flowerdew, Jonathan; Zanna, Laure
2013-10-01
For a simple dynamical system, such as a pendulum, it is easy to deduce where and when applied forcing might produce a particular response. However, for a complex nonlinear dynamical system such as the ocean or atmosphere, this is not as obvious. Knowing when or where the system is most sensitive, to observational uncertainty or otherwise, is key to understanding the physical processes, improving and providing reliable forecasts. We describe the application of adjoint modeling to determine the sensitivity of sea level at a UK coastal location, Sheerness, to perturbations in wind stress preceding an extreme North Sea storm surge event on 9 November 2007. Sea level at Sheerness is one of the most important factors used to decide whether to close the Thames Flood Barrier, which protects London. Adjoint modeling has been used by meteorologists since the 1990s, but is a relatively new technique for ocean modeling. It may be used to determine system sensitivity beyond the scope of ensemble modeling and in a computationally efficient way. Using estimates of wind stress error from Met Office forecasts, we find that for this event total sea level at Sheerness is most sensitive in the 3 h preceding the time of its unperturbed maximum level and over a radius of approximately 300 km. We also find that the pattern of sensitivity follows a simple sequence when considered in the reverse-time direction.
Energy Technology Data Exchange (ETDEWEB)
Abhyankar, Shrirang [Argonne National Lab. (ANL), Argonne, IL (United States); Anitescu, Mihai [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil [Argonne National Lab. (ANL), Argonne, IL (United States); Zhang, Hong [Argonne National Lab. (ANL), Argonne, IL (United States)
2016-03-31
Sensitivity analysis is an important tool to describe 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 work, 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 trajectory sensitivities of larger systems and is consistent, within machine precision, with the function whose 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 and time-dependent discontinuities. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach.
Adjoint Tomography of Taiwan Region: From Travel-Time Toward Waveform Inversion
Huang, H. H.; Lee, S. J.; Tromp, J.
2014-12-01
The complicated tectonic environment such as Taiwan region can modulate the seismic waveform severely and hamper the discrimination and the utilization of later phases. Restricted to the use of only first arrivals of P- and S-wave, the travel-time tomographic models of Taiwan can simulate the seismic waveform barely to a frequency of 0.2 Hz to date. While it has been sufficient for long-period studies, e.g. source inversion, this frequency band is still far from the applications to the community and high-resolution studies. To achieve a higher-frequency simulation, more data and the considerations of off-path and finite-frequency effects are necessary. Based on the spectral-element and the adjoint method recently developed, we prepared 94 MW 3.5-6.0 earthquakes with well-defined location and focal mechanism solutions from Real-Time Moment Tensor Monitoring System (RMT), and preformed an iterative gradient-based inversion employing waveform modeling and finite-frequency measurements of adjoint method. By which the 3-D sensitivity kernels are taken into account realistically and the full waveform information are naturally sought, without a need of any phase pick. A preliminary model m003 using 10-50 sec data was demonstrated and compared with previous travel-time models. The primary difference appears in the mountainous area, where the previous travel-time model may underestimate the S-wave speed in the upper crust, but overestimates in the lower crust.
Yu, Jia; Ji, Lucheng; Li, Weiwei; Yi, Weilin
2016-06-01
Adjoint method is an important tool for design refinement of multistage compressors. However, the radial static pressure distribution deviates during the optimization procedure and deteriorates the overall performance, producing final designs that are not well suited for realistic engineering applications. In previous development work on multistage turbomachinery blade optimization using adjoint method and thin shear-layer N-S equations, the entropy production is selected as the objective function with given mass flow rate and total pressure ratio as imposed constraints. The radial static pressure distribution at the interfaces between rows is introduced as a new constraint in the present paper. The approach is applied to the redesign of a five-stage axial compressor, and the results obtained with and without the constraint on the radial static pressure distribution at the interfaces between rows are discussed in detail. The results show that the redesign without the radial static pressure distribution constraint (RSPDC) gives an optimal solution that shows deviations on radial static pressure distribution, especially at rotor exit tip region. On the other hand, the redesign with the RSPDC successfully keeps the radial static pressure distribution at the interfaces between rows and make sure that the optimization results are applicable in a practical engineering design.
Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation
Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David
1996-01-01
This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.
Aerodynamic Optimization of the Nose Shape of a Train Using the Adjoint Method
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Jorge Munoz-Paniagua
2015-01-01
Full Text Available The adjoint method is used in this paper for the aerodynamic optimization of the nose shape of a train. This method has been extensively applied in aircraft or ground vehicle aerodynamic optimization, but is still in progress in train aerodynamics. Here we consider this innovative optimization method and present its application to reduce the aerodynamic drag when the train is subjected to front wind. The objective of this paper is to demonstrate the effectiveness of the method, highlighting the requirements, limitations and capabilities of it. Furthermore, a significant reduction of the aerodynamic drag in a short number of solver calls is aimed as well. The independence of the computational cost with respect to the number of design variables that define the optimal candidate is stressed as the most interesting characteristic of the adjoint method. This behavior permits a more complete modification of the shape of the train nose because the number of design variables is not a constraint anymore. The information obtained from the sensitivity field permits determining the regions of the geometry where a small modification of the nose shape might introduce a larger improvement of the train performance. A good agreement between this information and the successive geometry modifications is observed here.
Decomposition of almost Poisson structure of non-self-adjoint dynamical systems
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the almost Poisson structure is investigated based on a decompo- sition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding rela- tion between Poisson structure and symplectic structure is proved, making use of Jacobiizer and symplecticizer. Based on analysis of pseudo-symplectic structure of constraint submanifold of Chaplygin’s nonholonomic systems, an almost Poisson bracket for the systems is constructed and decomposed into a sum of a canonical Poisson one and an almost Poisson one. Similarly, an almost Poisson structure, which can be decomposed into a sum of canonical one and an almost "Lie-Poisson" one, is also constructed on an affine space with torsion whose autoparallels are utilized to describe the free motion of some non-self-adjoint systems. The decomposition of the almost Poisson bracket di- rectly leads to a decomposition of a dynamical vector field into a sum of usual Hamiltionian vector field and an almost Hamiltonian one, which is useful to simplifying the integration of vector fields.
Infrared conformality and bulk critical points: SU(2) with heavy adjoint quarks
Lucini, Biagio; Rago, Antonio; Rinaldi, Enrico
2013-01-01
The lattice phase structure of a gauge theory can be a serious obstruction to Monte Carlo studies of its continuum behaviour. This issue is particularly delicate when numerical studies are performed to determine whether a theory is in a (near-)conformal phase. In this work we investigate the heavy mass limit of the SU(2) gauge theory with Nf=2 adjoint fermions and its lattice phase diagram, showing the presence of a critical point ending a line of first order bulk phase transition. The relevant gauge observables and the low-lying spectrum are monitored in the vicinity of the critical point with very good control over different systematic effects. The scaling properties of masses and susceptibilities open the possibility that the effective theory at criticality is a scalar theory in the universality class of the four-dimensional Gaussian model. This behaviour is clearly different from what is observed for SU(2) gauge theory with two dynamical adjoint fermions, whose (near-)conformal numerical signature is henc...
Estimation of Oceanic Eddy Viscosity Profile and Wind Stress Drag Coefficient Using Adjoint Method
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Qilin Zhang
2015-01-01
Full Text Available Adjoint method is used to assimilate pseudoobservations to simultaneously estimate the OEVP and the WSDC in an oceanic Ekman layer model. Five groups of experiments are designed to investigate the influences that the optimization algorithms, step-length, inverse integral time of the adjoint model, prescribed vertical distribution of eddy viscosity, and regularization parameter exert on the inversion results. Experimental results show that the best estimation results are obtained with the GD algorithm; the best estimation results are obtained when the step-length is equal to 1 in Group 2; in Group 3, 8 days of inverse integral time yields the best estimation results, and good assimilation efficiency is achieved by increasing iteration steps when the inverse integral time is reduced; in Group 4, the OEVP can be estimated for some specific distributions; however, when the VEVCs increase along with the depth at the bottom of water, the estimation results are relatively poor. For this problem, we use extrapolation method to deal with the VEVCs in layers in which the estimation results are poor; the regularization method with appropriate regularization parameter can indeed improve the experiment result to some extent. In all experiments in Groups 2-3, the WSDCs are inverted successfully within 100 iterations.
Coupling of MASH-MORSE Adjoint Leakages with Space- and Time-Dependent Plume Radiation Sources
Energy Technology Data Exchange (ETDEWEB)
Slater, C.O.
2001-04-20
In the past, forward-adjoint coupling procedures in air-over-ground geometry have typically involved forward fluences arising from a point source a great distance from a target or vehicle system. Various processing codes were used to create localized forward fluence files that could be used to couple with the MASH-MORSE adjoint leakages. In recent years, radiation plumes that result from reactor accidents or similar incidents have been modeled by others, and the source space and energy distributions as a function of time have been calculated. Additionally, with the point kernel method, they were able to calculate in relatively quick fashion free-field radiation doses for targets moving within the fluence field or for stationary targets within the field, the time dependence for the latter case coming from the changes in position, shape, source strength, and spectra of the plume with time. The work described herein applies the plume source to the MASH-MORSE coupling procedure. The plume source replaces the point source for generating the forward fluences that are folded with MASH-MORSE adjoint leakages. Two types of source calculations are described. The first is a ''rigorous'' calculation using the TORT code and a spatially large air-over-ground geometry. For each time step desired, directional fluences are calculated and are saved over a predetermined region that encompasses a structure within which it is desired to calculate dose rates. Processing codes then create the surface fluences (which may include contributions from radiation sources that deposit on the roof or plateout) that will be coupled with the MASH-MORSE adjoint leakages. Unlike the point kernel calculations of the free-field dose rates, the TORT calculations in practice include the effects of ground scatter on dose rates and directional fluences, although the effects may be underestimated or overestimated because of the use of necessarily coarse mesh and quadrature in order to
Directory of Open Access Journals (Sweden)
K. C. Wells
2015-07-01
Full Text Available We describe a new 4D-Var inversion framework for N2O based on the GEOS-Chem chemical transport model and its adjoint, and apply this framework in a series of observing system simulation experiments to assess how well N2O sources and sinks can be constrained by the current global observing network. The employed measurement ensemble includes approximately weekly and quasi-continuous N2O measurements (hourly averages used from several long-term monitoring networks, N2O measurements collected from discrete air samples aboard a commercial aircraft (CARIBIC, and quasi-continuous measurements from an airborne pole-to-pole sampling campaign (HIPPO. For a two-year inversion, we find that the surface and HIPPO observations can accurately resolve a uniform bias in emissions during the first year; CARIBIC data provide a somewhat weaker constraint. Variable emission errors are much more difficult to resolve given the long lifetime of N2O, and major parts of the world lack significant constraints on the seasonal cycle of fluxes. Current observations can largely correct a global bias in the stratospheric sink of N2O if emissions are known, but do not provide information on the temporal and spatial distribution of the sink. However, for the more realistic scenario where source and sink are both uncertain, we find that simultaneously optimizing both would require unrealistically small errors in model transport. Regardless, a bias in the magnitude of the N2O sink would not affect the a posteriori N2O emissions for the two-year timescale used here, given realistic initial conditions, due to the timescale required for stratosphere–troposphere exchange (STE. The same does not apply to model errors in the rate of STE itself, which we show exerts a larger influence on the tropospheric burden of N2O than does the chemical loss rate over short (2O emissions. There, averaging kernels are highly smeared spatially and extend even to the midlatitudes, so that tropical
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.
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Guo Feng
2008-01-01
Full Text Available Abstract We consider the classes of periodic functions with formal self-adjoint linear differential operators , which include the classical Sobolev class as its special case. With the help of the spectral of linear differential equations, we find the exact values of Bernstein -width of the classes in the for .
Bondarenko, S
2015-01-01
We revisit the next-to-leading order~(NLO) correction to the eigenvalue of the BFKL equation in the adjoint representation and investigate its properties in analogy with the singlet BFKL in planar $\\mathcal{N}=4$ super Yang-Mills Theory~(SYM). We show that the adjoint NLO BFKL eigenvalue is needed to be slightly modified in order to have a property of hermitian separability present for the singlet BFKL. After this modification the adjoint NLO BFKL eigenvalue is expressed through holomorphic and antiholomophic parts of the leading order eigenvalue and their derivatives. The proposed choice of the modified NLO expression is supported by the fact that it is possible to obtain the same result in a relatively straightforward way directly from the singlet NLO BFKL eigenvalue replacing alternating series by series of constant sign. This transformation corresponds to changing cylindrical topology of the singlet BFKL to the planar topology of the adjoint BFKL. We believe that the original NLO calculation of Fadin and ...
Brezillon, J.; Dwight, R.P.
2009-01-01
Within the next few years, numerical shape optimization based on high fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimization problems, and the adjoint approach - which allows fast
Rozvany, G. I. N.; Sobieszczanski-Sobieski, J.
1992-01-01
In new, iterative continuum-based optimality criteria (COC) methods, the strain in the adjoint structure becomes non-unique if the number of active local constraints is greater than the number of design variables for an element. This brief note discusses the use of smooth envelope functions (SEFs) in overcoming economically computational problems caused by the above non-uniqueness.
Using Adjoint Methods to Improve 3-D Velocity Models of Southern California
Liu, Q.; Tape, C.; Maggi, A.; Tromp, J.
2006-12-01
We use adjoint methods popular in climate and ocean dynamics to calculate Fréchet derivatives for tomographic inversions in southern California. The Fréchet derivative of an objective function χ(m), where m denotes the Earth model, may be written in the generic form δχ=int Km(x) δln m(x) d3x, where δln m=δ m/m denotes the relative model perturbation. For illustrative purposes, we construct the 3-D finite-frequency banana-doughnut kernel Km, corresponding to the misfit of a single traveltime measurement, by simultaneously computing the 'adjoint' wave field s† forward in time and reconstructing the regular wave field s backward in time. The adjoint wave field is produced by using the time-reversed velocity at the receiver as a fictitious source, while the regular wave field is reconstructed on the fly by propagating the last frame of the wave field saved by a previous forward simulation backward in time. The approach is based upon the spectral-element method, and only two simulations are needed to produce density, shear-wave, and compressional-wave sensitivity kernels. This method is applied to the SCEC southern California velocity model. Various density, shear-wave, and compressional-wave sensitivity kernels are presented for different phases in the seismograms. We also generate 'event' kernels for Pnl, S and surface waves, which are the Fréchet kernels of misfit functions that measure the P, S or surface wave traveltime residuals at all the receivers simultaneously for one particular event. Effectively, an event kernel is a sum of weighted Fréchet kernels, with weights determined by the associated traveltime anomalies. By the nature of the 3-D simulation, every event kernel is also computed based upon just two simulations, i.e., its construction costs the same amount of computation time as an individual banana-doughnut kernel. One can think of the sum of the event kernels for all available earthquakes, called the 'misfit' kernel, as a graphical
Pseudo limits, bi-adjoints, and pseudo algebras: Categorical foundations of conformal field theory
Fiore, Thomas M.
In this paper we develop categorical foundations needed for a rigorous approach to the definition of conformal field theory outlined by Graeme Segal. We discuss pseudo algebras over theories and 2-theories, their pseudo morphisms, bilimits, bicolimits, bi-adjoints, stacks, and related concepts. These 2-categorical concepts are used to describe the algebraic structure on the class of rigged surfaces. A rigged surface is a real, compact, not necessarily connected, two dimensional manifold with complex structure and analytically parametrized boundary components. This class admits algebraic operations of disjoint union and gluing as well as a unit given by the empty rigged surface. These operations satisfy axioms of commutivity, associativity, unitality, transitivity, distributivity, and unit cancellation up to coherence isomorphism. Furthermore, these coherence isomorphisms satisfy coherence diagrams. These operations, coherences, and their diagrams are neatly encoded as a pseudo algebra over the 2-theory of commutative monoids with cancellation . A conformal field theory is a morphism of stacks of such structures. This thesis begins with a review of 2-categorical concepts, Lawvere theories, and algebras over Lawvere theories. We prove that the 2-categories of small categories and small pseudo algebras over a theory admit weighted pseudo limits and weighted bicolimits. The 2-category of pseudo algebras over a theory is bi-equivalent to the 2-category of algebras over a 2-monad with pseudo morphisms. We prove that a pseudo functor admits a left bi-adjoint if and only if it admits certain bi-universal arrows. An application of this theorem implies that the forgetful functor for pseudo algebras admits a left bi-adjoint. We introduce stacks for Grothendieck topologies and prove that the traditional definition of stacks in terms of descent data is equivalent to our definition via bilimits. The final chapter contains a proof that the 2-category of pseudo algebras over a 2
Adjoint Sensitivity Experiments of a Meso-β-scale Vortex in the Middle Reaches of the Yangtze River
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A relatively independent and small-scale heavy rainfall event occurred to the south of a slow eastward-moving meso-α-scale vortex. The analysis shows that a meso-β-scale system is heavily responsible for the intense precipitation. An attempt to simulate it met with some failures. In view of its small scale, short lifetime and relatively sparse observations at the initial time, an adjoint model was used to examine the sensitivity of the meso-β-scale vortex simulation with respect to initial conditions. The adjoint sensitivity indicates how small perturbations of initial model variables anywhere in the model domain can influence the central vorticity of the vortex. The largest sensitivity for both the wind and temperature perturbation is located below 700 hPa, especially at the low level. The largest sensitivity for the water vapor perturbation is located below 500 hPa, especially at the middle and low levels. The horizontal adjoint sensitivity for all variables is mainly located toward the upper reaches of the Yangtze River with respect to the simulated meso-β-scale system in Hunan and Jiangxi provinces with strong locality. The sensitivity shows that warm cyclonic perturbations in the upper reaches can have a great effect on the development of the meso-β-scale vortex. Based on adjoint sensitivity, forward sensitivity experiments were conducted to identify factors influencing the development of the meso-β-scale vortex and to explore ways of improving the prediction. A realistic prediction was achieved by using adjoint sensitivity to modify the initial conditions and implanting a warm cyclone at the initial time in the upper reaches of the river with respect to the meso-β-scale vortex,as is commonly done in tropical cyclone prediction.
Zahr, M. J.; Persson, P.-O.
2016-12-01
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian-Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge-Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space-time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization. The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier-Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.
One-loop adjoint masses for non-supersymmetric intersecting branes
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Anastasopoulos, P. [Technische Univ., Vienna (Austria). 1. Inst. fuer Theoretische Physik; Antoniadis, I. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Benakli, K. [CNRS, UPMC Univ. Paris (France). Lab. de Physique Theorique et Haute Energies; Goodsell, M.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Vichi, A. [Institute de Theorie des Phenomenes Physiques, EPFL, Lausanne (Switzerland)
2011-05-15
We consider breaking of supersymmetry in intersecting D-brane configurations by slight deviation of the angles from their supersymmetric values. We compute the masses generated by radiative corrections for the adjoint scalars on the brane world-volumes. In the open string channel, the string two-point function receives contributions only from the infrared and the ultraviolet limits. The latter is due to tree-level closed string uncanceled NS-NS tadpoles, which we explicitly reproduce from the effective Born-Infeld action. On the other hand, the infrared region reproduces the one-loop mediation of supersymmetry breaking in the effective gauge theory, via messengers and their Kaluza-Klein excitations. In the toroidal set-up considered here, it receives contributions only from N {approx} 4 and N {approx} 2 supersymmetric configurations, and thus always leads at leading order to a tachyonic direction, in agreement with effective field theory expectations. (orig.)
Chiba, G.; Tsuji, M.; Narabayashi, T.
2014-04-01
In order to better predict a kinetic behavior of a nuclear fission reactor, an improvement of the delayed neutron parameters is essential. The present paper specifies important nuclear data for a reactor kinetics: Fission yield and decay constant data of 86Ge, some bromine isotopes, 94Rb, 98mY and some iodine isotopes. Their importance is quantified as sensitivities with a help of the adjoint kinetic equation, and it is found that they are dependent on an inserted reactivity (or a reactor period). Moreover, dependence of sensitivities on nuclear data files is also quantified using the latest files. Even though the currently evaluated data are used, there are large differences among different data files from a view point of the delayed neutrons.
Adjoint-based optimization of flapping plates hinged with a trailing-edge flap
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Min Xu
2015-01-01
Full Text Available It is important to understand the impact of wing-morphing on aerodynamic performance in the study of flapping-wing flight of birds and insects. We use a flapping plate hinged with a trailing-edge flap as a simplified model for flexible/morphing wings in hovering. The trailing-edge flapping motion is optimized by an adjoint-based approach. The optimized configuration suggests that the trailing-edge flap can substantially enhance the overall lift. Further analysis indicates that the lift enhancement by the trailing-edge flapping is from the change of circulation in two ways: the local circulation change by the rotational motion of the flap, and the modification of vortex shedding process by the relative location between the trailing-edge flap and leading-edge main plate.
Numerical Study on Initial Field of Pollution in the Bohai Sea with an Adjoint Method
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Chunhui Wang
2013-01-01
Full Text Available Based on the simulation of a marine ecosystem dynamical model in the Bohai Sea, routine monitoring data are assimilated to study the initial field of pollution by using the adjoint method. In order to reduce variables that need to be optimized and make the simulation results more reasonable, an independent grid is selected every four grids both in longitude and latitude, and only the pollutant concentrations of these independent grids needed to be optimized while the other grids were calculated by interpolation method. Based on this method, the stability and reliability of this model were proved by a set of twin experiments. Therefore, this model could be applied in real experiment to simulate the initial field of the total nitrogen (totalN in May, 2009. Moreover, the distribution of totalN in any time step could be calculated by this model, and the monthly mean distribution in May in the Bohai Sea could be obtained.
An adjoint data assimilation method for optimizing frictional parameters on the afterslip area
Kano, Masayuki; Miyazaki, Shin'ichi; Ito, Kosuke; Hirahara, Kazuro
2013-12-01
Afterslip sometimes triggers subsequent earthquakes within a timescale of days to several years. Thus, it may be possible to predict the occurrence of such a triggered earthquake by simulating the spatio-temporal evolution of afterslip with estimated frictional parameters. To demonstrate the feasibility of this idea, we consider a plate interface model where afterslip propagates between two asperities following a rate-and-state friction law, and we adopt an adjoint data assimilation method to optimize frictional parameters. Synthetic observation data are sampled as the slip velocities on the plate interface during 20 days. It is found that: (1) all frictional parameters are optimized if the data sets consists not only of the early phase of afterslip or acceleration, but also of the decaying phase or deceleration; and (2) the prediction of the timing of the triggered earthquake is improved by using adjusted frictional parameters.
Adjoint Inversion for Extended Earthquake Source Kinematics From Very Dense Strong Motion Data
Ampuero, J. P.; Somala, S.; Lapusta, N.
2010-12-01
Addressing key open questions about earthquake dynamics requires a radical improvement of the robustness and resolution of seismic observations of large earthquakes. Proposals for a new generation of earthquake observation systems include the deployment of “community seismic networks” of low-cost accelerometers in urban areas and the extraction of strong ground motions from high-rate optical images of the Earth's surface recorded by a large space telescope in geostationary orbit. Both systems could deliver strong motion data with a spatial density orders of magnitude higher than current seismic networks. In particular, a “space seismometer” could sample the seismic wave field at a spatio-temporal resolution of 100 m, 1 Hz over areas several 100 km wide with an amplitude resolution of few cm/s in ground velocity. The amount of data to process would be immensely larger than what current extended source inversion algorithms can handle, which hampers the quantitative assessment of the cost-benefit trade-offs that can guide the practical design of the proposed earthquake observation systems. We report here on the development of a scalable source imaging technique based on iterative adjoint inversion and its application to the proof-of-concept of a space seismometer. We generated synthetic ground motions for M7 earthquake rupture scenarios based on dynamic rupture simulations on a vertical strike-slip fault embedded in an elastic half-space. A range of scenarios include increasing levels of complexity and interesting features such as supershear rupture speed. The resulting ground shaking is then processed accordingly to what would be captured by an optical satellite. Based on the resulting data, we perform source inversion by an adjoint/time-reversal method. The gradient of a cost function quantifying the waveform misfit between data and synthetics is efficiently obtained by applying the time-reversed ground velocity residuals as surface force sources, back
Spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavors
Bergner, Georg; Giudice, Pietro; Münster, Gernot; Montvay, Istvan; Piemonte, Stefano
2017-08-01
In this work we present the results of our investigation of SU(2) gauge theory with two Dirac fermions in the adjoint representation (aQCD2), which belongs to the class of strongly interacting gauge theories that are of basic interest for extensions of the Standard Model. We have done numerical lattice simulations of this theory at two different values of the gauge coupling and several fermion masses. Our results include the particle spectrum and the mass anomalous dimension. The spectrum contains new exotic fermion-gluon states and flavor-singlet mesons. The mass anomalous dimension is determined from the scaling of the masses and the mode number. The remnant dependence of the universal mass ratios and mass anomalous dimension on the gauge coupling indicates the relevance of scaling corrections, such that earlier estimations for the universal fixed point value of the mass anomalous dimension are incomplete without their inclusion.
The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours
Bergner, Georg; Montvay, Istvan; Münster, Gernot; Piemonte, Stefano
2016-01-01
In this work we present the results of our investigation of SU(2) gauge theory with two Dirac fermions in the adjoint representation, also known as Minimal Walking Technicolour. We have done numerical lattice simulations of this theory at two different values of the gauge coupling and several fermion masses. Our results include the particle spectrum and the mass anomalous dimension. The spectrum contains so far unconsidered states, a fermion-gluon state and flavour singlet mesons. The mass anomalous dimension is determined from the scaling of the masses and the mode number. The remnant dependence of the universal mass ratios and mass anomalous dimension on the gauge coupling indicates the relevance of scaling corrections.
Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks
Catterall, Simon; Sannino, Francesco; Schneible, Joe
2008-01-01
We report on numerical simulations of SU(2) lattice gauge theory with two flavors of light dynamical quarks in the adjoint of the gauge group. The dynamics of this theory is thought to be very different from QCD -- the theory exhibiting conformal or near conformal behavior in the infrared. We make a high resolution survey of the phase diagram of this model in the plane of the bare coupling and quark mass on lattices of size 8^3 \\times 16. Our simulations reveal a line of first order phase transitions extending from beta=0 to beta=beta_c \\sim 2.0. For beta > beta_c the line is no longer first order but continues as the locus of minimum meson mass. For beta > 2.0 we observe the critical pion and rho masses to be light, independent of bare coupling and approximately degenerate. We discuss possible interpretations of these observations and corresponding continuum limits.
Adjoint-optimization algorithm for spatial reconstruction of a scalar source
Wang, Qi; Hasegawa, Yosuke; Meneveau, Charles; Zaki, Tamer
2016-11-01
Identifying the location of the source of passive scalar transported in a turbulent environment based on remote measurements is an ill-posed problem. A conjugate-gradient algorithm is proposed, and relies on eddy-resolving simulations of both the forward and adjoint scalar transport equations to reconstruct the spatial distribution of the source. The formulation can naturally accommodate measurements from multiple sensors. The algorithm is evaluated for scalar dispersion in turbulent channel flow (Reτ = 180). As the distance between the source and sensor increases, the accuracy of the source recovery deteriorates due to diffusive effects. Improvement in performance is demonstrated for higher Prantl numbers and also with increasing number of sensors. This study is supported by the National Science Foundation (Grant CNS 1461870).
F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
Morita, Takeshi
2011-01-01
We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S^3 partition functions computed via localization. An explicit illustration based on the known analytic solution of the Chern-Simons matrix model is presented.
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Koshmanenko, Volodymyr; Koshmanenko, Nataliia
2016-01-01
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...
Scaling properties of SU(2) gauge theory with mixed fundamental-adjoint action
Rinaldi, Enrico; Lucini, Biagio; Patella, Agostino; Rago, Antonio
2012-01-01
We study the phase diagram of the SU(2) lattice gauge theory with fundamental-adjoint Wilson plaquette action. We confirm the presence of a first order bulk phase transition and we estimate the location of its end-point in the bare parameter space. If this point is second order, the theory is one of the simplest realizations of a lattice gauge theory admitting a continuum limit at finite bare couplings. All the relevant gauge observables are monitored in the vicinity of the fixed point with very good control over finite-size effects. The scaling properties of the low-lying glueball spectrum are studied while approaching the end-point in a controlled manner.
Confining vs. conformal scenario for SU(2) with adjoint fermions. Gluonic observables
Patella, Agostino; Lucini, Biagio; Pica, Claudio; Rago, Antonio
2010-01-01
Walking technicolor is a mechanism for electroweak symmetry breaking without Higgs field. The Higgs mechanism is provided by chiral symmetry breaking in the technicolor theory. An essential ingredient is the vicinity to an IR fixed point, which could reconcile technicolor with the electroweak precision tests. SU(2) gauge theory with two Dirac adjoint fermions has been proposed as a candidate for walking technicolor. Understanding whether this theory is confining or IR-conformal is a challenging problem, which can be addressed by means of numerical simulations. We have pointed out that a clean signal for the existence of an IR fixed point in this theory can be obtained by comparing the mesonic and gluonic sectors. We review some technical details of our calculations. Possible systematic errors are discussed.
Lemke, Mathias; Reiss, Julius; Sesterhenn, Jörn
2016-06-01
Particle image velocimetry (PIV) is one of the major tools to measure velocity fields in experiments. However, other flow properties like density or pressure are often of vital interest, but usually cannot be measured non-intrusively. There are many approaches to overcome this problem, but none is fully satisfactory. Here the computational method of an adjoint based data assimilation for this purpose is discussed. A numerical simulation of a flow is adapted to given velocity data. After successful adaption, previously unknown quantities can be taken from the - necessarily complete - simulation data. The main focus of this work is the efficient implementation of this approach by boundary driven optimisation. Synthetic test cases are presented to allow an assessment of the method.
Solution of the self-adjoint radiative transfer equation on hybrid computer systems
Gasilov, V. A.; Kuchugov, P. A.; Olkhovskaya, O. G.; Chetverushkin, B. N.
2016-06-01
A new technique for simulating three-dimensional radiative energy transfer for the use in the software designed for the predictive simulation of plasma with high energy density on parallel computers is proposed. A highly scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is developed based on the solution of a second-order equation with a self-adjoint operator. A distinctive feature of this algorithm is a preliminary transformation of rotation to eliminate mixed derivatives with respect to the spatial variables, simplify the structure of the difference operator, and accelerate the convergence of the iterative solution of the equation. It is shown that the proposed method correctly reproduces the limiting cases—isotropic radiation and the directed radiation with a δ-shaped angular distribution.
Fermions in higher representations. Some results about SU(2) with adjoint fermions
Del Debbio, L; Pica, C
2008-01-01
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present the implementation of the RHMC algorithm for simulating dynamical Wilson fermions. A first dataset is presented for the SU(2) gauge theory with two fermions in the adjoint representation, which has been proposed as a possible technicolor candidate. Simulations are performed on 8^3x16 lattices, at fixed lattice spacing. The PCAC mass, the pseudoscalar, vector and axial meson masses, the pseudoscalar meson decay constant are computed. The extrapolation to the chiral limit is discussed. However more extensive investigations are needed in order to control the systematic errors in the numerical results, and then understand in detail the phase structure of these theories.
Multi-objective optimization strategies using adjoint method and game theory in aerodynamics
Institute of Scientific and Technical Information of China (English)
Zhili Tang
2006-01-01
There are currently three different game strategies originated in economics:(1) Cooperative games (Pareto front),(2)Competitive games (Nash game) and (3)Hierarchical games (Stackelberg game).Each game achieves different equilibria with different performance,and their players play different roles in the games.Here,we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multicriteria aerodynamic optimization problems.The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments.We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method.The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front.Non-dominated Pareto front solutions are obtained,however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.
Energy Technology Data Exchange (ETDEWEB)
Barbone, Paul E; Rivas, Carlos E [College of Engineering, Boston University, Boston, MA (United States); Harari, Isaac; Albocher, Uri [Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv (Israel); Oberai, Assad A; Goenzen, Sevan [Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Inst., Troy, NY (United States)], E-mail: barbone@bu.edu, E-mail: harari@eng.tau.ac.il, E-mail: oberaa@rpi.edu
2008-11-01
We describe a novel variational formulation of the inverse elasticity problem given interior data. The strong form of this problem is governed by equations of pure advective transport. To address this problem, we generalize the adjoint-weighted variational equation (AWE) formulation, originally developed for flow of a passive scalar. Here, we shall study the properties of the AWE formulation in the context of inverse plane stress elasticity imaging. We show that the solution of the AWE formulation is equivalent to that of the strong form when both are well posed. We prove that the Galerkin discretization of the AWE formulation leads to a stable, convergent numerical method, and prove optimal rates of convergence.
Neutrino masses in $SU(5)\\times U(1)_F$ with adjoint flavons
Nardi, Enrico; Velasquez, Mauricio
2011-01-01
We present a $SU(5)\\times U(1)_F$ supersymmetric model for neutrino masses and mixings that includes three heavy singlet neutrinos and two flavons. We discuss how Abelian $U(1)_F$ symmetries can naturally yield non-hierarchical light neutrinos even when the heavy states are strongly hierarchical, and how it can also ensure that $R$--parity arises as an exact accidental symmetry. By assigning flavons to the adjoint representation of SU(5) and assuming universality for all the fundamental couplings, the coefficients of the effective Yukawa and Majorana mass operators become calculable in terms of group theoretical quantities. There is a single free parameter in the model, however, at leading order the structure of the light neutrinos mass matrix is determined in a parameter independent way.
Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators
Directory of Open Access Journals (Sweden)
Wen Zhang
2014-01-01
Full Text Available Let A1 and A2 be standard real Jordan algebras of self-adjoint operators on complex Hilbert spaces H1 and H2, respectively. For k≥2, let (i1,…,im be a fixed sequence with i1,…,im∈{1,…,k} and assume that at least one of the terms in (i1,…,im appears exactly once. Define the generalized Jordan product T1∘T2∘⋯∘Tk=Ti1Ti2⋯Tim+Tim⋯Ti2Ti1 on elements in Ai. Let Φ:A1→A2 be a map with the range containing all rank-one projections and trace zero-rank two self-adjoint operators. We show that Φ satisfies that σπ(Φ(A1∘⋯∘Φ(Ak=σπ(A1∘⋯∘Ak for all A1,…,Ak, where σπ(A stands for the peripheral spectrum of A, if and only if there exist a scalar c∈{-1,1} and a unitary operator U:H1→H2 such that Φ(A=cUAU* for all A∈A1, or Φ(A=cUAtU* for all A∈A1, where At is the transpose of A for an arbitrarily fixed orthonormal basis of H1. Moreover, c=1 whenever m is odd.
Miyoshi, Takayuki
2017-10-04
A three-dimensional seismic wave speed model in the Kanto region of Japan was developed using adjoint tomography for application in the effective reproduction of observed waveforms. Starting with a model based on previous travel time tomographic results, we inverted the waveforms obtained at seismic broadband stations from 140 local earthquakes in the Kanto region to obtain the P- and S-wave speeds Vp and Vs. Additionally, all centroid times of the source solutions were determined before the structural inversion. The synthetic displacements were calculated using the spectral-element method (SEM) in which the Kanto region was parameterized using 16 million grid points. The model parameters Vp and Vs were updated iteratively by Newton’s method using the misfit and Hessian kernels until the misfit between the observed and synthetic waveforms was minimized. Computations of the forward and adjoint simulations were conducted on the K computer in Japan. The optimized SEM code required a total of 6720 simulations using approximately 62,000 node hours to obtain the final model after 16 iterations. The proposed model reveals several anomalous areas with extremely low-Vs values in comparison with those of the initial model. These anomalies were found to correspond to geological features, earthquake sources, and volcanic regions with good data coverage and resolution. The synthetic waveforms obtained using the newly proposed model for the selected earthquakes showed better fit than the initial model to the observed waveforms in different period ranges within 5–30 s. This result indicates that the model can accurately predict actual waveforms.
Data assimilation for massive autonomous systems based on a second-order adjoint method
Ito, Shin-ichi; Nagao, Hiromichi; Yamanaka, Akinori; Tsukada, Yuhki; Koyama, Toshiyuki; Kano, Masayuki; Inoue, Junya
2016-10-01
Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA is now an accepted technique in various scientific fields. One key issue that remains controversial is the implementation of DA in massive simulation models under the constraints of limited computation time and resources. In this paper, we propose an adjoint-based DA method for massive autonomous models that produces optimum estimates and their uncertainties within reasonable computation time and resource constraints. The uncertainties are given as several diagonal elements of an inverse Hessian matrix, which is the covariance matrix of a normal distribution that approximates the target posterior probability density function in the neighborhood of the optimum. Conventional algorithms for deriving the inverse Hessian matrix require O (C N2+N3) computations and O (N2) memory, where N is the number of degrees of freedom of a given autonomous system and C is the number of computations needed to simulate time series of suitable length. The proposed method using a second-order adjoint method allows us to directly evaluate the diagonal elements of the inverse Hessian matrix without computing all of its elements. This drastically reduces the number of computations to O (C ) and the amount of memory to O (N ) for each diagonal element. The proposed method is validated through numerical tests using a massive two-dimensional Kobayashi phase-field model. We confirm that the proposed method correctly reproduces the parameter and initial state assumed in advance, and successfully evaluates the uncertainty of the parameter. Such information regarding uncertainty is valuable, as it can be used to optimize the design of experiments.
Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation
Canet, Elisabeth; Fournier, Alexandre; Jault, Dominique
2009-11-01
We introduce a quasi-geostrophic model of core dynamics, which aims at describing core processes on geomagnetic secular variation timescales. It extends the formalism of Alfvén torsional oscillations by incorporating nonzonal motions. Within this framework, the magnetohydrodynamics takes place in the equatorial plane; it involves quadratic magnetic quantities, which are averaged along the direction of rotation of the Earth. In addition, the equatorial flow is projected on the core-mantle boundary. It interacts with the magnetic field at the core surface, through the radial component of the magnetic induction equation. That part of the model connects the dynamics and the observed secular variation, with the radial component of the magnetic field acting as a passive tracer. We resort to variational data assimilation to formally construct the relationship between model predictions and observations. Variational data assimilation seeks to minimize an objective function by computing its sensitivity to its control variables. The sensitivity is efficiently calculated after integration of the adjoint model. We illustrate that framework with twin experiments, performed first in the case of the kinematic core flow inverse problem and then in the case of Alfvén torsional oscillations. In both cases, using the adjoint model allows us to retrieve core state variables which, while taking part in the dynamics, are not directly sampled at the core surface. We study the effect of several factors on the solution (width of the assimilation time window, amount and quality of data), and we discuss the potential of the model to deal with real geomagnetic observations.
Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity
Li, Dunzhu; Gurnis, Michael; Stadler, Georg
2017-01-01
We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature- and strain rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a preconditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.
Adjoint analysis of the source and path sensitivities of basin-guided waves
Day, Steven M.; Roten, Daniel; Olsen, Kim B.
2012-05-01
Simulations of earthquake rupture on the southern San Andreas Fault (SAF) reveal large amplifications in the San Gabriel and Los Angeles Basins (SGB and LAB) apparently associated with long-range path effects. Geometrically similar excitation patterns can be recognized repeatedly in different SAF simulations (e.g. Love wave-like energy with predominant period around 4 s, channelled southwestwardly from the SGB into LAB), yet the amplitudes with which these distinctive wavefield patterns are excited change, depending upon source details (slip distribution, direction and velocity of rupture). We describe a method for rapid calculation of the sensitivity of such predicted wavefield features to perturbations of the source kinematics, using a time-reversed (adjoint) wavefield simulation. The calculations are analogous to those done in adjoint tomography, and the same time-reversed calculation also yields path-sensitivity kernels that give further insight into the excitation mechanism. For rupture on the southernmost 300 km of SAF, LAB excitation is greatest for slip concentrated between the northern Coachella Valley and the transverse ranges, propagating to the NE and with rupture velocities between 3250 and 3500 m s-1 along that fault segment; that is, within or slightly above the velocity range (between Rayleigh and S velocities) that is energetically precluded in the limit of a sharp rupture front, highlighting the potential value of imposing physical constraints (such as from spontaneous rupture models) on source parametrizations. LAB excitation is weak for rupture to the SW and for ruptures in either direction located north of the transverse transverse ranges, whereas Ventura Basin (VTB) is preferentially excited by NE ruptures situated north of the transverse ranges. Path kernels show that LAB excitation is mediated by surface waves deflected by the velocity contrast along the southern margin of the transverse ranges, having most of their energy in basement rock
McGovern, Jonathan; Rutt, Ian; Murray, Tavi; Utke, Jean
2013-04-01
Studying the future behaviour of the Greenland Ice Sheet is important considering the ice sheet has a sea-level equivalent of 7 metres and the rate of mass loss from it is increasing (Velicogna, 2009). Examining the modelled response of the Greenland Ice Sheet to changes in forcing parameters can give insight into how it will behave in the future. The response of the ice sheet to specific changes in forcing parameters is referred to as the sensitivity. Being able to obtain model sensitivities in as little computation time as possible would be useful for examining the future response of the Greenland Ice Sheet. Adjoint models allow sensitivities to be obtained more efficiently than the conventional way, when considering spatially varying parameters. Conventionally, such sensitivities are obtained by perturbing a parameter at every grid point in turn and calculating the sensitivity at every grid point. Adjoint sensitivities, though, are calculated in a single step. This reduces the computational cost when obtaining sensitivities over large model domains. The adjoint method also has the advantage that it gives the exact value of the model sensitivity, rather than a finite difference approximation to it. We present the adjoint of a finite difference, shallow ice, thermomechanical ice sheet model with basal sliding, applied to the Greenland Ice Sheet. This adjoint model is obtained using the OpenAD automatic differentiation tool (Utke, 2006), which is open source. The adjoint model is validated by comparing adjoint and forward model sensitivities over 100 years. This work builds on the work of Heimbach (2009). We use the adjoint model to examine the sensitivity of the model to changes in basal sliding. About half the mass loss from the Greenland Ice Sheet occurs from surface runoff and half from dynamic mass loss (Broeke, 2009). Melt-water from Greenland Ice Sheet supra-glacial lakes can percolate to the bed through moulins. The melt-water that reaches the bed can then
Flux-P: Automating Metabolic Flux Analysis
Ebert, Birgitta E.; Anna-Lena Lamprecht; Bernhard Steffen; Blank, Lars M.
2012-01-01
Quantitative knowledge of intracellular fluxes in metabolic networks is invaluable for inferring metabolic system behavior and the design principles of biological systems. However, intracellular reaction rates can not often be calculated directly but have to be estimated; for instance, via 13C-based metabolic flux analysis, a model-based interpretation of stable carbon isotope patterns in intermediates of metabolism. Existing software such as FiatFlux, OpenFLUX or 13CFLUX supports experts in ...
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.
Directory of Open Access Journals (Sweden)
Mohammad W. Alomari
2014-01-01
Full Text Available Several new error bounds for the Čebyšev functional under various assumptions are proved. Applications for functions of self-adjoint operators on complex Hilbert spaces are provided as well.
Flux-tubes in three-dimensional lattice gauge theories
Trottier, H D; Trottier, Howard D.
1993-01-01
Flux-tubes in different representations of SU(2) and U(1) lattice gauge theories in three dimensions are measured. Wilson loops generate heavy ``quark-antiquark'' pairs in fundamental ($j=1/2$), adjoint ($j=1$), and quartet ($j=3/2$) representations of SU(2). The first direct lattice measurements of the flux-tube cross-section ${\\cal A}_j$ as a function of representation are made. It is found that ${\\cal A}_j \\approx {\\rm constant}$, to about 10\\%. Results are consistent with a connection between the string tension $\\sigma_j$ and ${\\cal A}_j$ suggested by a simplified flux-tube model, $\\sigma_j = g^2 j(j+1) / (2 {\\cal A}_j)$ [$g$ is the gauge coupling], given that $\\sigma_j$ scales like the Casimir $j(j+1)$, as observed in previous lattice studies in both three and four dimensions. The results can discriminate among phenomenological models of the physics underlying confinement. Flux-tubes for singly- and doubly-charged Wilson loops in compact QED$_3$ are also measured. It is found that the string tension scal...
An, Xing Qin; Xian Zhai, Shi; Jin, Min; Gong, Sunling; Wang, Yu
2016-06-01
The aerosol adjoint module of the atmospheric chemical modeling system GRAPES-CUACE (Global-Regional Assimilation and Prediction System coupled with the CMA Unified Atmospheric Chemistry Environment) is constructed based on the adjoint theory. This includes the development and validation of the tangent linear and the adjoint models of the three parts involved in the GRAPES-CUACE aerosol module: CAM (Canadian Aerosol Module), interface programs that connect GRAPES and CUACE, and the aerosol transport processes that are embedded in GRAPES. Meanwhile, strict mathematical validation schemes for the tangent linear and the adjoint models are implemented for all input variables. After each part of the module and the assembled tangent linear and adjoint models is verified, the adjoint model of the GRAPES-CUACE aerosol is developed and used in a black carbon (BC) receptor-source sensitivity analysis to track influential haze source areas in north China. The sensitivity of the average BC concentration over Beijing at the highest concentration time point (referred to as the Objective Function) is calculated with respect to the BC amount emitted over the Beijing-Tianjin-Hebei region. Four types of regions are selected based on the administrative division or the sensitivity coefficient distribution. The adjoint sensitivity results are then used to quantify the effect of reducing the emission sources at different time intervals over different regions. It is indicated that the more influential regions (with relatively larger sensitivity coefficients) do not necessarily correspond to the administrative regions. Instead, the influence per unit area of the sensitivity selected regions is greater. Therefore, controlling the most influential regions during critical time intervals based on the results of the adjoint sensitivity analysis is much more efficient than controlling administrative regions during an experimental time period.
Mineev, V S
2003-01-01
In the paper the one-dimensional one-center scattering problem with the initial potential $\\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as necessary conditions in the singular point alongside with account of the analytical structure of fundamental solutions, it allows us to receive exact expressions for the wave functions (i.e. for the boundary conditions), scattering coefficients and the singular corrections to the potential, as well as the corresponding bound state spectrum. It turns out that the point $\\delta$-shaped correction to the potential should be present without fail at any choice of the allowable self-adjoint extension, moreover a form of these corrections corresponds to the form of renormalization terms obtained in quantum electrodynamics. Thus, the proposed method shows the unequivocal connection among the boundary conditions, scattering coefficients and $\\delta$-shaped additions to the potential. Ta...
Han, Shuzong; Yang, Hua; Xue, Wenhu; Wang, Xingchi
2017-06-01
This paper introduces the assimilation technology in an ocean dynamics model and discusses the feasibility of inverting the sea surface current in the detection zone by assimilating the sea current radial velocity detected by single station HF ground wave radar in ocean dynamics model. Based on the adjoint assimilation and POM model, the paper successfully inverts the sea surface current through single station HF ground wave radar in the Zhoushan sea area. The single station HF radar inversion results are also compared with the bistatic HF radar composite results and the fixed point measured results by Annderaa current meter. The error analysis shows that acquisition of flow velocity and flow direction data from the single station HF radar based on adjoint assimilation and POM model is viable and the data obtained have a high correlation and consistency with the flow field observed by HF radar.
Energy Technology Data Exchange (ETDEWEB)
Klasen, D.
2003-07-01
In recent years high resolution data have become available due to the deployment of satellite born instruments observing the state of a large number of stratospheric constituents with unprecedentedly high horizontal and vertical resolution. These measurements are valuable for accessing the state of the atmosphere and for helping to develop guidelines for its preservation as a protection layer for terrestrial life. Nevertheless, the measurements alone offer limited direct information. They require interpretation and combination with other information sources to accurately describe the state of the atmosphere. By combining measurements with atmospheric models, the measurements' scatter in time and space can be mitigated and their interpretation improved. A chemistry-transport model (CTM) version of the Cologne model of the middle atmosphere (COMMA) has been developed to model transport and chemical transformation of atmospheric trace gases. In this thesis, the method of four-dimensional variational data assimilation is used to realize the above-mentioned combination in a mathematically rigorous way. The goal is to identify the most probable chemical state of the atmosphere using all available information. As chemistry-transport modelling is an initial value problem, those initial conditions are sought which result in best compliance of the model state with available information during the time period considered. As a measure of compliance, a cost function is specified, whose gradient is needed for minimising the cost function, and which can be obtained by means of an adjoint model. To this end, the adjoint code to the CTM was developed. As a last building block of the data assimilation system, the L-BFGS algorithm for the minimization of the cost function was added. The adjoint model of the middle atmosphere of Cologne CTM (AMMOC-CTM) data-assimilation system thereby developed was tested by applying it to data measured by the cryogenic infrared spectrometer and
Gelaro, Ron; Liu, Emily; Sienkiewicz, Meta
2011-01-01
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. In this talk, we present results from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. The tool has been running in various off-line configurations for some time, and is scheduled to run as a regular part of the real-time forecast suite beginning in autumn 20 I O. We focus on the impacts of the newest components of the satellite observing system, including AIRS, IASI and GPS. For AIRS and IASI, it is shown that the vast majority of the channels assimilated have systematic positive impacts (of varying magnitudes), although some channels degrade the forecast. Of the latter, most are moisture-sensitive or near-surface channels. The impact of GPS observations in the southern hemisphere is found to be a considerable overall benefit to the system. In addition, the spatial variability of observation impacts reveals coherent patterns of positive and negative impacts that may point to deficiencies in the use of certain observations over, for example, specific surface types. When performed in conjunction with selected 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 appears to pose a major challenge for optimizing the use of the current observational network and
Finster, Felix
2015-01-01
We consider a boundary value problem for the Dirac equation in a four-dimensional, smooth, asymptotically flat Lorentzian manifold admitting a Killing field which is timelike near and tangential to the boundary. A self-adjoint extension of the Dirac Hamiltonian is constructed. Our results also apply to the situation that the space-time includes horizons, where the Hamiltonian fails to be elliptic.
Spak, S.; Henze, D. K.; Carmichael, G. R.
2013-12-01
The science and policy communities both need common metrics that clearly, comprehensively, and intuitively communicate the relative sensitivities of air quality and climate to emissions control strategies, include emissions and process uncertainties, and minimize the range of error that is transferred to the metric. This is particularly important because most emissions control policies impact multiple short-lived climate forcing agents, and non-linear climate and health responses in space and time limit the accuracy and policy value of simple emissions-based calculations. Here we describe and apply new second-order elasticity metrics to support the direct comparison of emissions control policies for air quality and health co-benefits analyses using adjoint chemical transport and chemistry-climate models. Borrowing an econometric concept, the simplest elasticities in the atmospheric system are the percentage changes in concentrations due to a percentage change in the emissions. We propose a second-order elasticity metric, the Emissions Reduction Efficiency, which supports comparison across compounds, to long-lived climate forcing agents like CO2, and to other air quality impacts, at any temporal or spatial scale. These adjoint-based metrics (1) possess a single uncertainty range; (2) allow for the inclusion of related health and other impacts effects within the same framework; (3) take advantage of adjoint and forward sensitivity models; and (4) are easily understood. Using global simulations with the adjoint of GEOS-Chem, we apply these metrics to identify spatial and sectoral variability in the climate and health co-benefits of sectoral emissions controls on black carbon, sulfur dioxide, and PM2.5. We find spatial gradients in optimal control strategies on every continent, along with differences among megacities.
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.
Sources of springtime surface black carbon in the Arctic: an adjoint analysis for April 2008
Qi, Ling; Li, Qinbin; Henze, Daven K.; Tseng, Hsien-Liang; He, Cenlin
2017-08-01
We quantify source contributions to springtime (April 2008) surface black carbon (BC) in the Arctic by interpreting surface observations of BC at five receptor sites (Denali, Barrow, Alert, Zeppelin, and Summit) using a global chemical transport model (GEOS-Chem) and its adjoint. Contributions to BC at Barrow, Alert, and Zeppelin are dominated by Asian anthropogenic sources (40-43 %) before 18 April and by Siberian open biomass burning emissions (29-41 %) afterward. In contrast, Summit, a mostly free tropospheric site, has predominantly an Asian anthropogenic source contribution (24-68 %, with an average of 45 %). We compute the adjoint sensitivity of BC concentrations at the five sites during a pollution episode (20-25 April) to global emissions from 1 March to 25 April. The associated contributions are the combined results of these sensitivities and BC emissions. Local and regional anthropogenic sources in Alaska are the largest anthropogenic sources of BC at Denali (63 % of total anthropogenic contributions), and natural gas flaring emissions in the western extreme north of Russia (WENR) are the largest anthropogenic sources of BC at Zeppelin (26 %) and Alert (13 %). We find that long-range transport of emissions from Beijing-Tianjin-Hebei (also known as Jing-Jin-Ji), the biggest urbanized region in northern China, contribute significantly (˜ 10 %) to surface BC across the Arctic. On average, it takes ˜ 12 days for Asian anthropogenic emissions and Siberian biomass burning emissions to reach the Arctic lower troposphere, supporting earlier studies. Natural gas flaring emissions from the WENR reach Zeppelin in about a week. We find that episodic transport events dominate BC at Denali (87 %), a site outside the Arctic front, which is a strong transport barrier. The relative contribution of these events to surface BC within the polar dome is much smaller (˜ 50 % at Barrow and Zeppelin and ˜ 10 % at Alert). The large contributions from Asian anthropogenic
Seismic structure of the European crust and upper mantle based on adjoint tomography
Zhu, Hejun
We use adjoint tomography to estimate three-dimensional variations in seismic parameters within the crust and upper mantle beneath Europe and the North Atlantic Ocean. Spectral-element and adjoint methods are used to numerically calculate synthetic seismograms and sensitivity kernels in three-dimensional Earth models. Combined with gradient- based optimization algorithms, e.g., preconditioned conjugate-gradient and L-BFGS methods, we iteratively update seismic models of Earth's interior. A three-stage inversion strategy is designed to estimate variations in elastic wavespeeds, anelastic attenuation and radial & azimuthal anisotropy. In stage one, frequency-dependent phase differences between observed and simulated seismograms are used to determine a new radially anisotropic wavespeed model for the European crust and upper mantle, namely EU30. Long-wavelength structures in EU30 compare favorably with previous body- and surface-wave tomographic models. Some hitherto unidentified features naturally emerge from the smooth starting model. In stage two, frequency-dependent amplitude differences combined with remaining phase anomalies are used to simultaneously constrain elastic and anelastic structures. A new anelastic model, named EU50, is constructed in this stage. We observe several notable features, such as enhanced attenuation within the mantle transition zone beneath the North Atlantic Ocean. In the first two stages, long-period surface waves and short-period body waves in three-component seismograms are combined to simultaneously constrain shallow and deep structures. In stage three, frequency-dependent phase and amplitude anomalies of three-component surface waves are used to construct a radially and azimuthally anisotropic model EU60. We find that the direction of the fast axis is closely tied to the tectonic evolution in this region, such as extension along the North Atlantic Ridge, trench retreat in the Mediterranean, and counterclockwise rotation of the
Sources of springtime surface black carbon in the Arctic: an adjoint analysis for April 2008
Directory of Open Access Journals (Sweden)
L. Qi
2017-08-01
Full Text Available We quantify source contributions to springtime (April 2008 surface black carbon (BC in the Arctic by interpreting surface observations of BC at five receptor sites (Denali, Barrow, Alert, Zeppelin, and Summit using a global chemical transport model (GEOS-Chem and its adjoint. Contributions to BC at Barrow, Alert, and Zeppelin are dominated by Asian anthropogenic sources (40–43 % before 18 April and by Siberian open biomass burning emissions (29–41 % afterward. In contrast, Summit, a mostly free tropospheric site, has predominantly an Asian anthropogenic source contribution (24–68 %, with an average of 45 %. We compute the adjoint sensitivity of BC concentrations at the five sites during a pollution episode (20–25 April to global emissions from 1 March to 25 April. The associated contributions are the combined results of these sensitivities and BC emissions. Local and regional anthropogenic sources in Alaska are the largest anthropogenic sources of BC at Denali (63 % of total anthropogenic contributions, and natural gas flaring emissions in the western extreme north of Russia (WENR are the largest anthropogenic sources of BC at Zeppelin (26 % and Alert (13 %. We find that long-range transport of emissions from Beijing–Tianjin–Hebei (also known as Jing–Jin–Ji, the biggest urbanized region in northern China, contribute significantly (∼ 10 % to surface BC across the Arctic. On average, it takes ∼ 12 days for Asian anthropogenic emissions and Siberian biomass burning emissions to reach the Arctic lower troposphere, supporting earlier studies. Natural gas flaring emissions from the WENR reach Zeppelin in about a week. We find that episodic transport events dominate BC at Denali (87 %, a site outside the Arctic front, which is a strong transport barrier. The relative contribution of these events to surface BC within the polar dome is much smaller (∼ 50 % at Barrow and Zeppelin and ∼ 10 % at
Verdugo, Francesc; Parés, Núria; Díez, Pedro
2014-08-01
This article presents a space-time adaptive strategy for transient elastodynamics. The method aims at computing an optimal space-time discretization such that the computed solution has an error in the quantity of interest below a user-defined tolerance. The methodology is based on a goal-oriented error estimate that requires accounting for an auxiliary adjoint problem. The major novelty of this paper is using modal analysis to obtain a proper approximation of the adjoint solution. The idea of using a modal-based description was introduced in a previous work for error estimation purposes. Here this approach is used for the first time in the context of adaptivity. With respect to the standard direct time-integration methods, the modal solution of the adjoint problem is highly competitive in terms of computational effort and memory requirements. The performance of the proposed strategy is tested in two numerical examples. The two examples are selected to be representative of different wave propagation phenomena, one being a 2D bulky continuum and the second a 2D domain representing a structural frame.
Adjoint-based shape optimization of fin geometry for enhanced solid/liquid phase-change process
Morimoto, Kenichi; Suzuki, Yuji
2015-11-01
In recent years, the control of heat transfer processes, which play a critical role in various engineering devices/systems, has gained renewed attention. The present study aims to establish an adjoint-based shape optimization method for high-performance heat transfer processes involving phase-change phenomena. A possible example includes the application to the thermal management technique using phase-change material. Adjoint-based shape optimization scheme is useful to optimal shape design and optimal control of systems, for which the base function of the solution is unknown and the solution includes an infinite number of degrees of freedom. Here we formulate the shape-optimization scheme based on adjoint heat conduction analyses, focusing on the shape optimization of fin geometry. In the computation of the developed scheme, a meshless local Petrov-Galerkin (MLPG) method that is suited for dealing with complex boundary geometry is employed, and the enthalpy method is adopted for analyzing the motion of the phase-change interface. We examine in detail the effect of the initial geometry and the node distribution in the MLPG analysis upon the final solution of the shape optimization. Also, we present a new strategy for the computation using bubble mesh.
Curvature theory for point-path and plane-envelope in spherical kinematics by new adjoint approach
Wang, Wei; Wang, Delun
2014-11-01
Planar kinematics has been studied systematically based on centrodes, however axodes are underutilized to set up the curvature theories in spherical and spatial kinematics. Through a spherical adjoint approach, an axode-based theoretical system of spherical kinematics is established. The spherical motion is re-described by the adjoint approach and vector equation of spherical instant center is concisely derived. The moving and fixed axodes for spherical motion are mapped onto a unit sphere to obtain spherical centrodes, whose kinematic invariants totally reflect the intrinsic property of spherical motion. Based on the spherical centrodes, the curvature theories for a point and a plane of a rigid body in spherical motion are revealed by spherical fixed point and plane conditions. The Euler-Savary analogue for point-path is presented. Tracing points with higher order curvature features are located in the moving body by means of algebraic equations. For plane-envelope, the construction parameters are obtained. The osculating conditions for plane-envelope and circular cylindrical surface or circular conical surface are given. A spherical four-bar linkage is taken as an example to demonstrate the spherical adjoint approach and the curvature theories. The research proposes systematic spherical curvature theories with the axode as logical starting-point, and sets up a bridge from the centrode-based planar kinematics to the axode-based spatial kinematics.
Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach
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.
Curvature Theory for Point-Path and Plane-Envelope in Spherical Kinematics by New Adjoint Approach
Institute of Scientific and Technical Information of China (English)
WANG Wei; WANG Delun
2014-01-01
Planar kinematics has been studied systematically based on centrodes, however axodes are underutilized to set up the curvature theories in spherical and spatial kinematics. Through a spherical adjoint approach, an axode-based theoretical system of spherical kinematics is established. The spherical motion is re-described by the adjoint approach and vector equation of spherical instant center is concisely derived. The moving and fixed axodes for spherical motion are mapped onto a unit sphere to obtain spherical centrodes, whose kinematic invariants totally reflect the intrinsic property of spherical motion. Based on the spherical centrodes, the curvature theories for a point and a plane of a rigid body in spherical motion are revealed by spherical fixed point and plane conditions. The Euler-Savary analogue for point-path is presented. Tracing points with higher order curvature features are located in the moving body by means of algebraic equations. For plane-envelope, the construction parameters are obtained. The osculating conditions for plane-envelope and circular cylindrical surface or circular conical surface are given. A spherical four-bar linkage is taken as an example to demonstrate the spherical adjoint approach and the curvature theories. The research proposes systematic spherical curvature theories with the axode as logical starting-point, and sets up a bridge from the centrode-based planar kinematics to the axode-based spatial kinematics.
Directory of Open Access Journals (Sweden)
C. M. Hoppe
2014-05-01
Full Text Available This paper presents the development and implementation of a spatio-temporal variational data assimilation system (4D-var for the soil–vegetation–atmosphere transfer model "Community Land Model" (CLM3.5, along with the development of the adjoint code for the core soil–atmosphere transfer scheme of energy and soil moisture. The purpose of this work is to obtain an improved estimation technique for the energy fluxes (sensible and latent heat fluxes between the soil and the atmosphere. Optimal assessments of these fluxes are neither available from model simulations nor measurements alone, while a 4D-var data assimilation has the potential to combine both information sources by a Best Linear Unbiased Estimate (BLUE. The 4D-var method requires the development of the adjoint model of the CLM which is established in this work. The new data assimilation algorithm is able to assimilate soil temperature and soil moisture measurements for one-dimensional columns of the model grid. Numerical experiments were first used to test the algorithm under idealised conditions. It was found that the analysis delivers improved results whenever there is a dependence between the initial values and the assimilated quantity. Furthermore, soil temperature and soil moisture from in situ field measurements were assimilated. These calculations demonstrate the improved performance of flux estimates, whenever soil property parameters are available of sufficient quality. Misspecifications could also be identified by the performance of the variational scheme.
Energy Technology Data Exchange (ETDEWEB)
Gu, Grace [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Brown, Judith Alice [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bishop, Joseph E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-08-01
The texture of a polycrystalline material refers to the preferred orientation of the grains within the material. In metallic materials, texture can significantly affect the mechanical properties such as elastic moduli, yield stress, strain hardening, and fracture toughness. Recent advances in additive manufacturing of metallic materials offer the possibility in the not too distant future of controlling the spatial variation of texture. In this work, we investigate the advantages, in terms of mechanical performance, of allowing the texture to vary spatially. We use an adjoint-based gradient optimization algorithm within a finite element solver (COMSOL) to optimize several engineering quantities of interest in a simple structure (hole in a plate) and loading (uniaxial tension) condition. As a first step to general texture optimization, we consider the idealized case of a pure fiber texture in which the homogenized properties are transversely isotropic. In this special case, the only spatially varying design variables are the three Euler angles that prescribe the orientation of the homogenized material at each point within the structure. This work paves a new way to design metallic materials for tunable mechanical properties at the microstructure level.
Muon g -2 in gauge mediated supersymmetry breaking models with adjoint messengers
Gogoladze, Ilia; Ün, Cem Salih
2017-02-01
We explored the sparticle mass spectrum in light of the muon g -2 anomaly and the little hierarchy problem in a class of the gauge mediated supersymmetry breaking model. Here, the messenger fields transform in the adjoint representation of the Standard Model gauge symmetry. To avoid unacceptably light right-handed slepton masses, the Standard Model is supplemented by the additional U (1 )B-L gauge symmetry. A nonzero U (1 )B-L D term makes the right-handed slepton masses compatible with the current experimental bounds. We show that in the framework of Λ3muon g -2 anomaly and the observed 125 GeV Higgs boson mass can be simultaneously accommodated. The slepton masses in this case are predicted to lie in the few hundred GeV range, which can be tested at the LHC. Despite the heavy colored sparticle spectrum, the little hierarchy problem in this model can be ameliorated, and the electroweak fine-tuning parameter can be as low as 10 or so.
Komatitsch, Dimitri
2016-06-13
We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.
Ito, Shin-Ichi; Nagao, Hiromichi; Yamanaka, Akinori; Tsukada, Yuhki; Koyama, Toshiyuki; Inoue, Junya
Phase field (PF) method, which phenomenologically describes dynamics of microstructure evolutions during solidification and phase transformation, has progressed in the fields of hydromechanics and materials engineering. How to determine, based on observation data, an initial state and model parameters involved in a PF model is one of important issues since previous estimation methods require too much computational cost. We propose data assimilation (DA), which enables us to estimate the parameters and states by integrating the PF model and observation data on the basis of the Bayesian statistics. The adjoint method implemented on DA not only finds an optimum solution by maximizing a posterior distribution but also evaluates the uncertainty in the estimations by utilizing the second order information of the posterior distribution. We carried out an estimation test using synthetic data generated by the two-dimensional Kobayashi's PF model. The proposed method is confirmed to reproduce the true initial state and model parameters we assume in advance, and simultaneously estimate their uncertainties due to quality and quantity of the data. This result indicates that the proposed method is capable of suggesting the experimental design to achieve the required accuracy.
Morimoto, Kenichi; Kinoshita, Hidenori; Suzuki, Yuji
2016-11-01
In the present study, an adjoint-based shape-optimization method has been developed for designing extended heat transfer surfaces in conjugate heat transfer problems. Here we specifically consider heat conduction-dominated solidification problem under different thermal boundary conditions: (i) the isothermal condition, and (ii) the conjugate condition with thermal coupling between the solidified liquid and the solid wall inside the domain bounded by the extended heat transfer surface. In the present shape-optimization scheme, extended heat transfer surfaces are successively refined in a local way based on the variational information of a cost functional with respect to the shape modification. In the computation of the developed scheme, a meshless method is employed for dealing with the complex boundary shape. For high-resolution analyses with boundary-fitted node arrangement, we have introduced a bubble-mesh method combined with a high-efficiency algorithm for searching neighboring bubbles within a cut-off distance. The present technique can be easily applied to convection problems including high Reynolds number flow. We demonstrate, for the isothermal boundary condition, that the present optimization leads to tree-like fin shapes, which achieve the temperature field with global similarity for different initial fin shapes. We will also show the computational results for the conjugate condition, which would regularize the present optimization due to the fin-efficiency effect.
Komatitsch, Dimitri; Xie, Zhinan; Bozdaǧ, Ebru; Sales de Andrade, Elliott; Peter, Daniel; Liu, Qinya; Tromp, Jeroen
2016-09-01
We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.
Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation
Boujo, E.; Noiray, N.
2017-04-01
We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations-for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker-Planck equation is solved to compute Kramers-Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.
Adjoint LMS (ALMS Algorithm Based Active Noise Control with Feedback Path Modeling
Directory of Open Access Journals (Sweden)
U Ramachandraiah,
2010-12-01
Full Text Available In active noise control (ANC systems, there exists an inherent feedback from the loudspeaker to the primary microphone. Adjoint least mean square (ALMS algorithm is known to be an alternative to the widely used filtered x LMS (FxLMS for reducing the computational complexity and memory requirements, especially in the case of multi-channel systems. Further FxLMS algorithm is based on the assumptionthat the order of the weighing filter and secondary path can be commuted which is not always true in practice. Though ALMS do not make such an assumption, neither FxLMS nor the ALMS algorithms onsider the feedback path effect that is inherent in ANC systems.We propose a feedback ANC system based on ALMS algorithm which is analogous to the system based on FxLMS. Detailed computational complexity analysis for addition and multiplication requirements ispresented and are compared with those of its counterpart to establish its usefulness. Simulation results show the convergence characteristics of the ALMS based ANC with feedback path modeling is on par with that based on FxLMS.
Forward and adjoint radiance Monte Carlo models for quantitative photoacoustic imaging
Hochuli, Roman; Powell, Samuel; Arridge, Simon; Cox, Ben
2015-03-01
In quantitative photoacoustic imaging, the aim is to recover physiologically relevant tissue parameters such as chromophore concentrations or oxygen saturation. Obtaining accurate estimates is challenging due to the non-linear relationship between the concentrations and the photoacoustic images. Nonlinear least squares inversions designed to tackle this problem require a model of light transport, the most accurate of which is the radiative transfer equation. This paper presents a highly scalable Monte Carlo model of light transport that computes the radiance in 2D using a Fourier basis to discretise in angle. The model was validated against a 2D finite element model of the radiative transfer equation, and was used to compute gradients of an error functional with respect to the absorption and scattering coefficient. It was found that adjoint-based gradient calculations were much more robust to inherent Monte Carlo noise than a finite difference approach. Furthermore, the Fourier angular discretisation allowed very efficient gradient calculations as sums of Fourier coefficients. These advantages, along with the high parallelisability of Monte Carlo models, makes this approach an attractive candidate as a light model for quantitative inversion in photoacoustic imaging.
The adjoint method for general EEG and MEG sensor-based lead field equations
Energy Technology Data Exchange (ETDEWEB)
Vallaghe, Sylvain; Papadopoulo, Theodore; Clerc, Maureen [INRIA, Projet Odyssee, Sophia Antipolis (France)], E-mail: Sylvain.Vallaghe@sophia.inria.fr
2009-01-07
Most of the methods for the inverse source problem in electroencephalography (EEG) and magnetoencephalography (MEG) use a lead field as an input. The lead field is the function which relates any source in the brain to its measurements at the sensors. For complex geometries, there is no analytical formula of the lead field. The common approach is to numerically compute the value of the lead field for a finite number of point sources (dipoles). There are several drawbacks: the model of the source space is fixed (a set of dipoles), and the computation can be expensive for as much as 10 000 dipoles. The common idea to bypass these problems is to compute the lead field from a sensor point of view. In this paper, we use the adjoint method to derive general EEG and MEG sensor-based lead field equations. Within a simple framework, we provide a complete review of the explicit lead field equations, and we are able to extend these equations to non-pointlike sensors.
Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.
2016-09-01
A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.
Comparison of Ensemble and Adjoint Approaches to Variational Optimization of Observational Arrays
Nechaev, D.; Panteleev, G.; Yaremchuk, M.
2015-12-01
Comprehensive monitoring of the circulation in the Chukchi Sea and Bering Strait is one of the key prerequisites of the successful long-term forecast of the Arctic Ocean state. Since the number of continuously maintained observational platforms is restricted by logistical and political constraints, the configuration of such an observing system should be guided by an objective strategy that optimizes the observing system coverage, design, and the expenses of monitoring. The presented study addresses optimization of system consisting of a limited number of observational platforms with respect to reduction of the uncertainties in monitoring the volume/freshwater/heat transports through a set of key sections in the Chukchi Sea and Bering Strait. Variational algorithms for optimization of observational arrays are verified in the test bed of the set of 4Dvar optimized summer-fall circulations in the Pacific sector of the Arctic Ocean. The results of an optimization approach based on low-dimensional ensemble of model solutions is compared against a more conventional algorithm involving application of the tangent linear and adjoint models. Special attention is paid to the computational efficiency and portability of the optimization procedure.
Poirier, Vincent
Mesh deformation schemes play an important role in numerical aerodynamic optimization. As the aerodynamic shape changes, the computational mesh must adapt to conform to the deformed geometry. In this work, an extension to an existing fast and robust Radial Basis Function (RBF) mesh movement scheme is presented. Using a reduced set of surface points to define the mesh deformation increases the efficiency of the RBF method; however, at the cost of introducing errors into the parameterization by not recovering the exact displacement of all surface points. A secondary mesh movement is implemented, within an adjoint-based optimization framework, to eliminate these errors. The proposed scheme is tested within a 3D Euler flow by reducing the pressure drag while maintaining lift of a wing-body configured Boeing-747 and an Onera-M6 wing. As well, an inverse pressure design is executed on the Onera-M6 wing and an inverse span loading case is presented for a wing-body configured DLR-F6 aircraft.
Komatitsch, Dimitri; Bozdag, Ebru; de Andrade, Elliott Sales; Peter, Daniel B; Liu, Qinya; Tromp, Jeroen
2016-01-01
We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the $K_\\alpha$ sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersi...
Directory of Open Access Journals (Sweden)
Xiaoyan Zhang
2015-01-01
Full Text Available This study evaluates the impact of Tropospheric Airborne Meteorological Data Reporting (TAMDAR observations on regional 24-hour forecast error reduction over the Continental United States (CONUS domain using adjoint-based forecast sensitivity to observation (FSO method as the diagnostic tool. The relative impact of TAMDAR observations on reducing the forecast error was assessed by conducting the WRFDA FSO experiments for two two-week-long periods, one in January and one in June 2010. These experiments assimilated operational TAMDAR data and other conventional observations, as well as GPS refractivity (GPSREF. FSO results show that rawinsonde soundings (SOUND and TAMDAR exhibit the largest observation impact on 24 h WRF forecast, followed by GeoAMV, aviation routine weather reports (METAR, GPSREF, and synoptic observations (SYNOP. At 0000 and 1200 UTC, TAMDAR has an equivalent impact to SOUND in reducing the 24-hour forecast error. However, at 1800 UTC, TAMDAR has a distinct advantage over SOUND, which has the sparse observation report at these times. In addition, TAMDAR humidity observations at lower levels of the atmosphere (700 and 850 hPa have a significant impact on 24 h forecast error reductions. TAMDAR and SOUND observations present a qualitatively similar observation impact between FSO and Observation System Experiments (OSEs.
Higher representations on the lattice: numerical simulations. SU(2) with adjoint fermions
Del Debbio, Luigi; Pica, Claudio
2008-01-01
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present in detail the implementation of the HMC/RHMC algorithm for simulating dynamical fermions. Working with two flavors of Wilson fermions in the adjoint representation, we start mapping the phase diagram of the SU(2) theory. Preliminary runs to tune the algorithm are performed on 4^3*8 lattices, and a first exploration of the approach to the chiral limit is discussed from data for the PCAC mass and the pseudoscalar meson mass, generated on an 8^3*16 lattice. First computations of the lattice spacing and the vector mass are presented; since these models are candidates for realistic technicolor theories, our results yield a first estimate of the mass of the technirho. However more extensive investigations are needed in order to control the systematic errors in the numerical results, and then understand in detail the phase structure of these theories and their viability as candidates for st...
Using adjoint sensitivity as a local structure function in variational data assimilation
Directory of Open Access Journals (Sweden)
G. Hello
2001-01-01
Full Text Available One approach recently proposed in order to improve the forecast of weather events, such as cyclogenesis, is to increase the number of observations in areas depending on the flow configuration. These areas are obtained using, for example, the sensitivity to initial conditions of a selected predicted cyclone. An alternative or complementary way is proposed here. The idea is to employ such an adjoint sensitivity field as a local structure function within variational data assimilation, 3D-Var in this instance. Away from the sensitive area, observation increments project on the initial fields with the usual climatological (or weakly flow-dependent, in the case of 4D-Var structure functions. Within the sensitive area, the gradient fields are projected using all the available data in the zone, conventional or extra, if any. The formulation of the technique is given and the approach is further explained by using a simple 1D scheme. The technique is implemented in the ARPEGE/IFS code and applied to 11 FASTEX (Fronts and Atlantic Storm-Track Experiment cyclone cases, together with the targeted observations performed at the time of the campaign. The new approach is shown to allow for the desired stronger impact of the available observations and to systematically improve the forecasts of the FASTEX cyclones, unlike the standard 3D-Var.
Damage Detection of Bridges Using Vibration Data by Adjoint Variable Method
Directory of Open Access Journals (Sweden)
Akbar Mirzaee
2014-01-01
Full Text Available This research entails a theoretical and numerical study on a new damage detection method for bridges, using response sensitivity in time domain. This method, referred to as “adjoint variable method,” is a finite element model updating sensitivity based method. Governing equation of the bridge-vehicle system is established based on finite element formulation. In the inverse analysis, the new approach is presented to identify elemental flexural rigidity of the structure from acceleration responses of several measurement points. The computational cost of sensitivity matrix is the main concern associated with damage detection by these methods. The main advantage of the proposed method is the inclusion of an analytical method to augment the accuracy and speed of the solution. The reliable performance of the method to precisely identify the location and intensity of all types of predetermined single, multiple, and random damages over the whole domain of moving vehicle speed is shown. A comparison study is also carried out to demonstrate the relative effectiveness and upgraded performance of the proposed method in comparison to the similar ordinary sensitivity analysis methods. Moreover, various sources of errors including the effects of noise and primary errors on the numerical stability of the proposed method are discussed.
Large-N reduction in QCD-like theories with massive adjoint fermions
Energy Technology Data Exchange (ETDEWEB)
Azeyanagi, Tatsuo; /Kyoto U.; Hanada, Masanori; /Weizmann Inst.; Unsal, Mithat; /Weizmann Inst. /SLAC /Stanford U., Phys. Dept.; Yacoby, Ran; /Weizmann Inst.
2010-08-26
Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R3 x S1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1{sup 3} x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.
Adjoint $QCD_{1+1}$ in Light-cone Gauge, Quantized at Equal Time
Vianello, E
2004-01-01
SU(2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with "twisted" boundary conditions, periodic for one color component (the diagonal 3- component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-color component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the fr...
Nonperturbative Effects from Perturbation Theory in Adjoint QCD_{1+1}
Vianello, E
2004-01-01
SU(2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with "twisted" boundary conditions, periodic for one colour component (the diagonal 3- component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-colour component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the ...
Sikarwar, Nidhi
multiple experiments or numerical simulations. Alternatively an inverse design method can be used. An adjoint optimization method can be used to achieve the optimum blowing rate. It is shown that the method works for both geometry optimization and active control of the flow in order to deflect the flow in desirable ways. An adjoint optimization method is described. It is used to determine the blowing distribution in the diverging section of a convergent-divergent nozzle that gives a desired pressure distribution in the nozzle. Both the direct and adjoint problems and their associated boundary conditions are developed. The adjoint method is used to determine the blowing distribution required to minimize the shock strength in the nozzle to achieve a known target pressure and to achieve close to an ideally expanded flow pressure. A multi-block structured solver is developed to calculate the flow solution and associated adjoint variables. Two and three-dimensional calculations are performed for internal and external of the nozzle domains. A two step MacCormack scheme based on predictor- corrector technique is was used for some calculations. The four and five stage Runge-Kutta schemes are also used to artificially march in time. A modified Runge-Kutta scheme is used to accelerate the convergence to a steady state. Second order artificial dissipation has been added to stabilize the calculations. The steepest decent method has been used for the optimization of the blowing velocity after the gradients of the cost function with respect to the blowing velocity are calculated using adjoint method. Several examples are given of the optimization of blowing using the adjoint method.
Flux-P: Automating Metabolic Flux Analysis
Directory of Open Access Journals (Sweden)
Birgitta E. Ebert
2012-11-01
Full Text Available Quantitative knowledge of intracellular fluxes in metabolic networks is invaluable for inferring metabolic system behavior and the design principles of biological systems. However, intracellular reaction rates can not often be calculated directly but have to be estimated; for instance, via 13C-based metabolic flux analysis, a model-based interpretation of stable carbon isotope patterns in intermediates of metabolism. Existing software such as FiatFlux, OpenFLUX or 13CFLUX supports experts in this complex analysis, but requires several steps that have to be carried out manually, hence restricting the use of this software for data interpretation to a rather small number of experiments. In this paper, we present Flux-P as an approach to automate and standardize 13C-based metabolic flux analysis, using the Bio-jETI workflow framework. Exemplarily based on the FiatFlux software, it demonstrates how services can be created that carry out the different analysis steps autonomously and how these can subsequently be assembled into software workflows that perform automated, high-throughput intracellular flux analysis of high quality and reproducibility. Besides significant acceleration and standardization of the data analysis, the agile workflow-based realization supports flexible changes of the analysis workflows on the user level, making it easy to perform custom analyses.
Towards magnetic sounding of the Earth's core by an adjoint method
Li, K.; Jackson, A.; Livermore, P. W.
2013-12-01
Earth's magnetic field is generated and sustained by the so called geodynamo system in the core. Measurements of the geomagnetic field taken at the surface, downwards continued through the electrically insulating mantle to the core-mantle boundary (CMB), provide important constraints on the time evolution of the velocity, magnetic field and temperature anomaly in the fluid outer core. The aim of any study in data assimilation applied to the Earth's core is to produce a time-dependent model consistent with these observations [1]. Snapshots of these ``tuned" models provide a window through which the inner workings of the Earth's core, usually hidden from view, can be probed. We apply a variational data assimilation framework to an inertia-free magnetohydrodynamic system (MHD) [2]. Such a model is close to magnetostrophic balance [3], to which we have added viscosity to the dominant forces of Coriolis, pressure, Lorentz and buoyancy, believed to be a good approximation of the Earth's dynamo in the convective time scale. We chose to study the MHD system driven by a static temperature anomaly to mimic the actual inner working of Earth's dynamo system, avoiding at this stage the further complication of solving for the time dependent temperature field. At the heart of the models is a time-dependent magnetic field to which the core-flow is enslaved. In previous work we laid the foundation of the adjoint methodology, applied to a subset of the full equations [4]. As an intermediate step towards our ultimate vision of applying the techniques to a fully dynamic mode of the Earth's core tuned to geomagnetic observations, we present the intermediate step of applying the adjoint technique to the inertia-free Navier-Stokes equation in continuous form. We use synthetic observations derived from evolving a geophysically-reasonable magnetic field profile as the initial condition of our MHD system. Based on our study, we also propose several different strategies for accurately
Aerosol Health Impact Source Attribution Studies with the CMAQ Adjoint Air Quality Model
Turner, M. D.
Fine particulate matter (PM2.5) is an air pollutant consisting of a mixture of solid and liquid particles suspended in the atmosphere. Knowledge of the sources and distributions of PM2.5 is important for many reasons, two of which are that PM2.5 has an adverse effect on human health and also an effect on climate change. Recent studies have suggested that health benefits resulting from a unit decrease in black carbon (BC) are four to nine times larger than benefits resulting from an equivalent change in PM2.5 mass. The goal of this thesis is to quantify the role of emissions from different sectors and different locations in governing the total health impacts, risk, and maximum individual risk of exposure to BC both nationally and regionally in the US. We develop and use the CMAQ adjoint model to quantify the role of emissions from all modeled sectors, times, and locations on premature deaths attributed to exposure to BC. From a national analysis, we find that damages resulting from anthropogenic emissions of BC are strongly correlated with population and premature death. However, we find little correlation between damages and emission magnitude, suggesting that controls on the largest emissions may not be the most efficient means of reducing damages resulting from BC emissions. Rather, the best proxy for locations with damaging BC emissions is locations where premature deaths occur. Onroad diesel and nonroad vehicle emissions are the largest contributors to premature deaths attributed to exposure to BC, while onroad gasoline emissions cause the highest deaths per amount emitted. Additionally, emissions in fall and winter contribute to more premature deaths (and more per amount emitted) than emissions in spring and summer. From a regional analysis, we find that emissions from outside each of six urban areas account for 7% to 27% of the premature deaths attributed to exposure to BC within the region. Within the region encompassing New York City and Philadelphia
Ruzmaikin, A.
1997-01-01
Observations show that newly emerging flux tends to appear on the Solar surface at sites where there is flux already. This results in clustering of solar activity. Standard dynamo theories do not predict this effect.
Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model
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
Peter, Daniel; Videau, Brice; Pouget, Kevin; Komatitsch, Dimitri
2015-04-01
Improving the resolution of tomographic images is crucial to answer important questions on the nature of Earth's subsurface structure and internal processes. Seismic tomography is the most prominent approach where seismic signals from ground-motion records are used to infer physical properties of internal structures such as compressional- and shear-wave speeds, anisotropy and attenuation. Recent advances in regional- and global-scale seismic inversions move towards full-waveform inversions which require accurate simulations of seismic wave propagation in complex 3D media, providing access to the full 3D seismic wavefields. However, these numerical simulations are computationally very expensive and need high-performance computing (HPC) facilities for further improving the current state of knowledge. During recent years, many-core architectures such as graphics processing units (GPUs) have been added to available large HPC systems. Such GPU-accelerated computing together with advances in multi-core central processing units (CPUs) can greatly accelerate scientific applications. There are mainly two possible choices of language support for GPU cards, the CUDA programming environment and OpenCL language standard. CUDA software development targets NVIDIA graphic cards while OpenCL was adopted mainly by AMD graphic cards. In order to employ such hardware accelerators for seismic wave propagation simulations, we incorporated a code generation tool BOAST into an existing spectral-element code package SPECFEM3D_GLOBE. This allows us to use meta-programming of computational kernels and generate optimized source code for both CUDA and OpenCL languages, running simulations on either CUDA or OpenCL hardware accelerators. We show here applications of forward and adjoint seismic wave propagation on CUDA/OpenCL GPUs, validating results and comparing performances for different simulations and hardware usages.
Comparison of Observation Impacts in Two Forecast Systems using Adjoint Methods
Gelaro, Ronald; Langland, Rolf; Todling, Ricardo
2009-01-01
An experiment is being conducted to compare directly the impact of all assimilated observations on short-range forecast errors in different operational forecast systems. We use the adjoint-based method developed by Langland and Baker (2004), which allows these impacts to be efficiently calculated. This presentation describes preliminary results for a "baseline" set of observations, including both satellite radiances and conventional observations, used by the Navy/NOGAPS and NASA/GEOS-5 forecast systems for the month of January 2007. In each system, about 65% of the total reduction in 24-h forecast error is provided by satellite observations, although the impact of rawinsonde, aircraft, land, and ship-based observations remains significant. Only a small majority (50- 55%) of all observations assimilated improves the forecast, while the rest degrade it. It is found that most of the total forecast error reduction comes from observations with moderate-size innovations providing small to moderate impacts, not from outliers with very large positive or negative innovations. In a global context, the relative impacts of the major observation types are fairly similar in each system, although regional differences in observation impact can be significant. Of particular interest is the fact that while satellite radiances have a large positive impact overall, they degrade the forecast in certain locations common to both systems, especially over land and ice surfaces. Ongoing comparisons of this type, with results expected from other operational centers, should lead to more robust conclusions about the impacts of the various components of the observing system as well as about the strengths and weaknesses of the methodologies used to assimilate them.
Guven, B.; Olaguer, E. P.; Herndon, S. C.; Kolb, C. E.; Cuclis, A.
2012-12-01
During the "Formaldehyde and Olefins from Large Industrial Sources" (FLAIR) study in 2009, the Aerodyne Research Inc. (ARI) mobile laboratory performed real-time in situ measurements of VOCs, NOx and HCHO in Texas City, TX on May 7, 2009 from 11 am to 3 pm. This high resolution dataset collected in a predominantly industrial area provides an ideal test bed for advanced source attribution. Our goal was to identify and quantify emission sources within the largest facility in Texas City most likely responsible for measured benzene concentrations. For this purpose, fine horizontal resolution (200 m x 200 m) 4D variational (4Dvar) inverse modeling was performed by running the HARC air quality transport model in adjoint mode based on ambient concentrations measured by the mobile laboratory. The simulations were conducted with a horizontal domain size of 4 km x 4 km for a four-hour period (11 am to 3 pm). Potential emission unit locations within the facility were specified using a high spatial resolution digital model of the largest industrial complex in the area. The HARC model was used to infer benzene emission rates from all potential source locations that would account for the benzene concentrations measured by the Aerodyne mobile laboratory in the vicinity of the facility. A Positive Matrix Factorization receptor model was also applied to the concentrations of other compounds measured by the mobile lab to support the source attribution by the inverse model. Although previous studies attributed measured benzene concentrations during the same time period to a cooling tower unit at the industrial complex, this study found that some of the flare units in the facility were also associated with the elevated benzene concentrations. The emissions of some of these flare units were found to be greater than reported in emission inventories, by up to two orders of magnitude.
Directory of Open Access Journals (Sweden)
R. H. Moore
2013-04-01
Full Text Available We use the Global Modelling Initiative (GMI chemical transport model with a cloud droplet parameterisation adjoint to quantify the sensitivity of cloud droplet number concentration to uncertainties in predicting CCN concentrations. Published CCN closure uncertainties for six different sets of simplifying compositional and mixing state assumptions are used as proxies for modelled CCN uncertainty arising from application of those scenarios. It is found that cloud droplet number concentrations (Nd are fairly insensitive to the number concentration (Na of aerosol which act as CCN over the continents (∂lnNd/∂lnNa ~10–30%, but the sensitivities exceed 70% in pristine regions such as the Alaskan Arctic and remote oceans. This means that CCN concentration uncertainties of 4–71% translate into only 1–23% uncertainty in cloud droplet number, on average. Since most of the anthropogenic indirect forcing is concentrated over the continents, this work shows that the application of Köhler theory and attendant simplifying assumptions in models is not a major source of uncertainty in predicting cloud droplet number or anthropogenic aerosol indirect forcing for the liquid, stratiform clouds simulated in these models. However, it does highlight the sensitivity of some remote areas to pollution brought into the region via long-range transport (e.g., biomass burning or from seasonal biogenic sources (e.g., phytoplankton as a source of dimethylsulfide in the southern oceans. Since these transient processes are not captured well by the climatological emissions inventories employed by current large-scale models, the uncertainties in aerosol-cloud interactions during these events could be much larger than those uncovered here. This finding motivates additional measurements in these pristine regions, for which few observations exist, to quantify the impact (and associated uncertainty of transient aerosol processes on cloud properties.
Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony
1996-01-01
This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.
Dirac lattices, zero-range potentials, and self-adjoint extension
Bordag, M.; Muñoz-Castañeda, J. M.
2015-03-01
We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches handling these: the self-adjoint extension, regularization/renormalization and the zero range potential methods. Their close interrelations are discussed in detail and compared with the electrostatic approach which drops the contributions from the self fields. For a homogeneous two dimensional lattice of dipoles we write down the complete solutions, which allow, for example, for an easy numerical treatment of the scattering of the electromagnetic field on the lattice or for investigating plasmons. Using these formulas, we consider the limiting case of vanishing lattice spacing, i.e., the transition to a continuous sheet. For a scalar field and for the TE polarization of the electromagnetic field this transition is smooth and results in the results known from the continuous sheet. Especially for the TE polarization, we reproduce the results known from the hydrodynamic model describing a two dimensional electron gas. For the TM polarization, for polarizability parallel and perpendicular to the lattice, in both cases, the transition is singular. For the parallel polarizability this is surprising and different from the hydrodynamic model. For perpendicular polarizability this is what was known in literature. We also investigate the case when the transition is done with dipoles described by smeared delta function, i.e., keeping a regularization. Here, for TM polarization for parallel polarizability, when subsequently doing the limit of vanishing lattice spacing, we reproduce the result known from the hydrodynamic model. In case of perpendicular polarizability we need an additional renormalization to reproduce the result obtained previously by stepping back from the dipole approximation.
Directory of Open Access Journals (Sweden)
R. H. Moore
2012-08-01
Full Text Available We use the Global Modeling Initiative (GMI chemical transport model with a cloud droplet parameterization adjoint to quantify the sensitivity of cloud droplet number concentration to uncertainties in predicting CCN concentrations. Published CCN closure prediction uncertainties for six different sets of simplifying compositional and mixing state assumptions are used as proxies for modeled CCN uncertainty arising from application of those scenarios. It is found that cloud droplet number concentrations are fairly insensitive to CCN-active aerosol number concentrations over the continents (∂Nd/∂N_{a} ~ 10–30%, but the sensitivities exceed 70% in pristine regions such as the Alaskan Arctic and remote oceans. Since most of the anthropogenic indirect forcing is concentrated over the continents, this work shows that the application of Köhler theory and attendant simplifying assumptions in models is not a major source of uncertainty in predicting cloud droplet number or anthropogenic aerosol indirect forcing for the liquid, stratiform clouds simulated in these models. However, it does highlight the sensitivity of some remote areas to pollution brought into the region via long-range transport (e.g. biomass burning or from seasonal biogenic sources (e.g. phytoplankton as a source of dimethylsulfide in the southern oceans. Since these transient processes are not captured well by the climatological emissions inventories employed by current large-scale models, the uncertainties in aerosol-cloud interactions during these events could be much larger than those uncovered here. This finding motivates additional measurements in these pristine regions, which have recieved little attention to date, in order to quantify the impact of, and uncertainty associated with, transient processes in effecting changes in cloud properties.
Adjoint-tomography for a Local Surface Structure: Methodology and a Blind Test
Kubina, Filip; Michlik, Filip; Moczo, Peter; Kristek, Jozef; Stripajova, Svetlana
2017-04-01
We have developed a multiscale full-waveform adjoint-tomography method for local surface sedimentary structures with complicated interference wavefields. The local surface sedimentary basins and valleys are often responsible for anomalous earthquake ground motions and corresponding damage in earthquakes. In many cases only relatively small number of records of a few local earthquakes is available for a site of interest. Consequently, prediction of earthquake ground motion at the site has to include numerical modeling for a realistic model of the local structure. Though limited, the information about the local structure encoded in the records is important and irreplaceable. It is therefore reasonable to have a method capable of using the limited information in records for improving a model of the local structure. A local surface structure and its interference wavefield require a specific multiscale approach. In order to verify our inversion method, we performed a blind test. We obtained synthetic seismograms at 8 receivers for 2 local sources, complete description of the sources, positions of the receivers and material parameters of the bedrock. We considered the simplest possible starting model - a homogeneous halfspace made of the bedrock. Using our inversion method we obtained an inverted model. Given the starting model, synthetic seismograms simulated for the inverted model are surprisingly close to the synthetic seismograms simulated for the true structure in the target frequency range up to 4.5 Hz. We quantify the level of agreement between the true and inverted seismograms using the L2 and time-frequency misfits, and, more importantly for earthquake-engineering applications, also using the goodness-of-fit criteria based on the earthquake-engineering characteristics of earthquake ground motion. We also verified the inverted model for other source-receiver configurations not used in the inversion.
A user`s manual for MASH 1.0: A Monte Carlo Adjoint Shielding Code System
Energy Technology Data Exchange (ETDEWEB)
Johnson, J.O. [ed.
1992-03-01
The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the ``dose importance`` of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user`s manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.
A user's manual for MASH 1. 0: A Monte Carlo Adjoint Shielding Code System
Energy Technology Data Exchange (ETDEWEB)
Johnson, J.O. (ed.)
1992-03-01
The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the dose importance'' of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.
FLUXES FOR MECHANIZED ELECTRIC WELDING,
WELDING FLUXES, WELDING ), (* WELDING , WELDING FLUXES), ARC WELDING , WELDS, STABILITY, POROSITY, WELDING RODS, STEEL, CERAMIC MATERIALS, FLUXES(FUSION), TITANIUM ALLOYS, ALUMINUM ALLOYS, COPPER ALLOYS, ELECTRODEPOSITION
Roeck, Wojciech De; Schütz, Marius
2016-11-01
Since its introduction by Hastings (Phys Rev B 69:104431, 2004), the technique of quasi-adiabatic continuation has become a central tool in the discussion and classification of ground-state phases. It connects the ground states of self-adjoint Hamiltonians in the same phase by a unitary quasi-local transformation. This paper takes a step towards extending this result to non-self-adjoint perturbations, though, for technical reason, we restrict ourselves here to weak perturbations of non-interacting spins. The extension to non-self-adjoint perturbation is important for potential applications to Glauber dynamics (and its quantum analogues). In contrast to the standard quasi-adiabatic transformation, the transformation constructed here is exponentially local. Our scheme is inspired by KAM theory, with frustration-free operators playing the role of integrable Hamiltonians.
Institute of Scientific and Technical Information of China (English)
郑召文; 刘宝圣
2012-01-01
本文讨论了极限圆型Hamilton算子乘积的自伴性，利用Calkin方法及奇异Hamilton系统自伴扩张的一般构造理论，给出了在极限圆型时判定Hamilton算子乘积自伴的一个充要条件．%In this paper, the self-adjointness of the product of two Hamiltonian op- erators under the limit circle case is considered. Using the Calkin method and the construction of self-adjoint extension for singular Hamiltonian systems, the necessary and sufficient conditions which make the product of two Hamiltonian operators under the limit circle case being a self-adjoint operator are obtained.
Title, A.; Cheung, M.
2008-05-01
The high spatial resolution and high cadence of the Solar Optical Telescope on the JAXA Hinode spacecraft have allowed capturing many examples of magnetic flux emergence from the scale of granulation to active regions. The observed patterns of emergence are quite similar. Flux emerges as a array of small bipoles on scales from 1 to 5 arc seconds throughout the region that the flux eventually condenses. Because the fields emerging from the underlying flux rope my appear many in small segments and the total flux (absolute sum) is not a conserved quantity the amount of total flux on the surface may vary significantly during the emergence process. Numerical simulations of flux emergence exhibit patterns similar to observations. Movies of both observations and numerical simulations will be presented.
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.
Radial anisotropy of the North American upper mantle based on adjoint tomography with USArray
Zhu, Hejun; Komatitsch, Dimitri; Tromp, Jeroen
2017-10-01
We use seismic data from USArray to image the upper mantle underneath the United States based on a so-called `adjoint tomography', an iterative full waveform inversion technique. The inversion uses data from 180 regional earthquakes recorded by 4516 seismographic stations, resulting in 586 185 frequency-dependent measurements. Three-component short-period body waves and long-period surface waves are combined to simultaneously constrain deep and shallow structures. The transversely isotropic model US22 is the result of 22 pre-conditioned conjugate-gradient iterations. Approximate Hessian maps and point-spread function tests demonstrate good illumination of the study region and limited trade-offs among different model parameters. We observe a distinct wave-speed contrast between the stable eastern US and the tectonically active western US. This boundary is well correlated with the Rocky Mountain Front. Stable cratonic regions are characterized by fast anomalies down to 250-300 km, reflecting the thickness of the North American lithosphere. Several fast anomalies are observed beneath the North American lithosphere, suggesting the possibility of lithospheric delamination. Slow wave-speed channels are imaged beneath the lithosphere, which might indicate weak asthenosphere. Beneath the mantle transition zone of the central US, an elongated north-south fast anomaly is observed, which might be the ancient subducted Farallon slab. The tectonically active western US is dominated by prominent slow anomalies with magnitudes greater than -6 per cent down to approximately 250 km. No continuous lower to upper mantle upwellings are observed beneath Yellowstone. In addition, our results confirm previously observed differences between oceans and continents in the anisotropic parameter ξ = (βh/βv)2. A slow wave-speed channel with ξ > 1 is imaged beneath the eastern Pacific at depths from 100 to 200 km, reflecting horizontal shear within the asthenosphere. Underneath continental
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.
Adjoint-based sensitivity of flames to ignition parameters in non-premixed shear-flow turbulence
Capecelatro, Jesse; Bodony, Daniel; Freund, Jonathan
2016-11-01
The adjoint of the linearized and perturbed compressible flow equations for a mixture of chemically reacting ideal gases is used to assess the sensitivity of ignition in non-premixed shear-flow turbulence. Direct numerical simulations are used to provide an initial prediction, and the corresponding space-time discrete-exact adjoint is used to provide a sensitivity gradient for a specific quantity of interest (QoI). Owing to the ultimately binary outcome of ignition (i.e., it succeeds or fails after some period), a QoI is defined that both quantifies ignition success and varies smoothly near its threshold based on the heat release parameter in a short-time horizon during the ignition process. We use the resulting gradient to quantify the flow properties and model parameters that most affect the initiation of a sustained flame. A line-search algorithm is used to identify regions of high ignition probability and map the boundary between successful and failed ignition. The approach is demonstrated on a non-premixed turbulent shear layer and on a reacting jet-in-crossflow.
Prompt atmospheric neutrino flux
Jeong, Yu Seon; Enberg, Rikard; Kim, C S; Reno, Mary Hall; Sarcevic, Ina; Stasto, Anna
2016-01-01
We evaluate the prompt atmospheric neutrino flux including nuclear correction and $B$ hadron contribution in the different frameworks: NLO perturbative QCD and dipole models. The nuclear effect is larger in the prompt neutrino flux than in the total charm production cross section, and it reduces the fluxes by $10\\% - 30\\%$ depending on the model. We also investigate the uncertainty using the QCD scales allowed by the charm cross section data from RHIC and LHC experiments.
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
Bowman, K. W.; Liu, J.; Parazoo, N.; Lee, M.; Menemenlis, D.; Gierach, M. M.; Brix, H.; Gurney, K. R.; Collatz, G. J.; Bousserez, N.; Henze, D. K.
2014-12-01
Interannual variations in the atmospheric growth rate of CO2 have been attributed to the tropical regions and the controls are correlated with temperature anomalies. We investigate the spatial drivers of the atmospheric growth rate and the processes controlling them over the exceptional period of 2010-2011. This period was marked by a marked shift from an El Nino to La Nina period resulting in historically high sea surface temperature anomalies in the tropical Atlantic leading to serious droughts in the Amazon. However, in 2011, unusual precipitation in Australia was linked to gross primary productivity anomalies in semi-arid regions. We use satellite observations of CO2, CO, and solar induced fluorescence assimilated into the NASA Carbon Monitoring System Project (CMS-Flux) to attribute the atmospheric growth rate to global, spatially resolved fluxes. This system is based upon observationally-constrained "bottom-up" estimates from the Fossil Fuel Data Assimilation System (FFDAS), the ECCO2-Darwin physical and biogeochemical adjoint ocean state estimation system, and CASA-GFED3 land-surface biogeochemical model. The system is used to compute regional tropical and extra-tropical fluxes and quantify the role of biomass burning and gross primary productivity in controlling those fluxes.
Bowman, K. W.; Liu, J.; Parazoo, N.; Jiang, Z.; Bloom, A. A.; Lee, M.; Menemenlis, D.; Gierach, M.; Collatz, G. J.; Gurney, K. R.
2015-12-01
The La Nina between 2011-2012 led to significant droughts in the US and Northeastern Brazil while the historic drought in Amazon in 2010 was caused in part by the historic central Pacific El Nino. In order to investigate the role of drought on the atmospheric CO2 growth rate, we use satellite observations of CO2 and CO to infer spatially resolved carbon fluxes and attribute those fluxes to combustion sources correlated with drought conditions. Solar induced fluorescence in turn is used to estimate the impact of drought on productivity and its relationship to total flux. Preliminary results indicate that carbon losses in Mexico are comparable to the total fossil fuel production for that region. These in turn played an important role in the acceleration of the atmospheric growth rate from 2011-2012. These results were enabled using the NASA Carbon Monitoring System Project (CMS-Flux), which is based upon a 4D-variational assimilation system that incorporates observationally-constrained "bottom-up" estimates from the Fossil Fuel Data Assimilation System (FFDAS), the ECCO2-Darwin physical and biogeochemical adjoint ocean state estimation system, and CASA-GFED3 land-surface biogeochemical model.
Nievaart, V.A.; Legrady, D.; Moss, R.L.; Kloosterman, J.L.; Van der Hagen, T.H.; Van Dam, H.
2007-01-01
This paper deals with the application of the adjoint transport theory in order to optimize Monte Carlo based radiotherapy treatment planning. The technique is applied to Boron Neutron Capture Therapy where most often mixed beams of neutrons and gammas are involved. In normal forward Monte Carlo simu
Weiss, M.; Vermeulen, A.; Bos, J.; Bucco, D.
2011-01-01
The Adjoint Method is a well establised tool for assessement of guidance loops in conceptual design studies. It allows one to perform quick assessments of the performance both in deterministic settings, to determine a nominal or average miss distance, and in stochastic settings, to determine the
Institute of Scientific and Technical Information of China (English)
王兴涛
2002-01-01
Control equation and adjoint equation are established by using block-pulse functions, which trans-forms the linear time-varying systems with time delays into a system of algebraic equations and the optimal con-trol problems are transformed into an optimization problem of multivariate functions thereby achieving the opti-mal control of linear systems with time delays.
Electron heat flux instability
Saeed, Sundas; Sarfraz, M.; Yoon, P. H.; Lazar, M.; Qureshi, M. N. S.
2017-02-01
The heat flux instability is an electromagnetic mode excited by a relative drift between the protons and two-component core-halo electrons. The most prominent application may be in association with the solar wind where drifting electron velocity distributions are observed. The heat flux instability is somewhat analogous to the electrostatic Buneman or ion-acoustic instability driven by the net drift between the protons and bulk electrons, except that the heat flux instability operates in magnetized plasmas and possesses transverse electromagnetic polarization. The heat flux instability is also distinct from the electrostatic counterpart in that it requires two electron species with relative drifts with each other. In the literature, the heat flux instability is often called the 'whistler' heat flux instability, but it is actually polarized in the opposite sense to the whistler wave. This paper elucidates all of these fundamental plasma physical properties associated with the heat flux instability starting from a simple model, and gradually building up more complexity towards a solar wind-like distribution functions. It is found that the essential properties of the instability are already present in the cold counter-streaming electron model, and that the instability is absent if the protons are ignored. These instability characteristics are highly reminiscent of the electron firehose instability driven by excessive parallel temperature anisotropy, propagating in parallel direction with respect to the ambient magnetic field, except that the free energy source for the heat flux instability resides in the effective parallel pressure provided by the counter-streaming electrons.
The forward sensitivity and adjoint-state methods of glacial isostatic adjustment
Martinec, Zdeněk; Sasgen, Ingo; Velímský, Jakub
2015-01-01
In this study, a new method for computing the sensitivity of the glacial isostatic adjustment (GIA) forward solution with respect to the Earth's mantle viscosity, the so-called the forward sensitivity method (FSM), and a method for computing the gradient of data misfit with respect to viscosity parameters, the so-called adjoint-state method (ASM), are presented. These advanced formal methods complement each other in the inverse modelling of GIA-related observations. When solving this inverse problem, the first step is to calculate the forward sensitivities by the FSM and use them to fix the model parameters that do not affect the forward model solution, as well as identifying and removing redundant parts of the inferred viscosity structure. Once the viscosity model is optimized in view of the forward sensitivities, the minimization of the data misfit with respect to the viscosity parameters can be carried out by a gradient technique which makes use of the ASM. The aim is this paper is to derive the FSM and ASM in the forms that are closely associated with the forward solver of GIA developed by Martinec. Since this method is based on a continuous form of the forward model equations, which are then discretized by spectral and finite elements, we first derive the continuous forms of the FSM and ASM and then discretize them by the spectral and finite elements used in the discretization of the forward model equations. The advantage of this approach is that all three methods (forward, FSM and ASM) have the same matrix of equations and use the same methodology for the implementation of the time evolution of stresses. The only difference between the forward method and the FSM and ASM is that the different numerical differencing schemes for the time evolution of the Maxwell and generalized Maxwell viscous stresses are applied in the respective methods. However, it requires only a little extra computational time for carrying out the FSM and ASM numerically. An
Morency, C.; Tromp, J.
2008-12-01
successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.
Sengupta, T. K.; Bhaumik, S.; Shameem, U.
2011-03-01
A single-parameter family of self-adjoint compact difference (SACD) schemes is developed for discretizing the Laplacian operator in self-adjoint form. Developed implicit scheme is formally second-order accurate (with respect to truncation error) with a free parameter, α which helps control the numerical properties in the spectral plane. The SACD scheme is analyzed in the spectral plane for its resolution properties for both periodic and non-periodic problems using the matrix spectral analysis [T.K. Sengupta, G. Ganeriwal, S. De, Analysis of central and upwind schemes, J. Comput. Phys. 192 (2) (2003) 677-694]. The major objective here is to identify the advantages of the new scheme over the traditional explicit second order CD2 scheme, in discretizing the Laplacian operator in self-adjoint form. This appears in Navier-Stokes equation and in other transport equations and boundary value problems (bvp) expressed in orthogonal co-ordinate systems, either in physical or in transformed plane. We also compare the developed method with the higher order compact schemes for non-uniform grids. To demonstrate the accuracy of SACD scheme we have tested it for: (i) bi-directional wave propagation problem, given by the second order wave equation and (ii) an elliptic bvp, as in the Stommel ocean model for the stream function. These examples help infer the properties of SACD scheme when solving different types of partial differential equations. Most importantly the effects of grid-stretching and choice of value of the free parameter ( α) are investigated here. We also compare the present implicit compact method with explicit compact method known as the higher order compact (HOC) method. Also, the practical applications of the SACD scheme are explored by solving the Navier-Stokes equation for the cases of: (a) a flow inside a lid-driven cavity and (b) the receptivity and instability of an external adverse pressure gradient flow over a flat plate. In the former, unsteadiness of the
Santillana, Mauricio
2013-01-01
It is of crucial importance to be able to identify the location of atmospheric pollution sources in our planet. Global models of atmospheric transport in combination with diverse Earth observing systems are a natural choice to achieve this goal. It is shown that the ability to successfully reconstruct the location and magnitude of an instantaneous source in global chemical transport models (CTMs) decreases rapidly as a function of the time interval between the pollution release and the observation time. A simple way to quantitatively characterize this phenomenon is proposed based on the effective -undesired- numerical diffusion present in current Eulerian CTMs and verified using idealized numerical experiments. The approach presented consists of using the adjoint-based optimization method in a state-of-the-art CTM, GEOS-Chem, to reconstruct the location and magnitude of a realistic pollution plume for multiple time scales. The findings obtained from these numerical experiments suggest a time scale of 2 days a...
Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel
Nguyen, Nhan; Ardema, Mark
2006-01-01
This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch
Cagnetti, Filippo
2013-11-01
We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞ norm and O(h) in terms of the L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper. © 2013 IMACS.
DEFF Research Database (Denmark)
Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland
2014-01-01
an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D...... in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems...... with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and the main domain only, thus avoiding the need to solve a backward wave propagation problem inside the CFS-UPML, which is known to be highly...
Large-N reduction of SU(N) Yang-Mills theory with massive adjoint overlap fermions
Hietanen, A
2010-01-01
We study four dimensional large-N SU(N) Yang-Mills theory coupled to adjoint overlap fermions on a single site lattice. Lattice simulations along with perturbation theory show that the bare quark mass has to be taken to zero as one takes the continuum limit in order to be in the physically relevant center-symmetric phase. But, it seems that it is possible to take the continuum limit with any renormalized quark mass and still be in the center-symmetric physics. We have also conducted a study of the correlations between Polyakov loop operators in different directions and obtained the range for the Wilson mass parameter that enters the overlap Dirac operator.
Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter
Başar, Gökçe; Dienes, Keith R; McGady, David A
2015-01-01
In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and $(-1)^F$-twisted partition functions, and collectively suggest that the spectra of large-$N$ confining gauge theories are organized by the symmetries of two-dimensional conformal field theories.
A User's Manual for MASH V1.5 - A Monte Carlo Adjoint Shielding Code System
Energy Technology Data Exchange (ETDEWEB)
C. O. Slater; J. M. Barnes; J. O. Johnson; J.D. Drischler
1998-10-01
The Monte Carlo ~djoint ~ielding Code System, MASH, calculates neutron and gamma- ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air- over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system includes the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. The current version, MASH v 1.5, is the successor to the original MASH v 1.0 code system initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the "dose importance" of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response as a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem.
Lu, Xianqing; Zhang, Jicai
2006-10-01
Based on the simulation of M2 tide in the Bohai Sea, the Yellow Sea and the East China Sea, TOPEX/Poseidon altimeter data are assimilated into a 2D tidal model to study the spatially varying bottom friction coefficient (BFC) by using the adjoint method. In this study, the BFC at some grid points are selected as the independent BFC, while the BFC at other grid points can be obtained through linear interpolation with the independent BFC. Two strategies for selecting the independent BFC are discussed. In the first strategy, one independent BFC is uniformly selected from each 1°×1° area. In the second one, the independent BFC are selected based on the spatial distribution of water depth. Twin and practical experiments are carried out to compare the two strategies. In the twin experiments, the adjoint method has a strong ability of inverting the prescribed BFC distributions combined with the spatially varying BFC. In the practical experiments, reasonable simulation results can be obtained by optimizing the spatially varying independent BFC. In both twin and practical experiments, the simulation results with the second strategy are better than those with the first one. The BFC distribution obtained from the practical experiment indicates that the BFC in shallow water are larger than those in deep water in the Bohai Sea, the North Yellow Sea, the South Yellow Sea and the East China Sea individually. However, the BFC in the East China Sea are larger than those in the other areas perhaps because of the large difference of water depth or bottom roughness. The sensitivity analysis indicates that the model results are more sensitive to the independent BFC near the land.
U.S. Geological Survey, Department of the Interior — Net Ecosystem Carbon Flux is defined as the year-over-year change in Total Ecosystem Carbon Stock, or the net rate of carbon exchange between an ecosystem and the...
National Aeronautics and Space Administration — SolRad-Net (Solar Radiation Network) is an established network of ground-based sensors providing high-frequency solar flux measurements in quasi-realtime to the...
2004-01-01
Rahvusvahelise elektroonilise kunsti sümpoosioni ISEA2004 klubiõhtu "Flux in Tallinn" klubis Bon Bon. Eestit esindasid Ropotator, Ars Intel Inc., Urmas Puhkan, Joel Tammik, Taavi Tulev (pseud. Wochtzchee). Klubiõhtu koordinaator Andres Lõo
2004-01-01
Rahvusvahelise elektroonilise kunsti sümpoosioni ISEA2004 klubiõhtu "Flux in Tallinn" klubis Bon Bon. Eestit esindasid Ropotator, Ars Intel Inc., Urmas Puhkan, Joel Tammik, Taavi Tulev (pseud. Wochtzchee). Klubiõhtu koordinaator Andres Lõo
U.S. Geological Survey, Department of the Interior — Nitrous Oxide (N20) flux is the net rate of nitrous oxide exchange between an ecosystem and the atmosphere. Data of this variable were generated by the USGS...
Carbon Dioxide Flux Measurement Systems
Oak Ridge National Laboratory — The Southern Great Plains (SGP) carbon dioxide flux (CO2 flux) measurement systems provide half-hour average fluxes of CO2, H2O (latent heat), and sensible heat. The...
Cheung, Mark C. M.; Isobe, Hiroaki
2014-12-01
Magnetic flux emergence from the solar convection zone into the overlying atmosphere is the driver of a diverse range of phenomena associated with solar activity. In this article, we introduce theoretical concepts central to the study of flux emergence and discuss how the inclusion of different physical effects (e.g., magnetic buoyancy, magnetoconvection, reconnection, magnetic twist, interaction with ambient field) in models impact the evolution of the emerging field and plasma.
Theoretical magnetic flux emergence
MacTaggart, David
2011-01-01
Magnetic flux emergence is the subject of how magnetic fields from the solar interior can rise and expand into the atmosphere to produce active regions. It is the link that joins dynamics in the convection zone with dynamics in the atmosphere. In this thesis, we study many aspects of magnetic flux emergence through mathematical modelling and computer simulations. Our primary aim is to understand the key physical processes that lie behind emergence. The first chapter intro...
Directory of Open Access Journals (Sweden)
Mark C. M. Cheung
2014-07-01
Full Text Available Magnetic flux emergence from the solar convection zone into the overlying atmosphere is the driver of a diverse range of phenomena associated with solar activity. In this article, we introduce theoretical concepts central to the study of flux emergence and discuss how the inclusion of different physical effects (e.g., magnetic buoyancy, magnetoconvection, reconnection, magnetic twist, interaction with ambient field in models impact the evolution of the emerging field and plasma.
Estimation of surface heat flux for ablation and charring of thermal protection material
Qian, Wei-qi; He, Kai-feng; Zhou, Yu
2016-07-01
Ablation of the thermal protection material of the reentry hypersonic flight vehicle is a complex physical and chemical process. To estimate the surface heat flux from internal temperature measurement is much more complex than the conventional inverse heat conduction problem case. In the paper, by utilizing a two-layer pyrogeneration-plane ablation model to model the ablation and charring of the material, modifying the finite control volume method to suit for the numerical simulation of the heat conduction equation with variable-geometry, the CGM along with the associated adjoint problem is developed to estimate the surface heat flux. This estimation method is verified with a numerical example at first, the results show that the estimation method is feasible and robust. The larger is the measurement noise, the greater is the deviation of the estimated result from the exact value, and the measurement noise of ablated surface position has a significant and more direct influence on the estimated result of surface heat flux. Furthermore, the estimation method is used to analyze the experimental data of ablation of blunt Carbon-phenolic material Narmco4028 in an arc-heater. It is shown that the estimated surface heat flux agrees with the heating power value of the arc-heater, and the estimation method is basically effective and potential to treat the engineering heat conduction problem with ablation.
Joint CO2 state and flux estimation with the 4D-Var system EURAD-IM
Klimpt, Johannes; Elbern, Hendrik
2016-04-01
Atmospheric CO2 inversion studies seek to improve CO2 surface-atmosphere fluxes with the usage of adjoint transport models and CO2 concentration measurements. Terrestrial CO2 fluxes -anthropogenic emissions, photosynthesis, and respiration- bear large spatial and temporal variability and are highly uncertain. Additionally to the high uncertainty of the three CO2 fluxes itself, regional inversion studies suffer from uncertainty of the boundary layer height and atmospheric transport especially during night, leading to uncertainty of atmospheric CO2 mixing ratios during sunrise. This study assesses the potential of the 4-dimensional variational (4D-Var) method to estimate CO2 fluxes and atmospheric CO2 concentrations jointly at each grid cell on a regional scale. Identical twin experiments are executed with the nested EURopean Air pollution Dispersion-Inverse Model (EURAD-IM) with 5 km resolution in Central Europe with synthetic half hourly measurements from eleven concentration towers. The assimilation window is chosen to start from sunrise for 12 hours. We find that joint estimation of CO2 fluxes and initial states requires a more careful balance of the background error covariance matrices but enables a more detailed analysis of atmospheric CO2 and the surface-atmosphere fluxes.
Numerical methods for 3D tokamak simulations using a flux-surface independent grid
Energy Technology Data Exchange (ETDEWEB)
Stegmeir, A.; Coster, D.; Maj, O.; Lackner, K. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, 85748 Garching (Germany)
2014-06-15
A numerical approach for 3D Tokamak simulations using a flux surface independent grid is presented. The grid consists of few poloidal planes with a Cartesian isotropic grid within each poloidal plane. Perpendicular operators can be discretised within a poloidal plane using standard second order finite difference methods. The discretisation of parallel operators is achieved with a field line following map and an interpolation. The application of the support operator method to the parallel diffusion operator conserves the self-adjointness of the operator on the discrete level and keeps the numerical decay rate at a low level. The developed numerical methods can be applied to geometries where an X-point is present. (copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
The Flux-Flux Correlation Function for Anharmonic Barriers
Goussev, Arseni; Waalkens, Holger; Wiggins, Stephen
2010-01-01
The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classical and quantum flux-flux correlation functions for anharmonic barriers essentially analytically through the use of the classical and quantum normal forms. In the quantum case we show that the quantum normal form reduces the computation of the flux-flux correlation function to that of an effective one dimensional anharmonic barrier. The example of the computation of the quantum flux-flux correlation function for a fourth order anharmonic barrier is worked out in detail, and we present an analytical expression for the quantum mechanical microcanonical flux-flux correlation function. We then give a discussion of the short-time and harmonic limits.
Flux pinning in superconductors
Matsushita, Teruo
2014-01-01
The book covers the flux pinning mechanisms and properties and the electromagnetic phenomena caused by the flux pinning common for metallic, high-Tc and MgB2 superconductors. The condensation energy interaction known for normal precipitates or grain boundaries and the kinetic energy interaction proposed for artificial Nb pins in Nb-Ti, etc., are introduced for the pinning mechanism. Summation theories to derive the critical current density are discussed in detail. Irreversible magnetization and AC loss caused by the flux pinning are also discussed. The loss originally stems from the ohmic dissipation of normal electrons in the normal core driven by the electric field induced by the flux motion. The readers will learn why the resultant loss is of hysteresis type in spite of such mechanism. The influence of the flux pinning on the vortex phase diagram in high Tc superconductors is discussed, and the dependencies of the irreversibility field are also described on other quantities such as anisotropy of supercondu...
Flux Pinning in Superconductors
Matsushita, Teruo
2007-01-01
The book covers the flux pinning mechanisms and properties and the electromagnetic phenomena caused by the flux pinning common for metallic, high-Tc and MgB2 superconductors. The condensation energy interaction known for normal precipitates or grain boundaries and the kinetic energy interaction proposed for artificial Nb pins in Nb-Ti, etc., are introduced for the pinning mechanism. Summation theories to derive the critical current density are discussed in detail. Irreversible magnetization and AC loss caused by the flux pinning are also discussed. The loss originally stems from the ohmic dissipation of normal electrons in the normal core driven by the electric field induced by the flux motion. The readers will learn why the resultant loss is of hysteresis type in spite of such mechanism. The influence of the flux pinning on the vortex phase diagram in high Tc superconductors is discussed, and the dependencies of the irreversibility field are also described on other quantities such as anisotropy of supercondu...
Institute of Scientific and Technical Information of China (English)
Cheng Yongcun; Lu Xianqing; Liu Yuguang; Xu Qing
2007-01-01
Considering the interaction of different tidal waves, an adjoint numerical model is developed to simulate M2, S2, K1 and O1 tidal waves in the Bohai Sea, the Yellow Sea and the East China Sea(B-Y-E) simultaneously. Compared with previous researches, by using the adjoint assimilation technique to inverse open boundary conditions and bottom friction coefficients based on altimetric data from TOPEX/Poseidon (T/P)and tidal gauges data, the precision of the numerical simulation is significantly improved. Selecting 14 days of simulated results after t11e initial warming run to conduct harmonic analysis, the results can show the characteristics of M2, S2, K1 and O1 tidal wave systems perfectly in B-Y-E. Compared with 9 current stations, the calculated harmonic constants of tidal currents for M2 and K1 are in good agreement With the observed ones.
Bell, Matthew; Zhang, Wenyuan; Ioffe, Lev; Gershenson, Michael
2014-03-01
We have studied the coherent flux tunneling in a qubit containing two submicron Josephson junctions shunted by a superinductor (a dissipationless inductor with an impedance much greater than the resistance quantum). The two low energy quantum states of this device, " open="|"> 0 and " open="|"> 1, are represented by even and odd number of fluxes in the loop, respectively. This device is dual to the charge pairing Josephson rhombi qubit. The spectrum of the device, studied by microwave spectroscopy, reflects the interference between coherent quantum phase slips in the two junctions (the Aharonov-Casher effect). The time domain measurements demonstrate the suppression of the qubit's energy relaxation in the protected regime, which illustrates the potential of this flux pairing device as a protected quantum circuit. Templeton Foundation, NSF, and ARO.
Indian Academy of Sciences (India)
Boris Filippov; Olesya Martsenyuk; Abhishek K. Srivastava; Wahab Uddin
2015-03-01
In the early 1990s, it was found that the strongest disturbances of the space–weather were associated with huge ejections of plasma from the solar corona, which took the form of magnetic clouds when moved from the Sun. It is the collisions of the magnetic clouds with the Earth's magnetosphere that lead to strong, sometimes catastrophic changes in space–weather. The onset of a coronal mass ejection (CME) is sudden and no reliable forerunners of CMEs have been found till date. The CME prediction methodologies are less developed compared to the methods developed for the prediction of solar flares. The most probable initial magnetic configuration of a CME is a flux rope consisting of twisted field lines which fill the whole volume of a dark coronal cavity. The flux ropes can be in stable equilibrium in the coronal magnetic field for weeks and even months, but suddenly they lose their stability and erupt with high speed. Their transition to the unstable phase depends on the parameters of the flux rope (i.e., total electric current, twist, mass loading, etc.), as well as on the properties of the ambient coronal magnetic field. One of the major governing factors is the vertical gradient of the coronal magnetic field, which is estimated as decay index (). Cold dense prominence material can be collected in the lower parts of the helical flux tubes. Filaments are, therefore, good tracers of the flux ropes in the corona, which become visible long before the beginning of the eruption. The perspectives of the filament eruptions and following CMEs can be estimated by a comparison of observed filament heights with calculated decay index distributions. The present paper reviews the formation of magnetic flux ropes, their stable and unstable phases, eruption conditions, and also discusses their physical implications in the solar corona.
Schlichenmaier, Martin
2011-01-01
By elementary and direct calculations the vanishing of the (algebraic) second Lie algebra cohomology of the Witt and the Virasoro algebra with values in the adjoint module is shown. This yields infinitesimal and formal rigidity or these algebras. The first (and up to now only) proof of this important result was given 1989 by Fialowski in an unpublished note. It is based on cumbersome calculations. Compared to the original proof the presented one is quite elegant and considerably simpler.
Energy Technology Data Exchange (ETDEWEB)
Finn, John M., E-mail: finn@lanl.gov [T-5, Applied Mathematics and Plasma Physics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
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. 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
SELF-ADJOINTNESS OF PRODUCTS OF n SCHR(O..)DINGER OPERATORS%n个Schrodinger算子积自伴域
Institute of Scientific and Technical Information of China (English)
杨传富; 黄振友; 杨孝平
2004-01-01
In this paper, the problem of self-adjointness of products of n Schrodinger opera tors Li(i=1,… ,n;n∈Z and n≥2) generated by the differential expression l=- d2/dt2+q(t) on finite interval [a,b] (b》a) is considered. We show that Ln…L2L1 is a self-adjoint operator if and only if (Li=L*n+1-i(i=1，…，[n+1/2]).)whereL*n+1-i denotes the Hilbert space adjoint of Ln+1-i.%本文讨论了由微分算式l=-d2/dt2+q(t)生成的具有某种边界条件的n个正则Schrodinger算子Li(i=1,…,n)的积Ln…L2L1自伴性问题,证明了积算子Lm…L2L1自伴的充分必要条件为=L*n+1-i(i=1,…,[n+1/2]).
Galapon, E A
1999-01-01
Pauli's well known theorem (W. Pauli, Hanbuch der Physik vol. 5/1, ed. S. Flugge, (1926) p.60) asserts that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian implies that the time operator and the Hamitlonian posses completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate to a Hamiltonian with a spectrum which is a proper subspace of the real line. But we challenge this conclusion. We show rigourously the consitency of assuming a bounded, self-adjoint time operator conjugate to a Hamiltonian with an unbounded, or semibounded, or finitely countable point spectrum. Pauli implicitly assumed unconditionally that the domain of the Hamiltonian is invariant under the action of $U_\\beta=\\exp(-i\\beta T)$, where $T$ is the time operator, for arbitrary real number $\\betaA$. But we show that the $\\beta$'s are at most the differences of the eigenvalues of the Hamiltonian. And this happens, under some ...
Edwards, P. G.; Protheroe, R. J.
1985-01-01
The result of a new calculation of the atmospheric muon and neutrino fluxes and the energy spectrum of muon-neutrinos produced in individual extensive air showers (EAS) initiated by proton and gamma-ray primaries is reported. Also explained is the possibility of detecting atmospheric nu sub mu's due to gamma-rays from these sources.
Coupled superconducting flux qubits
Plantenberg, J.H.
2007-01-01
This thesis presents results of theoretical and experimental work on superconducting persistent-current quantum bits. These qubits offer an attractive route towards scalable solid-state quantum computing. The focus of this work is on the gradiometer flux qubit which has a special geometric design, t
Generic flux coupling analysis
Reimers, A.C.; Goldstein, Y.; Bockmayr, A.
2015-01-01
Flux coupling analysis (FCA) has become a useful tool for aiding metabolic reconstructions and guiding genetic manipulations. Originally, it was introduced for constraint-based models of metabolic networks that are based on the steady-state assumption. Recently, we have shown that the steady-state a
Lobotomy of flux compactifications
Dibitetto, Giuseppe; Guarino, Adolfo; Roest, Diederik
2014-01-01
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on (6) with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification
Disconnecting Solar Magnetic Flux
DeForest, C E; McComas, D J
2011-01-01
Disconnection of open magnetic flux by reconnection is required to balance the injection of open flux by CMEs and other eruptive events. Making use of recent advances in heliospheric background subtraction, we have imaged many abrupt disconnection events. These events produce dense plasma clouds whose distinctie shape can now be traced from the corona across the inner solar system via heliospheric imaging. The morphology of each initial event is characteristic of magnetic reconnection across a current sheet, and the newly-disconnected flux takes the form of a "U"-shaped loop that moves outward, accreting coronal and solar wind material. We analyzed one such event on 2008 December 18 as it formed and accelerated at 20 m/s^2 to 320 km/s, expanding self-similarly until it exited our field of view 1.2 AU from the Sun. From acceleration and photometric mass estimates we derive the coronal magnetic field strength to be 8uT, 6 Rs above the photosphere, and the entrained flux to be 1.6x10^11 Wb (1.6x10^19 Mx). We mod...
Coupled superconducting flux qubits
Plantenberg, J.H.
2007-01-01
This thesis presents results of theoretical and experimental work on superconducting persistent-current quantum bits. These qubits offer an attractive route towards scalable solid-state quantum computing. The focus of this work is on the gradiometer flux qubit which has a special geometric design, t
Directory of Open Access Journals (Sweden)
Haibo Chen
2013-01-01
Full Text Available Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS method and two gradient descent (GD methods (the normal one with Wolfe’s line search and the simplified one are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.
Directory of Open Access Journals (Sweden)
Maria Malejki
2007-01-01
Full Text Available We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space \\(l^2(\\mathbb{N}\\ by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator is bounded from below with compact resolvent. In our research we estimate the asymptotics (with \\(n\\to \\infty\\ of the joint error of approximation for the first \\(n\\ eigenvalues and eigenvectors of the operator by the eigenvalues and eigenvectors of the finite submatrix of order \\(n \\times n\\. The method applied in our research is based on the Rayleigh-Ritz method and Volkmer's results included in [H. Volkmer, Error Estimates for Rayleigh-Ritz Approximations of Eigenvalues and Eigenfunctions of the Mathieu and Spheroidal Wave Equation, Constr. Approx. 20 (2004, 39-54]. We extend the method to cover a class of infinite symmetric Jacobi matrices with three diagonals satisfying some polynomial growth estimates.
Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach
Magri, Luca
2013-01-01
We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We ...
Directory of Open Access Journals (Sweden)
Anzhou Cao
2013-01-01
Full Text Available Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients of M2 internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs. In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, the M2 internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.
Galanti, Eli
2016-01-01
During 2016-17 the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. This data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus allowing only calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model, is developed to relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for examination of various scenarios, simulating cases in which the depth of the wind depends...
Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.
2000-01-01
This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.
Energy Technology Data Exchange (ETDEWEB)
D.L. Henderson; S. Yoo; M. Kowalok; T.R. Mackie; B.R. Thomadsen
2001-10-30
The goal of this project is to investigate the use of the adjoint method, commonly used in the reactor physics community, for the optimization of radiation therapy patient treatment plans. Two different types of radiation therapy are being examined, interstitial brachytherapy and radiotherapy. In brachytherapy radioactive sources are surgically implanted within the diseased organ such as the prostate to treat the cancerous tissue. With radiotherapy, the x-ray source is usually located at a distance of about 1-metere from the patient and focused on the treatment area. For brachytherapy the optimization phase of the treatment plan consists of determining the optimal placement of the radioactive sources, which delivers the prescribed dose to the disease tissue while simultaneously sparing (reducing) the dose to sensitive tissue and organs. For external beam radiation therapy the optimization phase of the treatment plan consists of determining the optimal direction and intensity of beam, which provides complete coverage of the tumor region with the prescribed dose while simultaneously avoiding sensitive tissue areas. For both therapy methods, the optimal treatment plan is one in which the diseased tissue has been treated with the prescribed dose and dose to the sensitive tissue and organs has been kept to a minimum.
Domain Walls and Flux Tubes in N=2 SQCD D-Brane Prototypes
Shifman, M
2003-01-01
This paper could have been entitled "D branes and strings from flesh and blood." We study field theoretic prototypes of D branes/strings. To this end we consider (2+1)-dimensional domain walls in (3+1)-dimensional N=2 SQCD with SU(2) gauge group and two quark flavors in the fundamental representation. This theory is perturbed by a small mass term of the adjoint matter which, in the leading order in the mass parameter, does not break N=2 supersymmetry, and reduces to a (generalized) Fayet-Iliopoulos term in the effective low-energy N=2 SQED. We find 1/2 BPS-saturated domain wall solution interpolating between two quark vacua at weak coupling, and show that this domain wall localizes a U(1) gauge field. To make contact with the brane/string picture we consider the Abrikosov-Nielsen-Olesen magnetic flux tube in one of two quark vacua and demonstrate that it can end on the domain wall. We find an explicit 1/4 BPS-saturated solution for the wall/flux tube junction. We verify that the end point of the flux tube on ...
De Boer, J; Hori, K; Keurentjes, A; Morgan, J; Morrison, Douglas Robert Ogston; Sethi, S K; Boer, Jan de; Dijkgraaf, Robbert; Hori, Kentaro; Keurentjes, Arjan; Morgan, John; Morrison, David R.; Sethi, Savdeep
2002-01-01
We study string compactifications with sixteen supersymmetries. The moduli space for these compactifications becomes quite intricate in lower dimensions, partly because there are many different irreducible components. We focus primarily, but not exclusively, on compactifications to seven or more dimensions. These vacua can be realized in a number ways: the perturbative constructions we study include toroidal compactifications of the heterotic/type I strings, asymmetric orbifolds, and orientifolds. In addition, we describe less conventional M and F theory compactifications on smooth spaces. The last class of vacua considered are compactifications on singular spaces with non-trivial discrete fluxes. We find a number of new components in the string moduli space. Contained in some of these components are M theory compactifications with novel kinds of ``frozen'' singularities. We are naturally led to conjecture the existence of new dualities relating spaces with different singular geometries and fluxes. As our stu...
Directory of Open Access Journals (Sweden)
Gaisser Thomas K.
2015-01-01
Full Text Available This review of atmospheric muons and neutrinos emphasizes the high energy range relevant for backgrounds to high-energy neutrinos of astrophysical origin. After a brief historical introduction, the main distinguishing features of atmospheric νμ and νe are discussed, along with the implications of the muon charge ratio for the νµ / ν̅µ ratio. Methods to account for effects of the knee in the primary cosmic-ray spectrum and the energy-dependence of hadronic interactions on the neutrino fluxes are discussed and illustrated in the context of recent results from IceCube. A simple numerical/analytic method is proposed for systematic investigation of uncertainties in neutrino fluxes arising from uncertainties in the primary cosmic-ray spectrum/composition and hadronic interactions.
Lobotomy of flux compactifications
Dibitetto, Giuseppe; Guarino, Adolfo; Roest, Diederik
2014-05-01
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on 6 with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge algebra. Besides the known four AdS solutions surviving the orientifold projection to = 4 induced by O6-planes, this theory contains a novel AdS solution that requires non-trivial orientifold-odd fluxes, hence being a genuine critical point of the = 8 theory.
Lobotomy of flux compactifications
Energy Technology Data Exchange (ETDEWEB)
Dibitetto, Giuseppe [Institutionen för fysik och astronomi, University of Uppsala,Box 803, SE-751 08 Uppsala (Sweden); Guarino, Adolfo [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics,Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Roest, Diederik [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4 9747 AG Groningen (Netherlands)
2014-05-15
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on T{sup 6} with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge algebra. Besides the known four AdS solutions surviving the orientifold projection to N=4 induced by O6-planes, this theory contains a novel AdS solution that requires non-trivial orientifold-odd fluxes, hence being a genuine critical point of the N=8 theory.
1984-05-05
These approaches are based on proven principles which have served the thermal test community well for years. Other concepts hold promise of being able to...8217. --......- - ... .... - - The thermal test community has developed instrumentation which is quite suitable for the moderate, and relatively constant, flux...on the maximum phase II system fluence of 400 cal/cm2 . Second, the present thermal test community will have confidence in the performance of an
Lobotomy of Flux Compactifications
Giuseppe Dibitetto; Adolfo Guarino(Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern, Switzerland); Diederik Roest
2014-01-01
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on $ \\mathbb{T} $ 6 with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge...
Eddy Correlation Flux Measurement System
Oak Ridge National Laboratory — The eddy correlation (ECOR) flux measurement system provides in situ, half-hour measurements of the surface turbulent fluxes of momentum, sensible heat, latent heat,...
Martinec, Zdenek; Sasgen, Ingo; Velimsky, Jakub
2014-05-01
In this study, two new methods for computing the sensitivity of the glacial isostatic adjustment (GIA) forward solution with respect to the Earth's mantle viscosity are presented: the forward sensitivity method (FSM) and the adjoint sensitivity method (ASM). These advanced formal methods are based on the time-domain,spectral-finite element method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec (2000). There are many similarities between the forward method and the FSM and ASM for a general physical system. However, in the case of GIA, there are also important differences between the forward and sensitivity methods. The analysis carried out in this study results in the following findings. First, the forward method of GIA is unconditionally solvable, regardless of whether or not a combined ice and ocean-water load contains the first-degree spherical harmonics. This is also the case for the FSM, however, the ASM must in addition be supplemented by nine conditions on the misfit between the given GIA-related data and the forward model predictions to guarantee the existence of a solution. This constrains the definition of data least-squares misfit. Second, the forward method of GIA implements an ocean load as a free boundary-value function over an ocean area with a free geometry. That is, an ocean load and the shape of ocean, the so-called ocean function, are being sought, in addition to deformation and gravity-increment fields, by solving the forward method. The FSM and ASM also apply the adjoint ocean load as a free boundary-value function, but instead over an ocean area with the fixed geometry given by the ocean function determined by the forward method. In other words, a boundary-value problem for the forward method of GIA is free with respect to determining (i) the boundary-value data over an ocean area and (ii) the ocean function itself, while the boundary-value problems for the FSM and ASM are free only with respect to
Energy Technology Data Exchange (ETDEWEB)
Galanti, Eli; Kaspi, Yohai, E-mail: eli.galanti@weizmann.ac.il [Weizmann Institute of Science, Rehovot (Israel)
2016-04-01
During 2016–17, the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. These data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus only allowing the calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model is developed to relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for the examination of various scenarios, simulating cases in which the depth of the wind depends on latitude. We show that it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn, also taking into account measurement errors. Calculating the solution uncertainties, we show that the wind depth can be determined more precisely in the low-to-mid-latitudes. In addition, the gravitational moments are found to be particularly sensitive to flows at the equatorial intermediate depths. Therefore, we expect that if deep winds exist on these planets they will have a measurable signature by Juno and Cassini.
Mazzolini, R G
2001-01-01
The author places Grmek's editorial within the flux of the historiographical debate which, since the middle of the 1970s, has concentrated on two major crises due to the end of social science-oriented 'scientific history' and to the 'linguistic turn'. He also argues that Grmek's historiographical work of the 1980s and 1990s was to some extent an alternative to certain observed changes in historical fashion and has achieved greater intelligibility because of its commitment to a rational vision of science and historiography.
Henze, D. K.; Lacey, F.; Seltzer, M.; Vallack, H.; Kuylenstierna, J.; Bowman, K. W.; Anenberg, S.; Sasser, E.; Lee, C. J.; Martin, R.
2013-12-01
The Climate and Clean Air Coalition (CCAC) was initiated in 2012 to develop, understand and promote measures to reduce short lived climate forcers such as aerosol, ozone and methane. The Coalition now includes over 30 nations, and as a service to these nations is committed to providing a decision support toolkit that allows member nations to explore the benefits of a range of emissions mitigation measures in terms of the combined impacts on air quality and climate and so help in the development of their National Action Plans. Here we will present recent modeling work to support the development of the CCAC National Action Plans toolkit. Adjoint sensitivity analysis is presented as a means of efficiently relating air quality, climate and crop impacts back to changes in emissions from each species, sector and location at the grid-scale resolution of typical global air quality model applications. The GEOS-Chem adjoint model is used to estimate the damages per ton of emissions of PM2.5 related mortality, the impacts of ozone precursors on crops and ozone-related health effects, and the combined impacts of these species on regional surface temperature changes. We show how the benefits-per-emission vary spatially as a function of the surrounding environment, and how this impacts the overall benefit of sector-specific control strategies. We present initial findings for Bangladesh, as well as Mexico, Ghana and Colombia, some of the first countries to join the CCAC, and discuss general issues related to adjoint-based metrics for quantifying air quality and climate co-benefits.
Martin, William G.; Cairns, Brian; Bal, Guillaume
2014-01-01
This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth?s atmosphere.
Critical heat flux thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Collado, F.J. E-mail: fjk@posta.unizar.es
2002-11-01
Convective boiling in subcooled water flowing through a heated channel is essential in many engineering applications where high heat flux need to be accommodated, such as in the divertor plates of fusion reactors. There are many available correlations for predicting heat transfer in the individual regimes of the empirical Nukiyama boiling curve, although unfortunately there is no physical fundamentals of such curve. Recently, the author has shown that the classical entropy balance could contain key information about boiling heat transfer. So, it was found that the average thermal gap in the heated channel (the wall temperature minus the average temperature of the coolant fluid) was strongly correlated with the efficiency of a theoretical reversible engine placed in this thermal gap. In this work and from the new proposed correlation, a new expression of the wall temperature in function of the average fluid temperature is derived and successfully checked against experimental data from General Electric. This expression suggests a new and simple definition of the critical heat flux (CHF), a key parameter of the thermal-hydraulic design of fusion reactors. Finally, based on the new definition, the CHF trends are commented.
Energy Technology Data Exchange (ETDEWEB)
Fadin, V.S. [Budker Institute of Nuclear Physics, SD RAS, Novosibirsk (Russian Federation); Novosibirsk State University, Novosibirsk (Russian Federation); Fiore, R. [Universita della Calabria, Dipartimento di Fisica, Cosenza (Italy); Istituto Nazionale di Fisica, Nucleare Gruppo Collegato di Cosenza (Italy)
2016-05-15
We analyze a modification of the BFKL kernel for the adjoint representation of the color group in the maximally supersymmetric (N = 4) Yang-Mills theory in the limit of a large number of colors, related to the modification of the eigenvalues of the kernel suggested by Bondarenko and Prygarin in order to obtain Hermitian separability of the eigenvalues. We restore the modified kernel in the momentum space. It turns out that the modification is related only to the real part of the kernel and that the correction to the kernel cannot be presented by a single analytic function in the entire momentum region, which contradicts the known properties of the kernel. (orig.)
Institute of Scientific and Technical Information of China (English)
王建丰; 黄琼湘; 刘儒英; 冶成福
2008-01-01
For a graph G,let h(G;x)=h(G)and[G]h denote the adjoint polynomial and the adjoint equivalence class of G,respectively.In this paper,a new application of[G]h is given.Making use of[G]h,we give a necessary and suffcient condition for adjoint uniqueness of the graph H such that H≠G,where H=(Ui∈APi)U(Uj∈BUj),A(∈)A'={1,2,3,5}U{2n|n∈N,n≥3},B(∈)B'={7,2n|n∈N,n(>)5)and G=a p1UaoP2Ua1P3Ua2P5U(U(n i)=3aiP2i).
Permanent magnet flux-biased magnetic actuator with flux feedback
Groom, Nelson J. (Inventor)
1991-01-01
The invention is a permanent magnet flux-biased magnetic actuator with flux feedback for adjustably suspending an element on a single axis. The magnetic actuator includes a pair of opposing electromagnets and provides bi-directional forces along the single axis to the suspended element. Permanent magnets in flux feedback loops from the opposing electromagnets establish a reference permanent magnet flux-bias to linearize the force characteristics of the electromagnets to extend the linear range of the actuator without the need for continuous bias currents in the electromagnets.
Kanno, S; Wands, D; Kanno, Sugumi; Soda, Jiro; Wands, David
2005-01-01
We propose a geometrical model of brane inflation where inflation is driven by the flux generated by opposing brane charges and terminated by the collision of the branes, with charge annihilation. We assume the collision process is completely inelastic and the kinetic energy is transformed into the thermal energy after collision. Thereafter the two branes coalesce together and behave as a single brane universe with zero effective cosmological constant. In the Einstein frame, the 4-dimensional effective theory changes abruptly at the collision point. Therefore, our inflationary model is necessarily 5-dimensional in nature. As the collision process has no singularity in 5-dimensional gravity, we can follow the evolution of fluctuations during the whole history of the universe. It turns out that the radion field fluctuations have a steeply tilted, red spectrum, while the primordial gravitational waves have a flat spectrum. Instead, primordial density perturbations could be generated by a curvaton mechanism.
Optimal fluxes and Reynolds stresses
Jimenez, Javier
2016-01-01
It is remarked that fluxes in conservation laws, such as the Reynolds stresses in the momentum equation of turbulent shear flows, or the spectral energy flux in isotropic turbulence, are only defined up to an arbitrary solenoidal field. While this is not usually significant for long-time averages, it becomes important when fluxes are modelled locally in large-eddy simulations, or in the analysis of intermittency and cascades. As an example, a numerical procedure is introduced to compute fluxes in scalar conservation equations in such a way that their total integrated magnitude is minimised. The result is an irrotational vector field that derives from a potential, thus minimising sterile flux `circuits'. The algorithm is generalised to tensor fluxes and applied to the transfer of momentum in a turbulent channel. The resulting instantaneous Reynolds stresses are compared with their traditional expressions, and found to be substantially different.
Zhang, Li; Henze, David K.; Grell, Georg A.; Carmichael. Gregory R.; Bousserez, Nicolas; Zhang, Qiang; Torres, Omar; Ahn, Changwoo; Lu, Zifeng; Cao, Junji; Mao, Yuhao
2015-01-01
Accurate estimates of the emissions and distribution of black carbon (BC) in the region referred to here as Southeastern Asia (70degE-l50degE, 11degS-55degN) are critical to studies of the atmospheric environment and climate change. Analysis of modeled BC concentrations compared to in situ observations indicates levels are underestimated over most of Southeast Asia when using any of four different emission inventories. We thus attempt to reduce uncertainties in BC emissions and improve BC model simulations by developing top-down, spatially resolved, estimates of BC emissions through assimilation of OMI observations of aerosol absorption optical depth (AAOD) with the GEOS-Chem model and its adjoint for April and October of 2006. Overwhelming enhancements, up to 500%, in anthropogenic BC emissions are shown after optimization over broad areas of Southeast Asia in April. In October, the optimization of anthropogenic emissions yields a slight reduction (1-5%) over India and parts of southern China, while emissions increase by 10-50% over eastern China. Observational data from in situ measurements and AERONET observations are used to evaluate the BC inversions and assess the bias between OMI and AERONET AAOD. Low biases in BC concentrations are improved or corrected in most eastern and central sites over China after optimization, while the constrained model still underestimates concentrations in Indian sites in both April and October, possibly as a. consequence of low prior emissions. Model resolution errors may contribute up to a factor of 2.5 to the underestimate of surface BC concentrations over northern India. We also compare the optimized results using different anthropogenic emission inventories and discuss the sensitivity of top-down constraints on anthropogenic emissions with respect to biomass burning emissions. In addition, the impacts of brown carbon, the formulation of the observation operator, and different a priori constraints on the optimization are
Heat Flux Apportionment to Heterogeneous Surfaces Using Flux Footprint Analysis
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Heat flux data collected from the Baiyangdian Heterogeneous Field Experiment were analyzed using the footprint method. High resolution (25 m) Landsat-5 satellite imaging was used to determine the land cover as one of four surface types: farmland, lake, wetland, or village. Data from two observation sites in September 2005 were used. One site (Wangjiazhai) was characterized by highly heterogeneous surfaces in the central area of the Baiyangdian: lake/wetland. The other site (Xiongxian) was on land with more uniform surface cover. An improved Eulerian analytical flux footprint model was used to determine "source areas" of the heat fluxes measured at towers located at each site from surrounding landscapes of mixed surface types.In relative terms results show that wetland and lake areas generally contributed most to the observed heat flux at Wangjiazhai, while farmland contributed most at Xiongxian. Given the areal distribution of surface type contributions, calculations were made to obtain the magnitudes of the heat flux from lake, wetland and farmland to the total observed flux and apportioned contributions of each surface type to the sensible and latent heat fluxes. Results show that on average the sensible heat flux from wetland and farmland were comparable over the diurnal cycle, while the latent heat flux from farmland was somewhat larger by about 30-50 W m-2 during daytime. The latent and sensible fluxes from the lake source in daytime were about 50 W m-2 and 100 W m-2 less, respectively, than from wetland and farmland. The results are judged reasonable and serve to demonstrate the potential for flux apportionment over heterogeneous surfaces.
Simon, Moritz
2014-11-14
© 2014, Springer Science+Business Media New York. With the target of optimizing CO
Maxfield, Travis; Robbins, Daniel; Sethi, Savdeep
2013-01-01
Type IIB toroidal orientifolds are among the earliest examples of flux vacua. By applying T-duality, we construct the first examples of massive IIA flux vacua with Minkowski space-times, along with new examples of type IIA flux vacua. The backgrounds are surprisingly simple with no four-form flux at all. They serve as illustrations of the ingredients needed to build type IIA and massive IIA solutions with scale separation. To check that these backgrounds are actually solutions, we formulate the complete set of type II supergravity equations of motion in a very useful form that treats the R-R fields democratically.
Heat Flux Instrumentation Laboratory (HFIL)
Federal Laboratory Consortium — Description: The Heat Flux Instrumentation Laboratory is used to develop advanced, flexible, thin film gauge instrumentation for the Air Force Research Laboratory....
Bretaudeau, F.; Metivier, L.; Brossier, R.; Virieux, J.
2013-12-01
Traveltime tomography algorithms generally use ray tracing. The use of rays in tomography may not be suitable for handling very large datasets and perform tomography in very complex media. Traveltime maps can be computed through finite-difference approach (FD) and avoid complex ray-tracing algorithm for the forward modeling (Vidale 1998, Zhao 2004). However, rays back-traced from receiver to source following the gradient of traveltime are still used to compute the Fréchet derivatives. As a consequence, the sensitivity information computed using back-traced rays is not numerically consistent with the FD modeling used (the derivatives are only a rough approximation of the true derivatives of the forward modeling). Leung & Quian (2006) proposed a new approach that avoid ray tracing where the gradient of the misfit function is computed using the adjoint-state method. An adjoint-state variable is thus computed simultaneously for all receivers using a numerical method consistent with the forward modeling, and for the computational cost of one forward modeling. However, in their formulation, the receivers have to be located at the boundary of the investigated model, and the optimization approach is limited to simple gradient-based method (i.e. steepest descent, conjugate gradient) as only the gradient is computed. However, the Hessian operator has an important role in gradient-based reconstruction methods, providing the necessary information to rescale the gradient, correct for illumination deficit and remove artifacts. Leung & Quian (2006) uses LBFGS, a quasi-Newton method that provides an improved estimation of the influence of the inverse Hessian. Lelievre et al. (2011) also proposed a tomography approach in which the Fréchet derivatives are computed directly during the forward modeling using explicit symbolic differentiation of the modeling equations, resulting in a consistent Gauss-Newton inversion. We are interested here in the use of a new optimization approach
Klamt, Steffen; Regensburger, Georg; Gerstl, Matthias P; Jungreuthmayer, Christian; Schuster, Stefan; Mahadevan, Radhakrishnan; Zanghellini, Jürgen; Müller, Stefan
2017-04-01
Elementary flux modes (EFMs) emerged as a formal concept to describe metabolic pathways and have become an established tool for constraint-based modeling and metabolic network analysis. EFMs are characteristic (support-minimal) vectors of the flux cone that contains all feasible steady-state flux vectors of a given metabolic network. EFMs account for (homogeneous) linear constraints arising from reaction irreversibilities and the assumption of steady state; however, other (inhomogeneous) linear constraints, such as minimal and maximal reaction rates frequently used by other constraint-based techniques (such as flux balance analysis [FBA]), cannot be directly integrated. These additional constraints further restrict the space of feasible flux vectors and turn the flux cone into a general flux polyhedron in which the concept of EFMs is not directly applicable anymore. For this reason, there has been a conceptual gap between EFM-based (pathway) analysis methods and linear optimization (FBA) techniques, as they operate on different geometric objects. One approach to overcome these limitations was proposed ten years ago and is based on the concept of elementary flux vectors (EFVs). Only recently has the community started to recognize the potential of EFVs for metabolic network analysis. In fact, EFVs exactly represent the conceptual development required to generalize the idea of EFMs from flux cones to flux polyhedra. This work aims to present a concise theoretical and practical introduction to EFVs that is accessible to a broad audience. We highlight the close relationship between EFMs and EFVs and demonstrate that almost all applications of EFMs (in flux cones) are possible for EFVs (in flux polyhedra) as well. In fact, certain properties can only be studied with EFVs. Thus, we conclude that EFVs provide a powerful and unifying framework for constraint-based modeling of metabolic networks.
Directory of Open Access Journals (Sweden)
J. H. Davies
2009-11-01
Full Text Available We present a revised estimate of Earth's surface heat flux that is based upon a heat flow data-set with 38 347 measurements, which is 55% more than used in previous estimates. Our methodology, like others, accounts for hydrothermal circulation in young oceanic crust by utilising a half-space cooling approximation. For the rest of Earth's surface, we estimate the average heat flow for different geologic domains as defined by global digital geology maps; and then produce the global estimate by multiplying it by the total global area of that geologic domain. The averaging is done on a polygon set which results from an intersection of a 1 degree equal area grid with the original geology polygons; this minimises the adverse influence of clustering. These operations and estimates are derived accurately using methodologies from Geographical Information Science. We consider the virtually un-sampled Antarctica separately and also make a small correction for hot-spots in young oceanic lithosphere. A range of analyses is presented. These, combined with statistical estimates of the error, provide a measure of robustness. Our final preferred estimate is 47±2 TW, which is greater than previous estimates.
Data Acquisition and Flux Calculations
DEFF Research Database (Denmark)
Rebmann, C.; Kolle, O; Heinesch, B;
2012-01-01
In this chapter, the basic theory and the procedures used to obtain turbulent fluxes of energy, mass, and momentum with the eddy covariance technique will be detailed. This includes a description of data acquisition, pretreatment of high-frequency data and flux calculation....
Superconducting wires and fractional flux
Sá de Melo, C. A. R.
1996-05-01
The quantization of flux quanta in superconductors is revisited and analyzed in a new geometry. The system analyzed is a superconducting wire. The geometry is such that the superconducting wire winds N times around an insulating cylinder and that the wire has its end connected back to its beginning, thus producing an N-loop short circuited solenoid. The winding number N acts as a topological index that controls flux quantization. In this case, fractional flux quanta can be measured through the center of the insulating cylinder, provided that the cylinder radius is small enough. The Little-Parks experiment for an identical geometry is discussed. The period of oscillation of the transition temperature of the wire is found to vary as 1/N in units of flux Φ relative to the flux quantum Φ0. When a SQUID is made in such a geometry the maximal current through the SQUID varies with period Φ0/N.
Interpreting Flux from Broadband Photometry
Brown, Peter J; Roming, Peter W A; Siegel, Michael
2016-01-01
We discuss the transformation of observed photometry into flux for the creation of spectral energy distributions and the computation of bolometric luminosities. We do this in the context of supernova studies, particularly as observed with the Swift spacecraft, but the concepts and techniques should be applicable to many other types of sources and wavelength regimes. Traditional methods of converting observed magnitudes to flux densities are not very accurate when applied to UV photometry. Common methods for extinction and the integration of pseudo-bolometric fluxes can also lead to inaccurate results. The sources of inaccuracy, though, also apply to other wavelengths. Because of the complicated nature of translating broad-band photometry into monochromatic flux densities, comparison between observed photometry and a spectroscopic model is best done by comparing in the natural units of the observations. We recommend that integrated flux measurements be made using a spectrum or spectral energy distribution whic...
Virieux, J.; Bretaudeau, F.; Metivier, L.; Brossier, R.
2013-12-01
Simultaneous inversion of seismic velocities and source parameters have been a long standing challenge in seismology since the first attempts to mitigate trade-off between very different parameters influencing travel-times (Spencer and Gubbins 1980, Pavlis and Booker 1980) since the early development in the 1970s (Aki et al 1976, Aki and Lee 1976, Crosson 1976). There is a strong trade-off between earthquake source positions, initial times and velocities during the tomographic inversion: mitigating these trade-offs is usually carried empirically (Lemeur et al 1997). This procedure is not optimal and may lead to errors in the velocity reconstruction as well as in the source localization. For a better simultaneous estimation of such multi-parametric reconstruction problem, one may take benefit of improved local optimization such as full Newton method where the Hessian influence helps balancing between different physical parameter quantities and improving the coverage at the point of reconstruction. Unfortunately, the computation of the full Hessian operator is not easily computed in large models and with large datasets. Truncated Newton (TCN) is an alternative optimization approach (Métivier et al. 2012) that allows resolution of the normal equation H Δm = - g using a matrix-free conjugate gradient algorithm. It only requires to be able to compute the gradient of the misfit function and Hessian-vector products. Traveltime maps can be computed in the whole domain by numerical modeling (Vidale 1998, Zhao 2004). The gradient and the Hessian-vector products for velocities can be computed without ray-tracing using 1st and 2nd order adjoint-state methods for the cost of 1 and 2 additional modeling step (Plessix 2006, Métivier et al. 2012). Reciprocity allows to compute accurately the gradient and the full Hessian for each coordinates of the sources and for their initial times. Then the resolution of the problem is done through two nested loops. The model update Δm is
Zhao, S.; Soltanzadeh, M.; Pappin, A. J.; Hakami, A.; Turner, M. D.; Capps, S.; Henze, D. K.; Percell, P.; Bash, J. O.; Napelenok, S. L.; Pinder, R. W.; Russell, A. G.; Nenes, A.; Baek, J.; Carmichael, G. R.; Stanier, C. O.; Chai, T.; Byun, D.; Fahey, K.; Resler, J.; Mashayekhi, R.
2016-12-01
Scenario-based studies evaluate air quality co-benefits by adopting collective measures introduced under a climate policy scenario cannot distinguish between benefits accrued from CO2 reductions among sources of different types and at different locations. Location and sector dependencies are important factors that can be captured in an adjoint-based analysis of CO2 reduction co-benefits. The present study aims to quantify how the ancillary benefits of reducing criteria co-pollutants vary spatially and by sector. The adjoint of USEPA's CMAQ was applied to quantify the health benefits associated with emission reduction of criteria pollutants (NOX) in on-road mobile, Electric Generation Units (EGUs), and other select sectors on a location-by-location basis across the US and Canada. These health benefits are then converted to CO2 emission reduction co-benefits by accounting for source-specific emission rates of criteria pollutants in comparison to CO2. We integrate the results from the adjoint of CMAQ with emission estimates from 2011 NEI at the county level, and point source data from EPA's Air Markets Program Data and National Pollutant Release Inventory (NPRI) for Canada. Our preliminary results show that the monetized health benefits (due to averted chronic mortality) associated with reductions of 1 ton of CO2 emissions is up to 65/ton in Canada and 200/ton in US for mobile on-road sector. For EGU sources, co-benefits are estimated at up to 100/ton and 10/ton for the US and Canada respectively. For Canada, the calculated co-benefits through gaseous pollutants including NOx is larger than those through PM2.5 due to the official association between NO2 exposure and chronic mortality. Calculated co-benefits show a great deal of spatial variability across emission locations for different sectors and sub-sectors. Implications of such spatial variability in devising control policy options that effectively address both climate and air quality objectives will be discussed.
Interpreting Flux from Broadband Photometry
Brown, Peter J.; Breeveld, Alice; Roming, Peter W. A.; Siegel, Michael
2016-10-01
We discuss the transformation of observed photometry into flux for the creation of spectral energy distributions (SED) and the computation of bolometric luminosities. We do this in the context of supernova studies, particularly as observed with the Swift spacecraft, but the concepts and techniques should be applicable to many other types of sources and wavelength regimes. Traditional methods of converting observed magnitudes to flux densities are not very accurate when applied to UV photometry. Common methods for extinction and the integration of pseudo-bolometric fluxes can also lead to inaccurate results. The sources of inaccuracy, though, also apply to other wavelengths. Because of the complicated nature of translating broadband photometry into monochromatic flux densities, comparison between observed photometry and a spectroscopic model is best done by forward modeling the spectrum into the count rates or magnitudes of the observations. We recommend that integrated flux measurements be made using a spectrum or SED which is consistent with the multi-band photometry rather than converting individual photometric measurements to flux densities, linearly interpolating between the points, and integrating. We also highlight some specific areas where the UV flux can be mischaracterized.
A Reconnecting Flux Rope Dynamo
Baggaley, Andrew W.; Barenghi, Carlo F.; Shukurov, Anvar; Subramanian, Kandaswamy
2009-01-01
We develop a new model of the fluctuation dynamo in which the magnetic field is confined in thin flux ropes advected by a multi-scale flow modeling turbulence. Magnetic dissipation occurs only via reconnection of the flux ropes. We investigate the kinetic energy release into heat, mediated by the dynamo action, both in our model and by solving the induction equation with the same flow. We find that a flux rope dynamo is an order of magnitude more efficient at converting mechanical energy into...
Generalised Geometry and Flux Vacua
Larfors, Magdalena
2015-01-01
This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.
Liu, Junjie; Bowman, Kevin W.; Lee, Memong; Henze, David K.; Bousserez, Nicolas; Brix, Holger; Collatz, G. James; Menemenlis, Dimitris; Ott, Lesley; Pawson, Steven; Jones, Dylan; Nassar, Ray
2014-01-01
Using an Observing System Simulation Experiment (OSSE), we investigate the impact of JAXA Greenhouse gases Observing SATellite 'IBUKI' (GOSAT) sampling on the estimation of terrestrial biospheric flux with the NASA Carbon Monitoring System Flux (CMS-Flux) estimation and attribution strategy. The simulated observations in the OSSE use the actual column carbon dioxide (X(CO2)) b2.9 retrieval sensitivity and quality control for the year 2010 processed through the Atmospheric CO2 Observations from Space algorithm. CMS-Flux is a variational inversion system that uses the GEOS-Chem forward and adjoint model forced by a suite of observationally constrained fluxes from ocean, land and anthropogenic models. We investigate the impact of GOSAT sampling on flux estimation in two aspects: 1) random error uncertainty reduction and 2) the global and regional bias in posterior flux resulted from the spatiotemporally biased GOSAT sampling. Based on Monte Carlo calculations, we find that global average flux uncertainty reduction ranges from 25% in September to 60% in July. When aggregated to the 11 land regions designated by the phase 3 of the Atmospheric Tracer Transport Model Intercomparison Project, the annual mean uncertainty reduction ranges from 10% over North American boreal to 38% over South American temperate, which is driven by observational coverage and the magnitude of prior flux uncertainty. The uncertainty reduction over the South American tropical region is 30%, even with sparse observation coverage. We show that this reduction results from the large prior flux uncertainty and the impact of non-local observations. Given the assumed prior error statistics, the degree of freedom for signal is approx.1132 for 1-yr of the 74 055 GOSAT X(CO2) observations, which indicates that GOSAT provides approx.1132 independent pieces of information about surface fluxes. We quantify the impact of GOSAT's spatiotemporally sampling on the posterior flux, and find that a 0.7 gigatons of
Lin, Ching-Long; Chai, Tianfeng
2001-06-01
In the digital information era one of the challenges is to extract useful information from accessible data. In this paper, we will present a four-dimensional variational data assimilation (4DVAR) technique and apply it to retrieving micro-scale turbulent structures in a convective boundary layer from high-resolution Doppler lidar radial velocity data. The 4DVAR is based on the calculus of variations and optimal control theories to recover complete data by assimilating limited data into a dynamic model. Several features are implemented into the 4DVAR model, e.g. a surface flux model, a buffer zone and smoothness constraints. The surface flux model provides appropriate momentum and temperature fluxes to the 4DVAR. The buffer zone is found to improve retrieval quality by reducing the effect of lateral boundary conditions. A generic algorithm is proposed to estimate weights of the smoothness constraints. The approach of identical twin experiments is first used to assess the performance of the model and its sensitivity to observational errors. The 4DVAR is then applied to real lidar data and reveals a micro-front like structure passing through the boundary layer.
Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li
2017-01-01
This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41
Büskens, Christof; Maurer, Helmut
2000-08-01
Parametric nonlinear optimal control problems subject to control and state constraints are studied. Two discretization methods are discussed that transcribe optimal control problems into nonlinear programming problems for which SQP-methods provide efficient solution methods. It is shown that SQP-methods can be used also for a check of second-order sufficient conditions and for a postoptimal calculation of adjoint variables. In addition, SQP-methods lead to a robust computation of sensitivity differentials of optimal solutions with respect to perturbation parameters. Numerical sensitivity analysis is the basis for real-time control approximations of perturbed solutions which are obtained by evaluating a first-order Taylor expansion with respect to the parameter. The proposed numerical methods are illustrated by the optimal control of a low-thrust satellite transfer to geosynchronous orbit and a complex control problem from aquanautics. The examples illustrate the robustness, accuracy and efficiency of the proposed numerical algorithms.
Bondarenko, Sergey
2016-01-01
We discuss a residual freedom of the next-to-leading BFKL eigenvalue that originates from ambiguity in redistributing the next-to-leading~(NLO) corrections between the adjoint BFKL eigenvalue and eigenfunctions in planar $\\mathcal{N}=4$ super-Yang-Mills~(SYM) Theory. In terms of the remainder function of the Bern-Dixon-Smirnov~(BDS) amplitude this freedom is translated to reshuffling correction between the eigenvalue and the impact factors in the multi-Regge kinematics~(MRK) in the next-to-leading logarithm approximation~(NLA). We show that the modified NLO BFKL eigenvalue suggested by the authors can be introduced in the MRK expression for the remainder function by shifting the anomalous dimension in the impact factor in such a way that the two and three loop remainder function is left unchanged to the NLA accuracy.
Bondarenko, Sergey; Prygarin, Alex
2016-07-01
We discuss a residual freedom of the next-to-leading BFKL eigenvalue that originates from ambiguity in redistributing the next-to-leading (NLO) corrections between the adjoint BFKL eigenvalue and eigenfunctions in planar {N}=4 super-Yang-Mills (SYM) Theory. In terms of the remainder function of the Bern-Dixon-Smirnov (BDS) amplitude this freedom is translated to reshuffling correction between the eigenvalue and the impact factors in the multi-Regge kinematics (MRK) in the next-to-leading logarithm approximation (NLA). We show that the modified NLO BFKL eigenvalue suggested by the authors in ref. [1] can be introduced in the MRK expression for the remainder function by shifting the anomalous dimension in the impact factor in such a way that the two and three loop remainder function is left unchanged to the NLA accuracy.
Energy Technology Data Exchange (ETDEWEB)
Fadin, V.S. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Budker Nuclear Physics Institute, Novosibirsk (Russian Federation); Novosibirskij Gosudarstvennyj Univ., Novosibirsk (Russian Federation); Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); St. Petersburg State Univ., Gatchina (Russian Federation)
2011-12-15
We calculate the eigenvalues of the next-to-leading kernel for the BFKL equation in the adjoint representation of the gauge group SU(N{sub c}) in the N=4 supersymmetric Yang-Mills model. These eigenvalues are used to obtain the high energy behavior of the remainder function for the 6-point scattering amplitude with the maximal helicity violation in the kinematical regions containing the Mandelstam cut contribution. The leading and next-to-leading singularities of the corresponding collinear anomalous dimension are calculated in all orders of perturbation theory. We compare our result with the known collinear limit and with the recently suggested ansatz for the remainder function in three loops and obtain the full agreement providing that the numerical parameters in this anzatz are chosen in an appropriate way.
Physics of Magnetic Flux Ropes
Priest, E R; Lee, L C
1990-01-01
The American Geophysical Union Chapman Conference on the Physics of Magnetic Flux Ropes was held at the Hamilton Princess Hotel, Hamilton, Bermuda on March 27–31, 1989. Topics discussed ranged from solar flux ropes, such as photospheric flux tubes, coronal loops and prominences, to flux ropes in the solar wind, in planetary ionospheres, at the Earth's magnetopause, in the geomagnetic tail and deep in the Earth's magnetosphere. Papers presented at that conference form the nucleus of this book, but the book is more than just a proceedings of the conference. We have solicited articles from all interested in this topic. Thus, there is some material in the book not discussed at the conference. Even in the case of papers presented at the conference, there is generally a much more detailed and rigorous presentation than was possible in the time allowed by the oral and poster presentations.
High Flux Isotope Reactor (HFIR)
Federal Laboratory Consortium — The HFIR at Oak Ridge National Laboratory is a light-water cooled and moderated reactor that is the United States’ highest flux reactor-based neutron source. HFIR...
What is flux balance analysis?
Orth, Jeffrey D.; Thiele, Ines; Palsson, Bernhard Ø
2010-01-01
Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network. This primer covers the theoretical basis of the approach, several practical examples and a software toolbox for performing the calculations.
Conical electromagnetic radiation flux concentrator
Miller, E. R.
1972-01-01
Concentrator provides method of concentrating a beam of electromagnetic radiation into a smaller beam, presenting a higher flux density. Smaller beam may be made larger by sending radiation through the device in the reverse direction.
Specification of ROP flux shape
Energy Technology Data Exchange (ETDEWEB)
Min, Byung Joo [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Gray, A. [Atomic Energy of Canada Ltd., Chalk River, ON (Canada)
1997-06-01
The CANDU 9 480/SEU core uses 0.9% SEU (Slightly Enriched Uranium) fuel. The use f SEU fuel enables the reactor to increase the radial power form factor from 0.865, which is typical in current natural uranium CANDU reactors, to 0.97 in the nominal CANDU 9 480/SEU core. The difference is a 12% increase in reactor power. An additional 5% increase can be achieved due to a reduced refuelling ripple. The channel power limits were also increased by 3% for a total reactor power increase of 20%. This report describes the calculation of neutron flux distributions in the CANDU 9 480/SEU core under conditions specified by the C and I engineers. The RFSP code was used to calculate of neutron flux shapes for ROP analysis. Detailed flux values at numerous potential detector sites were calculated for each flux shape. (author). 6 tabs., 70 figs., 4 refs.
Flux Emergence at the Photosphere
Cheung, M. C. M.; Schüssler, M.; Moreno-Insertis, F.
2006-12-01
To model the emergence of magnetic fields at the photosphere, we carried out 3D magneto-hydrodynamics (MHD) simulations using the MURaM code. Our simulations take into account the effects of compressibility, energy exchange via radiative transfer and partial ionization in the equation of state. All these physical ingredients are essential for a proper treatment of the problem. In the simulations, an initially buoyant magnetic flux tube is embedded in the upper layers of the convection zone. We find that the interaction between the flux tube and the external flow field has an important influence on the emergent morphology of the magnetic field. Depending on the initial properties of the flux tube (e.g. field strength, twist, entropy etc.), the emergence process can also modify the local granulation pattern. The inclusion of radiative transfer allows us to directly compare the simulation results with real observations of emerging flux.
Periodicities in photospheric magnetic flux
Institute of Scientific and Technical Information of China (English)
SONG; Wenbin; WANG; Jingxiu
2006-01-01
Magnetic field plays an important role in solar structure and activity. In principle, the determination of magnetic flux would provide the best general-purpose index of solar activity. Currently, the periodicity studies corresponding to photospheric magnetic flux (PMF) are very few possibly due to the absence of a uniform flux sequence. In this paper, by using 383 NSO/Kitt Peak magnetic synoptic charts we reconstruct a flux sequence from February 1975 to August 2003 and perform a relatively systemic periodicity analysis with two methods of the Scargle periodogram and the Morlet wavelet transform. As a result, four periods are found at around 1050, 500, 300 and 160 days. We analyze these periods' temporal variabilities in detail and discuss their respective origins briefly.
Energy Technology Data Exchange (ETDEWEB)
Endres, Sebastian; Steiner, Frank, E-mail: sebastian.endres@uni-ulm.d, E-mail: frank.steiner@uni-ulm.d [Institut fuer Theoretische Physik, Universitaet Ulm Albert-Einstein-Allee 11, 89081 Ulm (Germany)
2010-03-05
The Berry-Keating operator H{sub BK} := -i h-bar (x d/dx + 1/2) (Berry and Keating 1999 SIAM Rev. 41 236) governing the Schroedinger dynamics is discussed in the Hilbert space L{sup 2}(R{sub >},dx) and on compact quantum graphs. It has been proved that the spectrum of H{sub BK} defined on L{sup 2}(R{sub >},dx) is purely continuous and thus this quantization of H{sub BK} cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of H{sub BK} acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of H{sub BK}. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the 'squared' Berry-Keating operator H{sub BK}{sup 2} := -x{sup 2} d{sup 2}/dx{sup 2} -2x d/dx - 1/4 which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for H{sup 2}{sub BK} on compact quantum graphs. While the spectra of both H{sub BK} and H{sup 2}{sub BK} on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither H{sub BK} nor H{sup 2}{sub BK} can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In the first paper in this series, a variational data assimilation of ideal tropical cyclone (TC) tracks was performed for the statistical-dynamical prediction model SD-90 by the adjoint method, and a prediction of TC tracks was made with good accuracy for tracks containing no sharp turns. In the present paper, the cases of real TC tracks are studied. Due to the complexity of TC motion, attention is paid to the diagnostic research of TC motion. First, five TC tracks are studied. Using the data of each entire TC track, by the adjoint method, five TC tracks are fitted well, and the forces acting on the TCs are retrieved. For a given TC, the distribution of the resultant of the retrieved force and Coriolis force well matches the corresponding TC track, i.e., when a TC turns, the resultant of the retrieved force and Coriolis force acts as a centripetal force, which means that the TC indeed moves like a particle; in particular, for TC 9911, the clockwise looping motion is also fitted well. And the distribution of the resultant appears to be periodic in some cases. Then, the present method is carried out for a portion of the track data for TC 9804, which indicates that when the amount of data for a TC track is sufficient, the algorithm is stable. And finally, the same algorithm is implemented for TCs with a double-eyewall structure, namely Bilis (2000) and Winnie (1997),and the results prove the applicability of the algorithm to TCs with complicated mesoscale structures if the TC track data are obtained every three hours.