Construction of adjoint operators for coupled equations depending on different variables

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1986-01-01

A procedure is described for the construction of the adjoint operator matrix in case of coupled equations defining quantities that depend on different sets of variables. This case is not properly treated in the literature. From this procedure a simple rule can be deduced for the construction of such adjoint operator matrices

An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

Science.gov (United States)

Subramanian, Ramanathan Vishnampet Ganapathi

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 improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is 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. 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

Approximation for the adjoint neutron spectrum

International Nuclear Information System (INIS)

Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2002-01-01

The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

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

International Nuclear Information System (INIS)

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

2018-01-01

Highlights: • We demonstrate adjoint methods for atmospheric remote sensing in a two-dimensional setting. • Searchlight functions are used to handle the singularity of measurement response functions. • Adjoint methods require two radiative transfer calculations to evaluate the measurement misfit function and its derivatives with respect to all unknown parameters. • Synthetic retrieval studies show the scalability of adjoint methods to problems with thousands of measurements and unknown parameters. • Adjoint methods and the searchlight function technique are generalizable to 3D remote sensing. - Abstract: In previous work, we derived the adjoint method as a computationally efficient path to three-dimensional (3D) retrievals of clouds and aerosols. In this paper we will demonstrate the use of adjoint methods for retrieving two-dimensional (2D) fields of cloud extinction. The demonstration uses a new 2D radiative transfer solver (FSDOM). This radiation code was augmented with adjoint methods to allow efficient derivative calculations needed to retrieve cloud and surface properties from multi-angle reflectance measurements. The code was then used in three synthetic retrieval studies. Our retrieval algorithm adjusts the cloud extinction field and surface albedo to minimize the measurement misfit function with a gradient-based, quasi-Newton approach. At each step we compute the value of the misfit function and its gradient with two calls to the solver FSDOM. First we solve the forward radiative transfer equation to compute the residual misfit with measurements, and second we solve the adjoint radiative transfer equation to compute the gradient of the misfit function with respect to all unknowns. The synthetic retrieval studies verify that adjoint methods are scalable to retrieval problems with many measurements and unknowns. We can retrieve the vertically-integrated optical depth of moderately thick clouds as a function of the horizontal coordinate. It is also

Comparing Mass Balance and Adjoint-Based 4D-VAR Methods for Inverse Modeling of Nitrogen Dioxide Columns for Nitrogen Oxide Emissions

Science.gov (United States)

Cooper, M.; Martin, R.; Henze, D. K.

2016-12-01

Nitrogen oxide (NOx ≡ NO + NO2) emission inventories can be improved through top-down constraints provided by inverse modeling of observed nitrogen dioxide (NO2) columns. Here we compare two methods of inverse modeling for emissions of NOx from synthetic NO2 columns generated from known emissions using the GEOS-Chem chemical transport model and its adjoint. We treat the adjoint-based 4D-VAR approach for estimating top-down emissions as a benchmark against which to evaluate variations on the mass balance method. We find that the standard mass balance algorithm can be improved by using an iterative process and using finite difference to calculate the local sensitivity of a change in NO2 columns to a change in emissions, resulting in a factor of two reduction in inversion error. In a simplified case study to recover local emission perturbations, horizontal smearing effects due to NOx transport were better resolved by the adjoint-based approach than by mass balance. For more complex emission changes that reflect real world scenarios, the iterative finite difference mass balance and adjoint methods produce similar top-down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3-4. Inversions of data sets that simulate satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint-based 4D-VAR method, it offers the ability to efficiently estimate top-down emissions using models that do not have an adjoint.

Iteration of adjoint equations

International Nuclear Information System (INIS)

Lewins, J.D.

1994-01-01

Adjoint functions are the basis of variational methods and now widely used for perturbation theory and its extension to higher order theory as used, for example, in modelling fuel burnup and optimization. In such models, the adjoint equation is to be solved in a critical system with an adjoint source distribution that is not zero but has special properties related to ratios of interest in critical systems. Consequently the methods of solving equations by iteration and accumulation are reviewed to show how conventional methods may be utilized in these circumstances with adequate accuracy. (author). 3 refs., 6 figs., 3 tabs

Deterministic sensitivity analysis of two-phase flow systems: forward and adjoint methods. Final report

International Nuclear Information System (INIS)

Cacuci, D.G.

1984-07-01

This report presents a self-contained mathematical formalism for deterministic sensitivity analysis of two-phase flow systems, a detailed application to sensitivity analysis of the homogeneous equilibrium model of two-phase flow, and a representative application to sensitivity analysis of a model (simulating pump-trip-type accidents in BWRs) where a transition between single phase and two phase occurs. The rigor and generality of this sensitivity analysis formalism stem from the use of Gateaux (G-) differentials. This report highlights the major aspects of deterministic (forward and adjoint) sensitivity analysis, including derivation of the forward sensitivity equations, derivation of sensitivity expressions in terms of adjoint functions, explicit construction of the adjoint system satisfied by these adjoint functions, determination of the characteristics of this adjoint system, and demonstration that these characteristics are the same as those of the original quasilinear two-phase flow equations. This proves that whenever the original two-phase flow problem is solvable, the adjoint system is also solvable and, in principle, the same numerical methods can be used to solve both the original and adjoint equations

Sensitivity kernels for viscoelastic loading based on adjoint methods

Science.gov (United States)

Al-Attar, David; Tromp, Jeroen

2014-01-01

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

Generalization of Spectral Green's Function nodal method for slab-geometry fixed-source adjoint transport problems in SN formulation

International Nuclear Information System (INIS)

Curbelo, Jesus P.; Silva, Odair P. da; Barros, Ricardo C.

2017-01-01

Presented here is the application of the adjoint technique for solving source{detector discrete ordinates (S N ) transport problems by using a spectral nodal method. For slab-geometry adjoint S-N model, the adjoint spectral Green's function method (SGF † ) is extended to multigroup problems considering arbitrary L'th-order of scattering anisotropy, and the possibility of non{zero prescribed boundary conditions for the forward S N transport problems. The SGF † method converges numerical solutions that are completely free from spatial truncation errors. In order to generate numerical solutions of the SGF † equations, we use the partial adjoint one{node block inversion (NBI) iterative scheme. Partial adjoint NBI scheme uses the most recent estimates for the node-edge adjoint angular Fluxes in the outgoing directions of a given discretization node, to solve the resulting adjoint SN problem in that node for all the adjoint angular fluxes in the incoming directions, which constitute the outgoing adjoint angular fluxes for the adjacent node in the sweeping directions. Numerical results are given to illustrate the present spectral nodal method features and some advantages of using the adjoint technique in source-detector problems. author)

A response matrix method for slab-geometry discrete ordinates adjoint calculations in energy-dependent source-detector problems

Energy Technology Data Exchange (ETDEWEB)

Mansur, Ralph S.; Moura, Carlos A., E-mail: ralph@ime.uerj.br, E-mail: demoura@ime.uerj.br [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil). Departamento de Engenharia Mecanica; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional

2017-07-01

Presented here is an application of the Response Matrix (RM) method for adjoint discrete ordinates (S{sub N}) problems in slab geometry applied to energy-dependent source-detector problems. The adjoint RM method is free from spatial truncation errors, as it generates numerical results for the adjoint angular fluxes in multilayer slabs that agree with the numerical values obtained from the analytical solution of the energy multigroup adjoint SN equations. Numerical results are given for two typical source-detector problems to illustrate the accuracy and the efficiency of the offered RM computer code. (author)

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.

Passive control of thermoacoustic oscillations with adjoint methods

Science.gov (United States)

Aguilar, Jose; Juniper, Matthew

2017-11-01

Strict pollutant regulations are driving gas turbine manufacturers to develop devices that operate under lean premixed conditions, which produce less NOx but encourage thermoacoustic oscillations. These are a form of unstable combustion that arise due to the coupling between the acoustic field and the fluctuating heat release in a combustion chamber. In such devices, in which safety is paramount, thermoacoustic oscillations must be eliminated passively, rather than through feedback control. The ideal way to eliminate thermoacoustic oscillations is by subtly changing the shape of the device. To achieve this, one must calculate the sensitivity of each unstable thermoacoustic mode to every geometric parameter. This is prohibitively expensive with standard methods, but is relatively cheap with adjoint methods. In this study we first present low-order network models as a tool to model and study the thermoacoustic behaviour of combustion chambers. Then we compute the continuous adjoint equations and the sensitivities to relevant parameters. With this, we run an optimization routine that modifies the parameters in order to stabilize all the resonant modes of a laboratory combustor rig.

Adjoint electron Monte Carlo calculations

International Nuclear Information System (INIS)

Jordan, T.M.

1986-01-01

Adjoint Monte Carlo is the most efficient method for accurate analysis of space systems exposed to natural and artificially enhanced electron environments. Recent adjoint calculations for isotropic electron environments include: comparative data for experimental measurements on electronics boxes; benchmark problem solutions for comparing total dose prediction methodologies; preliminary assessment of sectoring methods used during space system design; and total dose predictions on an electronics package. Adjoint Monte Carlo, forward Monte Carlo, and experiment are in excellent agreement for electron sources that simulate space environments. For electron space environments, adjoint Monte Carlo is clearly superior to forward Monte Carlo, requiring one to two orders of magnitude less computer time for relatively simple geometries. The solid-angle sectoring approximations used for routine design calculations can err by more than a factor of 2 on dose in simple shield geometries. For critical space systems exposed to severe electron environments, these potential sectoring errors demand the establishment of large design margins and/or verification of shield design by adjoint Monte Carlo/experiment

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

Science.gov (United States)

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

2018-01-01

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

An adjoint sensitivity-based data assimilation method and its comparison with existing variational methods

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.

A reduced adjoint approach to variational data assimilation

KAUST Repository

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.

A reduced adjoint approach to variational data assimilation

KAUST Repository

Altaf, Muhammad; El Gharamti, Mohamad; Heemink, Arnold W.; Hoteit, Ibrahim

2013-01-01

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.

Generalization of Spectral Green's Function nodal method for slab-geometry fixed-source adjoint transport problems in S{sub N} formulation

Energy Technology Data Exchange (ETDEWEB)

Curbelo, Jesus P.; Silva, Odair P. da; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-graduacao em Modelagem Computacional; Garcia, Carlos R., E-mail: cgh@instec.cu [Departamento de Ingenieria Nuclear, Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)

2017-07-01

Presented here is the application of the adjoint technique for solving source-detector discrete ordinates (S{sub N}) transport problems by using a spectral nodal method. For slab-geometry adjoint S-N model, the adjoint spectral Green's function method (SGF{sup †}) is extended to multigroup problems considering arbitrary L'th-order of scattering anisotropy, and the possibility of non-zero prescribed boundary conditions for the forward S{sub N} transport problems. The SGF{sup †} method converges numerical solutions that are completely free from spatial truncation errors. In order to generate numerical solutions of the SGF{sup †} equations, we use the partial adjoint one-node block inversion (NBI) iterative scheme. Partial adjoint NBI scheme uses the most recent estimates for the node-edge adjoint angular Fluxes in the outgoing directions of a given discretization node, to solve the resulting adjoint SN problem in that node for all the adjoint angular fluxes in the incoming directions, which constitute the outgoing adjoint angular fluxes for the adjacent node in the sweeping directions. Numerical results are given to illustrate the present spectral nodal method features and some advantages of using the adjoint technique in source-detector problems. author)

Adjoint Monte-Carlo method with fictitious scattering in deep penetration and long-distance detector calculations

International Nuclear Information System (INIS)

Andreucci, N.

1985-04-01

Deep penetration transport problems in complex systems joint to heterogeneous source (Q) sampling give rise to some difficulties in evaluating leakage and fluxes on a detector point. To overcome these difficulties we have solved both the adjoint Boltzmann flux (phi*) equation and following scalar-dual equation: ∫Qphi* dP - ∫Q*phi dP = ∫phiphi* Ω . n dΣ dΩ dE dt + ∫ [phiphi*]sub(0)sup(T)/v dr dΩ dE D = (phase space). With a suitable choice for the domain D, for Q* and for the boundary conditions, an adjoint flux calculation allows us to obtain simultaneously the Q-source contribution and the detection (or leakage) spectrum. Compared to direct methods with importance sampling, the adjoint methods give very low-cost and faithful results

Recent advances in the spectral green's function method for monoenergetic slab-geometry fixed-source adjoint transport problems in S{sub N} formulation

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)

Effect of lattice-level adjoint-weighting on the kinetics parameters of CANDU reactors

International Nuclear Information System (INIS)

Nichita, Eleodor

2009-01-01

Space-time kinetics calculations for CANDU reactors are routinely performed using the Improved Quasistatic (IQS) method. The IQS method calculates kinetics parameters such as the effective delayed-neutron fraction and generation time using adjoint weighting. In the current implementation of IQS, the direct flux, as well as the adjoint, is calculated using a two-group cell-homogenized reactor model which is inadequate for capturing the effect of the softer energy spectrum of the delayed neutrons. Additionally, there may also be fine spatial effects that are lost because the intra-cell adjoint shape is ignored. The purpose of this work is to compare the kinetics parameters calculated using the two-group cell-homogenized model with those calculated using lattice-level fine-group heterogeneous adjoint weighting and to assess whether the differences are large enough to justify further work on incorporating lattice-level adjoint weighting into the IQS method. A second goal is to evaluate whether the use of a fine-group cell-homogenized lattice-level adjoint, such as is the current practice for Light Water Reactors (LWRs), is sufficient to capture the lattice effects in question. It is found that, for CANDU lattices, the generation time is almost unaffected by the type of adjoint used to calculate it, but that the effective delayed-neutron fraction is affected by the type of adjoint used. The effective delayed-neutron fraction calculated using the two-group cell-homogenized adjoint is 5.2% higher than the 'best' effective delayed-neutron fraction value obtained using the detailed lattice-level fine-group heterogeneous adjoint. The effective delayed-neutron fraction calculated using the fine-group cell-homogenized adjoint is only 1.7% higher than the 'best' effective delayed-neutron fraction value but is still not equal to it. This situation is different from that encountered in LWRs where weighting by a fine-group cell-homogenized adjoint is sufficient to calculate the

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

Science.gov (United States)

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

2012-04-01

The problem of generating and maintaining adjoint models is sufficiently difficult that typically only the most advanced and well-resourced community ocean models achieve it. There are two current technologies which each suffer from their own limitations. Algorithmic differentiation, also called automatic differentiation, is employed by models such as the MITGCM [2] and the Alfred Wegener Institute model FESOM [3]. This technique is very difficult to apply to existing code, and requires a major initial investment to prepare the code for automatic adjoint generation. AD tools may also have difficulty with code employing modern software constructs such as derived data types. An alternative is to formulate the adjoint differential equation and to discretise this separately. This approach, known as the continuous adjoint and employed in ROMS [4], has the disadvantage that two different model code bases must be maintained and manually kept synchronised as the model develops. The discretisation of the continuous adjoint is not automatically consistent with that of the forward model, producing an additional source of error. The alternative presented here is to formulate the flow model in the high level language UFL (Unified Form Language) and to automatically generate the model using the software of the FEniCS project. In this approach it is the high level code specification which is differentiated, a task very similar to the formulation of the continuous adjoint [5]. However since the forward and adjoint models are generated automatically, the difficulty of maintaining them vanishes and the software engineering process is therefore robust. The scheduling and execution of the adjoint model, including the application of an appropriate checkpointing strategy is managed by libadjoint [1]. In contrast to the conventional algorithmic differentiation description of a model as a series of primitive mathematical operations, libadjoint employs a new abstraction of the simulation

Adjoint P1 equations solution for neutron slowing down

International Nuclear Information System (INIS)

Cardoso, Carlos Eduardo Santos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2002-01-01

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, the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. The direct and adjoint neutron fluxes resulting from the solution of P 1 equations were used to three different weighting processes, to obtain the macrogroup macroscopic cross sections. It was found out noticeable differences among them. (author)

Development of a Matlab/Simulink tool to facilitate system analysis and simulation via the adjoint and covariance methods

NARCIS (Netherlands)

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

Multi-objective Optimization Strategies Using Adjoint Method and Game Theory in Aerodynamics

Science.gov (United States)

Tang, Zhili

2006-08-01

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 multi-criteria 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.

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.

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.

ADGEN: ADjoint GENerator for computer models

International Nuclear Information System (INIS)

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

FOCUS: a non-multigroup adjoint Monte Carlo code with improved variance reduction

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1974-01-01

A description is given of the selection mechanism in the adjoint Monte Carlo code FOCUS in which the energy is treated as a continuous variable. The method of Kalos who introduced the idea of adjoint cross sections is followed to derive a sampling scheme for the adjoint equation solved in FOCUS which is in most aspects analogous to the normal Monte Carlo game. The disadvantages of the use of these adjoint cross sections are removed to some extent by introduction of a new definition for the adjoint cross sections resulting in appreciable variance reduction. At the cost of introducing a weight factor slightly different from unity, the direction and energy are selected in a simple way without the need of two-dimensional probability tables. Finally the handling of geometry and cross section in FOCUS is briefly discussed. 6 references. (U.S.)

Weak self-adjoint differential equations

International Nuclear Information System (INIS)

Gandarias, M L

2011-01-01

The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006 J. Math. Anal. Appl. 318 742-57; 2007 Arch. ALGA 4 55-60). In Ibragimov (2007 J. Math. Anal. Appl. 333 311-28), a general theorem on conservation laws was proved. In this paper, we generalize the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. We find a class of weak self-adjoint quasi-linear parabolic equations. The property of a differential equation to be weak self-adjoint is important for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)

First-arrival traveltime tomography for anisotropic media using the adjoint-state method

KAUST Repository

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.

First-arrival traveltime tomography for anisotropic media using the adjoint-state method

KAUST Repository

Waheed, Umair bin; Flagg, Garret; Yarman, Can Evren

2016-01-01

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.

Probability density adjoint for sensitivity analysis of the Mean of Chaos

Energy Technology Data Exchange (ETDEWEB)

Blonigan, Patrick J., E-mail: blonigan@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu

2014-08-01

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.

Adjoint current-based approaches to prostate brachytherapy optimization

International Nuclear Information System (INIS)

Roberts, J. A.; Henderson, D. L.

2009-01-01

This paper builds on previous work done at the Univ. of Wisconsin - Madison to employ the adjoint concept of nuclear reactor physics in the so-called greedy heuristic of brachytherapy optimization. Whereas that previous work focused on the adjoint flux, i.e. the importance, this work has included use of the adjoint current to increase the amount of information available in optimizing. Two current-based approaches were developed for 2-D problems, and each was compared to the most recent form of the flux-based methodology. The first method aimed to take a treatment plan from the flux-based greedy heuristic and adjust via application of the current-displacement, or a vector displacement based on a combination of tissue (adjoint) and seed (forward) currents acting as forces on a seed. This method showed promise in improving key urethral and rectal dosimetric quantities. The second method uses the normed current-displacement as the greedy criterion such that seeds are placed in regions of least force. This method, coupled with the dose-update scheme, generated treatment plans with better target irradiation and sparing of the urethra and normal tissues than the flux-based approach. Tables of these parameters are given for both approaches. In summary, these preliminary results indicate adjoint current methods are useful in optimization and further work in 3-D should be performed. (authors)

Adjoint entropy vs topological entropy

OpenAIRE

Giordano Bruno, Anna

2012-01-01

Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...

Approximation for the adjoint neutron spectrum; Aproximacao para o espectro adjunto de neutrons

Energy Technology Data Exchange (ETDEWEB)

Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2002-07-01

The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

The Adjoint Method for the Inverse Problem of Option Pricing

Directory of Open Access Journals (Sweden)

Shou-Lei Wang

2014-01-01

Full Text Available The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the TV-L1 model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS to find the optimal and numerical examples shows the effectiveness of the presented method.

Formulation of coarse mesh finite difference to calculate mathematical adjoint flux; Formulacao de diferencas finitas de malha grossa para calculo do fluxo adjunto matematico

Energy Technology Data Exchange (ETDEWEB)

Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2002-07-01

The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)

Adjoint-Based Aerodynamic Design of Complex Aerospace Configurations

Science.gov (United States)

Nielsen, Eric J.

2016-01-01

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

The Laplace transformation of adjoint transport equations

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1985-01-01

A clarification is given of the difference between the equation adjoint to the Laplace-transformed time-dependent transport equation and the Laplace-transformed time-dependent adjoint transport equation. Proper procedures are derived to obtain the Laplace transform of the instantaneous detector response. (author)

Ambient noise adjoint tomography for a linear array in North China

Science.gov (United States)

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

2017-12-01

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

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

International Nuclear Information System (INIS)

Baldiotti, M C; Gitman, D M; Tyutin, I V; Voronov, B L

2011-01-01

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x)=g 1 x -1 +g 2 x -2 , x is an element of R + = [0, ∞). For g 2 >0 and g 1 K (x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schroedinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein's method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.

Sensitivity analysis of predictive models with an automated adjoint generator

International Nuclear Information System (INIS)

Pin, F.G.; Oblow, E.M.

1987-01-01

The adjoint method is a well established sensitivity analysis methodology that is particularly efficient in large-scale modeling problems. The coefficients of sensitivity of a given response with respect to every parameter involved in the modeling code can be calculated from the solution of a single adjoint run of the code. Sensitivity coefficients provide a quantitative measure of the importance of the model data in calculating the final results. The major drawback of the adjoint method is the requirement for calculations of very large numbers of partial derivatives to set up the adjoint equations of the model. ADGEN is a software system that has been designed to eliminate this drawback and automatically implement the adjoint formulation in computer codes. The ADGEN system will be described and its use for improving performance assessments and predictive simulations will be discussed. 8 refs., 1 fig

An investigation of the adjoint method for external beam radiation therapy treatment planning using Monte Carlo transport

International Nuclear Information System (INIS)

Kowalok, M.; Mackie, T.R.

2001-01-01

A relatively new technique for achieving the right dose to the right tissue, is intensity modulated radiation therapy (IMRT). In this technique, a megavoltage x-ray beam is rotated around a patient, and the intensity and shape of the beam is modulated as a function of source position and patient anatomy. The relationship between beam-let intensity and patient dose can be expressed under a matrix form where the matrix D ij represents the dose delivered to voxel i by beam-let j per unit fluence. The D ij influence matrix is the key element that enables this approach. In this regard, sensitivity theory lends itself in a natural way to the process of computing beam weights for treatment planning. The solution of the adjoint form of the Boltzmann equation is an adjoint function that describes the importance of particles throughout the system in contributing to the detector response. In this case, adjoint methods can provide the sensitivity of the dose at a single point in the patient with respect to all points in the source field. The purpose of this study is to investigate the feasibility of using the adjoint method and Monte Carlo transport for radiation therapy treatment planning

Identification of the Parameters of the Instantaneous Point Pollution Source in the Azov Sea Based on the Adjoint Method

Directory of Open Access Journals (Sweden)

V.S. Kochergin

2017-02-01

Full Text Available The passive admixture transport model in the Azov Sea is considered. The problem of cartelistic impulse local source identification at the sea surface based on adjoint method is solving by integration of independent series of adjoint tasks. Simultaneous solution of this problem at the parallel mode is realized by the aforementioned approach. The efficiency of the algorithm optimal value power of source search agreed with the data measurements is shown in the test example. The measurement data assimilation algorithm in the passive admixture transfer model is implemented applying variational methods of filtration for optimal estimate retrieval. The retrieval is carried out by means of the method of adjoint equations and solving of linear systems. On the basis of the variational filtration method of data assimilation, the optimal estimate retrieval algorithm for pollution source power identification is constructed. In application of the algorithm, the integration of the main, linked and adjoint problems is implemented. Integration problems are solved using TVD approximations. For the application of the procedure, the Azov current fields and turbulent diffusion coefficients are obtained using the sigma coordinate ocean model (POM under the eastern wind stress conditions being dominant at the observed time period. Furthermore, the results can be used to perform numerical data assimilation on loads of suspended matter.

Adjoint Parameter Sensitivity Analysis for the Hydrodynamic Lattice Boltzmann Method with Applications to Design Optimization

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...

Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems

KAUST Repository

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.

Finite-fault source inversion using adjoint methods in 3D heterogeneous media

Science.gov (United States)

Somala, Surendra Nadh; Ampuero, Jean-Paul; Lapusta, Nadia

2018-04-01

Accounting for lateral heterogeneities in the 3D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3D heterogeneity in source inversion involves pre-computing 3D Green's functions, which requires a number of 3D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense datasets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green's functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green's functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3D heterogeneous velocity model. The velocity model comprises a uniform background and a 3D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3D velocity model are performed for two different station configurations, a dense and a sparse network with 1 km and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect

Adjoint sensitivity analysis of high frequency structures with Matlab

CERN Document Server

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.

Estimation of Adjoint-Weighted Kinetics Parameters in Monte Carlo Wieland Calculations

International Nuclear Information System (INIS)

Choi, Sung Hoon; Shim, Hyung Jin

2013-01-01

The effective delayed neutron fraction, β eff , and the prompt neutron generation time, Λ, in the point kinetics equation are weighted by the adjoint flux to improve the accuracy of the reactivity estimate. Recently the Monte Carlo (MC) kinetics parameter estimation methods by using the self-consistent adjoint flux calculated in the MC forward simulations have been developed and successfully applied for the research reactor analyses. However these adjoint estimation methods based on the cycle-by-cycle genealogical table require a huge memory size to store the pedigree hierarchy. In this paper, we present a new adjoint estimation in which the pedigree of a single history is utilized by applying the MC Wielandt method. The effectiveness of the new method is demonstrated in the kinetics parameter estimations for infinite homogeneous two-group problems and the Godiva critical facility

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

Energy Technology Data Exchange (ETDEWEB)

Baldiotti, M C; Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: baldiott@fma.if.usp.br, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)

2011-06-01

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x)=g{sub 1}x{sup -1}+g{sub 2}x{sup -2}, x is an element of R{sub +} = [0, {infinity}). For g{sub 2}>0 and g{sub 1}<0, the potential is known as the Kratzer potential V{sub K}(x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schroedinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein's method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.

Self-adjointness of the fast flux in a pressurized water reactor

International Nuclear Information System (INIS)

Mosteller, R.D.

1985-01-01

Most computer codes for the analysis of systems transients rely on a simplified representation of the active core, typically employing either a one-dimensional or a point kinetics model. The collapsing of neutronics data from multidimensional steady-state calculations normally employs flux/flux-adjoint weighting. The multidimensional calculations, however, usually are performed only for the forward problem, not the adjoint. The collapsing methodologies employed in generating the neutronics input for transient codes typically construct adjoint fluxes from the assumption that the fast flux is self-adjoint. Until now, no further verification of this assumption has been undertaken for thermal reactors. As part of the verification effort for EPRI's reactor analysis support package, the validity of this assumption now has been investigated for a modern pressurized water reactor (PWR). The PDQ-7 code was employed to perform two-group fine-mesh forward and adjoint calculations for a two-dimensional representation of Zion Unit 2 at beginning of life, based on the standard PWR ARMP model. It has been verified that the fast flux is very nearly self-adjoint in a PWR. However, a significant error can arise during the subsequent construction of the thermal adjoint flux unless allowance is made for the difference between the forward and adjoint thermal buckling terms. When such a difference is included, the thermal adjoint flux can be estimated very accurately

Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2

International Nuclear Information System (INIS)

Velarde, G.

1976-01-01

Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)

A midway forward-adjoint coupling method for neutron and photon Monte Carlo transport

International Nuclear Information System (INIS)

Serov, I.V.; John, T.M.; Hoogenboom, J.E.

1999-01-01

The midway Monte Carlo method for calculating detector responses combines a forward and an adjoint Monte Carlo calculation. In both calculations, particle scores are registered at a surface to be chosen by the user somewhere between the source and detector domains. The theory of the midway response determination is developed within the framework of transport theory for external sources and for criticality theory. The theory is also developed for photons, which are generated at inelastic scattering or capture of neutrons. In either the forward or the adjoint calculation a so-called black absorber technique can be applied; i.e., particles need not be followed after passing the midway surface. The midway Monte Carlo method is implemented in the general-purpose MCNP Monte Carlo code. The midway Monte Carlo method is demonstrated to be very efficient in problems with deep penetration, small source and detector domains, and complicated streaming paths. All the problems considered pose difficult variance reduction challenges. Calculations were performed using existing variance reduction methods of normal MCNP runs and using the midway method. The performed comparative analyses show that the midway method appears to be much more efficient than the standard techniques in an overwhelming majority of cases and can be recommended for use in many difficult variance reduction problems of neutral particle transport

Continuous-energy adjoint flux and perturbation calculation using the iterated fission probability method in Monte-Carlo code TRIPOLI-4 and underlying applications

International Nuclear Information System (INIS)

Truchet, G.; Leconte, P.; Peneliau, Y.; Santamarina, A.

2013-01-01

The first goal of this paper is to present an exact method able to precisely evaluate very small reactivity effects with a Monte Carlo code (<10 pcm). 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 efficiency 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. It offers the possibility to split reactivity contributions on both isotopes and reactions. Other applications of this perturbation method are presented and tested like the calculation of exact kinetic parameters (βeff, Λeff) or sensitivity parameters

Self-adjoint extensions and spectral analysis in the Calogero problem

International Nuclear Information System (INIS)

Gitman, D M; Tyutin, I V; Voronov, B L

2010-01-01

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential αx -2 . Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some 'paradoxes' inherent in the 'naive' quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

Variation estimation of the averaged cross sections in the direct and adjoint fluxes

International Nuclear Information System (INIS)

Cardoso, Carlos Eduardo Santos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

1995-01-01

There are several applications of the perturbation theory to specifics problems of reactor physics, such as nonuniform fuel burnup, nonuniform poison accumulation and evaluations of Doppler effects on reactivity. The neutron fluxes obtained from the solutions of direct and adjoint diffusion equations, are used in these applications. In the adjoint diffusion equation has been used the group constants averaged in the energy-dependent direct neutron flux, that it is not theoretically consistent. In this paper it is presented a method to calculate the energy-dependent adjoint neutron flux, to obtain the average group-constant that will be used in the adjoint diffusion equation. The method is based on the solution of the adjoint neutron balance equations, that were derived for a two regions cell. (author). 5 refs, 2 figs, 1 tab

Solution of the mathematical adjoint equations for an interface current nodal formulation

International Nuclear Information System (INIS)

Yang, W.S.; Taiwo, T.A.; Khalil, H.

1994-01-01

Two techniques for solving the mathematical adjoint equations of an interface current nodal method are described. These techniques are the ''similarity transformation'' procedure and a direct solution scheme. A theoretical basis is provided for the similarity transformation procedure originally proposed by Lawrence. It is shown that the matrices associated with the mathematical and physical adjoint equations are similar to each other for the flat transverse leakage approximation but not for the quadratic leakage approximation. It is also shown that a good approximate solution of the mathematical adjoint for the quadratic transverse leakage approximation is obtained by applying the similarity transformation for the flat transverse leakage approximation to the physical adjoint solution. The direct solution scheme, which was developed as an alternative to the similarity transformation procedure, yields the correct mathematical adjoint solution for both flat and quadratic transverse leakage approximations. In this scheme, adjoint nodal equations are cast in a form very similar to that of the forward equations by employing a linear transformation of the adjoint partial currents. This enables the use of the forward solution algorithm with only minor modifications for solving the mathematical adjoint equations. By using the direct solution scheme as a reference method, it is shown that while the results computed with the similarity transformation procedure are approximate, they are sufficiently accurate for calculations of global and local reactivity changes resulting from coolant voiding in a liquid-metal reactor

Self-adjoint extensions and spectral analysis in the Calogero problem

Energy Technology Data Exchange (ETDEWEB)

Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L [Lebedev Physical Institute, Moscow (Russian Federation)], E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru

2010-04-09

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential {alpha}x{sup -2}. Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some 'paradoxes' inherent in the 'naive' quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

Lecture 1. Monte Carlo basics. Lecture 2. Adjoint Monte Carlo. Lecture 3. Coupled Forward-Adjoint calculations

Energy Technology Data Exchange (ETDEWEB)

Hoogenboom, J.E. [Delft University of Technology, Interfaculty Reactor Institute, Delft (Netherlands)

2000-07-01

The Monte Carlo method is a statistical method to solve mathematical and physical problems using random numbers. The principle of the methods will be demonstrated for a simple mathematical problem and for neutron transport. Various types of estimators will be discussed, as well as generally applied variance reduction methods like splitting, Russian roulette and importance biasing. The theoretical formulation for solving eigenvalue problems for multiplying systems will be shown. Some reflections will be given about the applicability of the Monte Carlo method, its limitations and its future prospects for reactor physics calculations. Adjoint Monte Carlo is a Monte Carlo game to solve the adjoint neutron (or photon) transport equation. The adjoint transport equation can be interpreted in terms of simulating histories of artificial particles, which show properties of neutrons that move backwards in history. These particles will start their history at the detector from which the response must be estimated and give a contribution to the estimated quantity when they hit or pass through the neutron source. Application to multigroup transport formulation will be demonstrated Possible implementation for the continuous energy case will be outlined. The inherent advantages and disadvantages of the method will be discussed. The Midway Monte Carlo method will be presented for calculating a detector response due to a (neutron or photon) source. A derivation will be given of the basic formula for the Midway Monte Carlo method The black absorber technique, allowing for a cutoff of particle histories when reaching the midway surface in one of the calculations will be derived. An extension of the theory to coupled neutron-photon problems is given. The method will be demonstrated for an oil well logging problem, comprising a neutron source in a borehole and photon detectors to register the photons generated by inelastic neutron scattering. (author)

Lecture 1. Monte Carlo basics. Lecture 2. Adjoint Monte Carlo. Lecture 3. Coupled Forward-Adjoint calculations

International Nuclear Information System (INIS)

Hoogenboom, J.E.

2000-01-01

The Monte Carlo method is a statistical method to solve mathematical and physical problems using random numbers. The principle of the methods will be demonstrated for a simple mathematical problem and for neutron transport. Various types of estimators will be discussed, as well as generally applied variance reduction methods like splitting, Russian roulette and importance biasing. The theoretical formulation for solving eigenvalue problems for multiplying systems will be shown. Some reflections will be given about the applicability of the Monte Carlo method, its limitations and its future prospects for reactor physics calculations. Adjoint Monte Carlo is a Monte Carlo game to solve the adjoint neutron (or photon) transport equation. The adjoint transport equation can be interpreted in terms of simulating histories of artificial particles, which show properties of neutrons that move backwards in history. These particles will start their history at the detector from which the response must be estimated and give a contribution to the estimated quantity when they hit or pass through the neutron source. Application to multigroup transport formulation will be demonstrated Possible implementation for the continuous energy case will be outlined. The inherent advantages and disadvantages of the method will be discussed. The Midway Monte Carlo method will be presented for calculating a detector response due to a (neutron or photon) source. A derivation will be given of the basic formula for the Midway Monte Carlo method The black absorber technique, allowing for a cutoff of particle histories when reaching the midway surface in one of the calculations will be derived. An extension of the theory to coupled neutron-photon problems is given. The method will be demonstrated for an oil well logging problem, comprising a neutron source in a borehole and photon detectors to register the photons generated by inelastic neutron scattering. (author)

Phenomenology of spinless adjoints in two universal extra dimensions

International Nuclear Information System (INIS)

Ghosh, Kirtiman; Datta, Anindya

2008-01-01

We discuss the phenomenology of (1,1)-mode adjoint scalars in the framework of two Universal Extra Dimensions. The Kaluza-Klein (KK) towers of these adjoint scalars arise in the 4-dimensional effective theory from the 6th component of the gauge fields after compactification. Adjoint scalars can have KK-number conserving as well as KK-number violating interactions. We calculate the KK-number violating operators involving these scalars and two Standard Model fields. Decay widths of these scalars into different channels have been estimated. We have also briefly discussed pair-production and single production of such scalars at the Large Hadron Collider

An Analysis on the Calculation Efficiency of the Responses Caused by the Biased Adjoint Fluxes in Hybrid Monte Carlo Simulation

International Nuclear Information System (INIS)

Khuat, Quang Huy; Kim, Song Hyun; Kim, Do Hyun; Shin, Chang Ho

2015-01-01

This technique is known as Consistent Adjoint Driven Importance Sampling (CADIS) method and it is implemented in SCALE code system. In the CADIS method, adjoint transport equation has to be solved to determine deterministic importance functions. Using the CADIS method, a problem was noted that the biased adjoint flux estimated by deterministic methods can affect the calculation efficiency and error. The biases of adjoint function are caused by the methodology, calculation strategy, tolerance of result calculated by the deterministic method and inaccurate multi-group cross section libraries. In this paper, a study to analyze the influence of the biased adjoint functions into Monte Carlo computational efficiency is pursued. In this study, a method to estimate the calculation efficiency was proposed for applying the biased adjoint fluxes in the CADIS approach. For a benchmark problem, the responses and FOMs using SCALE code system were evaluated as applying the adjoint fluxes. The results show that the biased adjoint fluxes significantly affects the calculation efficiencies

Application of Adjoint Method and Spectral-Element Method to Tomographic Inversion of Regional Seismological Structure Beneath Japanese Islands

Science.gov (United States)

Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.

2014-12-01

Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.

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

Science.gov (United States)

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

2014-06-01

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

Sensitivity Analysis for Steady State Groundwater Flow Using Adjoint Operators

Science.gov (United States)

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

1985-03-01

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

Spatial discretizations for self-adjoint forms of the radiative transfer equations

International Nuclear Information System (INIS)

Morel, Jim E.; Adams, B. Todd; Noh, Taewan; McGhee, John M.; Evans, Thomas M.; Urbatsch, Todd J.

2006-01-01

There are three commonly recognized second-order self-adjoint forms of the neutron transport equation: the even-parity equations, the odd-parity equations, and the self-adjoint angular flux equations. Because all of these equations contain second-order spatial derivatives and are self-adjoint for the mono-energetic case, standard continuous finite-element discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of time-dependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the self-adjoint angular flux equation is referred to as the self-adjoint angular intensity equation. Then we describe a general, arbitrary-order, continuous spatial finite-element approach that is applied to each of the three equations in conjunction with backward-Euler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the self-adjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes

New Monte Carlo approach to the adjoint Boltzmann equation

International Nuclear Information System (INIS)

De Matteis, A.; Simonini, R.

1978-01-01

A class of stochastic models for the Monte Carlo integration of the adjoint neutron transport equation is described. Some current general methods are brought within this class, thus preparing the ground for subsequent comparisons. Monte Carlo integration of the adjoint Boltzmann equation can be seen as a simulation of the transport of mathematical particles with reaction kernels not normalized to unity. This last feature is a source of difficulty: It can influence the variance of the result negatively and also often leads to preparation of special ''libraries'' consisting of tables of normalization factors as functions of energy, presently used by several methods. These are the two main points that are discussed and that are taken into account to devise a nonmultigroup method of solution for a certain class of problems. Reactions considered in detail are radiative capture, elastic scattering, discrete levels and continuum inelastic scattering, for which the need for tables has been almost completely eliminated. The basic policy pursued to avoid a source of statistical fluctuations is to try to make the statistical weight of the traveling particle dependent only on its starting and current energies, at least in simple cases. The effectiveness of the sampling schemes proposed is supported by numerical comparison with other more general adjoint Monte Carlo methods. Computation of neutron flux at a point by means of an adjoint formulation is the problem taken as a test for numerical experiments. Very good results have been obtained in the difficult case of resonant cross sections

Development and validation of continuous energy adjoint-weighted calculations

International Nuclear Information System (INIS)

Truchet, Guillaume

2015-01-01

A key issue in nowadays Reactor Physics is to propagate input data uncertainties (e.g. nuclear data, manufacturing tolerances, etc.) to nuclear codes final results (e.g. k(eff), reaction rate, etc.). In order to propagate uncertainties, one typically assumes small variations around a reference and evaluates at first sensitivity profiles. Problem is that nuclear Monte Carlo codes are not - or were not until very recently - able to straightforwardly process such sensitivity profiles, even thought they are considered as reference codes. First goal of this PhD thesis is to implement a method to calculate k(eff)-sensitivity profiles to nuclear data or any perturbations in TRIPOLI-4, the CEA Monte Carlo neutrons transport code. To achieve such a goal, a method has first been developed to calculate the adjoint flux using the Iterated Fission Probability (IFP) principle that states that the adjoint flux at a given phase space point is proportional to the neutron importance in a just critical core after several power iterations. Thanks to our developments, it has been made possible, for the fist time, to calculate the continuous adjoint flux for an actual and complete reactor core configuration. From that new feature, we have elaborated a new method able to forwardly apply the exact perturbation theory in Monte Carlo codes. Exact perturbation theory does not rely on small variations which makes possible to calculate very complex experiments. Finally and after a deep analysis of the IFP method, this PhD thesis also reproduces and improves an already used method to calculate adjoint weighted kinetic parameters as well as reference migrations areas. (author) [fr

Radiation source reconstruction with known geometry and materials using the adjoint

International Nuclear Information System (INIS)

Hykes, Joshua M.; Azmy, Yousry Y.

2011-01-01

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)

An eddy-permitting, dynamically consistent adjoint-based assimilation system for the tropical Pacific: Hindcast experiments in 2000

KAUST Repository

Hoteit, Ibrahim; Cornuelle, B.; Heimbach, P.

2010-01-01

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

Verification of a hybrid adjoint methodology in Titan for single photon emission computed tomography - 316

International Nuclear Information System (INIS)

Royston, K.; Haghighat, A.; Yi, C.

2010-01-01

The hybrid deterministic transport code TITAN is being applied to a Single Photon Emission Computed Tomography (SPECT) simulation of a myocardial perfusion study. The TITAN code's hybrid methodology allows the use of a discrete ordinates solver in the phantom region and a characteristics method solver in the collimator region. Currently we seek to validate the adjoint methodology in TITAN for this application using a SPECT model that has been created in the MCNP5 Monte Carlo code. The TITAN methodology was examined based on the response of a single voxel detector placed in front of the heart with and without collimation. For the case without collimation, the TITAN response for single voxel-sized detector had a -9.96% difference relative to the MCNP5 response. To simulate collimation, the adjoint source was specified in directions located within the collimator acceptance angle. For a single collimator hole with a diameter matching the voxel dimension, a difference of -0.22% was observed. Comparisons to groupings of smaller collimator holes of two different sizes resulted in relative differences of 0.60% and 0.12%. The number of adjoint source directions within an acceptance angle was increased and showed no significant change in accuracy. Our results indicate that the hybrid adjoint methodology of TITAN yields accurate solutions greater than a factor of two faster than MCNP5. (authors)

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

Science.gov (United States)

Talnikar, Chaitanya; Wang, Qiqi; Laskowski, Gregory

2016-11-01

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

Toward regional-scale adjoint tomography in the deep earth

Science.gov (United States)

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

Fast parallel algorithms for the x-ray transform and its adjoint.

Science.gov (United States)

Gao, Hao

2012-11-01

Iterative reconstruction methods often offer better imaging quality and allow for reconstructions with lower imaging dose than classical methods in computed tomography. However, the computational speed is a major concern for these iterative methods, for which the x-ray transform and its adjoint are two most time-consuming components. The speed issue becomes even notable for the 3D imaging such as cone beam scans or helical scans, since the x-ray transform and its adjoint are frequently computed as there is usually not enough computer memory to save the corresponding system matrix. The purpose of this paper is to optimize the algorithm for computing the x-ray transform and its adjoint, and their parallel computation. The fast and highly parallelizable algorithms for the x-ray transform and its adjoint are proposed for the infinitely narrow beam in both 2D and 3D. The extension of these fast algorithms to the finite-size beam is proposed in 2D and discussed in 3D. The CPU and GPU codes are available at https://sites.google.com/site/fastxraytransform. The proposed algorithm is faster than Siddon's algorithm for computing the x-ray transform. In particular, the improvement for the parallel computation can be an order of magnitude. The authors have proposed fast and highly parallelizable algorithms for the x-ray transform and its adjoint, which are extendable for the finite-size beam. The proposed algorithms are suitable for parallel computing in the sense that the computational cost per parallel thread is O(1).

Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics

KAUST Repository

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.

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

Science.gov (United States)

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

2017-11-01

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

The dynamic adjoint as a Green’s function

International Nuclear Information System (INIS)

Pázsit, I.; Dykin, V.

2015-01-01

Highlight: • The relationship between the direct Green’s function and the dynamic adjoint function is discussed in two-group theory. • It is shown that the elements of the direct Greens’ function matrix are identical to those of the transpose of the adjoint Green’s function matrix, with an interchange of arguments. • It is also remarked how the dynamic adjoint function of van Dam can be given in terms of the direct Green’s function matrix. - Abstract: The concept of the dynamic adjoint was introduced by Hugo van Dam for calculating the in-core neutron noise in boiling water reactors in the mid-70’s. This successful approach found numerous applications for calculating the neutron noise in both PWRs and BWRs since then. Although the advantages and disadvantages of using the direct (forward) or the adjoint (backward) approach for the calculation of the neutron noise were analysed in a number of publications, the direct relationship between the forward Green’s function and the dynamic adjoint has not been discussed. On the other hand, in particle transport theory the relationship between the direct and adjoint Green’s function has been discussed in detail, in which Mike Williams has had many seminal contributions. In this note we analyse the relationship between the direct Green’s function and the dynamic adjoint in the spirit of Mike’s work in neutron transport and radiation damage theory. The paper is closed with some personal remarks and reminiscences.

The adjoint sensitivity method, a contribution to the code uncertainty evaluation

International Nuclear Information System (INIS)

Ounsy, A.; Crecy, F. de; Brun, B.

1993-01-01

The application of the ASM (Adjoint Sensitivity Method) to thermohydraulic codes, is examined. The advantage of the method is to be very few CPU time consuming in comparison with usual approach requiring one complete code run per sensitivity determination. The mathematical aspects of the problem are first described, and the applicability of the method of the functional-type response of a thermalhydraulic model is demonstrated. On a simple example of non linear hyperbolic equation (Burgers equation) the problem has been analyzed. It is shown that the formalism used in the literature treating this subject is not appropriate. A new mathematical formalism circumventing the problem is proposed. For the discretized form of the problem, two methods are possible: the Continuous ASM and the Discrete ASM. The equivalence of both methods is demonstrated; nevertheless only the DASM constitutes a practical solution for thermalhydraulic codes. The application of the DASM to the thermalhydraulic safety code CATHARE is then presented for two examples. They demonstrate that ASM constitutes an efficient tool for the analysis of code sensitivity. (authors) 7 figs., 5 tabs., 8 refs

The adjoint sensitivity method. A contribution to the code uncertainty evaluation

International Nuclear Information System (INIS)

Ounsy, A.; Brun, B.

1993-01-01

The application of the ASM (Adjoint Sensitivity Method) to thermohydraulic codes, is examined. The advantage of the method is to be very few CPU time consuming in comparison with usual approach requiring one complete code run per sensitivity determination. The mathematical aspects of the problem are first described, and the applicability of the method of the functional-type response of a thermalhydraulic model is demonstrated. On a simple example of non linear hyperbolic equation (Burgers equation) the problem has been analyzed. It is shown that the formalism used in the literature treating this subject is not appropriate. A new mathematical formalism circumventing the problem is proposed. For the discretized form of the problem, two methods are possible: the Continuous ASM and the Discrete ASM. The equivalence of both methods is demonstrated; nevertheless only the DASM constitutes a practical solution for thermalhydraulic codes. The application of the DASM to the thermalhydraulic safety code CATHARE is then presented for two examples. They demonstrate that ASM constitutes an efficient tool for the analysis of code sensitivity. (authors) 7 figs., 5 tabs., 8 refs

The adjoint sensitivity method. A contribution to the code uncertainty evaluation

Energy Technology Data Exchange (ETDEWEB)

Ounsy, A; Brun, B

1994-12-31

The application of the ASM (Adjoint Sensitivity Method) to thermohydraulic codes, is examined. The advantage of the method is to be very few CPU time consuming in comparison with usual approach requiring one complete code run per sensitivity determination. The mathematical aspects of the problem are first described, and the applicability of the method of the functional-type response of a thermalhydraulic model is demonstrated. On a simple example of non linear hyperbolic equation (Burgers equation) the problem has been analyzed. It is shown that the formalism used in the literature treating this subject is not appropriate. A new mathematical formalism circumventing the problem is proposed. For the discretized form of the problem, two methods are possible: the Continuous ASM and the Discrete ASM. The equivalence of both methods is demonstrated; nevertheless only the DASM constitutes a practical solution for thermalhydraulic codes. The application of the DASM to the thermalhydraulic safety code CATHARE is then presented for two examples. They demonstrate that ASM constitutes an efficient tool for the analysis of code sensitivity. (authors) 7 figs., 5 tabs., 8 refs.

The adjoint sensitivity method, a contribution to the code uncertainty evaluation

Energy Technology Data Exchange (ETDEWEB)

Ounsy, A; Crecy, F de; Brun, B

1994-12-31

The application of the ASM (Adjoint Sensitivity Method) to thermohydraulic codes, is examined. The advantage of the method is to be very few CPU time consuming in comparison with usual approach requiring one complete code run per sensitivity determination. The mathematical aspects of the problem are first described, and the applicability of the method of the functional-type response of a thermalhydraulic model is demonstrated. On a simple example of non linear hyperbolic equation (Burgers equation) the problem has been analyzed. It is shown that the formalism used in the literature treating this subject is not appropriate. A new mathematical formalism circumventing the problem is proposed. For the discretized form of the problem, two methods are possible: the Continuous ASM and the Discrete ASM. The equivalence of both methods is demonstrated; nevertheless only the DASM constitutes a practical solution for thermalhydraulic codes. The application of the DASM to the thermalhydraulic safety code CATHARE is then presented for two examples. They demonstrate that ASM constitutes an efficient tool for the analysis of code sensitivity. (authors) 7 figs., 5 tabs., 8 refs.

Estimation of ex-core detector responses by adjoint Monte Carlo

Energy Technology Data Exchange (ETDEWEB)

Hoogenboom, J. E. [Delft Univ. of Technology, Mekelweg 15, 2629 JB Delft (Netherlands)

2006-07-01

Ex-core detector responses can be efficiently calculated by combining an adjoint Monte Carlo calculation with the converged source distribution of a forward Monte Carlo calculation. As the fission source distribution from a Monte Carlo calculation is given only as a collection of discrete space positions, the coupling requires a point flux estimator for each collision in the adjoint calculation. To avoid the infinite variance problems of the point flux estimator, a next-event finite-variance point flux estimator has been applied, witch is an energy dependent form for heterogeneous media of a finite-variance estimator known from the literature. To test the effects of this combined adjoint-forward calculation a simple geometry of a homogeneous core with a reflector was adopted with a small detector in the reflector. To demonstrate the potential of the method the continuous-energy adjoint Monte Carlo technique with anisotropic scattering was implemented with energy dependent absorption and fission cross sections and constant scattering cross section. A gain in efficiency over a completely forward calculation of the detector response was obtained, which is strongly dependent on the specific system and especially the size and position of the ex-core detector and the energy range considered. Further improvements are possible. The method works without problems for small detectors, even for a point detector and a small or even zero energy range. (authors)

System of adjoint P1 equations for neutron moderation

International Nuclear Information System (INIS)

Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

2000-01-01

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)

Development of one-energy group, two-dimensional, frequency dependent detector adjoint function based on the nodal method

International Nuclear Information System (INIS)

Khericha, Soli T.

2000-01-01

One-energy group, two-dimensional computer code was developed to calculate the response of a detector to a vibrating absorber in a reactor core. A concept of local/global components, based on the frequency dependent detector adjoint function, and a nodalization technique were utilized. The frequency dependent detector adjoint functions presented by complex equations were expanded into real and imaginary parts. In the nodalization technique, the flux is expanded into polynomials about the center point of each node. The phase angle and the magnitude of the one-energy group detector adjoint function were calculated for a detector located in the center of a 200x200 cm reactor using a two-dimensional nodalization technique, the computer code EXTERMINATOR, and the analytical solution. The purpose of this research was to investigate the applicability of a polynomial nodal model technique to the calculations of the real and the imaginary parts of the detector adjoint function for one-energy group two-dimensional polynomial nodal model technique. From the results as discussed earlier, it is concluded that the nodal model technique can be used to calculate the detector adjoint function and the phase angle. Using the computer code developed for nodal model technique, the magnitude of one energy group frequency dependent detector adjoint function and the phase angle were calculated for the detector located in the center of a 200x200 cm homogenous reactor. The real part of the detector adjoint function was compared with the results obtained from the EXTERMINATOR computer code as well as the analytical solution based on a double sine series expansion using the classical Green's Function solution. The values were found to be less than 1% greater at 20 cm away from the source region and about 3% greater closer to the source compared to the values obtained from the analytical solution and the EXTERMINATOR code. The currents at the node interface matched within 1% of the average

Full Seismic Waveform Tomography of the Japan region using Adjoint Methods

Science.gov (United States)

Steptoe, Hamish; Fichtner, Andreas; Rickers, Florian; Trampert, Jeannot

2013-04-01

We present a full-waveform tomographic model of the Japan region based on spectral-element wave propagation, adjoint techniques and seismic data from dense station networks. This model is intended to further our understanding of both the complex regional tectonics and the finite rupture processes of large earthquakes. The shallow Earth structure of the Japan region has been the subject of considerable tomographic investigation. The islands of Japan exist in an area of significant plate complexity: subduction related to the Pacific and Philippine Sea plates is responsible for the majority of seismicity and volcanism of Japan, whilst smaller micro-plates in the region, including the Okhotsk, and Okinawa and Amur, part of the larger North America and Eurasia plates respectively, contribute significant local intricacy. In response to the need to monitor and understand the motion of these plates and their associated faults, numerous seismograph networks have been established, including the 768 station high-sensitivity Hi-net network, 84 station broadband F-net and the strong-motion seismograph networks K-net and KiK-net in Japan. We also include the 55 station BATS network of Taiwan. We use this exceptional coverage to construct a high-resolution model of the Japan region from the full-waveform inversion of over 15,000 individual component seismograms from 53 events that occurred between 1997 and 2012. We model these data using spectral-element simulations of seismic wave propagation at a regional scale over an area from 120°-150°E and 20°-50°N to a depth of around 500 km. We quantify differences between observed and synthetic waveforms using time-frequency misfits allowing us to separate both phase and amplitude measurements whilst exploiting the complete waveform at periods of 15-60 seconds. Fréchet kernels for these misfits are calculated via the adjoint method and subsequently used in an iterative non-linear conjugate-gradient optimization. Finally, we employ

Application of sensitivity analysis to a simplified coupled neutronic thermal-hydraulics transient in a fast reactor using Adjoint techniques

International Nuclear Information System (INIS)

Gilli, L.; Lathouwers, D.; Kloosterman, J.L.; Van der Hagen, T.H.J.J.

2011-01-01

In this paper a method to perform sensitivity analysis for a simplified multi-physics problem is presented. The method is based on the Adjoint Sensitivity Analysis Procedure which is used to apply first order perturbation theory to linear and nonlinear problems using adjoint techniques. The multi-physics problem considered includes a neutronic, a thermo-kinetics, and a thermal-hydraulics part and it is used to model the time dependent behavior of a sodium cooled fast reactor. The adjoint procedure is applied to calculate the sensitivity coefficients with respect to the kinetic parameters of the problem for two reference transients using two different model responses, the results obtained are then compared with the values given by a direct sampling of the forward nonlinear problem. Our first results show that, thanks to modern numerical techniques, the procedure is relatively easy to implement and provides good estimation for most perturbations, making the method appealing for more detailed problems. (author)

The adjoint sensitivity method, a contribution to the code uncertainty evaluation

International Nuclear Information System (INIS)

Ounsy, A.; Brun, B.; De Crecy, F.

1994-01-01

This paper deals with the application of the adjoint sensitivity method (ASM) to thermal hydraulic codes. The advantage of the method is to use small central processing unit time in comparison with the usual approach requiring one complete code run per sensitivity determination. In the first part the mathematical aspects of the problem are treated, and the applicability of the method of the functional-type response of a thermal hydraulic model is demonstrated. On a simple example of non-linear hyperbolic equation (Burgers equation) the problem has been analysed. It is shown that the formalism used in the literature treating this subject is not appropriate. A new mathematical formalism circumventing the problem is proposed. For the discretized form of the problem, two methods are possible: the continuous ASM and the discrete ASM. The equivalence of both methods is demonstrated; nevertheless only the discrete ASM constitutes a practical solution for thermal hydraulic codes. The application of the discrete ASM to the thermal hydraulic safety code CATHARE is then presented for two examples. They demonstrate that the discrete ASM constitutes an efficient tool for the analysis of code sensitivity. ((orig.))

Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

Directory of Open Access Journals (Sweden)

Encinas A.M.

2018-02-01

Full Text Available In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

Characterization and uniqueness of distinguished self-adjoint extensions of dirac operators

International Nuclear Information System (INIS)

Klaus, M.; Wuest, R.; Princeton Univ., NJ

1979-01-01

Distinguished self-adjoint extensions of Dirac operators are characterized by Nenciu and constructed by means of cut-off potentials by Wuest. In this paper it is shown that the existence and a more explicit characterization of Nenciu's self-adjoint extensions can be obtained as a consequence from results of the cut-off method, that these extensions are the same as the extensions constructed with cut-off potentials and that they are unique in some sense. (orig.) [de

Linear Array Ambient Noise Adjoint Tomography Reveals Intense Crust-Mantle Interactions in North China Craton

Science.gov (United States)

Zhang, Chao; Yao, Huajian; Liu, Qinya; Zhang, Ping; Yuan, Yanhua O.; Feng, Jikun; Fang, Lihua

2018-01-01

We present a 2-D ambient noise adjoint tomography technique for a linear array with a significant reduction in computational cost and show its application to an array in North China. We first convert the observed data for 3-D media, i.e., surface-wave empirical Green's functions (EGFs) to the reconstructed EGFs (REGFs) for 2-D media using a 3-D/2-D transformation scheme. Different from the conventional steps of measuring phase dispersion, this technology refines 2-D shear wave speeds along the profile directly from REGFs. With an initial model based on traditional ambient noise tomography, adjoint tomography updates the model by minimizing the frequency-dependent Rayleigh wave traveltime delays between the REGFs and synthetic Green functions calculated by the spectral-element method. The multitaper traveltime difference measurement is applied in four-period bands: 20-35 s, 15-30 s, 10-20 s, and 6-15 s. The recovered model shows detailed crustal structures including pronounced low-velocity anomalies in the lower crust and a gradual crust-mantle transition zone beneath the northern Trans-North China Orogen, which suggest the possible intense thermo-chemical interactions between mantle-derived upwelling melts and the lower crust, probably associated with the magmatic underplating during the Mesozoic to Cenozoic evolution of this region. To our knowledge, it is the first time that ambient noise adjoint tomography is implemented for a 2-D medium. Compared with the intensive computational cost and storage requirement of 3-D adjoint tomography, this method offers a computationally efficient and inexpensive alternative to imaging fine-scale crustal structures beneath linear arrays.

An Adjoint-Based Adaptive Ensemble Kalman Filter

KAUST Repository

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.

An Adjoint-Based Adaptive Ensemble Kalman Filter

KAUST Repository

Song, Hajoon; Hoteit, Ibrahim; Cornuelle, Bruce D.; Luo, Xiaodong; Subramanian, Aneesh C.

2013-01-01

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.

Continuous energy adjoint Monte Carlo for coupled neutron-photon transport

Energy Technology Data Exchange (ETDEWEB)

Hoogenboom, J.E. [Delft Univ. of Technology (Netherlands). Interfaculty Reactor Inst.

2001-07-01

Although the theory for adjoint Monte Carlo calculations with continuous energy treatment for neutrons as well as for photons is known, coupled neutron-photon transport problems present fundamental difficulties because of the discrete energies of the photons produced by neutron reactions. This problem was solved by forcing the energy of the adjoint photon to the required discrete value by an adjoint Compton scattering reaction or an adjoint pair production reaction. A mathematical derivation shows the exact procedures to follow for the generation of an adjoint neutron and its statistical weight. A numerical example demonstrates that correct detector responses are obtained compared to a standard forward Monte Carlo calculation. (orig.)

Adjoint P1 equations solution for neutron slowing down; Solucao das equacoes P1 adjuntas para moderacao de neutrons

Energy Technology Data Exchange (ETDEWEB)

Cardoso, Carlos Eduardo Santos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2002-07-01

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, the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. The direct and adjoint neutron fluxes resulting from the solution of P{sub 1} equations were used to three different weighting processes, to obtain the macrogroup macroscopic cross sections. It was found out noticeable differences among them. (author)

The adjoint space in heat transport theory

International Nuclear Information System (INIS)

Dam, H. van; Hoogenboom, J.E.

1980-01-01

The mathematical concept of adjoint operators is applied to the heat transport equation and an adjoint equation is defined with a detector function as source term. The physical meaning of the solutions for the latter equation is outlined together with an application in the field of perturbation analysis. (author)

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

Science.gov (United States)

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

2009-01-01

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

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

Science.gov (United States)

Wang, Mengze; Mons, Vincent; Zaki, Tamer

2017-11-01

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

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

Science.gov (United States)

Green, Lawrence; Carle, Alan; Fagan, Mike

1999-01-01

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop

Multigroup and coupled forward-adjoint Monte Carlo calculation efficiencies for secondary neutron doses from proton beams

International Nuclear Information System (INIS)

Kelsey IV, Charles T.; Prinja, Anil K.

2011-01-01

We evaluate the Monte Carlo calculation efficiency for multigroup transport relative to continuous energy transport using the MCNPX code system to evaluate secondary neutron doses from a proton beam. We consider both fully forward simulation and application of a midway forward adjoint coupling method to the problem. Previously we developed tools for building coupled multigroup proton/neutron cross section libraries and showed consistent results for continuous energy and multigroup proton/neutron transport calculations. We observed that forward multigroup transport could be more efficient than continuous energy. Here we quantify solution efficiency differences for a secondary radiation dose problem characteristic of proton beam therapy problems. We begin by comparing figures of merit for forward multigroup and continuous energy MCNPX transport and find that multigroup is 30 times more efficient. Next we evaluate efficiency gains for coupling out-of-beam adjoint solutions with forward in-beam solutions. We use a variation of a midway forward-adjoint coupling method developed by others for neutral particle transport. Our implementation makes use of the surface source feature in MCNPX and we use spherical harmonic expansions for coupling in angle rather than solid angle binning. The adjoint out-of-beam transport for organs of concern in a phantom or patient can be coupled with numerous forward, continuous energy or multigroup, in-beam perturbations of a therapy beam line configuration. Out-of-beam dose solutions are provided without repeating out-of-beam transport. (author)

Global Seismic Imaging Based on Adjoint Tomography

Science.gov (United States)

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

2013-12-01

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

The adjoint string at finite temperature

International Nuclear Information System (INIS)

Damgaard, P.H.

1986-10-01

Expectations for the behavior of the adjoint string at finite temperature are presented. In the Migdal-Kadanoff approximation a real-space renormalization group study of the effective Polyakov like action predicts a deconfinement-like crossover for adjoint sources at a temperature slightly below the deconfinement temperature of fundamental sources. This prediction is compared with a Monte Carlo simulation of SU(2) lattice gauge theory on an 8 3 x2 lattice. (orig.)

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle Multi-Pixel Polarimetric Measurements

Science.gov (United States)

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.

A new approach for developing adjoint models

Science.gov (United States)

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

2011-12-01

Many data assimilation algorithms rely on the availability of gradients of misfit functionals, which can be efficiently computed with adjoint models. However, the development of an adjoint model for a complex geophysical code is generally very difficult. Algorithmic differentiation (AD, also called automatic differentiation) offers one strategy for simplifying this task: it takes the abstraction that a model is a sequence of primitive instructions, each of which may be differentiated in turn. While extremely successful, this low-level abstraction runs into time-consuming difficulties when applied to the whole codebase of a model, such as differentiating through linear solves, model I/O, calls to external libraries, language features that are unsupported by the AD tool, and the use of multiple programming languages. While these difficulties can be overcome, it requires a large amount of technical expertise and an intimate familiarity with both the AD tool and the model. An alternative to applying the AD tool to the whole codebase is to assemble the discrete adjoint equations and use these to compute the necessary gradients. With this approach, the AD tool must be applied to the nonlinear assembly operators, which are typically small, self-contained units of the codebase. The disadvantage of this approach is that the assembly of the discrete adjoint equations is still very difficult to perform correctly, especially for complex multiphysics models that perform temporal integration; as it stands, this approach is as difficult and time-consuming as applying AD to the whole model. In this work, we have developed a library which greatly simplifies and automates the alternate approach of assembling the discrete adjoint equations. We propose a complementary, higher-level abstraction to that of AD: that a model is a sequence of linear solves. The developer annotates model source code with library calls that build a 'tape' of the operators involved and their dependencies, and

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

Science.gov (United States)

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.

Implementation of Generalized Adjoint Equation Solver for DeCART

International Nuclear Information System (INIS)

Han, Tae Young; Cho, Jin Young; Lee, Hyun Chul; Noh, Jae Man

2013-01-01

In this paper, the generalized adjoint solver based on the generalized perturbation theory is implemented on DeCART and the verification calculations were carried out. As the results, the adjoint flux for the general response coincides with the reference solution and it is expected that the solver could produce the parameters for the sensitivity and uncertainty analysis. Recently, MUSAD (Modules of Uncertainty and Sensitivity Analysis for DeCART) was developed for the uncertainty analysis of PMR200 core and the fundamental adjoint solver was implemented into DeCART. However, the application of the code was limited to the uncertainty to the multiplication factor, k eff , because it was based on the classical perturbation theory. For the uncertainty analysis to the general response as like the power density, it is necessary to develop the analysis module based on the generalized perturbation theory and it needs the generalized adjoint solutions from DeCART. In this paper, the generalized adjoint solver is implemented on DeCART and the calculation results are compared with the results by TSUNAMI of SCALE 6.1

Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach

Science.gov (United States)

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.

Wavelet-based multiscale adjoint waveform-difference tomography using body and surface waves

Science.gov (United States)

Yuan, Y. O.; Simons, F. J.; Bozdag, E.

2014-12-01

We present a multi-scale scheme for full elastic waveform-difference inversion. Using a wavelet transform proves to be a key factor to mitigate cycle-skipping effects. We start with coarse representations of the seismogram to correct a large-scale background model, and subsequently explain the residuals in the fine scales of the seismogram to map the heterogeneities with great complexity. We have previously applied the multi-scale approach successfully to body waves generated in a standard model from the exploration industry: a modified two-dimensional elastic Marmousi model. With this model we explored the optimal choice of wavelet family, number of vanishing moments and decomposition depth. For this presentation we explore the sensitivity of surface waves in waveform-difference tomography. The incorporation of surface waves is rife with cycle-skipping problems compared to the inversions considering body waves only. We implemented an envelope-based objective function probed via a multi-scale wavelet analysis to measure the distance between predicted and target surface-wave waveforms in a synthetic model of heterogeneous near-surface structure. Our proposed method successfully purges the local minima present in the waveform-difference misfit surface. An elastic shallow model with 100~m in depth is used to test the surface-wave inversion scheme. We also analyzed the sensitivities of surface waves and body waves in full waveform inversions, as well as the effects of incorrect density information on elastic parameter inversions. Based on those numerical experiments, we ultimately formalized a flexible scheme to consider both body and surface waves in adjoint tomography. While our early examples are constructed from exploration-style settings, our procedure will be very valuable for the study of global network data.

Imaging disturbance zones ahead of a tunnel by elastic full-waveform inversion: Adjoint gradient based inversion vs. parameter space reduction using a level-set method

Directory of Open Access Journals (Sweden)

Andre Lamert

2018-03-01

Full Text Available We present and compare two flexible and effective methodologies to predict disturbance zones ahead of underground tunnels by using elastic full-waveform inversion. One methodology uses a linearized, iterative approach based on misfit gradients computed with the adjoint method while the other uses iterative, gradient-free unscented Kalman filtering in conjunction with a level-set representation. Whereas the former does not involve a priori assumptions on the distribution of elastic properties ahead of the tunnel, the latter introduces a massive reduction in the number of explicit model parameters to be inverted for by focusing on the geometric form of potential disturbances and their average elastic properties. Both imaging methodologies are validated through successful reconstructions of simple disturbances. As an application, we consider an elastic multiple disturbance scenario. By using identical synthetic time-domain seismograms as test data, we obtain satisfactory, albeit different, reconstruction results from the two inversion methodologies. The computational costs of both approaches are of the same order of magnitude, with the gradient-based approach showing a slight advantage. The model parameter space reduction approach compensates for this by additionally providing a posteriori estimates of model parameter uncertainty. Keywords: Tunnel seismics, Full waveform inversion, Seismic waves, Level-set method, Adjoint method, Kalman filter

Solar wind reconstruction from magnetosheath data using an adjoint approach

International Nuclear Information System (INIS)

Nabert, C.; Othmer, C.

2015-01-01

We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradient-based minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.

Solar wind reconstruction from magnetosheath data using an adjoint approach

Energy Technology Data Exchange (ETDEWEB)

Nabert, C.; Othmer, C. [Technische Univ. Braunschweig (Germany). Inst. fuer Geophysik und extraterrestrische Physik; Glassmeier, K.H. [Technische Univ. Braunschweig (Germany). Inst. fuer Geophysik und extraterrestrische Physik; Max Planck Institute for Solar System Research, Goettingen (Germany)

2015-07-01

We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradient-based minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.

Advances in Global Adjoint Tomography -- Massive Data Assimilation

Science.gov (United States)

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

Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for Boron Neutron Capture Therapy

International Nuclear Information System (INIS)

Nievaart, V. A.; Legrady, D.; Moss, R. L.; Kloosterman, J. L.; Hagen, T. H. J. J. van der; Dam, H. van

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 simulations the particles start at a source and lose energy as they travel towards the region of interest, i.e., the designated point of detection. Conversely, with adjoint Monte Carlo simulations, the so-called adjoint particles start at the region of interest and gain energy as they travel towards the source where they are detected. In this respect, the particles travel backwards and the real source and real detector become the adjoint detector and adjoint source, respectively. At the adjoint detector, an adjoint function is obtained with which numerically the same result, e.g., dose or flux in the tumor, can be derived as with forward Monte Carlo. In many cases, the adjoint method is more efficient and by that is much quicker when, for example, the response in the tumor or organ at risk for many locations and orientations of the treatment beam around the patient is required. However, a problem occurs when the treatment beam is mono-directional as the probability of detecting adjoint Monte Carlo particles traversing the beam exit (detector plane in adjoint mode) in the negative direction of the incident beam is zero. This problem is addressed here and solved first with the use of next event estimators and second with the application of a Legendre expansion technique of the angular adjoint function. In the first approach, adjoint particles are tracked deterministically through a tube to a (adjoint) point detector far away from the geometric model. The adjoint particles will traverse the disk shaped entrance of this tube (the beam exit in the actual geometry) perpendicularly. This method is slow whenever many events are involved that are not contributing to the point

The method of rigged spaces in singular perturbation theory of self-adjoint operators

CERN Document Server

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...

On the use of flux-adjoint condensed nuclear data for 1-group AGR kinetics

International Nuclear Information System (INIS)

Hutt, P.K.

1979-03-01

Following previous work on the differences between one and two neutron group AGR kinetics the possible advantages of flux-adjoint condensed lattice data over the simple flux condensation procedure are investigated. Analytic arguments are given for expecting flux-adjoint condensation to give a better representation of rod worth slopes and flux shape changes associated with partially rodded cores. These areas have previously been found to yield most of the one to two neutron group differences. The validity of these arguments is demonstrated comparing various calculations. (U.K.)

Self-consistent adjoint analysis for topology optimization of electromagnetic waves

Science.gov (United States)

Deng, Yongbo; Korvink, Jan G.

2018-05-01

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

Almost commuting self-adjoint matrices: The real and self-dual cases

Science.gov (United States)

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.

The Hausdorff measure of chaotic sets of adjoint shift maps

Energy Technology Data Exchange (ETDEWEB)

Wang Huoyun [Department of Mathematics of Guangzhou University, Guangzhou 510006 (China)]. E-mail: wanghuoyun@sina.com; Song Wangan [Department of Computer, Huaibei Coal Industry Teacher College, Huaibei 235000 (China)

2006-11-15

In this paper, the size of chaotic sets of adjoint shift maps is estimated by Hausdorff measure. We prove that for any adjoint shift map there exists a finitely chaotic set with full Hausdorff measure.

Adjoint method provides phase response functions for delay-induced oscillations.

Science.gov (United States)

Kotani, Kiyoshi; Yamaguchi, Ikuhiro; Ogawa, Yutaro; Jimbo, Yasuhiko; Nakao, Hiroya; Ermentrout, G Bard

2012-07-27

Limit-cycle oscillations induced by time delay are widely observed in various systems, but a systematic phase-reduction theory for them has yet to be developed. Here we present a practical theoretical framework to calculate the phase response function Z(θ), a fundamental quantity for the theory, of delay-induced limit cycles with infinite-dimensional phase space. We show that Z(θ) can be obtained as a zero eigenfunction of the adjoint equation associated with an appropriate bilinear form for the delay differential equations. We confirm the validity of the proposed framework for two biological oscillators and demonstrate that the derived phase equation predicts intriguing multimodal locking behavior.

Optimization of a neutron detector design using adjoint transport simulation

International Nuclear Information System (INIS)

Yi, C.; Manalo, K.; Huang, M.; Chin, M.; Edgar, C.; Applegate, S.; Sjoden, G.

2012-01-01

A synthetic aperture approach has been developed and investigated for Special Nuclear Materials (SNM) detection in vehicles passing a checkpoint at highway speeds. SNM is postulated to be stored in a moving vehicle and detector assemblies are placed on the road-side or in chambers embedded below the road surface. Neutron and gamma spectral awareness is important for the detector assembly design besides high efficiencies, so that different SNMs can be detected and identified with various possible shielding settings. The detector assembly design is composed of a CsI gamma-ray detector block and five neutron detector blocks, with peak efficiencies targeting different energy ranges determined by adjoint simulations. In this study, formulations are derived using adjoint transport simulations to estimate detector efficiencies. The formulations is applied to investigate several neutron detector designs for Block IV, which has its peak efficiency in the thermal range, and Block V, designed to maximize the total neutron counts over the entire energy spectrum. Other Blocks detect different neutron energies. All five neutron detector blocks and the gamma-ray block are assembled in both MCNP and deterministic simulation models, with detector responses calculated to validate the fully assembled design using a 30-group library. The simulation results show that the 30-group library, collapsed from an 80-group library using an adjoint-weighting approach with the YGROUP code, significantly reduced the computational cost while maintaining accuracy. (authors)

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

Science.gov (United States)

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

2018-01-01

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

Optical properties reconstruction using the adjoint method based on the radiative transfer equation

Science.gov (United States)

Addoum, Ahmad; Farges, Olivier; Asllanaj, Fatmir

2018-01-01

An efficient algorithm is proposed to reconstruct the spatial distribution of optical properties in heterogeneous media like biological tissues. The light transport through such media is accurately described by the radiative transfer equation in the frequency-domain. The adjoint method is used to efficiently compute the objective function gradient with respect to optical parameters. Numerical tests show that the algorithm is accurate and robust to retrieve simultaneously the absorption μa and scattering μs coefficients for lowly and highly absorbing medium. Moreover, the simultaneous reconstruction of μs and the anisotropy factor g of the Henyey-Greenstein phase function is achieved with a reasonable accuracy. The main novelty in this work is the reconstruction of g which might open the possibility to image this parameter in tissues as an additional contrast agent in optical tomography.

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.

Adjoint Airfoil Optimization of Darrieus-Type Vertical Axis Wind Turbine

Science.gov (United States)

Fuchs, Roman; Nordborg, Henrik

2012-11-01

We present the feasibility of using an adjoint solver to optimize the torque of a Darrieus-type vertical axis wind turbine (VAWT). We start with a 2D cross section of a symmetrical airfoil and restrict us to low solidity ratios to minimize blade vortex interactions. The adjoint solver of the ANSYS FLUENT software package computes the sensitivities of airfoil surface forces based on a steady flow field. Hence, we find the torque of a full revolution using a weighted average of the sensitivities at different wind speeds and angles of attack. The weights are computed analytically, and the range of angles of attack is given by the tip speed ratio. Then the airfoil geometry is evolved, and the proposed methodology is evaluated by transient simulations.

The adjoint method for general EEG and MEG sensor-based lead field equations

International Nuclear Information System (INIS)

Vallaghe, Sylvain; Papadopoulo, Theodore; Clerc, Maureen

2009-01-01

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.

Adjoint string breaking in the pseudoparticle approach

International Nuclear Information System (INIS)

Szasz, Christian; Wagner, Marc

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.

Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems

KAUST Repository

Garg, Vikram V; Prudhomme, Serge; van der Zee, Kris G; Carey, Graham F

2014-01-01

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

Time reversal imaging, Inverse problems and Adjoint Tomography}

Science.gov (United States)

Montagner, J.; Larmat, C. S.; Capdeville, Y.; Kawakatsu, H.; Fink, M.

2010-12-01

With the increasing power of computers and numerical techniques (such as spectral element methods), it is possible to address a new class of seismological problems. The propagation of seismic waves in heterogeneous media is simulated more and more accurately and new applications developed, in particular time reversal methods and adjoint tomography in the three-dimensional Earth. Since the pioneering work of J. Claerbout, theorized by A. Tarantola, many similarities were found between time-reversal methods, cross-correlations techniques, inverse problems and adjoint tomography. By using normal mode theory, we generalize the scalar approach of Draeger and Fink (1999) and Lobkis and Weaver (2001) to the 3D- elastic Earth, for theoretically understanding time-reversal method on global scale. It is shown how to relate time-reversal methods on one hand, with auto-correlations of seismograms for source imaging and on the other hand, with cross-correlations between receivers for structural imaging and retrieving Green function. Time-reversal methods were successfully applied in the past to acoustic waves in many fields such as medical imaging, underwater acoustics, non destructive testing and to seismic waves in seismology for earthquake imaging. In the case of source imaging, time reversal techniques make it possible an automatic location in time and space as well as the retrieval of focal mechanism of earthquakes or unknown environmental sources . We present here some applications at the global scale of these techniques on synthetic tests and on real data, such as Sumatra-Andaman (Dec. 2004), Haiti (Jan. 2010), as well as glacial earthquakes and seismic hum.

Self-adjointness of the Gaffney Laplacian on Vector Bundles

International Nuclear Information System (INIS)

Bandara, Lashi; Milatovic, Ognjen

2015-01-01

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

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.

Self-Adjointness Criterion for Operators in Fock Spaces

International Nuclear Information System (INIS)

Falconi, Marco

2015-01-01

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

Treatment planning for prostate brachytherapy using region of interest adjoint functions and a greedy heuristic

International Nuclear Information System (INIS)

Yoo, Sua; Kowalok, Michael E; Thomadsen, Bruce R; Henderson, Douglass L

2003-01-01

We have developed an efficient treatment-planning algorithm for prostate implants that is based on region of interest (ROI) adjoint functions and a greedy heuristic. For this work, we define the adjoint function for an ROI as the sensitivity of the average dose in the ROI to a unit-strength brachytherapy source at any seed position. The greedy heuristic uses a ratio of target and critical structure adjoint functions to rank seed positions according to their ability to irradiate the target ROI while sparing critical structure ROIs. This ratio is computed once for each seed position prior to the optimization process. Optimization is performed by a greedy heuristic that selects seed positions according to their ratio values. With this method, clinically acceptable treatment plans are obtained in less than 2 s. For comparison, a branch-and-bound method to solve a mixed integer-programming model took more than 50 min to arrive at a feasible solution. Both methods achieved good treatment plans, but the speedup provided by the greedy heuristic was a factor of approximately 1500. This attribute makes this algorithm suitable for intra-operative real-time treatment planning

Variation estimation of the averaged cross sections in the direct and adjoint fluxes; Estimativa das variacoes das secoes de choque mediadas nos fluxos direto e adjunto

Energy Technology Data Exchange (ETDEWEB)

Cardoso, Carlos Eduardo Santos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia

1995-12-31

There are several applications of the perturbation theory to specifics problems of reactor physics, such as nonuniform fuel burnup, nonuniform poison accumulation and evaluations of Doppler effects on reactivity. The neutron fluxes obtained from the solutions of direct and adjoint diffusion equations, are used in these applications. In the adjoint diffusion equation has been used the group constants averaged in the energy-dependent direct neutron flux, that it is not theoretically consistent. In this paper it is presented a method to calculate the energy-dependent adjoint neutron flux, to obtain the average group-constant that will be used in the adjoint diffusion equation. The method is based on the solution of the adjoint neutron balance equations, that were derived for a two regions cell. (author). 5 refs, 2 figs, 1 tab.

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

Science.gov (United States)

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

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

Science.gov (United States)

Gonzales, Matthew Alejandro

version of MCNP6. Temperature feedback results from the cross sections themselves, changes in the probability density functions, as well as changes in the density of the materials. The focus of this work is specific to the Doppler temperature feedback which result from Doppler broadening of cross sections as well as changes in the probability density function within the scattering kernel. This method is compared against published results using Mosteller's numerical benchmark to show accurate evaluations of the Doppler temperature coefficient, fuel assembly calculations, and a benchmark solution based on the heavy gas model for free-gas elastic scattering. An infinite medium benchmark for neutron free gas elastic scattering for large scattering ratios and constant absorption cross section has been developed using the heavy gas model. An exact closed form solution for the neutron energy spectrum is obtained in terms of the confluent hypergeometric function and compared against spectra for the free gas scattering model in MCNP6. Results show a quick increase in convergence of the analytic energy spectrum to the MCNP6 code with increasing target size, showing absolute relative differences of less than 5% for neutrons scattering with carbon. The analytic solution has been generalized to accommodate piecewise constant in energy absorption cross section to produce temperature feedback. Results reinforce the constraints in which heavy gas theory may be applied resulting in a significant target size to accommodate increasing cross section structure. The energy dependent piecewise constant cross section heavy gas model was used to produce a benchmark calculation of the Doppler temperature coefficient to show accurate calculations when using the adjoint-weighted method. Results show the Doppler temperature coefficient using adjoint weighting and cross section derivatives accurately obtains the correct solution within statistics as well as reduce computer runtimes by a factor of 50.

Global Linear Representations of Nonlinear Systems and the Adjoint Map

OpenAIRE

Banks, S.P.

1988-01-01

In this paper we shall study the global linearization of nonlinear systems on a manifold by two methods. The first consists of an expansion of the vector field in the space of square integrable vector fields. In the second method we use the adjoint representation of the Lie algebra vector fields to obtain an infinite-dimensional matrix representation of the system. A connection between the two approaches will be developed.

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

Science.gov (United States)

Bergner, Georg; Piemonte, Stefano

2018-04-01

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

On the Incompleteness of Ibragimov’s Conservation Law Theorem and Its Equivalence to a Standard Formula Using Symmetries and Adjoint-Symmetries

Directory of Open Access Journals (Sweden)

Stephen C. Anco

2017-02-01

Full Text Available A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well-known Fréchet derivative identity. Furthermore, the connection of this formula (and of Ibragimov’s theorem to the standard action of symmetries on conservation laws is explained, which accounts for a number of major drawbacks that have appeared in recent work using the formula to generate conservation laws. In particular, the formula can generate trivial conservation laws and does not always yield all non-trivial conservation laws unless the symmetry action on the set of these conservation laws is transitive. It is emphasized that all local conservation laws for any given system of differential equations can be found instead by a general method using adjoint-symmetries. This general method is a kind of adjoint version of the standard Lie method to find all local symmetries and is completely algorithmic. The relationship between this method, Noether’s theorem and the symmetry/adjoint-symmetry formula is discussed.

Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators

International Nuclear Information System (INIS)

Jefferies, Brian; Johnson, Gerald W.; Nielsen, Lance

2007-01-01

The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A 1 ,..., A n and associated continuous Borel probability measures μ 1 , ?, μ n on [0,1]. Fix A 1 ,..., A n . Then each choice of an n-tuple (μ 1 ,...,μ n ) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A 1 , ..., A n are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi

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

Science.gov (United States)

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

A family of integrable differential–difference equations, its bi-Hamiltonian structure and binary nonlinearization of the Lax pairs and adjoint Lax pairs

International Nuclear Information System (INIS)

Xu Xixiang

2012-01-01

Highlights: ► We deduce a family of integrable differential–difference equations. ► We present a discrete Hamiltonian operator involving two arbitrary real parameters. ► We establish the bi-Hamiltonian structure for obtained integrable family. ► Liouvolle integrability of the obtained family is demonstrated. ► Every equation in obtained family is factored through the binary nonlinearization. - Abstract: A family of integrable differential–difference equations is derived by the method of Lax pairs. A discrete Hamiltonian operator involving two arbitrary real parameters is introduced. When the parameters are suitably selected, a pair of discrete Hamiltonian operators is presented. Bi-Hamiltonian structure of obtained family is established by discrete trace identity. Then, Liouville integrability for the obtained family is proved. Ultimately, through the binary nonlinearization of the Lax pairs and adjoint Lax pairs, every differential–difference equation in obtained family is factored by an integrable symplectic map and a finite-dimensional integrable system in Liouville sense.

An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

KAUST Repository

Festa, Adriano; Gomes, Diogo A.; Machado Velho, Roberto

2017-01-01

Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

KAUST Repository

Festa, Adriano

2017-03-22

Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

Variational variance reduction for particle transport eigenvalue calculations using Monte Carlo adjoint simulation

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Larsen, Edward W.

2003-01-01

The Variational Variance Reduction (VVR) method is an effective technique for increasing the efficiency of Monte Carlo simulations [Ann. Nucl. Energy 28 (2001) 457; Nucl. Sci. Eng., in press]. This method uses a variational functional, which employs first-order estimates of forward and adjoint fluxes, to yield a second-order estimate of a desired system characteristic - which, in this paper, is the criticality eigenvalue k. If Monte Carlo estimates of the forward and adjoint fluxes are used, each having global 'first-order' errors of O(1/√N), where N is the number of histories used in the Monte Carlo simulation, then the statistical error in the VVR estimation of k will in principle be O(1/N). In this paper, we develop this theoretical possibility and demonstrate with numerical examples that implementations of the VVR method for criticality problems can approximate O(1/N) convergence for significantly large values of N

Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel

Science.gov (United States)

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

Tracking sensitive source areas of different weather pollution types using GRAPES-CUACE adjoint model

Science.gov (United States)

Wang, Chao; An, Xingqin; Zhai, Shixian; Hou, Qing; Sun, Zhaobin

2018-02-01

In this study, the sustained pollution processes were selected during which daily PM2.5 concentration exceeded 75 μg/m3 for three days continuously based on the hourly data of Beijing observation sites from July 2012 to December 2015. Using the China Meteorological Administration (CMA) MICAPS meteorological processing system, synoptic situation during PM2.5 pollution processes was classified into five weather types: low pressure and weak high pressure alternating control, weak high pressure, low pressure control, high rear, and uniform pressure field. Then, we chose the representative pollution cases corresponding to each type, adopted the GRAPES-CUACE adjoint model tracking the sensitive source areas of the five types, and analyzed the critical discharge periods of Beijing and neighboring provinces as well as their contribution to the PM2.5 peak concentration in Beijing. The results showed that the local source plays the main theme in the 30 h before the objective time, and prior to 72 h before the objective time contribution of local sources for the five pollution types are 37.5%, 25.0%, 39.4%, 31.2%, and 42.4%, respectively; the Hebei source contributes constantly in the 57 h ahead of the objective time with the contribution proportion ranging from 37% to 64%; the contribution period and rate of Tianjin and Shanxi sources are shorter and smaller. Based on the adjoint sensitivity analysis, we further discussed the effect of emission reduction control measures in different types, finding that the effect of local source reduction in the first 20 h of the objective time is better, and if the local source is reduced 50% within 72 h before the objective time, the decline rates of PM2.5 in the five types are 11.6%, 9.4%, 13.8%, 9.9% and 15.2% respectively. And the reduction effect of the neighboring sources is better within the 3-57 h before the objective time.

An adjoint method of sensitivity analysis for residual vibrations of structures subject to impacts

Science.gov (United States)

Yan, Kun; Cheng, Gengdong

2018-03-01

For structures subject to impact loads, the residual vibration reduction is more and more important as the machines become faster and lighter. An efficient sensitivity analysis of residual vibration with respect to structural or operational parameters is indispensable for using a gradient based optimization algorithm, which reduces the residual vibration in either active or passive way. In this paper, an integrated quadratic performance index is used as the measure of the residual vibration, since it globally measures the residual vibration response and its calculation can be simplified greatly with Lyapunov equation. Several sensitivity analysis approaches for performance index were developed based on the assumption that the initial excitations of residual vibration were given and independent of structural design. Since the resulting excitations by the impact load often depend on structural design, this paper aims to propose a new efficient sensitivity analysis method for residual vibration of structures subject to impacts to consider the dependence. The new method is developed by combining two existing methods and using adjoint variable approach. Three numerical examples are carried out and demonstrate the accuracy of the proposed method. The numerical results show that the dependence of initial excitations on structural design variables may strongly affects the accuracy of sensitivities.

An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

International Nuclear Information System (INIS)

Arcos-Olalla, Rafael; Reyes, Marco A.; Rosu, Haret C.

2012-01-01

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.

An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

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.

An adjoint-based framework for maximizing mixing in binary fluids

Science.gov (United States)

Eggl, Maximilian; Schmid, Peter

2017-11-01

Mixing in the inertial, but laminar parameter regime is a common application in a wide range of industries. Enhancing the efficiency of mixing processes thus has a fundamental effect on product quality, material homogeneity and, last but not least, production costs. In this project, we address mixing efficiency in the above mentioned regime (Reynolds number Re = 1000 , Peclet number Pe = 1000) by developing and demonstrating an algorithm based on nonlinear adjoint looping that minimizes the variance of a passive scalar field which models our binary Newtonian fluids. The numerical method is based on the FLUSI code (Engels et al. 2016), a Fourier pseudo-spectral code, which we modified and augmented by scalar transport and adjoint equations. Mixing is accomplished by moving stirrers which are numerically modeled using a penalization approach. In our two-dimensional simulations we consider rotating circular and elliptic stirrers and extract optimal mixing strategies from the iterative scheme. The case of optimizing shape and rotational speed of the stirrers will be demonstrated.

Adjoint sensitivity theory for steady-state ground-water flow

International Nuclear Information System (INIS)

1983-11-01

In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady-state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah and the Wolcamp carbonate/sandstone aquifer of the Palo Duro Basin in the Texas Panhandle. Two performance measures are evaluated, local heads and velocity in the vicinity of potential high-level nuclear waste repositories. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Local velocity-related performance measures are more sensitive to hydraulic conductivities. The uncertainty in the performance measure is a function of the parameter sensitivity, parameter variance and the correlation between parameters. Given a parameter covariance matrix, the uncertainty of the performance measure can be calculated. Although no results are presented here, the implications of uncertainty calculations for the two studies are discussed. 18 references, 25 figures

Spectral monodromy of non-self-adjoint operators

International Nuclear Information System (INIS)

Phan, Quang Sang

2014-01-01

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

Spectral monodromy of non-self-adjoint operators

Science.gov (United States)

Phan, Quang Sang

2014-01-01

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

Spectral monodromy of non-self-adjoint operators

Energy Technology Data Exchange (ETDEWEB)

Phan, Quang Sang, E-mail: quang.phan@uj.edu.pl [Université de Rennes 1, Institut de Recherche Mathématique de Rennes (UMR 6625), Campus de Beaulieu, 35042 Rennes (France)

2014-01-15

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

Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

Science.gov (United States)

Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

2015-04-01

The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface

Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico

KAUST Repository

Gopalakrishnan, Ganesh; Cornuelle, Bruce D.; Hoteit, Ibrahim

2013-01-01

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

Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico

KAUST Repository

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

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

Science.gov (United States)

Marcotte, Christopher D; Grigoriev, Roman O

2016-09-01

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

A generalized adjoint framework for sensitivity and global error estimation in time-dependent nuclear reactor simulations

International Nuclear Information System (INIS)

Stripling, H.F.; Anitescu, M.; Adams, M.L.

2013-01-01

Highlights: ► We develop an abstract framework for computing the adjoint to the neutron/nuclide burnup equations posed as a system of differential algebraic equations. ► We validate use of the adjoint for computing both sensitivity to uncertain inputs and for estimating global time discretization error. ► Flexibility of the framework is leveraged to add heat transfer physics and compute its adjoint without a reformulation of the adjoint system. ► Such flexibility is crucial for high performance computing applications. -- Abstract: We develop a general framework for computing the adjoint variable to nuclear engineering problems governed by a set of differential–algebraic equations (DAEs). The nuclear engineering community has a rich history of developing and applying adjoints for sensitivity calculations; many such formulations, however, are specific to a certain set of equations, variables, or solution techniques. Any change or addition to the physics model would require a reformulation of the adjoint problem and substantial difficulties in its software implementation. In this work we propose an abstract framework that allows for the modification and expansion of the governing equations, leverages the existing theory of adjoint formulation for DAEs, and results in adjoint equations that can be used to efficiently compute sensitivities for parametric uncertainty quantification. Moreover, as we justify theoretically and demonstrate numerically, the same framework can be used to estimate global time discretization error. We first motivate the framework and show that the coupled Bateman and transport equations, which govern the time-dependent neutronic behavior of a nuclear reactor, may be formulated as a DAE system with a power constraint. We then use a variational approach to develop the parameter-dependent adjoint framework and apply existing theory to give formulations for sensitivity and global time discretization error estimates using the adjoint

Adjoint assimilation of altimetric, surface drifter, and hydrographic data in a quasi-geostrophic model of the Azores Current

Science.gov (United States)

Morrow, Rosemary; de Mey, Pierre

1995-12-01

The flow characteristics in the region of the Azores Current are investigated by assimilating TOPEX/POSEIDON and ERS 1 altimeter data into the multilevel Harvard quasigeostrophic (QG) model with open boundaries (Miller et al., 1983) using an adjoint variational scheme (Moore, 1991). The study site lies in the path of the Azores Current, where a branch retroflects to the south in the vicinity of the Madeira Rise. The region was the site of an intensive field program in 1993, SEMAPHORE. We had two main aims in this adjoint assimilation project. The first was to see whether the adjoint method could be applied locally to optimize an initial guess field, derived from the continous assimilation of altimetry data using optimal interpolation (OI). The second aim was to assimilate a variety of different data sets and evaluate their importance in constraining our QG model. The adjoint assimilation of surface data was effective in optimizing the initial conditions from OI. After 20 iterations the cost function was generally reduced by 50-80%, depending on the chosen data constraints. The primary adjustment process was via the barotropic mode. Altimetry proved to be a good constraint on the variable flow field, in particular, for constraining the barotropic field. The excellent data quality of the TOPEX/POSEIDON (T/P) altimeter data provided smooth and reliable forcing; but for our mesoscale study in a region of long decorrelation times O(30 days), the spatial coverage from the combined T/P and ERS 1 data sets was more important for constraining the solution and providing stable flow at all levels. Surface drifters provided an excellent constraint on both the barotropic and baroclinic model fields. More importantly, the drifters provided a reliable measure of the mean field. Hydrographic data were also applied as a constraint; in general, hydrography provided a weak but effective constraint on the vertical Rossby modes in the model. Finally, forecasts run over a 2-month period

Discrete SLn-connections and self-adjoint difference operators on 2-dimensional manifolds

International Nuclear Information System (INIS)

Grinevich, P G; Novikov, S P

2013-01-01

The programme of discretization of famous completely integrable systems and associated linear operators was launched in the 1990s. In particular, the properties of second-order difference operators on triangulated manifolds and equilateral triangular lattices have been studied by Novikov and Dynnikov since 1996. This study included Laplace transformations, new discretizations of complex analysis, and new discretizations of GL n -connections on triangulated n-dimensional manifolds. A general theory of discrete GL n -connections 'of rank one' has been developed (see the Introduction for definitions). The problem of distinguishing the subclass of SL n -connections (and unimodular SL n ± -connections, which satisfy detA = ±1) has not been solved. In the present paper it is shown that these connections play an important role (which is similar to the role of magnetic fields in the continuous case) in the theory of self-adjoint Schrödinger difference operators on equilateral triangular lattices in ℝ 2 . In Appendix 1 a complete characterization is given of unimodular SL n ± -connections of rank 1 for all n > 1, thus correcting a mistake (it was wrongly claimed that they reduce to a canonical connection for n > 2). With the help of a communication from Korepanov, a complete clarification is provided of how the classical theory of electrical circuits and star-triangle transformations is connected with the discrete Laplace transformations on triangular lattices. Bibliography: 29 titles

Geostatistical and adjoint sensitivity techniques applied to a conceptual model of ground-water flow in the Paradox Basin, Utah

International Nuclear Information System (INIS)

Metcalfe, D.E.; Campbell, J.E.; RamaRao, B.S.; Harper, W.V.; Battelle Project Management Div., Columbus, OH)

1985-01-01

Sensitivity and uncertainty analysis are important components of performance assessment activities for potential high-level radioactive waste repositories. The application of geostatistical and adjoint sensitivity techniques to aid in the calibration of an existing conceptual model of ground-water flow is demonstrated for the Leadville Limestone in Paradox Basin, Utah. The geostatistical method called kriging is used to statistically analyze the measured potentiometric data for the Leadville. This analysis consists of identifying anomalous data and data trends and characterizing the correlation structure between data points. Adjoint sensitivity analysis is then performed to aid in the calibration of a conceptual model of ground-water flow to the Leadville measured potentiometric data. Sensitivity derivatives of the fit between the modeled Leadville potentiometric surface and the measured potentiometric data to model parameters and boundary conditions are calculated by the adjoint method. These sensitivity derivatives are used to determine which model parameter and boundary condition values should be modified to most efficiently improve the fit of modeled to measured potentiometric conditions

Infrared conformality and bulk critical points: SU(2) with heavy adjoint quarks

CERN Document Server

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...

GPU-accelerated adjoint algorithmic differentiation

Science.gov (United States)

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.

On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems

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 ...

Application of the adjoint optimisation of shock control bump for ONERA-M6 wing

Science.gov (United States)

Nejati, A.; Mazaheri, K.

2017-11-01

This article is devoted to the numerical investigation of the shock wave/boundary layer interaction (SWBLI) as the main factor influencing the aerodynamic performance of transonic bumped airfoils and wings. The numerical analysis is conducted for the ONERA-M6 wing through a shock control bump (SCB) shape optimisation process using the adjoint optimisation method. SWBLI is analyzed for both clean and bumped airfoils and wings, and it is shown how the modified wave structure originating from upstream of the SCB reduces the wave drag, by improving the boundary layer velocity profile downstream of the shock wave. The numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm are used to find the optimum location and shape of the SCB for the ONERA-M6 airfoil and wing. Two different geometrical models are introduced for the 3D SCB, one with linear variations, and another with periodic variations. Both configurations result in drag reduction and improvement in the aerodynamic efficiency, but the periodic model is more effective. Although the three-dimensional flow structure involves much more complexities, the overall results are shown to be similar to the two-dimensional case.

Adjoint optimization of natural convection problems: differentially heated cavity

Science.gov (United States)

Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.

2017-12-01

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 for

An introduction to the self-adjointness and spectral analysis of Schroedinger operators

International Nuclear Information System (INIS)

Simon, B.

1977-01-01

The author first explains the basic results about self adjointness, from a point of view which emphasizes the connection with solvability of the Schroedinger equation. He then describes four methods that define self ajoint Hamiltonians, for most Schroedinger operators and discusses types of spectra, closing by considering the essential spectrum in the two body case. (P.D.)

The Adjoint Method for The Optimization of Brachytherapy and Radiotherapy Patient Treatment Planning Procedures Using Monte Carlo Calculations

International Nuclear Information System (INIS)

Henderson, D.L.; Yoo, S.; Kowalok, M.; Mackie, T.R.; Thomadsen, B.R.

2001-01-01

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-meter 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

LTSN solution of the adjoint neutron transport equation with arbitrary source for high order of quadrature in a homogeneous slab

International Nuclear Information System (INIS)

Goncalves, Glenio A.; Orengo, Gilberto; Vilhena, Marco Tullio M.B. de; Graca, Claudio O.

2002-01-01

In this work we present the LTS N solution of the adjoint transport equation for an arbitrary source, testing the aptness of this analytical solution for high order of quadrature in transport problems and comparing some preliminary results with the ANISN computations in a homogeneneous slab geometry. In order to do that we apply the new formulation for the LTS N method based on the invariance projection property, becoming possible to handle problems with arbitrary sources and demanding high order of quadrature or deep penetration. This new approach for the LTS N method is important both for direct and adjoint transport calculations and its development was inspired by the necessity of using generalized adjoint sources for important calculations. Although the mathematical convergence has been proved for an arbitrary source, when the quadrature order or deep penetration is required the LTS N method presents computational overflow even for simple sources (sin, cos, exp, polynomial). With the new formulation we eliminate this drawback and in this work we report the numerical simulations testing the new approach

Adjoint sensitivity analysis of the thermomechanical behavior of repositories

International Nuclear Information System (INIS)

Wilson, J.L.; Thompson, B.M.

1984-01-01

The adjoint sensitivity method is applied to thermomechanical models for the first time. The method provides an efficient and inexpensive answer to the question: how sensitive are thermomechanical predictions to assumed parameters. The answer is exact, in the sense that it yields exact derivatives of response measures to parameters, and approximate, in the sense that projections of the response fo other parameter assumptions are only first order correct. The method is applied to linear finite element models of thermomechanical behavior. Extensions to more complicated models are straight-forward but often laborious. An illustration of the method with a two-dimensional repository corridor model reveals that the chosen stress response measure was most sensitive to Poisson's ratio for the rock matrix

Estimating a planetary magnetic field with time-dependent global MHD simulations using an adjoint approach

Directory of Open Access Journals (Sweden)

C. Nabert

2017-05-01

Full Text Available 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.

Perturbation of self-adjoint operators by Dirac distributions

International Nuclear Information System (INIS)

Zorbas, J.

1980-01-01

The existence of a family of self-adjoint Hamiltonians H/sub theta/, theta element of [0, 2π), corresponding to the formal expression H 0 +νdelta (x) is shown for a general class of self-adjoint operators H 0 . Expressions for the Green's function and wavefunction corresponding to H/sub theta/ are obtained in terms of the Green's function and wavefunction corresponding to H 0 . Similar results are shown for the perturbation of H 0 by a finite sum of Dirac distributions. A prescription is given for obtaining H/sub theta/ as the strong resolvent limit of a family of momentum cutoff Hamiltonians H/sup N/. The relationship between the scattering theories corresponding to H/sup N/ and H/sub theta/ is examined

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

Science.gov (United States)

Mantile, Andrea; Posilicano, Andrea; Sini, Mourad

2016-07-01

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

Global adjoint tomography: first-generation model

KAUST Repository

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

Mimetic finite difference method

Science.gov (United States)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Relationship between different approaches to derive weighting functions related to atmospheric remote sensing problems

International Nuclear Information System (INIS)

Rozanov, Vladimir V.; Rozanov, Alexei V.

2007-01-01

The paper is devoted to the investigation of the relationship between different methods used to derive weighting functions required to solve numerous inverse problems related to the remote sensing of the Earth's atmosphere by means of scattered solar light observations. The first method commonly referred to as the forward-adjoint approach is based on a joint solution of the forward and adjoint radiative transfer equations and the second one requires the linearized forward radiative transfer equation to be solved. In the framework of the forward-adjoint method we consider two approaches commonly used to derive the weighting functions. These approaches are referenced as the 'response function' and the 'formal solution' techniques, respectively. We demonstrate here that the weighting functions derived employing the formal solution technique can also be obtained substituting the analytical representations for the direct forward and direct adjoint intensities into corresponding expressions obtained in the framework of the response function technique. The advantages and disadvantages of different techniques are discussed

The Adjoint Monte Carlo - a viable option for efficient radiotherapy treatment planning

Energy Technology Data Exchange (ETDEWEB)

Goldstein, M [Israel Atomic Energy Commission, Beersheba (Israel). Nuclear Research Center-Negev

1996-12-01

In cancer therapy using collimated beams of photons, the radiation oncologist must determine a set of beams that delivers the required dose to each point in the tumor and minimizes the risk of damage to the healthy tissue and vital organs. Currently, the oncologist determines these beams iteratively, by using a sequence of dose calculations using approximate numerical methods. In this paper, a more accurate and potentially faster approach, based on the Adjoint Monte Carlo method, is presented (authors).

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.

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...

NESTLE: Few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems

International Nuclear Information System (INIS)

Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.

1994-06-01

NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation

Methodology of Continuous-Energy Adjoint Monte Carlo for Neutron, Photon, and Coupled Neutron-Photon Transport

International Nuclear Information System (INIS)

Hoogenboom, J. Eduard

2003-01-01

Adjoint Monte Carlo may be a useful alternative to regular Monte Carlo calculations in cases where a small detector inhibits an efficient Monte Carlo calculation as only very few particle histories will cross the detector. However, in general purpose Monte Carlo codes, normally only the multigroup form of adjoint Monte Carlo is implemented. In this article the general methodology for continuous-energy adjoint Monte Carlo neutron transport is reviewed and extended for photon and coupled neutron-photon transport. In the latter cases the discrete photons generated by annihilation or by neutron capture or inelastic scattering prevent a direct application of the general methodology. Two successive reaction events must be combined in the selection process to accommodate the adjoint analog of a reaction resulting in a photon with a discrete energy. Numerical examples illustrate the application of the theory for some simplified problems

Objective-function Hybridization in Adjoint Seismic Tomography

Science.gov (United States)

Yuan, Y. O.; Bozdag, E.; Simons, F.; Gao, F.

2016-12-01

In the realm of seismic tomography, we are at the threshold of a new era of huge seismic datasets. However, how to assimilate as much information as possible from every seismogram is still a challenge. Cross-correlation measurements are generally tailored to some window selection algorithms, such as FLEXWIN (Maggie et al. 2008), to balance amplitude differences between seismic phases. However, these measurements naturally favor maximum picks in selected windows. It is also difficult to select all usable portions of seismograms in an optimum way that lots of information is generally lost, particularly the scattered waves. Instantaneous phase type of misfits extract information from every wiggle without cutting seismograms into small pieces, however, dealing with cycle skips at short periods can be challenging. For this purpose, we introduce a flexible hybrid approach for adjoint seismic tomography, to combine various objective functions. We initially focus on phase measurements and propose using instantaneous phase to take into account relatively small-magnitude scattered waves at long periods while using cross-correlation measurements on FLEXWIN windows to select distinct body-wave arrivals without complicating measurements due to non-linearities at short periods. To better deal with cycle skips and reliably measure instantaneous phases we design a new misfit function that incorporates instantaneous phase information implicitly instead of measuring it explicitly, through using normalized analytic signals. We present in our synthetic experiments how instantaneous phase, cross-correlation and their hybridization affect tomographic results. The combination of two different phase measurements in a hybrid approach constitutes progress towards using "anything and everything" in a data set, addressing data quality and measurement challenges simultaneously. We further extend hybridisation of misfit functions for amplitude measurements such as cross-correlation amplitude

Application of adjoint sensitivity theory to performance assessment of hydrogeologic concerns

International Nuclear Information System (INIS)

Metcalfe, D.E.; Harper, W.V.

1986-01-01

Sensitivity and uncertainty analyses are important components of performance assessment activities for potential high-level radioactive waste repositories. The application of the adjoint sensitivity technique is demonstrated for the Leadville Limestone in the Paradox Basin, Utah. The adjoint technique is used sequentially to first assist in the calibration of the regional conceptual ground-water flow model to measured potentiometric data. Second, it is used to evaluate the sensitivities of the calculated pressures used to define local scale boundary conditions to regional parameters and boundary conditions

Convergence problems associated with the iteration of adjoint equations in nuclear reactor theory

International Nuclear Information System (INIS)

Ngcobo, E.

2003-01-01

Convergence problems associated with the iteration of adjoint equations based on two-group neutron diffusion theory approximations in slab geometry are considered. For this purpose first-order variational techniques are adopted to minimise numerical errors involved. The importance of deriving the adjoint source from a breeding ratio is illustrated. The results obtained are consistent with the expected improvement in accuracy

Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

Science.gov (United States)

Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

2010-01-01

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

An Adjoint Sensitivity Method Applied to Time Reverse Imaging of Tsunami Source for the 2009 Samoa Earthquake

Science.gov (United States)

Hossen, M. Jakir; Gusman, Aditya; Satake, Kenji; Cummins, Phil R.

2018-01-01

We have previously developed a tsunami source inversion method based on "Time Reverse Imaging" and demonstrated that it is computationally very efficient and has the ability to reproduce the tsunami source model with good accuracy using tsunami data of the 2011 Tohoku earthquake tsunami. In this paper, we implemented this approach in the 2009 Samoa earthquake tsunami triggered by a doublet earthquake consisting of both normal and thrust faulting. Our result showed that the method is quite capable of recovering the source model associated with normal and thrust faulting. We found that the inversion result is highly sensitive to some stations that must be removed from the inversion. We applied an adjoint sensitivity method to find the optimal set of stations in order to estimate a realistic source model. We found that the inversion result is improved significantly once the optimal set of stations is used. In addition, from the reconstructed source model we estimated the slip distribution of the fault from which we successfully determined the dipping orientation of the fault plane for the normal fault earthquake. Our result suggests that the fault plane dip toward the northeast.

Adjoint shape optimization for fluid-structure interaction of ducted flows

Science.gov (United States)

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

2018-03-01

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

Exploring the use of a deterministic adjoint flux calculation in criticality Monte Carlo simulations

International Nuclear Information System (INIS)

Jinaphanh, A.; Miss, J.; Richet, Y.; Martin, N.; Hebert, A.

2011-01-01

The paper presents a preliminary study on the use of a deterministic adjoint flux calculation to improve source convergence issues by reducing the number of iterations needed to reach the converged distribution in criticality Monte Carlo calculations. Slow source convergence in Monte Carlo eigenvalue calculations may lead to underestimate the effective multiplication factor or reaction rates. The convergence speed depends on the initial distribution and the dominance ratio. We propose using an adjoint flux estimation to modify the transition kernel according to the Importance Sampling technique. This adjoint flux is also used as the initial guess of the first generation distribution for the Monte Carlo simulation. Calculated Variance of a local estimator of current is being checked. (author)

Oscillator representations for self-adjoint Calogero Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)

2011-10-21

In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

Oscillator representations for self-adjoint Calogero Hamiltonians

International Nuclear Information System (INIS)

Gitman, D M; Tyutin, I V; Voronov, B L

2011-01-01

In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

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

Science.gov (United States)

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

2017-09-01

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

System of adjoint P1 equations for neutron moderation; Sistema de equacoes P1 adjuntas para a moderacao de neutrons

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)

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.

Adaptive mesh refinement and adjoint methods in geophysics simulations

Science.gov (United States)

Burstedde, Carsten

2013-04-01

required by human intervention and analysis. Specifying an objective functional that quantifies the misfit between the simulation outcome and known constraints and then minimizing it through numerical optimization can serve as an automated technique for parameter identification. As suggested by the similarity in formulation, the numerical algorithm is closely related to the one used for goal-oriented error estimation. One common point is that the so-called adjoint equation needs to be solved numerically. We will outline the derivation and implementation of these methods and discuss some of their pros and cons, supported by numerical results.

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.

Visualising Earth's Mantle based on Global Adjoint Tomography

Science.gov (United States)

Bozdag, E.; Pugmire, D.; Lefebvre, M. P.; Hill, J.; Komatitsch, D.; Peter, D. B.; Podhorszki, N.; Tromp, J.

2017-12-01

Recent advances in 3D wave propagation solvers and high-performance computing have enabled regional and global full-waveform inversions. Interpretation of tomographic models is often done on visually. Robust and efficient visualization tools are necessary to thoroughly investigate large model files, particularly at the global scale. In collaboration with Oak Ridge National Laboratory (ORNL), we have developed effective visualization tools and used for visualization of our first-generation global model, GLAD-M15 (Bozdag et al. 2016). VisIt (https://wci.llnl.gov/simulation/computer-codes/visit/) is used for initial exploration of the models and for extraction of seismological features. The broad capability of VisIt, and its demonstrated scalability proved valuable for experimenting with different visualization techniques, and in the creation of timely results. Utilizing VisIt's plugin-architecture, a data reader plugin was developed, which reads the ADIOS (https://www.olcf.ornl.gov/center-projects/adios/) format of our model files. Blender (https://www.blender.org) is used for the setup of lighting, materials, camera paths and rendering of geometry. Python scripting was used to control the orchestration of different geometries, as well as camera animation for 3D movies. While we continue producing 3D contour plots and movies for various seismic parameters to better visualize plume- and slab-like features as well as anisotropy throughout the mantle, our aim is to make visualization an integral part of our global adjoint tomography workflow to routinely produce various 2D cross-sections to facilitate examination of our models after each iteration. This will ultimately form the basis for use of pattern recognition techniques in our investigations. Simulations for global adjoint tomography are performed on ORNL's Titan system and visualization is done in parallel on ORNL's post-processing cluster Rhea.

Nefness of adjoint bundles for ample vector bundles

Directory of Open Access Journals (Sweden)

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.

A greedy heuristic using adjoint functions for the optimization of seed and needle configurations in prostate seed implant

Energy Technology Data Exchange (ETDEWEB)

Yoo, Sua [Department of Radiation Oncology, Duke University Medical Center, Box 3295, Durham, NC 27710 (United States); Kowalok, Michael E [Department of Radiation Oncology, Virginia Commonwealth University Health System, 401 College St., PO Box 980058, Richmond, VA 23298-0058 (United States); Thomadsen, Bruce R [Department of Medical Physics, University of Wisconsin-Madison, 1530 MSC, 1300 University Ave., Madison, WI 53706 (United States); Henderson, Douglass L [Department of Engineering Physics, University of Wisconsin-Madison, 153 Engineering Research Bldg., 1500 Engineering Dr., Madison, WI 53706 (United States)

2007-02-07

We continue our work on the development of an efficient treatment-planning algorithm for prostate seed implants by incorporation of an automated seed and needle configuration routine. The treatment-planning algorithm is based on region of interest (ROI) adjoint functions and a greedy heuristic. As defined in this work, the adjoint function of an ROI is the sensitivity of the average dose in the ROI to a unit-strength brachytherapy source at any seed position. The greedy heuristic uses a ratio of target and critical structure adjoint functions to rank seed positions according to their ability to irradiate the target ROI while sparing critical structure ROIs. Because seed positions are ranked in advance and because the greedy heuristic does not modify previously selected seed positions, the greedy heuristic constructs a complete seed configuration quickly. Isodose surface constraints determine the search space and the needle constraint limits the number of needles. This study additionally includes a methodology that scans possible combinations of these constraint values automatically. This automated selection scheme saves the user the effort of manually searching constraint values. With this method, clinically acceptable treatment plans are obtained in less than 2 min. For comparison, the branch-and-bound method used to solve a mixed integer-programming model took close to 2.5 h to arrive at a feasible solution. Both methods achieved good treatment plans, but the speedup provided by the greedy heuristic was a factor of approximately 100. This attribute makes this algorithm suitable for intra-operative real-time treatment planning.

A greedy heuristic using adjoint functions for the optimization of seed and needle configurations in prostate seed implant

International Nuclear Information System (INIS)

Yoo, Sua; Kowalok, Michael E; Thomadsen, Bruce R; Henderson, Douglass L

2007-01-01

We continue our work on the development of an efficient treatment-planning algorithm for prostate seed implants by incorporation of an automated seed and needle configuration routine. The treatment-planning algorithm is based on region of interest (ROI) adjoint functions and a greedy heuristic. As defined in this work, the adjoint function of an ROI is the sensitivity of the average dose in the ROI to a unit-strength brachytherapy source at any seed position. The greedy heuristic uses a ratio of target and critical structure adjoint functions to rank seed positions according to their ability to irradiate the target ROI while sparing critical structure ROIs. Because seed positions are ranked in advance and because the greedy heuristic does not modify previously selected seed positions, the greedy heuristic constructs a complete seed configuration quickly. Isodose surface constraints determine the search space and the needle constraint limits the number of needles. This study additionally includes a methodology that scans possible combinations of these constraint values automatically. This automated selection scheme saves the user the effort of manually searching constraint values. With this method, clinically acceptable treatment plans are obtained in less than 2 min. For comparison, the branch-and-bound method used to solve a mixed integer-programming model took close to 2.5 h to arrive at a feasible solution. Both methods achieved good treatment plans, but the speedup provided by the greedy heuristic was a factor of approximately 100. This attribute makes this algorithm suitable for intra-operative real-time treatment planning

Application of the adjoint function methodology for neutron fluence determination

International Nuclear Information System (INIS)

Haghighat, A.; Nanayakkara, B.; Livingston, J.; Mahgerefteh, M.; Luoma, J.

1991-01-01

In previous studies, the neutron fluence at a reactor pressure vessel has been estimated based on consolidation of transport theory calculations and experimental data obtained from in-vessel capsules and/or cavity dosimeters. Normally, a forward neutron transport calculation is performed for each fuel cycle and the neutron fluxes are integrated over the reactor operating time to estimate the neutron fluence. Such calculations are performed for a geometrical model which is composed of one-eighth (0 to 45 deg) of the reactor core and its surroundings; i.e., core barrel, thermal shield, downcomer, reactor vessel, cavity region, concrete wall, and instrumentation well. Because the model is large, transport theory calculations generally require a significant amount of computer memory and time; hence, more efficient methodologies such as the adjoint transport approach have been proposed. These studies, however, do not address the necessary sensitivity studies needed for adjoint function calculations. The adjoint methodology has been employed to estimate the activity of a cavity dosimeter and that of an in-vessel capsule. A sensitivity study has been performed on the mesh distribution used in and around the cavity dosimeter and the in-vessel capsule. Further, since a major portion of the detector response is due to the neutrons originated in the peripheral fuel assemblies, a study on the use of a smaller calculational model has been performed

Adjoint-based Sensitivity of Jet Noise to Near-nozzle Forcing

Science.gov (United States)

Chung, Seung Whan; Vishnampet, Ramanathan; Bodony, Daniel; Freund, Jonathan

2017-11-01

Past efforts have used optimal control theory, based on the numerical solution of the adjoint flow equations, to perturb turbulent jets in order to reduce their radiated sound. These efforts have been successful in that sound is reduced, with concomitant changes to the large-scale turbulence structures in the flow. However, they have also been inconclusive, in that the ultimate level of reduction seemed to depend upon the accuracy of the adjoint-based gradient rather than a physical limitation of the flow. The chaotic dynamics of the turbulence can degrade the smoothness of cost functional in the control-parameter space, which is necessary for gradient-based optimization. We introduce a route to overcoming this challenge, in part by leveraging the regularity and accuracy with a dual-consistent, discrete-exact adjoint formulation. We confirm its properties and use it to study the sensitivity and controllability of the acoustic radiation from a simulation of a M = 1.3 turbulent jet, whose statistics matches data. The smoothness of the cost functional over time is quantified by a minimum optimization step size beyond which the gradient cannot have a certain degree of accuracy. Based on this, we achieve a moderate level of sound reduction in the first few optimization steps. This material is based [in part] upon work supported by the Department of Energy, National Nuclear Security Administration, under Award Number DE-NA0002374.

Adjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO2 sequestration in underground reservoirs

KAUST Repository

Simon, Moritz

2014-11-14

© 2014, Springer Science+Business Media New York. With the target of optimizing CO2 sequestration in underground reservoirs, we investigate constrained optimal control problems with partially miscible two-phase flow in porous media. Our objective is to maximize the amount of trapped CO2 in an underground reservoir after a fixed period of CO2 injection, while time-dependent injection rates in multiple wells are used as control parameters. We describe the governing two-phase two-component Darcy flow PDE system, formulate the optimal control problem and derive the continuous adjoint equations. For the discretization we apply a variant of the so-called BOX method, a locally conservative control-volume FE method that we further stabilize by a periodic averaging feature to reduce oscillations. The timestep-wise Lagrange function of the control problem is implemented as a variational form in Sundance, a toolbox for rapid development of parallel FE simulations, which is part of the HPC software Trilinos. We discuss the BOX method and our implementation in Sundance. The MPI parallelized Sundance state and adjoint solvers are linked to the interior point optimization package IPOPT, using limited-memory BFGS updates for approximating second derivatives. Finally, we present and discuss different types of optimal control results.

The sensitivity analysis by adjoint method for the uncertainty evaluation of the CATHARE-2 code

Energy Technology Data Exchange (ETDEWEB)

Barre, F.; de Crecy, A.; Perret, C. [French Atomic Energy Commission (CEA), Grenoble (France)

1995-09-01

This paper presents the application of the DASM (Discrete Adjoint Sensitivity Method) to CATHARE 2 thermal-hydraulics code. In a first part, the basis of this method is presented. The mathematical model of the CATHARE 2 code is based on the two fluid six equation model. It is discretized using implicit time discretization and it is relatively easy to implement this method in the code. The DASM is the ASM directly applied to the algebraic system of the discretized code equations which has been demonstrated to be the only solution of the mathematical model. The ASM is an integral part of the new version 1.4 of CATHARE. It acts as a post-processing module. It has been qualified by comparison with the {open_quotes}brute force{close_quotes} technique. In a second part, an application of the DASM in CATHARE 2 is presented. It deals with the determination of the uncertainties of the constitutive relationships, which is a compulsory step for calculating the final uncertainty of a given response. First, the general principles of the method are explained: the constitutive relationship are represented by several parameters and the aim is to calculate the variance-covariance matrix of these parameters. The experimental results of the separate effect tests used to establish the correlation are considered. The variance of the corresponding results calculated by CATHARE are estimated by comparing experiment and calculation. A DASM calculation is carried out to provide the derivatives of the responses. The final covariance matrix is obtained by combination of the variance of the responses and those derivatives. Then, the application of this method to a simple case-the blowdown Canon experiment-is presented. This application has been successfully performed.

The sensitivity analysis by adjoint method for the uncertainty evaluation of the CATHARE-2 code

International Nuclear Information System (INIS)

Barre, F.; de Crecy, A.; Perret, C.

1995-01-01

This paper presents the application of the DASM (Discrete Adjoint Sensitivity Method) to CATHARE 2 thermal-hydraulics code. In a first part, the basis of this method is presented. The mathematical model of the CATHARE 2 code is based on the two fluid six equation model. It is discretized using implicit time discretization and it is relatively easy to implement this method in the code. The DASM is the ASM directly applied to the algebraic system of the discretized code equations which has been demonstrated to be the only solution of the mathematical model. The ASM is an integral part of the new version 1.4 of CATHARE. It acts as a post-processing module. It has been qualified by comparison with the open-quotes brute forceclose quotes technique. In a second part, an application of the DASM in CATHARE 2 is presented. It deals with the determination of the uncertainties of the constitutive relationships, which is a compulsory step for calculating the final uncertainty of a given response. First, the general principles of the method are explained: the constitutive relationship are represented by several parameters and the aim is to calculate the variance-covariance matrix of these parameters. The experimental results of the separate effect tests used to establish the correlation are considered. The variance of the corresponding results calculated by CATHARE are estimated by comparing experiment and calculation. A DASM calculation is carried out to provide the derivatives of the responses. The final covariance matrix is obtained by combination of the variance of the responses and those derivatives. Then, the application of this method to a simple case-the blowdown Canon experiment-is presented. This application has been successfully performed

Adjoint-state inversion of electric resistivity tomography data of seawater intrusion at the Argentona coastal aquifer (Spain)

Science.gov (United States)

Fernández-López, Sheila; Carrera, Jesús; Ledo, Juanjo; Queralt, Pilar; Luquot, Linda; Martínez, Laura; Bellmunt, Fabián

2016-04-01

Seawater intrusion in aquifers is a complex phenomenon that can be characterized with the help of electric resistivity tomography (ERT) because of the low resistivity of seawater, which underlies the freshwater floating on top. The problem is complex because of the need for joint inversion of electrical and hydraulic (density dependent flow) data. Here we present an adjoint-state algorithm to treat electrical data. This method is a common technique to obtain derivatives of an objective function, depending on potentials with respect to model parameters. The main advantages of it are its simplicity in stationary problems and the reduction of computational cost respect others methodologies. The relationship between the concentration of chlorides and the resistivity values of the field is well known. Also, these resistivities are related to the values of potentials measured using ERT. Taking this into account, it will be possible to define the different resistivities zones from the field data of potential distribution using the basis of inverse problem. In this case, the studied zone is situated in Argentona (Baix Maresme, Catalonia), where the values of chlorides obtained in some wells of the zone are too high. The adjoint-state method will be used to invert the measured data using a new finite element code in C ++ language developed in an open-source framework called Kratos. Finally, the information obtained numerically with our code will be checked with the information obtained with other codes.

Comparison of three different methods of perturbing the potential vorticity field in mesoscale forecasts of Mediterranean heavy precipitation events: PV-gradient, PV-adjoint and PV-satellite

Science.gov (United States)

Vich, M.; Romero, R.; Richard, E.; Arbogast, P.; Maynard, K.

2010-09-01

Heavy precipitation events occur regularly in the western Mediterranean region. These events often have a high impact on the society due to economic and personal losses. The improvement of the mesoscale numerical forecasts of these events can be used to prevent or minimize their impact on the society. In previous studies, two ensemble prediction systems (EPSs) based on perturbing the model initial and boundary conditions were developed and tested for a collection of high-impact MEDEX cyclonic episodes. These EPSs perturb the initial and boundary potential vorticity (PV) field through a PV inversion algorithm. This technique ensures modifications of all the meteorological fields without compromising the mass-wind balance. One EPS introduces the perturbations along the zones of the three-dimensional PV structure presenting the local most intense values and gradients of the field (a semi-objective choice, PV-gradient), while the other perturbs the PV field over the MM5 adjoint model calculated sensitivity zones (an objective method, PV-adjoint). The PV perturbations are set from a PV error climatology (PVEC) that characterizes typical PV errors in the ECMWF forecasts, both in intensity and displacement. This intensity and displacement perturbation of the PV field is chosen randomly, while its location is given by the perturbation zones defined in each ensemble generation method. Encouraged by the good results obtained by these two EPSs that perturb the PV field, a new approach based on a manual perturbation of the PV field has been tested and compared with the previous results. This technique uses the satellite water vapor (WV) observations to guide the correction of initial PV structures. The correction of the PV field intents to improve the match between the PV distribution and the WV image, taking advantage of the relation between dark and bright features of WV images and PV anomalies, under some assumptions. Afterwards, the PV inversion algorithm is applied to run

[Purifying process of gynostemma pentaphyllum saponins based on "adjoint marker" online control technology and identification of their compositions by UPLC-QTOF-MS].

Science.gov (United States)

Fan, Dong-Dong; Kuang, Yan-Hui; Dong, Li-Hua; Ye, Xiao; Chen, Liang-Mian; Zhang, Dong; Ma, Zhen-Shan; Wang, Jin-Yu; Zhu, Jing-Jing; Wang, Zhi-Min; Wang, De-Qin; Li, Chu-Yuan

2017-04-01

To optimize the purification process of gynostemma pentaphyllum saponins (GPS) based on "adjoint marker" online control technology with GPS as the testing index. UPLC-QTOF-MS technology was used for qualitative analysis. "Adjoint marker" online control results showed that the end point of load sample was that the UV absorbance of effluent liquid was equal to half of that of load sample solution, and the absorbance was basically stable when the end point was stable. In UPLC-QTOF-MS qualitative analysis, 16 saponins were identified from GPS, including 13 known gynostemma saponins and 3 new saponins. This optimized method was proved to be simple, scientific, reasonable, easy for online determination, real-time record, and can be better applied to the mass production and automation of production. The results of qualitative analysis indicated that the "adjoint marker" online control technology can well retain main efficacy components of medicinal materials, and provide analysis tools for the process control and quality traceability. Copyright© by the Chinese Pharmaceutical Association.

Manipulating Rayleigh-Taylor Growth Using Adjoints

Science.gov (United States)

Kord, Ali; Capecelatro, Jesse

2017-11-01

It has been observed that initial interfacial perturbations affect the growth of Rayleigh-Taylor (RT) instabilities. However, it remains to be seen to what extent the perturbations alter the RT growth rate. Direct numerical simulations (DNS) provide a powerful means for studying the effects of initial conditions (IC) on the growth rate. However, a brute-force approach for identifying optimal initial perturbations is not practical via DNS. In addition, identifying sensitivity of the RT growth to the large number of parameters used in defining the IC is computationally expensive. A discrete adjoint is formulated to measure sensitivities of multi-mode RT growth to ICs in a high-order finite difference framework. The sensitivity is used as a search direction for adjusting the initial perturbations to both maximize and suppress the RT growth rate during its non-linear regime. The modes that contribute the greatest sensitivity are identified, and optimized perturbation energy spectrum are reported. PhD Student, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI.

Mass anomalous dimension of Adjoint QCD at large N from twisted volume reduction

CERN Document Server

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.

Mass anomalous dimension of adjoint QCD at large N from twisted volume reduction

Energy Technology Data Exchange (ETDEWEB)

Pérez, Margarita García [Instituto de Física Teórica UAM-CSIC, Nicolás Cabrera 13-15, Universidad Autónoma de Madrid,E-28049-Madrid (Spain); González-Arroyo, Antonio [Instituto de Física Teórica UAM-CSIC, Nicolás Cabrera 13-15, Universidad Autónoma de Madrid,E-28049-Madrid (Spain); Departamento de Física Teórica, C-XI, Universidad Autónoma de Madrid,E-28049-Madrid (Spain); Keegan, Liam [PH-TH, CERN,CH-1211 Geneva 23 (Switzerland); Okawa, Masanori [Graduate School of Science, Hiroshima University,Higashi-Hiroshima, Hiroshima 739-8526 (Japan); Core of Research for the Energetic Universe, Hiroshima University,Higashi-Hiroshima, Hiroshima 739-8526 (Japan)

2015-08-07

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.

Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: A new approach with the adjoint method

KAUST Repository

Cagnetti, Filippo; Gomes, Diogo A.; Tran, Hung Vinh

2013-01-01

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.

Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: A new approach with the adjoint method

KAUST Repository

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.

Fugitive emission source characterization using a gradient-based optimization scheme and scalar transport adjoint

Science.gov (United States)

Brereton, Carol A.; Joynes, Ian M.; Campbell, Lucy J.; Johnson, Matthew R.

2018-05-01

Fugitive emissions are important sources of greenhouse gases and lost product in the energy sector that can be difficult to detect, but are often easily mitigated once they are known, located, and quantified. In this paper, a scalar transport adjoint-based optimization method is presented to locate and quantify unknown emission sources from downstream measurements. This emission characterization approach correctly predicted locations to within 5 m and magnitudes to within 13% of experimental release data from Project Prairie Grass. The method was further demonstrated on simulated simultaneous releases in a complex 3-D geometry based on an Alberta gas plant. Reconstructions were performed using both the complex 3-D transient wind field used to generate the simulated release data and using a sequential series of steady-state RANS wind simulations (SSWS) representing 30 s intervals of physical time. Both the detailed transient and the simplified wind field series could be used to correctly locate major sources and predict their emission rates within 10%, while predicting total emission rates from all sources within 24%. This SSWS case would be much easier to implement in a real-world application, and gives rise to the possibility of developing pre-computed databases of both wind and scalar transport adjoints to reduce computational time.

Comparison of the Adjoint and Adjoint-Free 4dVar Assimilation of the Hydrographic and Velocity Observations in the Adriatic Sea

Science.gov (United States)

2015-11-10

approach is the ab- sence of the necessity to develop and maintain tangent linear and adjoint codes and its flexibility in adaptation to various...uadratic term in the right hand side of (B.10) is negligible. In the re- orted experiments we kept it in place since the value of ε was close o 0.01 and

Adjoint tomography of the crust and upper mantle structure beneath the Kanto region using broadband seismograms

KAUST Repository

Miyoshi, Takayuki; Obayashi, Masayuki; Peter, Daniel; Tono, Yoko; Tsuboi, Seiji

2017-01-01

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.

Adjoint tomography of the crust and upper mantle structure beneath the Kanto region using broadband seismograms

KAUST Repository

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.

Improved forward wave propagation and adjoint-based sensitivity kernel calculations using a numerically stable finite-element PML

DEFF Research Database (Denmark)

Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland

2014-01-01

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......In recent years, the application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint elastic wave propagation problems. An important challenge is to design...... convolution formulation of the complex-frequency-shifted unsplit-field perfectly matched layer (CFS-UPML) derived in previous work more flexible by providing a new treatment to analytically remove singular parameters in the formulation. We also extend this new formulation to 3-D. Furthermore, we derive...

An eddy-permitting, dynamically consistent adjoint-based assimilation system for the tropical Pacific: Hindcast experiments in 2000

KAUST Repository

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.

Four-fermi anomalous dimension with adjoint fermions

CERN Document Server

Del Debbio, Luigi; Ruano, Carlos Pena

2014-01-01

The four-fermi interaction can play an important role in models of strong dynamical EW sym- metry breaking if the anomalous dimensions of the four-fermi operators become large in the IR. We discuss a number of issues that are relevant for the nonperturbative computation of the four- fermi anomalous dimensions for the SU(2) gauge theory with two flavors of Dirac fermions in the adjoint representation, using a Schrödinger functional formalism.

Numerical study of dense adjoint 2-color matter

International Nuclear Information System (INIS)

Hands, S.; Scorzato, L.; Oevers, M.

2000-11-01

We study the global symmetries of SU(2) gauge theory with N flavors of staggered fermions in the presence of a chemical potential. We motivate the special interest of the case N=1 (staggered) with fermions in the adjoint representation of the gauge group. We present results from numerical simulations with both hybrid Monte Carlo and the two-step multi-bosonic algorithm. (orig.)

Elementary operators on self-adjoint operators

Science.gov (United States)

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, .

Validation of a new midway forward-adjoint coupling option in MCNP

Energy Technology Data Exchange (ETDEWEB)

Serov, I.V.; John, T.M.; Hoogenboom, J.E. [Technische Univ. Delft (Netherlands). Interfacultair Reactor Inst.

1996-09-01

The new midway Monte Carlo is based on the coupling of scores from a forward and an adjoint Monte Carlo calculation on a surface in between the source and the detector. The method is implemented in MCNP. The utilization of the method is fairly straight-forward and does not require any substantial expertise. The midway Monte Carlo method was tested against the gamma-ray skyshine MCNP benchmark problem. This problem involves deep penetration and streaming along complicated paths. The midway method supplied results, which agree with the results of the reference calculation within the limits of the estimated statistical uncertainties. The efficiency of the easy-to-implement midway calculation is higher than the efficiency of the reference calculation which is already optimized by use of an importance function. The midway method proves to be efficient in problems with complicated streaming paths towards small detectors. (author)

Validation of a new midway forward-adjoint coupling option in MCNP

International Nuclear Information System (INIS)

Serov, I.V.; John, T.M.; Hoogenboom, J.E.

1996-01-01

The new midway Monte Carlo is based on the coupling of scores from a forward and an adjoint Monte Carlo calculation on a surface in between the source and the detector. The method is implemented in MCNP. The utilization of the method is fairly straight-forward and does not require any substantial expertise. The midway Monte Carlo method was tested against the gamma-ray skyshine MCNP benchmark problem. This problem involves deep penetration and streaming along complicated paths. The midway method supplied results, which agree with the results of the reference calculation within the limits of the estimated statistical uncertainties. The efficiency of the easy-to-implement midway calculation is higher than the efficiency of the reference calculation which is already optimized by use of an importance function. The midway method proves to be efficient in problems with complicated streaming paths towards small detectors. (author)

Efficient Adjoint Computation of Hybrid Systems of Differential Algebraic Equations with Applications in Power Systems

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.

An optimal control method for fluid structure interaction systems via adjoint boundary pressure

Science.gov (United States)

Chirco, L.; Da Vià, R.; Manservisi, S.

2017-11-01

In recent year, in spite of the computational complexity, Fluid-structure interaction (FSI) problems have been widely studied due to their applicability in science and engineering. Fluid-structure interaction systems consist of one or more solid structures that deform by interacting with a surrounding fluid flow. FSI simulations evaluate the tensional state of the mechanical component and take into account the effects of the solid deformations on the motion of the interior fluids. The inverse FSI problem can be described as the achievement of a certain objective by changing some design parameters such as forces, boundary conditions and geometrical domain shapes. In this paper we would like to study the inverse FSI problem by using an optimal control approach. In particular we propose a pressure boundary optimal control method based on Lagrangian multipliers and adjoint variables. The objective is the minimization of a solid domain displacement matching functional obtained by finding the optimal pressure on the inlet boundary. The optimality system is derived from the first order necessary conditions by taking the Fréchet derivatives of the Lagrangian with respect to all the variables involved. The optimal solution is then obtained through a standard steepest descent algorithm applied to the optimality system. The approach presented in this work is general and could be used to assess other objective functionals and controls. In order to support the proposed approach we perform a few numerical tests where the fluid pressure on the domain inlet controls the displacement that occurs in a well defined region of the solid domain.

Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"

Science.gov (United States)

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...

Spectral Solutions of Self-adjoint Elliptic Problems with Immersed Interfaces

International Nuclear Information System (INIS)

Auchmuty, G.; Klouček, P.

2011-01-01

This paper describes a spectral representation of solutions of self-adjoint elliptic problems with immersed interfaces. The interface is assumed to be a simple non-self-intersecting closed curve that obeys some weak regularity conditions. The problem is decomposed into two problems, one with zero interface data and the other with zero exterior boundary data. The problem with zero interface data is solved by standard spectral methods. The problem with non-zero interface data is solved by introducing an interface space H Γ (Ω) and constructing an orthonormal basis of this space. This basis is constructed using a special class of orthogonal eigenfunctions analogously to the methods used for standard trace spaces by Auchmuty (SIAM J. Math. Anal. 38, 894–915, 2006). Analytical and numerical approximations of these eigenfunctions are described and some simulations are presented.

Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity

Science.gov (United States)

Li, Dunzhu; Gurnis, Michael; Stadler, Georg

2017-04-01

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-dependent 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 pre-conditioned 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.

BPS Center Vortices in Nonrelativistic SU(N) Gauge Models with Adjoint Higgs Fields

International Nuclear Information System (INIS)

Oxman, L. E.

2015-01-01

We propose a class of SU(N) Yang-Mills models, with adjoint Higgs fields, that accept BPS center vortex equations. The lack of a local magnetic flux that could serve as an energy bound is circumvented by including a new term in the energy functional. This term tends to align, in the Lie algebra, the magnetic field and one of the adjoint Higgs fields. Finally, a reduced set of equations for the center vortex profile functions is obtained (for N=2,3). In particular, Z(3) BPS vortices come in three colours and three anticolours, obtained from an ansatz based on the defining representation and its conjugate.

ADGEN: An automated adjoint code generator for large-scale sensitivity analysis

International Nuclear Information System (INIS)

Pin, F.G.; Oblow, E.M.; Horwedel, J.E.; Lucius, J.L.

1987-01-01

This paper describes a new automated system, named ADGEN, which makes use of the strengths of computer calculus to automate the costly and time-consuming calculation of derivatives in FORTRAN computer codes, and automatically generate adjoint solutions of computer codes

ORIGINAL ARTICLE Sixth Order Stable Central Difference Method ...

African Journals Online (AJOL)

for solving self-adjoint singularly perturbed two-point boundary value problems. ... semiconductor devices, diffraction theory, .... y x is continuously differentiable in the interval [0 1] and applying ...... known as boundary layer, is observed at the.

Surface spectra of Weyl semimetals through self-adjoint extensions

Science.gov (United States)

Seradjeh, Babak; Vennettilli, Michael

2018-02-01

We apply the method of self-adjoint extensions of Hermitian operators to the low-energy, continuum Hamiltonians of Weyl semimetals in bounded geometries and derive the spectrum of the surface states on the boundary. This allows for the full characterization of boundary conditions and the surface spectra on surfaces both normal to the Weyl node separation as well as parallel to it. We show that the boundary conditions for quadratic bulk dispersions are, in general, specified by a U (2 ) matrix relating the wave function and its derivatives normal to the surface. We give a general procedure to obtain the surface spectra from these boundary conditions and derive them in specific cases of bulk dispersion. We consider the role of global symmetries in the boundary conditions and their effect on the surface spectrum. We point out several interesting features of the surface spectra for different choices of boundary conditions, such as a Mexican-hat shaped dispersion on the surface normal to Weyl node separation. We find that the existence of bound states, Fermi arcs, and the shape of their dispersion, depend on the choice of boundary conditions. This illustrates the importance of the physics at and near the boundaries in the general statement of bulk-boundary correspondence.

Application of perturbation methods and sensitivity analysis to water hammer problems in hydraulic networks

International Nuclear Information System (INIS)

Balino, Jorge L.; Larreteguy, Axel E.; Andrade Lima, Fernando R.

1995-01-01

The differential method was applied to the sensitivity analysis for water hammer problems in hydraulic networks. Starting from the classical water hammer equations in a single-phase liquid with friction, the state vector comprising the piezometric head and the velocity was defined. Applying the differential method the adjoint operator, the adjoint equations with the general form of their boundary conditions, and the general form of the bilinear concomitant were calculated. The discretized adjoint equations and the corresponding boundary conditions were programmed and solved by using the so called method of characteristics. As an example, a constant-level tank connected through a pipe to a valve discharging to atmosphere was considered. The bilinear concomitant was calculated for this particular case. The corresponding sensitivity coefficients due to the variation of different parameters by using both the differential method and the response surface generated by the computer code WHAT were also calculated. The results obtained with these methods show excellent agreement. (author). 11 refs, 2 figs, 2 tabs

Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems

KAUST Repository

Asner, Liya; Tavener, Simon; Kay, David

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.

Factorization of the 3d superconformal index with an adjoint matter

Energy Technology Data Exchange (ETDEWEB)

Hwang, Chiung [Department of Physics, POSTECH,Pohang 790-784 (Korea, Republic of); Park, Jaemo [Department of Physics, POSTECH,Pohang 790-784 (Korea, Republic of); Postech Center for Theoretical Physics (PCTP), POSTECH,Pohang 790-784 (Korea, Republic of)

2015-11-05

We work out the factorization of the 3d superconformal index for N=2U(N{sub c}) gauge theory with one adjoint chiral multiplet as well as N{sub f} fundamental, N{sub a} anti-fundamental chiral multiplets. Using the factorization, one can prove the Seiberg-like duality for N=4U(N{sub c}) theory with N{sub f} hypermultiplets at the index level. We explicitly show that monopole operators violating unitarity bound in a bad theory are mapped to free hypermultiplets in the dual side. For N=2U(N{sub c}) theory with one adjoint matter X, N{sub f} fundamental, N{sub a} anti-fundamental chiral multiplets with superpotential W=trX{sup n+1}, we work out Seiberg-like duality for this theory. The index computation provides combinatorial identities for a dual pair, which we carry out intensive numerical checks.

Self-adjoint Hamiltonians with a mass jump: General matching conditions

International Nuclear Information System (INIS)

Gadella, M.; Kuru, S.; Negro, J.

2007-01-01

The simplest position-dependent mass Hamiltonian in one dimension, where the mass has the form of a step function with a jump discontinuity at one point, is considered. The most general matching conditions at the jumping point for the solutions of the Schroedinger equation that provide a self-adjoint Hamiltonian are characterized

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

KAUST Repository

Komatitsch, Dimitri; Xie, Zhinan; Bozdağ, Ebru; de Andrade, Elliott Sales; Peter, Daniel; 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 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.

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

KAUST Repository

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.

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

Science.gov (United States)

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.

Self-adjointness and spectral properties of Dirac operators with magnetic links

DEFF Research Database (Denmark)

Portmann, Fabian; Sok, Jérémy; Solovej, Jan Philip

2018-01-01

We define Dirac operators on $\\mathbb{S}^3$ (and $\\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among other things, that these operators have discrete spectrum...

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

Science.gov (United States)

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

2015-12-01

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

Four-loop vacuum energy density of the SU(Nc) + adjoint Higgs theory

International Nuclear Information System (INIS)

Kajantie, K.; Rummukainen, K.; Schroder, Y.; Laine, M.

2003-01-01

We compute the dimensionally regularised four-loop vacuum energy density of the SU(N c ) gauge + adjoint Higgs theory, in the disordered phase. 'Scalarisation', or reduction to a small set of master integrals of the type appearing in scalar field theories, is carried out in d dimensions, employing general partial integration identities through an algorithm developed by Laporta, while the remaining scalar integrals are evaluated in d=3-2ε dimensions, by expanding in ε 6 ln(1/g)), O(g 6 ) to the pressure, while the general methods are applicable also to studies of critical phenomena in QED-like statistical physics systems. (author)

Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

International Nuclear Information System (INIS)

Liscum-Powell, J.L.; Lorence, L.J. Jr.; Morel, J.E.; Prinja, A.K.

1999-01-01

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere and, like the even- and odd- parity form, S n source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here we apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross-sections from the CEPXS code and S n discretization

Self-adjoint angular flux equation for coupled electron-photon transport

International Nuclear Information System (INIS)

Liscum-Powell, J.L.; Prinja, A.K.; Morel, J.E.; Lorence, L.J. Jr.

1999-01-01

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self-adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere, and, like the even- and odd-parity form, S n source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here, the authors apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross sections from the CEPXS code and S n discretization

Practical adjoint Monte Carlo technique for fixed-source and eigenfunction neutron transport problems

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1981-01-01

An adjoint Monte Carlo technique is described for the solution of neutron transport problems. The optimum biasing function for a zero-variance collision estimator is derived. The optimum treatment of an analog of a non-velocity thermal group has also been derived. The method is extended to multiplying systems, especially for eigenfunction problems to enable the estimate of averages over the unknown fundamental neutron flux distribution. A versatile computer code, FOCUS, has been written, based on the described theory. Numerical examples are given for a shielding problem and a critical assembly, illustrating the performance of the FOCUS code. 19 refs

Deterministic calculation of the effective delayed neutron fraction without using the adjoint neutron flux - 299

International Nuclear Information System (INIS)

Talamo, A.; Gohar, Y.; Aliberti, G.; Zhong, Z.; Bournos, V.; Fokov, Y.; Kiyavitskaya, H.; Routkovskaya, C.; Serafimovich, I.

2010-01-01

In 1997, Bretscher calculated the effective delayed neutron fraction by the k-ratio method. The Bretscher's approach is based on calculating the multiplication factor of a nuclear reactor core with and without the contribution of delayed neutrons. The multiplication factor set by the delayed neutrons (the delayed multiplication factor) is obtained as the difference between the total and the prompt multiplication factors. Bretscher evaluated the effective delayed neutron fraction as the ratio between the delayed and total multiplication factors (therefore the method is often referred to as k-ratio method). In the present work, the k-ratio method is applied by deterministic nuclear codes. The ENDF/B nuclear data library of the fuel isotopes ( 238 U and 238 U) have been processed by the NJOY code with and without the delayed neutron data to prepare multigroup WIMSD nuclear data libraries for the DRAGON code. The DRAGON code has been used for preparing the PARTISN macroscopic cross sections. This calculation methodology has been applied to the YALINA-Thermal assembly of Belarus. The assembly has been modeled and analyzed using PARTISN code with 69 energy groups and 60 different material zones. The deterministic and Monte Carlo results for the effective delayed neutron fraction obtained by the k-ratio method agree very well. The results also agree with the values obtained by using the adjoint flux. (authors)

Running coupling in SU(2) gauge theory with two adjoint fermions

DEFF Research Database (Denmark)

Rantaharju, Jarno; Rantalaiho, Teemu; Rummukainen, Kari

2016-01-01

We study SU(2) gauge theory with two Dirac fermions in the adjoint representation of the gauge group on the lattice. Using clover improved Wilson fermion action with hypercubic truncated stout smearing we perform simulations at larger coupling than before. We measure the evolution of the coupling...... with the existence of a fixed point in the interval 2.2g∗23. We also measure the anomalous dimension and find that its value at the fixed point is γ∗≃0.2±0.03....... constant using the step scaling method with the Schrödinger functional and study the remaining discretization effects. At weak coupling we observe significant discretization effects, which make it difficult to obtain a fully controlled continuum limit. Nevertheless, the data remains consistent...

q-structure algebra of Uq(g-circumflex) from its adjoint action

International Nuclear Information System (INIS)

El Hassouni, A.; Hassouni, Y.; Zakkari, M.

1994-08-01

We prove that the adjoint action of the quantum affine Lie algebra U q (g-circumflex), where g is a simple finite dimensional Lie algebra, reproduces the q-commutation relationship of U q (g-circumflex) if and only if g is of type A n , n ≥ 1. (author). 4 refs

Adjoint Inversion for Extended Earthquake Source Kinematics From Very Dense Strong Motion Data

Science.gov (United States)

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

Asynchronous Two-Level Checkpointing Scheme for Large-Scale Adjoints in the Spectral-Element Solver Nek5000

Energy Technology Data Exchange (ETDEWEB)

Schanen, Michel; Marin, Oana; Zhang, Hong; Anitescu, Mihai

2016-01-01

Adjoints are an important computational tool for large-scale sensitivity evaluation, uncertainty quantification, and derivative-based optimization. An essential component of their performance is the storage/recomputation balance in which efficient checkpointing methods play a key role. We introduce a novel asynchronous two-level adjoint checkpointing scheme for multistep numerical time discretizations targeted at large-scale numerical simulations. The checkpointing scheme combines bandwidth-limited disk checkpointing and binomial memory checkpointing. Based on assumptions about the target petascale systems, which we later demonstrate to be realistic on the IBM Blue Gene/Q system Mira, we create a model of the expected performance of our checkpointing approach and validate it using the highly scalable Navier-Stokes spectralelement solver Nek5000 on small to moderate subsystems of the Mira supercomputer. In turn, this allows us to predict optimal algorithmic choices when using all of Mira. We also demonstrate that two-level checkpointing is significantly superior to single-level checkpointing when adjoining a large number of time integration steps. To our knowledge, this is the first time two-level checkpointing had been designed, implemented, tuned, and demonstrated on fluid dynamics codes at large scale of 50k+ cores.

Gradient-type methods in inverse parabolic problems

International Nuclear Information System (INIS)

Kabanikhin, Sergey; Penenko, Aleksey

2008-01-01

This article is devoted to gradient-based methods for inverse parabolic problems. In the first part, we present a priori convergence theorems based on the conditional stability estimates for linear inverse problems. These theorems are applied to backwards parabolic problem and sideways parabolic problem. The convergence conditions obtained coincide with sourcewise representability in the self-adjoint backwards parabolic case but they differ in the sideways case. In the second part, a variational approach is formulated for a coefficient identification problem. Using adjoint equations, a formal gradient of an objective functional is constructed. A numerical test illustrates the performance of conjugate gradient algorithm with the formal gradient.

Numerical study of dense adjoint matter in two color QCD

International Nuclear Information System (INIS)

Hands, S.; Morrison, S.; Scorzato, L.; Oevers, M.

2000-06-01

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential μ, for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N=1 adjoint flavor on a 4 3 x 8 lattice are presented, using both hybrid Monte Carlo and two-step multi-boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for N≥2. The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N=1. (orig.)

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

Science.gov (United States)

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

2015-04-01

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

Forward and adjoint sensitivity computation of chaotic dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Wang, Qiqi, E-mail: qiqi@mit.edu [Department of Aeronautics and Astronautics, MIT, 77 Mass Ave., Cambridge, MA 02139 (United States)

2013-02-15

This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.

State estimates and forecasts of the loop current in the Gulf of Mexico using the MITgcm and its adjoint

KAUST Repository

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.

State estimates and forecasts of the loop current in the Gulf of Mexico using the MITgcm and its adjoint

KAUST Repository

Gopalakrishnan, Ganesh; Cornuelle, Bruce D.; Hoteit, Ibrahim; Rudnick, Daniel L.; Owens, W. Brechner

2013-01-01

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.

Absence of singular continuous spectrum for certain self-adjoint operators

International Nuclear Information System (INIS)

Mourre, E.

1979-01-01

An adequate condition is given for a self-adjoint operator to show in the vinicity of a point E of its spectrum the following properties: its point spectrum is of finite size; its singular continuous spectrum is empty. In the way of new applications the absence of singular continuous spectrum is demonstrated in the following two cases: perturbations of pseudo-differential operators; Schroedinger operators of a three-body system [fr

Adjoint de programme régional (h/f) | CRDI - Centre de recherches ...

International Development Research Centre (IDRC) Digital Library (Canada)

L'adjoint de programme doit établir les priorités parmi les multiples ... sur un système de contrôle, en établissant l'ordre prioritaire afin de respecter les ... Au besoin, aider les agents de gestion de programme à entretenir et à mettre à jour les ...

Two linearization methods for atmospheric remote sensing

International Nuclear Information System (INIS)

Doicu, A.; Trautmann, T.

2009-01-01

We present two linearization methods for a pseudo-spherical atmosphere and general viewing geometries. The first approach is based on an analytical linearization of the discrete ordinate method with matrix exponential and incorporates two models for matrix exponential calculation: the matrix eigenvalue method and the Pade approximation. The second method referred to as the forward-adjoint approach is based on the adjoint radiative transfer for a pseudo-spherical atmosphere. We provide a compact description of the proposed methods as well as a numerical analysis of their accuracy and efficiency.

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

International Nuclear Information System (INIS)

Finn, John M.

2015-01-01

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (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

Monte Carlo methods for the reliability analysis of Markov systems

International Nuclear Information System (INIS)

Buslik, A.J.

1985-01-01

This paper presents Monte Carlo methods for the reliability analysis of Markov systems. Markov models are useful in treating dependencies between components. The present paper shows how the adjoint Monte Carlo method for the continuous time Markov process can be derived from the method for the discrete-time Markov process by a limiting process. The straightforward extensions to the treatment of mean unavailability (over a time interval) are given. System unavailabilities can also be estimated; this is done by making the system failed states absorbing, and not permitting repair from them. A forward Monte Carlo method is presented in which the weighting functions are related to the adjoint function. In particular, if the exact adjoint function is known then weighting factors can be constructed such that the exact answer can be obtained with a single Monte Carlo trial. Of course, if the exact adjoint function is known, there is no need to perform the Monte Carlo calculation. However, the formulation is useful since it gives insight into choices of the weight factors which will reduce the variance of the estimator

Objective function choice for control of a thermocapillary flow using an adjoint-based control strategy

International Nuclear Information System (INIS)

Muldoon, Frank H.; Kuhlmann, Hendrik C.

2015-01-01

Highlights: • Suppression of oscillations in a thermocapillary flow is addressed by optimization. • The gradient of the objective function is obtained by solving the adjoint equations. • The issue of choosing an objective function is investigated. - Abstract: The problem of suppressing flow oscillations in a thermocapillary flow is addressed using a gradient-based control strategy. The physical problem addressed is the “open boat” process of crystal growth, the flow in which is driven by thermocapillary and buoyancy effects. The problem is modeled by the two-dimensional unsteady incompressible Navier–Stokes and energy equations under the Boussinesq approximation. The goal of the control is to suppress flow oscillations which arise when the driving forces are such that the flow becomes unsteady. The control is a spatially and temporally varying temperature gradient boundary condition at the free surface. The control which minimizes the flow oscillations is found using a conjugate gradient method, where the gradient of the objective function with respect to the control variables is obtained from solving a set of adjoint equations. The issue of choosing an objective function that can be both optimized in a computationally efficient manner and optimization of which provides control that damps the flow oscillations is investigated. Almost complete suppression of the flow oscillations is obtained for certain choices of the objective function.

A symmetrized quasi-diffusion method for solving multidimensional transport problems

International Nuclear Information System (INIS)

Miften, M.M.; Larsen, E.W.

1992-01-01

In this paper, the authors propose a 'symmetrized' QD (SQD) method in which the non-self-adjoint QD diffusion problem is replaced by two self-adjoint diffusion problems. These problems are more easily discretized and more efficiently solved than in the standard QD method. They also give SQD calculational results for transport problems in x-y geometry

Fully automatic time-window selection using machine learning for global adjoint tomography

Science.gov (United States)

Chen, Y.; Hill, J.; Lei, W.; Lefebvre, M. P.; Bozdag, E.; Komatitsch, D.; Tromp, J.

2017-12-01

Selecting time windows from seismograms such that the synthetic measurements (from simulations) and measured observations are sufficiently close is indispensable in a global adjoint tomography framework. The increasing amount of seismic data collected everyday around the world demands "intelligent" algorithms for seismic window selection. While the traditional FLEXWIN algorithm can be "automatic" to some extent, it still requires both human input and human knowledge or experience, and thus is not deemed to be fully automatic. The goal of intelligent window selection is to automatically select windows based on a learnt engine that is built upon a huge number of existing windows generated through the adjoint tomography project. We have formulated the automatic window selection problem as a classification problem. All possible misfit calculation windows are classified as either usable or unusable. Given a large number of windows with a known selection mode (select or not select), we train a neural network to predict the selection mode of an arbitrary input window. Currently, the five features we extract from the windows are its cross-correlation value, cross-correlation time lag, amplitude ratio between observed and synthetic data, window length, and minimum STA/LTA value. More features can be included in the future. We use these features to characterize each window for training a multilayer perceptron neural network (MPNN). Training the MPNN is equivalent to solve a non-linear optimization problem. We use backward propagation to derive the gradient of the loss function with respect to the weighting matrices and bias vectors and use the mini-batch stochastic gradient method to iteratively optimize the MPNN. Numerical tests show that with a careful selection of the training data and a sufficient amount of training data, we are able to train a robust neural network that is capable of detecting the waveforms in an arbitrary earthquake data with negligible detection error

Application of perturbation theory to lattice calculations based on method of cyclic characteristics

Science.gov (United States)

Assawaroongruengchot, Monchai

Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the

Application of perturbation theory to lattice calculations based on method of cyclic characteristics

Energy Technology Data Exchange (ETDEWEB)

Assawaroongruengchot, M

2007-07-01

Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the

Application of perturbation theory to lattice calculations based on method of cyclic characteristics

International Nuclear Information System (INIS)

Assawaroongruengchot, M.

2007-01-01

Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the

Studying the properties of Variational Data Assimilation Methods by Applying a Set of Test-Examples

DEFF Research Database (Denmark)

Thomsen, Per Grove; Zlatev, Zahari

2007-01-01

and backward computations are carried out by using the model under consideration and its adjoint equations (both the model and its adjoint are defined by systems of differential equations). The major difficulty is caused by the huge increase of the computational load (normally by a factor more than 100...... assimilation method (numerical algorithms for solving differential equations, splitting procedures and optimization algorithms) have been studied by using these tests. The presentation will include results from testing carried out in the study.......he variational data assimilation methods can successfully be used in different fields of science and engineering. An attempt to utilize available sets of observations in the efforts to improve (i) the models used to study different phenomena (ii) the model results is systematically carried out when...

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

Science.gov (United States)

Xu, Xiao-Chuan; Yang, Chuan-Fu

2018-06-01

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

Data and Workflow Management Challenges in Global Adjoint Tomography

Science.gov (United States)

Lei, W.; Ruan, Y.; Smith, J. A.; Modrak, R. T.; Orsvuran, R.; Krischer, L.; Chen, Y.; Balasubramanian, V.; Hill, J.; Turilli, M.; Bozdag, E.; Lefebvre, M. P.; Jha, S.; Tromp, J.

2017-12-01

It is crucial to take the complete physics of wave propagation into account in seismic tomography to further improve the resolution of tomographic images. The adjoint method is an efficient way of incorporating 3D wave simulations in seismic tomography. However, global adjoint tomography is computationally expensive, requiring thousands of wavefield simulations and massive data processing. Through our collaboration with the Oak Ridge National Laboratory (ORNL) computing group and an allocation on Titan, ORNL's GPU-accelerated supercomputer, we are now performing our global inversions by assimilating waveform data from over 1,000 earthquakes. The first challenge we encountered is dealing with the sheer amount of seismic data. Data processing based on conventional data formats and processing tools (such as SAC), which are not designed for parallel systems, becomes our major bottleneck. To facilitate the data processing procedures, we designed the Adaptive Seismic Data Format (ASDF) and developed a set of Python-based processing tools to replace legacy FORTRAN-based software. These tools greatly enhance reproducibility and accountability while taking full advantage of highly parallel system and showing superior scaling on modern computational platforms. The second challenge is that the data processing workflow contains more than 10 sub-procedures, making it delicate to handle and prone to human mistakes. To reduce human intervention as much as possible, we are developing a framework specifically designed for seismic inversion based on the state-of-the art workflow management research, specifically the Ensemble Toolkit (EnTK), in collaboration with the RADICAL team from Rutgers University. Using the initial developments of the EnTK, we are able to utilize the full computing power of the data processing cluster RHEA at ORNL while keeping human interaction to a minimum and greatly reducing the data processing time. Thanks to all the improvements, we are now able to

Least-Squares PN Formulation of the Transport Equation Using Self-Adjoint-Angular-Flux Consistent Boundary Conditions

Energy Technology Data Exchange (ETDEWEB)

Laboure, Vincent M.; Wang, Yaqi; DeHart, Mark D.

2016-05-01

In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids [1] 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 [2], 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 [3] 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.

Least-Squares PN Formulation of the Transport Equation Using Self-Adjoint-Angular-Flux Consistent Boundary Conditions.

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.

Eguchi-Kawai reduction with one flavor of adjoint Moebius fermion

OpenAIRE

Cunningham, William; Giedt, Joel

2013-01-01

We study the single site lattice gauge theory of SU(N) coupled to one Dirac flavor of fermion in the adjoint representation. We utilize M\\"obius fermions for this study, and accelerate the calculation with graphics processing units (GPUs). Our Monte Carlo simulations indicate that for sufficiently large inverse 't Hooft coupling b = 1/g^2 N, and for N \\leq 10 the distribution of traced Polyakov loops has "fingers" that extend from the origin. However, in the massless case the distribution of ...

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

Science.gov (United States)

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.

Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions

Czech Academy of Sciences Publication Activity Database

Siegl, Petr; Štampach, F.

2017-01-01

Roč. 11, č. 4 (2017), s. 901-928 ISSN 1846-3886 Grant - others:GA ČR(CZ) GA13-11058S Institutional support: RVO:61389005 Keywords : Non-self-adjoint Jacobi operator * Weyl m-function * Jacobian elliptic functions Subject RIV: BE - Theoretical Physics OBOR OECD: Pure mathematics Impact factor: 0.440, year: 2016

An approach to computing discrete adjoints for MPI-parallelized models applied to Ice Sheet System Model 4.11

Directory of Open Access Journals (Sweden)

E. Larour

2016-11-01

Full Text Available 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.

Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws

International Nuclear Information System (INIS)

Ibragimov, N Kh; Avdonina, E D

2013-01-01

The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions. Bibliography: 23 titles

Green's matrix for a second-order self-adjoint matrix differential operator

International Nuclear Information System (INIS)

Sisman, Tahsin Cagri; Tekin, Bayram

2010-01-01

A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.

Non-analogue Monte Carlo method, application to neutron simulation; Methode de Monte Carlo non analogue, application a la simulation des neutrons

Energy Technology Data Exchange (ETDEWEB)

Morillon, B.

1996-12-31

With most of the traditional and contemporary techniques, it is still impossible to solve the transport equation if one takes into account a fully detailed geometry and if one studies precisely the interactions between particles and matters. Only the Monte Carlo method offers such a possibility. However with significant attenuation, the natural simulation remains inefficient: it becomes necessary to use biasing techniques where the solution of the adjoint transport equation is essential. The Monte Carlo code Tripoli has been using such techniques successfully for a long time with different approximate adjoint solutions: these methods require from the user to find out some parameters. If this parameters are not optimal or nearly optimal, the biases simulations may bring about small figures of merit. This paper presents a description of the most important biasing techniques of the Monte Carlo code Tripoli ; then we show how to calculate the importance function for general geometry with multigroup cases. We present a completely automatic biasing technique where the parameters of the biased simulation are deduced from the solution of the adjoint transport equation calculated by collision probabilities. In this study we shall estimate the importance function through collision probabilities method and we shall evaluate its possibilities thanks to a Monte Carlo calculation. We compare different biased simulations with the importance function calculated by collision probabilities for one-group and multigroup problems. We have run simulations with new biasing method for one-group transport problems with isotropic shocks and for multigroup problems with anisotropic shocks. The results show that for the one-group and homogeneous geometry transport problems the method is quite optimal without splitting and russian roulette technique but for the multigroup and heterogeneous X-Y geometry ones the figures of merit are higher if we add splitting and russian roulette technique.

Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems : Method Development for Multi-Physics in Reactors

NARCIS (Netherlands)

Perkó, Z.

2015-01-01

This thesis presents novel adjoint and spectral methods for the sensitivity and uncertainty (S&U) analysis of multi-physics problems encountered in the field of reactor physics. The first part focuses on the steady state of reactors and extends the adjoint sensitivity analysis methods well

Gradient-based methods for production optimization of oil reservoirs

Energy Technology Data Exchange (ETDEWEB)

Suwartadi, Eka

2012-07-01

Production optimization for water flooding in the secondary phase of oil recovery is the main topic in this thesis. The emphasis has been on numerical optimization algorithms, tested on case examples using simple hypothetical oil reservoirs. Gradientbased optimization, which utilizes adjoint-based gradient computation, is used to solve the optimization problems. The first contribution of this thesis is to address output constraint problems. These kinds of constraints are natural in production optimization. Limiting total water production and water cut at producer wells are examples of such constraints. To maintain the feasibility of an optimization solution, a Lagrangian barrier method is proposed to handle the output constraints. This method incorporates the output constraints into the objective function, thus avoiding additional computations for the constraints gradient (Jacobian) which may be detrimental to the efficiency of the adjoint method. The second contribution is the study of the use of second-order adjoint-gradient information for production optimization. In order to speedup convergence rate in the optimization, one usually uses quasi-Newton approaches such as BFGS and SR1 methods. These methods compute an approximation of the inverse of the Hessian matrix given the first-order gradient from the adjoint method. The methods may not give significant speedup if the Hessian is ill-conditioned. We have developed and implemented the Hessian matrix computation using the adjoint method. Due to high computational cost of the Newton method itself, we instead compute the Hessian-timesvector product which is used in a conjugate gradient algorithm. Finally, the last contribution of this thesis is on surrogate optimization for water flooding in the presence of the output constraints. Two kinds of model order reduction techniques are applied to build surrogate models. These are proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM

Four-loop vacuum energy density of the SU($N_c$) + adjoint Higgs theory

CERN Document Server

Kajantie, Keijo; Rummukainen, K; Schröder, Y

2003-01-01

We compute the dimensionally regularised four-loop vacuum energy density of the SU(N_c) gauge + adjoint Higgs theory, in the disordered phase. ``Scalarisation'', or reduction to a small set of master integrals of the type appearing in scalar field theories, is carried out in d dimensions, employing general partial integration identities through an algorithm developed by Laporta, while the remaining scalar integrals are evaluated in d = 3 - 2\\epsilon dimensions, by expanding in \\epsilon << 1 and evaluating a number of coefficients. The results have implications for the thermodynamics of finite temperature QCD, allowing to determine perturbative contributions of orders O(g^6 ln(1/g)), O(g^6) to the pressure, while the general methods are applicable also to studies of critical phenomena in QED-like statistical physics systems.

Detection of critical PM2.5 emission sources and their contributions to a heavy haze episode in Beijing, China, using an adjoint model

Science.gov (United States)

Zhai, Shixian; An, Xingqin; Zhao, Tianliang; Sun, Zhaobin; Wang, Wei; Hou, Qing; Guo, Zengyuan; Wang, Chao

2018-05-01

sensitivity simulations of the Models-3/CMAQ system. The two modeling approaches are highly comparable in their assessments of atmospheric pollution control schemes for critical emission regions, but the adjoint method has higher computational efficiency than the forward sensitivity method. The results also imply that critical regional emission reduction could be more efficient than individual peak emission control for improving regional PM2.5 air quality.

Application of adjoint sensitivity analysis to nuclear reactor fuel rod performance

International Nuclear Information System (INIS)

Wilderman, S.J.; Was, G.S.

1984-01-01

Adjoint sensitivity analysis in nuclear fuel behavior modeling is extended to operate on the entire power history for both Zircaloy and stainless steel cladding via the computer codes FCODE-ALPHA/SS and SCODE/SS. The sensitivities of key variables to input parameters are found to be highly non-intuitive and strongly dependent on the fuel-clad gap status and the history of the fuel during the cycle. The sensitivities of five key variables, clad circumferential stress and strain, fission gas release, fuel centerline temperature and fuel-clad gap, to eleven input parameters are studied. The most important input parameters (yielding significances between 1 and 100) are fabricated clad inner and outer radii and fuel radius. The least important significances (less than 0.01) are the time since reactor start-up and fuel-burnup densification rate. Intermediate to these are fabricated fuel porosity, linear heat generation rate, the power history scale factor, clad outer temperature, fill gas pressure and coolant pressure. Stainless steel and Zircaloy have similar sensitivities at start-up but these diverges a burnup proceeds due to the effect of the higher creep rate of Zircaloy which causes the system to be more responsive to changes in input parameters. The value of adjoint sensitivity analysis lies in its capability of uncovering dependencies of fuel variables on input parameters that cannot be determined by a sequential thought process. (orig.)

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.

Generalized perturbation theory based on the method of cyclic characteristics

Energy Technology Data Exchange (ETDEWEB)

Assawaroongruengchot, M.; Marleau, G. [Institut de Genie Nucleaire, Departement de Genie Physique, Ecole Polytechnique de Montreal, 2900 Boul. Edouard-Montpetit, Montreal, Que. H3T 1J4 (Canada)

2006-07-01

A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)

Generalized perturbation theory based on the method of cyclic characteristics

International Nuclear Information System (INIS)

Assawaroongruengchot, M.; Marleau, G.

2006-01-01

A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)

Adjoint-based model predictive control of wind farms : Beyond the quasi steady-state power maximization

NARCIS (Netherlands)

Vali, M.; Petrović, Vlaho; Boersma, S.; van Wingerden, J.W.; Kuhn, Martin; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri

2017-01-01

In this paper, we extend our closed-loop optimal control framework for wind farms to minimize wake-induced power losses. We develop an adjoint-based model predictive controller which employs a medium-fidelity 2D dynamic wind farm model. The wind turbine axial induction factors are considered here

An adjoint-based scheme for eigenvalue error improvement

International Nuclear Information System (INIS)

Merton, S.R.; Smedley-Stevenson, R.P.; Pain, C.C.; El-Sheikh, A.H.; Buchan, A.G.

2011-01-01

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)

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

International Nuclear Information System (INIS)

Shadid, J.N.; Smith, T.M.; Cyr, E.C.; Wildey, T.M.; Pawlowski, R.P.

2016-01-01

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.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

Energy Technology Data Exchange (ETDEWEB)

Shadid, J.N., E-mail: jnshadi@sandia.gov [Sandia National Laboratories, Computational Mathematics Department (United States); Department of Mathematics and Statistics, University of New Mexico (United States); Smith, T.M. [Sandia National Laboratories, Multiphysics Applications Department (United States); Cyr, E.C. [Sandia National Laboratories, Computational Mathematics Department (United States); Wildey, T.M. [Sandia National Laboratories, Optimization and UQ Department (United States); Pawlowski, R.P. [Sandia National Laboratories, Multiphysics Applications Department (United States)

2016-09-15

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.

Application of the variational method for calculation of neutron spectra and group constants - Master thesis

International Nuclear Information System (INIS)

Milosevic, M.

1979-01-01

One-dimensional variational method for cylindrical configuration was applied for calculating group constants, together with effects of elastic slowing down, anisotropic elastic scattering, inelastic scattering, heterogeneous resonance absorption with the aim to include the presence of a number of different isotopes and effects of neutron leakage from the reactor core. Neutron flux shape P 3 and adjoint function are proposed in order to enable calculation of smaller size reactors and inclusion of heterogeneity effects by cell calculations. Microscopic multigroup constants were prepared based on the UKNDL data library. Analytical-numerical approach was applied for solving the equations of the P 3 approximation to obtain neutron flux moments and adjoint functions

A fast finite-difference algorithm for topology optimization of permanent magnets

Science.gov (United States)

Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter

2017-09-01

We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.

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

Science.gov (United States)

Mottelet, Stephane; Gaullier, Gil; Sadaka, Georges

2017-01-01

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

Automated variance reduction of Monte Carlo shielding calculations using the discrete ordinates adjoint function

International Nuclear Information System (INIS)

Wagner, J.C.; Haghighat, A.

1998-01-01

Although the Monte Carlo method is considered to be the most accurate method available for solving radiation transport problems, its applicability is limited by its computational expense. Thus, biasing techniques, which require intuition, guesswork, and iterations involving manual adjustments, are employed to make reactor shielding calculations feasible. To overcome this difficulty, the authors have developed a method for using the S N adjoint function for automated variance reduction of Monte Carlo calculations through source biasing and consistent transport biasing with the weight window technique. They describe the implementation of this method into the standard production Monte Carlo code MCNP and its application to a realistic calculation, namely, the reactor cavity dosimetry calculation. The computational effectiveness of the method, as demonstrated through the increase in calculational efficiency, is demonstrated and quantified. Important issues associated with this method and its efficient use are addressed and analyzed. Additional benefits in terms of the reduction in time and effort required of the user are difficult to quantify but are possibly as important as the computational efficiency. In general, the automated variance reduction method presented is capable of increases in computational performance on the order of thousands, while at the same time significantly reducing the current requirements for user experience, time, and effort. Therefore, this method can substantially increase the applicability and reliability of Monte Carlo for large, real-world shielding applications

Application of Wielandt method in continuous-energy nuclear data sensitivity analysis with RMC code

International Nuclear Information System (INIS)

Qiu Yishu; Wang Kan; She Ding

2015-01-01

The Iterated Fission Probability (IFP) method, an accurate method to estimate adjoint-weighted quantities in the continuous-energy Monte Carlo criticality calculations, has been widely used for calculating kinetic parameters and nuclear data sensitivity coefficients. By using a strategy of waiting, however, this method faces the challenge of high memory usage to store the tallies of original contributions which size is proportional to the number of particle histories in each cycle. Recently, the Wielandt method, applied by Monte Carlo code McCARD to calculate kinetic parameters, estimates adjoint fluxes in a single particle history and thus can save memory usage. In this work, the Wielandt method has been applied in Rector Monte Carlo code RMC for nuclear data sensitivity analysis. The methodology and algorithm of applying Wielandt method in estimation of adjoint-based sensitivity coefficients are discussed. Verification is performed by comparing the sensitivity coefficients calculated by Wielandt method with analytical solutions, those computed by IFP method which is also implemented in RMC code for sensitivity analysis, and those from the multi-group TSUNAMI-3D module in SCALE code package. (author)

Topology optimization and lattice Boltzmann methods

DEFF Research Database (Denmark)

Nørgaard, Sebastian Arlund

This thesis demonstrates the application of the lattice Boltzmann method for topology optimization problems. Specifically, the focus is on problems in which time-dependent flow dynamics have significant impact on the performance of the devices to be optimized. The thesis introduces new topology...... a discrete adjoint approach. To handle the complexity of the discrete adjoint approach more easily, a method for computing it based on automatic differentiation is introduced, which can be adapted to any lattice Boltzmann type method. For example, while it is derived in the context of an isothermal lattice...... Boltzmann model, it is shown that the method can be easily extended to a thermal model as well. Finally, the predicted behavior of an optimized design is compared to the equiva-lent prediction from a commercial finite element solver. It is found that the weakly compressible nature of the lattice Boltzmann...

Analyticity spaces of self-adjoint operators subjected to perturbations with applications to Hankel invariant distribution spaces

NARCIS (Netherlands)

Eijndhoven, van S.J.L.; Graaf, de J.

1986-01-01

A new theory of generalized functions has been developed by one of the authors (de Graaf). In this theory the analyticity domain of each positive self-adjoint unbounded operator $\\mathcal{A}$ in a Hilbert space $X$ is regarded as a test space denoted by $\\mathcal{S}_{x,\\mathcal{A}} $. In the first

Gradient flow coupling in the SU(2) gauge theory with two adjoint fermions

DEFF Research Database (Denmark)

Rantaharju, Jarno

2016-01-01

We study SU(2) gauge theory with two fermion flavors in the adjoint representation. Using a clover improved HEX smeared action and the gradient flow running coupling allows us to simulate with larger lattice size than before. We find an infrared fixed point after a continuum extrapolation in the ...... in the range 4.3g∗24.8. We also measure the mass anomalous dimension and find the value 0.25γ∗0.28 at the fixed point....

Review and comparison of effective delayed neutron fraction calculation methods with Monte Carlo codes

International Nuclear Information System (INIS)

Bécares, V.; Pérez-Martín, S.; Vázquez-Antolín, M.; Villamarín, D.; Martín-Fuertes, F.; González-Romero, E.M.; Merino, I.

2014-01-01

Highlights: • Review of several Monte Carlo effective delayed neutron fraction calculation methods. • These methods have been implemented with the Monte Carlo code MCNPX. • They have been benchmarked against against some critical and subcritical systems. • Several nuclear data libraries have been used. - Abstract: The calculation of the effective delayed neutron fraction, β eff , with Monte Carlo codes is a complex task due to the requirement of properly considering the adjoint weighting of delayed neutrons. Nevertheless, several techniques have been proposed to circumvent this difficulty and obtain accurate Monte Carlo results for β eff without the need of explicitly determining the adjoint flux. In this paper, we make a review of some of these techniques; namely we have analyzed two variants of what we call the k-eigenvalue technique and other techniques based on different interpretations of the physical meaning of the adjoint weighting. To test the validity of all these techniques we have implemented them with the MCNPX code and we have benchmarked them against a range of critical and subcritical systems for which either experimental or deterministic values of β eff are available. Furthermore, several nuclear data libraries have been used in order to assess the impact of the uncertainty in nuclear data in the calculated value of β eff

On the discrete spectrum of non-self-adjoint Schroedinger differential equation with an operator coefficient

International Nuclear Information System (INIS)

Bayramoglu, Mehmet; Tasci, Fatih; Zeynalov, Djafar

2004-01-01

We study the discrete part of spectrum of a singular non-self-adjoint second-order differential equation on a semiaxis with an operator coefficient. Its boundedness is proved. The result is applied to the Schroedinger boundary value problem -Δu+q(x)u=λ 2 u, u vertical bar ∂D =0, with a complex potential q(x) in an angular domain

Full Waveform Adjoint Seismic Tomography of the Antarctic Plate

Science.gov (United States)

Lloyd, A. J.; Wiens, D.; Zhu, H.; Tromp, J.; Nyblade, A.; Anandakrishnan, S.; Aster, R. C.; Huerta, A. D.; Winberry, J. P.; Wilson, T. J.; Dalziel, I. W. D.; Hansen, S. E.; Shore, P.

2017-12-01

Recent studies investigating the response and influence of the solid Earth on the evolution of the cryosphere demonstrate the need to account for 3D rheological structure to better predict ice sheet dynamics, stability, and future sea level impact, as well as to improve glacial isostatic adjustment models and more accurately measure ice mass loss. Critical rheological properties like mantle viscosity and lithospheric thickness may be estimated from shear wave velocity models that, for Antarctica, would ideally possess regional-scale resolution extending down to at least the base of the transition zone (i.e. 670 km depth). However, current global- and continental-scale seismic velocity models are unable to obtain both the resolution and spatial coverage necessary, do not take advantage of the full set of available Antarctic data, and, in most instance, employ traditional seismic imaging techniques that utilize limited seismogram information. We utilize 3-component earthquake waveforms from almost 300 Antarctic broadband seismic stations and 26 southern mid-latitude stations from 270 earthquakes (5.5 ≤ Mw ≤ 7.0) between 2001-2003 and 2007-2016 to conduct a full-waveform adjoint inversion for Antarctica and surrounding regions of the Antarctic plate. Necessary forward and adjoint wavefield simulations are performed utilizing SPECFEM3D_GLOBE with the aid of the Texas Advanced Computing Center. We utilize phase observations from seismogram segments containing P, S, Rayleigh, and Love waves, including reflections and overtones, which are autonomously identified using FLEXWIN. The FLEXWIN analysis is carried out over a short (15-50 s) and long (initially 50-150 s) period band that target body waves, or body and surface waves, respectively. As our model is iteratively refined, the short-period corner of the long period band is gradually reduced to 25 s as the model converges over 20 linearized inversion iterations. We will briefly present this new high

Big Data Challenges in Global Seismic 'Adjoint Tomography' (Invited)

Science.gov (United States)

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

Determination of the potential for fundamental- and adjoint-representation sources in SU(2) in three dimensions

International Nuclear Information System (INIS)

Mawhinney, R.D.

1990-01-01

Pure SU(2) lattice gauge theory in three dimensions is studied by Monte Carlo simulation with a determination of the potential between fundamental- and adjoint-representation sources as a major goal. A 32 3 lattice is used and Wilson loops up to 16 by 16 are measured using a modification to the standard multihit variance reduction which improves the statistics by at least a factor of 3 at β=6.0. The integrated autocorrelation times measured for the loops show a peak for loops of size β by β. The fundamental- and adjoint-representation potentials are seen to have the same functional form to very high accuracy and their numerical values are in the ratio of their Casimir operators. The string tension is extracted and scaling is seen to within a few percent over a range of couplings which correspond to a factor of 2 change in the glueball mass. Correlated errors have been taken into account in the extraction of the potentials from the Wilson-loop values

A non-self-adjoint quadratic eigenvalue problem describing a fluid-solid interaction Part II : analysis of convergence

NARCIS (Netherlands)

Bourne, D.P.; Elman, H.; Osborn, J.E.

2009-01-01

This paper is the second part of a two-part paper treating a non-self-adjoint quadratic eigenvalue problem for the linear stability of solutions to the Taylor-Couette problem for flow of a viscous liquid in a deformable cylinder, with the cylinder modelled as a membrane. The first part formulated

Electron cyclotron current drive predictions for ITER: Comparison of different models

International Nuclear Information System (INIS)

Marushchenko, N.B.; Maassberg, H.; Beidler, C.D.; Turkin, Yu.

2007-01-01

Full text: Due to its high localization and operational flexibility, Electron Cyclotron Current Drive (ECCD) is envisaged for stabilizing the Neoclassical Tearing Mode (NTM) in tokamaks and correcting the rotational transform profile in stellarators. While the spatial location of the electron cyclotron resonant interaction is usually calculated by the ray-tracing technique, numerical tools for calculating the ECCD efficiency are not so common. Two different methods are often applied: i) direct calculation by Fokker-Planck modelling, and ii) by the adjoint approach technique. In the present report we analyze and compare different models used in the adjoint approach technique from the point of view of ITER applications. The numerical tools for calculating the ECCD efficiency developed to date do not completely cover the range of collisional regimes for the electrons involved in the current drive. Only two opposite limits are well developed, collisional and collisionless. Nevertheless, for the densities and temperatures expected for ECCD application in ITER, the collisionless limit model (with trapped particles taken into account) is quite suitable. We analyze the requisite ECCD scenarios with help of the new ray tracing code TRAVIS with the adjoint approach implemented. The (adjoint) Green's function applied for the current drive calculations is formulated with momentum conservation taken into account; this is especially important and even crucial for scenarios, in which mainly bulk electrons are responsible for absorption of the RF power. For comparison, the most common 'high speed limit' model in which the collision operator neglects the integral part and which is approximated by terms valid only for the tail electrons, produces an ECCD efficiency which is an underestimate for some cases by a factor of about 2. In order to select the appropriate model, a rough criterion of 'high speed limit' model applicability is formulated. The results are verified also by

Improvement of basal conditions knowledge in Antarctica using data assimilation methods

Science.gov (United States)

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

2017-12-01

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

Spectral multipliers on spaces of distributions associated with non-negative self-adjoint operators

DEFF Research Database (Denmark)

Georgiadis, Athanasios; Nielsen, Morten

2018-01-01

and Triebel–Lizorkin spaces with full range of indices is established too. As an application, we obtain equivalent norm characterizations for the spaces mentioned above. Non-classical spaces as well as Lebesgue, Hardy, (generalized) Sobolev and Lipschitz spaces are also covered by our approach.......We consider spaces of homogeneous type associated with a non-negative self-adjoint operator whose heat kernel satisfies certain upper Gaussian bounds. Spectral multipliers are introduced and studied on distributions associated with this operator. The boundedness of spectral multipliers on Besov...

Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

International Nuclear Information System (INIS)

Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.

2007-01-01

We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R 3

Tracking a Severe Pollution Event in Beijing in December 2016 with the GRAPES-CUACE Adjoint Model

Science.gov (United States)

Wang, Chao; An, Xingqin; Zhai, Shixian; Sun, Zhaobin

2018-02-01

We traced the adjoint sensitivity of a severe pollution event in December 2016 in Beijing using the adjoint model of the GRAPES-CUACE (Global/Regional Assimilation and Prediction System coupled with the China Meteorological Administration Unified Atmospheric Chemistry Environmental Forecasting System). The key emission sources and periods affecting this severe pollution event are analyzed. For comaprison, we define 2000 Beijing Time 3 December 2016 as the objective time when PM2.5 reached the maximum concentration in Beijing. It is found that the local hourly sensitivity coefficient amounts to a peak of 9.31 μg m-3 just 1 h before the objective time, suggesting that PM2.5 concentration responds rapidly to local emissions. The accumulated sensitivity coefficient in Beijing is large during the 20-h period prior to the objective time, showing that local emissions are the most important in this period. The accumulated contribution rates of emissions from Beijing, Tianjin, Hebei, and Shanxi are 34.2%, 3.0%, 49.4%, and 13.4%, respectively, in the 72-h period before the objective time. The evolution of hourly sensitivity coefficient shows that the main contribution from the Tianjin source occurs 1-26 h before the objective time and its peak hourly contribution is 0.59 μg m-3 at 4 h before the objective time. The main contributions of the Hebei and Shanxi emission sources occur 1-54 and 14-53 h, respectively, before the objective time and their hourly sensitivity coefficients both show periodic fluctuations. The Hebei source shows three sensitivity coefficient peaks of 3.45, 4.27, and 0.71 μg m-3 at 4, 16, and 38 h before the objective time, respectively. The sensitivity coefficient of the Shanxi source peaks twice, with values of 1.41 and 0.64 μg m-3 at 24 and 45 h before the objective time, respectively. Overall, the adjoint model is effective in tracking the crucial sources and key periods of emissions for the severe pollution event.

One-loop adjoint masses for non-supersymmetric intersecting branes

Energy Technology Data Exchange (ETDEWEB)

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.)

A hybrid method for the computation of quasi-3D seismograms.

Science.gov (United States)

Masson, Yder; Romanowicz, Barbara

2013-04-01

Green's functions are computed using 2D SEM simulation in a 1D Earth model. Such seismograms account for the 3D structure inside the region of interest in a quasi-exact manner. Later we plan to extrapolate the misfit function computed from such seismograms at the stations back into the SEM region in order to compute local adjoint kernels. This opens a new path toward regional adjoint tomography into the deep Earth. Capdeville, Y., et al. (2002). "Coupling the spectral element method with a modal solution for elastic wave propagation in global Earth models." Geophysical Journal International 152(1): 34-67. Lekic, V. and B. Romanowicz (2011). "Inferring upper-mantle structure by full waveform tomography with the spectral element method." Geophysical Journal International 185(2): 799-831. Nissen-Meyer, T., et al. (2007). "A two-dimensional spectral-element method for computing spherical-earth seismograms-I. Moment-tensor source." Geophysical Journal International 168(3): 1067-1092. Robertsson, J. O. A. and C. H. Chapman (2000). "An efficient method for calculating finite-difference seismograms after model alterations." Geophysics 65(3): 907-918. Tape, C., et al. (2009). "Adjoint tomography of the southern California crust." Science 325(5943): 988-992.

Optimisation of production from an oil-reservoir using augmented Lagrangian methods

Energy Technology Data Exchange (ETDEWEB)

Doublet, Daniel Christopher

2007-07-01

This work studies the use of augmented Lagrangian methods for water flooding production optimisation from an oil reservoir. Commonly, water flooding is used as a means to enhance oil recovery, and due to heterogeneous rock properties, water will flow with different velocities throughout the reservoir. Due to this, water breakthrough can occur when great regions of the reservoir are still unflooded so that much of the oil may become 'trapped' in the reservoir. To avoid or reduce this problem, one can control the production so that the oil recovery rate is maximised, or alternatively the net present value (NPV) of the reservoir is maximised. We have considered water flooding, using smart wells. Smart wells with down-hole valves gives us the possibility to control the injection/production at each of the valve openings along the well, so that it is possible to control the flowregime. One can control the injection/production at all valve openings, and the setting of the valves may be changed during the production period, which gives us a great deal of control over the production and we want to control the injection/ production so that the profit obtained from the reservoir is maximised. The problem is regarded as an optimal control problem, and it is formulated as an augmented Lagrangian saddle point problem. We develop a method for optimal control based on solving the Karush-Kuhn-Tucker conditions for the augmented Lagrangian functional, a method, which to my knowledge has not been presented in the literature before. The advantage of this method is that we do not need to solve the forward problem for each new estimate of the control variables, which reduces the computational effort compared to other methods that requires the solution of the forward problem every time we find a new estimate of the control variables, such as the adjoint method. We test this method on several examples, where it is compared to the adjoint method. Our numerical experiments show

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

Science.gov (United States)

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.

Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for Boron Neutron Capture Therapy

NARCIS (Netherlands)

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

Calculation of radiation effects in solids by direct numerical solution of the adjoint transport equation

International Nuclear Information System (INIS)

Matthes, W.K.

1998-01-01

The 'adjoint transport equation in its integro-differential form' is derived for the radiation damage produced by atoms injected into solids. We reduce it to the one-dimensional form and prepare it for a numerical solution by: --discretizing the continuous variables energy, space and direction, --replacing the partial differential quotients by finite differences and --evaluating the collision integral by a double sum. By a proper manipulation of this double sum the adjoint transport equation turns into a (very large) set of linear equations with tridiagonal matrix which can be solved by a special (simple and fast) algorithm. The solution of this set of linear equations contains complete information on a specified damage type (e.g. the energy deposited in a volume V) in terms of the function D(i,E,c,x) which gives the damage produced by all particles generated in a cascade initiated by a particle of type i starting at x with energy E in direction c. It is essential to remark that one calculation gives the damage function D for the complete ranges of the variables {i,E,c and x} (for numerical reasons of course on grid-points in the {E,c,x}-space). This is most useful to applications where a general source-distribution S(i,E,c,x) of particles is given by the experimental setup (e.g. beam-window and and target in proton accelerator work. The beam-protons along their path through the window--or target material generate recoil atoms by elastic collisions or nuclear reactions. These recoil atoms form the particle source S). The total damage produced then is eventually given by: D = (Σ)i ∫ ∫ ∫ S(i, E, c, x)*D(i, E, c, x)*dE*dc*dx A Fortran-77 program running on a PC-486 was written for the overall procedure and applied to some problems

Two different hematocrit detection methods: Different methods, different results?

Directory of Open Access Journals (Sweden)

Schuepbach Reto A

2010-03-01

Full Text Available Abstract Background Less is known about the influence of hematocrit detection methodology on transfusion triggers. Therefore, the aim of the present study was to compare two different hematocrit-assessing methods. In a total of 50 critically ill patients hematocrit was analyzed using (1 blood gas analyzer (ABLflex 800 and (2 the central laboratory method (ADVIA® 2120 and compared. Findings Bland-Altman analysis for repeated measurements showed a good correlation with a bias of +1.39% and 2 SD of ± 3.12%. The 24%-hematocrit-group showed a correlation of r2 = 0.87. With a kappa of 0.56, 22.7% of the cases would have been transfused differently. In the-28%-hematocrit group with a similar correlation (r2 = 0.8 and a kappa of 0.58, 21% of the cases would have been transfused differently. Conclusions Despite a good agreement between the two methods used to determine hematocrit in clinical routine, the calculated difference of 1.4% might substantially influence transfusion triggers depending on the employed method.

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

Energy Technology Data Exchange (ETDEWEB)

Aguilo Valentin, Miguel Alejandro [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Adjoint-Baed Optimal Control on the Pitch Angle of a Single-Bladed Vertical-Axis Wind Turbine

Science.gov (United States)

Tsai, Hsieh-Chen; Colonius, Tim

2017-11-01

Optimal control on the pitch angle of a NACA0018 single-bladed vertical-axis wind turbine (VAWT) is numerically investigated at a low Reynolds number of 1500. With fixed tip-speed ratio, the input power is minimized and mean tangential force is maximized over a specific time horizon. The immersed boundary method is used to simulate the two-dimensional, incompressible flow around a horizontal cross section of the VAWT. The problem is formulated as a PDE constrained optimization problem and an iterative solution is obtained using adjoint-based conjugate gradient methods. By the end of the longest control horizon examined, two controls end up with time-invariant pitch angles of about the same magnitude but with the opposite signs. The results show that both cases lead to a reduction in the input power but not necessarily an enhancement in the mean tangential force. These reductions in input power are due to the removal of a power-damaging phenomenon that occurs when a vortex pair is captured by the blade in the upwind-half region of a cycle. This project was supported by Caltech FLOWE center/Gordon and Betty Moore Foundation.

Sources and processes contributing to nitrogen deposition: an adjoint model analysis applied to biodiversity hotspots worldwide.

Science.gov (United States)

Paulot, Fabien; Jacob, Daniel J; Henze, Daven K

2013-04-02

Anthropogenic enrichment of reactive nitrogen (Nr) deposition is an ecological concern. We use the adjoint of a global 3-D chemical transport model (GEOS-Chem) to identify the sources and processes that control Nr deposition to an ensemble of biodiversity hotspots worldwide and two U.S. national parks (Cuyahoga and Rocky Mountain). We find that anthropogenic sources dominate deposition at all continental sites and are mainly regional (less than 1000 km) in origin. In Hawaii, Nr supply is controlled by oceanic emissions of ammonia (50%) and anthropogenic sources (50%), with important contributions from Asia and North America. Nr deposition is also sensitive in complicated ways to emissions of SO2, which affect Nr gas-aerosol partitioning, and of volatile organic compounds (VOCs), which affect oxidant concentrations and produce organic nitrate reservoirs. For example, VOC emissions generally inhibit deposition of locally emitted NOx but significantly increase Nr deposition downwind. However, in polluted boreal regions, anthropogenic VOC emissions can promote Nr deposition in winter. Uncertainties in chemical rate constants for OH + NO2 and NO2 hydrolysis also complicate the determination of source-receptor relationships for polluted sites in winter. Application of our adjoint sensitivities to the representative concentration pathways (RCPs) scenarios for 2010-2050 indicates that future decreases in Nr deposition due to NOx emission controls will be offset by concurrent increases in ammonia emissions from agriculture.

Mapping pan-Arctic CH4 emissions using an adjoint method by integrating process-based wetland and lake biogeochemical models and atmospheric CH4 concentrations

Science.gov (United States)

Tan, Z.; Zhuang, Q.; Henze, D. K.; Frankenberg, C.; Dlugokencky, E. J.; Sweeney, C.; Turner, A. J.

2015-12-01

Understanding CH4 emissions from wetlands and lakes are critical for the estimation of Arctic carbon balance under fast warming climatic conditions. To date, our knowledge about these two CH4 sources is almost solely built on the upscaling of discontinuous measurements in limited areas to the whole region. Many studies indicated that, the controls of CH4 emissions from wetlands and lakes including soil moisture, lake morphology and substrate content and quality are notoriously heterogeneous, thus the accuracy of those simple estimates could be questionable. Here we apply a high spatial resolution atmospheric inverse model (nested-grid GEOS-Chem Adjoint) over the Arctic by integrating SCIAMACHY and NOAA/ESRL CH4 measurements to constrain the CH4 emissions estimated with process-based wetland and lake biogeochemical models. Our modeling experiments using different wetland CH4 emission schemes and satellite and surface measurements show that the total amount of CH4 emitted from the Arctic wetlands is well constrained, but the spatial distribution of CH4 emissions is sensitive to priors. For CH4 emissions from lakes, our high-resolution inversion shows that the models overestimate CH4 emissions in Alaskan costal lowlands and East Siberian lowlands. Our study also indicates that the precision and coverage of measurements need to be improved to achieve more accurate high-resolution estimates.

Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations

International Nuclear Information System (INIS)

Xu Xixiang

2012-01-01

A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. (general)

Accurately bi-orthogonal direct and adjoint lambda modes via two-sided Eigen-solvers

International Nuclear Information System (INIS)

Roman, J.E.; Vidal, V.; Verdu, G.

2005-01-01

This work is concerned with the accurate computation of the dominant l-modes (Lambda mode) of the reactor core in order to approximate the solution of the neutron diffusion equation in different situations such as the transient modal analysis. In a previous work, the problem was already addressed by implementing a parallel program based on SLEPc (Scalable Library for Eigenvalue Problem Computations), a public domain software for the solution of eigenvalue problems. Now, the proposed solution is extended by incorporating also the computation of the adjoint l-modes in such a way that the bi-orthogonality condition is enforced very accurately. This feature is very desirable in some types of analyses, and in the proposed scheme it is achieved by making use of two-sided eigenvalue solving software. Current implementations of some of these software, while still susceptible of improvement, show that they can be competitive in terms of response time and accuracy with respect to other types of eigenvalue solving software. The code developed by the authors has parallel capabilities in order to be able to analyze reactors with a great level of detail in a short time. (authors)

Accurately bi-orthogonal direct and adjoint lambda modes via two-sided Eigen-solvers

Energy Technology Data Exchange (ETDEWEB)

Roman, J.E.; Vidal, V. [Valencia Univ. Politecnica, D. Sistemas Informaticos y Computacion (Spain); Verdu, G. [Valencia Univ. Politecnica, D. Ingenieria Quimica y Nuclear (Spain)

2005-07-01

This work is concerned with the accurate computation of the dominant l-modes (Lambda mode) of the reactor core in order to approximate the solution of the neutron diffusion equation in different situations such as the transient modal analysis. In a previous work, the problem was already addressed by implementing a parallel program based on SLEPc (Scalable Library for Eigenvalue Problem Computations), a public domain software for the solution of eigenvalue problems. Now, the proposed solution is extended by incorporating also the computation of the adjoint l-modes in such a way that the bi-orthogonality condition is enforced very accurately. This feature is very desirable in some types of analyses, and in the proposed scheme it is achieved by making use of two-sided eigenvalue solving software. Current implementations of some of these software, while still susceptible of improvement, show that they can be competitive in terms of response time and accuracy with respect to other types of eigenvalue solving software. The code developed by the authors has parallel capabilities in order to be able to analyze reactors with a great level of detail in a short time. (authors)

Application of the variational method for calculation of neutron spectra and group constants - Master thesis; Primena varijacione metode na odredjivanje spektra neutrona i grupnih konstanti - Magistarski rad

Energy Technology Data Exchange (ETDEWEB)

Milosevic, M [Institute of Nuclear Sciences Vinca, Beograd (Serbia and Montenegro)

1979-07-01

One-dimensional variational method for cylindrical configuration was applied for calculating group constants, together with effects of elastic slowing down, anisotropic elastic scattering, inelastic scattering, heterogeneous resonance absorption with the aim to include the presence of a number of different isotopes and effects of neutron leakage from the reactor core. Neutron flux shape P{sub 3} and adjoint function are proposed in order to enable calculation of smaller size reactors and inclusion of heterogeneity effects by cell calculations. Microscopic multigroup constants were prepared based on the UKNDL data library. Analytical-numerical approach was applied for solving the equations of the P{sub 3} approximation to obtain neutron flux moments and adjoint functions.

Open and closed string worldsheets from free large N gauge theories with adjoint and fundamental matter

International Nuclear Information System (INIS)

Yaakov, Itamar

2006-01-01

We extend Gopakumar's prescription for constructing closed string worldsheets from free field theory diagrams with adjoint matter to open and closed string worldsheets arising from free field theories with fundamental matter. We describe the extension of the gluing mechanism and the electrical circuit analogy to fundamental matter. We discuss the generalization of the existence and uniqueness theorem of Strebel differentials to open Riemann surfaces. Two examples are computed of correlators containing fundamental matter, and the resulting worldsheet OPE's are computed. Generic properties of Gopakumar's construction are discussed

Adjoint Optimization of a Wing Using the CSRT Method

NARCIS (Netherlands)

Straathof, M.H.; Van Tooren, M.J.L.

2011-01-01

This paper will demonstrate the potential of the Class-Shape-Refinement-Transformation (CSRT) method for aerodynamically optimizing three-dimensional surfaces. The CSRT method was coupled to an in-house Euler solver and this combination was used in an optimization framework to optimize the ONERA M6

The basis spline method and associated techniques

International Nuclear Information System (INIS)

Bottcher, C.; Strayer, M.R.

1989-01-01

We outline the Basis Spline and Collocation methods for the solution of Partial Differential Equations. Particular attention is paid to the theory of errors, and the handling of non-self-adjoint problems which are generated by the collocation method. We discuss applications to Poisson's equation, the Dirac equation, and the calculation of bound and continuum states of atomic and nuclear systems. 12 refs., 6 figs

Adjoint-based global variance reduction approach for reactor analysis problems

International Nuclear Information System (INIS)

Zhang, Qiong; Abdel-Khalik, Hany S.

2011-01-01

A new variant of a hybrid Monte Carlo-Deterministic approach for simulating particle transport problems is presented and compared to the SCALE FW-CADIS approach. The new approach, denoted by the Subspace approach, optimizes the selection of the weight windows for reactor analysis problems where detailed properties of all fuel assemblies are required everywhere in the reactor core. Like the FW-CADIS approach, the Subspace approach utilizes importance maps obtained from deterministic adjoint models to derive automatic weight-window biasing. In contrast to FW-CADIS, the Subspace approach identifies the correlations between weight window maps to minimize the computational time required for global variance reduction, i.e., when the solution is required everywhere in the phase space. The correlations are employed to reduce the number of maps required to achieve the same level of variance reduction that would be obtained with single-response maps. Numerical experiments, serving as proof of principle, are presented to compare the Subspace and FW-CADIS approaches in terms of the global reduction in standard deviation. (author)

``Use of perturbative methods to break down the variation of reactivity between two systems``; ``Decomposition par methodes perturbatives de la variation de reactivite de deux systemes``

Energy Technology Data Exchange (ETDEWEB)

Perruchot-Triboulet, S.; Sanchez, R.

1997-12-01

The modification of the isotopic composition, the temperature or even accounting for across section uncertainties in one part of a nuclear reactor core, affects the value of the effective multiplication factor. A new tool allows the analysis of the reactivity effect generated by the modification of the system. With the help of the direct and adjoint fluxes, a detailed balance of reactivity, between the compared systems, is done for each isotopic cross section. After the presentation of the direct and adjoint transport equations in the context of the multigroup code transport APOLLO2, this note describes the method, based on perturbation theory, for the analysis of the reactivity variation. An example application is also given. (author).

Coolant void reactivity adjustments in advanced CANDU lattices using adjoint sensitivity technique

International Nuclear Information System (INIS)

Assawaroongruengchot, M.; Marleau, G.

2008-01-01

Coolant void reactivity (CVR) is an important factor in reactor accident analysis. Here we study the adjustments of CVR at beginning of burnup cycle (BOC) and k eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice using the optimization and adjoint sensitivity techniques. The sensitivity coefficients are evaluated using the perturbation theory based on the integral neutron transport equations. The neutron and flux importance transport solutions are obtained by the method of cyclic characteristics (MOCC). Three sets of parameters for CVR-BOC and k eff -EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR-BOC (CBCVR-BOC). To approximate the EOC sensitivity coefficient, we perform constant-power burnup/depletion calculations using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Our aim is to achieve a desired negative CVR-BOC of -2 mk and k eff -EOC of 0.900 for the first two cases, and a CBCVR-BOC of -2 mk and k eff -EOC of 0.900 for the last case. Sensitivity analyses of CVR and eigenvalue are also included in our study

Coolant void reactivity adjustments in advanced CANDU lattices using adjoint sensitivity technique

Energy Technology Data Exchange (ETDEWEB)

Assawaroongruengchot, M. [Institut de Genie Nucleaire, Ecole Polytechnique de Montreal, P.O. Box 6079, stn. Centre-ville, Montreal, H3C3A7 (Canada)], E-mail: monchaia@gmail.com; Marleau, G. [Institut de Genie Nucleaire, Ecole Polytechnique de Montreal, P.O. Box 6079, stn. Centre-ville, Montreal, H3C3A7 (Canada)], E-mail: guy.marleau@polymtl.ca

2008-03-15

Coolant void reactivity (CVR) is an important factor in reactor accident analysis. Here we study the adjustments of CVR at beginning of burnup cycle (BOC) and k{sub eff} at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice using the optimization and adjoint sensitivity techniques. The sensitivity coefficients are evaluated using the perturbation theory based on the integral neutron transport equations. The neutron and flux importance transport solutions are obtained by the method of cyclic characteristics (MOCC). Three sets of parameters for CVR-BOC and k{sub eff}-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR-BOC (CBCVR-BOC). To approximate the EOC sensitivity coefficient, we perform constant-power burnup/depletion calculations using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Our aim is to achieve a desired negative CVR-BOC of -2 mk and k{sub eff}-EOC of 0.900 for the first two cases, and a CBCVR-BOC of -2 mk and k{sub eff}-EOC of 0.900 for the last case. Sensitivity analyses of CVR and eigenvalue are also included in our study.

Variational Multi-Scale method with spectral approximation of the sub-scales.

KAUST Repository

Dia, Ben Mansour; Chá con-Rebollo, Tomas

2015-01-01

A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base

Forward-weighted CADIS method for variance reduction of Monte Carlo calculations of distributions and multiple localized quantities

International Nuclear Information System (INIS)

Wagner, J. C.; Blakeman, E. D.; Peplow, D. E.

2009-01-01

This paper presents a new hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as responses at multiple localized detectors and spectra. This method, referred to as Forward-Weighted CADIS (FW-CADIS), is a variation on the Consistent Adjoint Driven Importance Sampling (CADIS) method, which has been used for some time to very effectively improve the efficiency of Monte Carlo calculations of localized quantities, e.g., flux, dose, or reaction rate at a specific location. The basis of this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. Implementation of this method utilizes the results from a forward deterministic calculation to develop a forward-weighted source for a deterministic adjoint calculation. The resulting adjoint function is then used to generate consistent space- and energy-dependent source biasing parameters and weight windows that are used in a forward Monte Carlo calculation to obtain approximately uniform statistical uncertainties in the desired tally regions. The FW-CADIS method has been implemented in the ADVANTG/MCNP framework and has been fully automated within the MAVRIC sequence of SCALE 6. Results of the application of the method to enabling the calculation of dose rates throughout an entire full-scale pressurized-water reactor facility are presented and discussed. (authors)

Calculation of neutron importance function in fissionable assemblies using Monte Carlo method

International Nuclear Information System (INIS)

Feghhi, S. A. H.; Afarideh, H.; Shahriari, M.

2007-01-01

The purpose of the present work is to develop an efficient solution method to calculate neutron importance function in fissionable assemblies for all criticality conditions, using Monte Carlo Method. The neutron importance function has a well important role in perturbation theory and reactor dynamic calculations. Usually this function can be determined by calculating adjoint flux through out solving the Adjoint weighted transport equation with deterministic methods. However, in complex geometries these calculations are very difficult. In this article, considering the capabilities of MCNP code in solving problems with complex geometries and its closeness to physical concepts, a comprehensive method based on physical concept of neutron importance has been introduced for calculating neutron importance function in sub-critical, critical and supercritical conditions. For this means a computer program has been developed. The results of the method has been benchmarked with ANISN code calculations in 1 and 2 group modes for simple geometries and their correctness has been approved for all three criticality conditions. Ultimately, the efficiency of the method for complex geometries has been shown by calculation of neutron importance in MNSR research reactor

Iterative methods for photoacoustic tomography in attenuating acoustic media

Science.gov (United States)

Haltmeier, Markus; Kowar, Richard; Nguyen, Linh V.

2017-11-01

The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation accounting for frequency dependent attenuation according to a wide class of attenuation laws that may include memory. We formulate the inverse problem of photoacoustic tomography in attenuating medium as an ill-posed operator equation in a Hilbert space framework that is tackled by iterative regularization methods. Our approach comes with a clear convergence analysis. For that purpose we derive explicit expressions for the adjoint problem that can efficiently be implemented. In contrast to time reversal, the employed adjoint wave equation is again damping and, thus has a stable solution. This stability property can be clearly seen in our numerical results. Moreover, the presented numerical results clearly demonstrate the efficiency and accuracy of the derived iterative reconstruction algorithms in various situations including the limited view case.

Extending the subspace hybrid method for eigenvalue problems in reactor physics calculation

International Nuclear Information System (INIS)

Zhang, Q.; Abdel-Khalik, H. S.

2013-01-01

This paper presents an innovative hybrid Monte-Carlo-Deterministic method denoted by the SUBSPACE method designed for improving the efficiency of hybrid methods for reactor analysis applications. The SUBSPACE method achieves its high computational efficiency by taking advantage of the existing correlations between desired responses. Recently, significant gains in computational efficiency have been demonstrated using this method for source driven problems. Within this work the mathematical theory behind the SUBSPACE method is introduced and extended to address core wide level k-eigenvalue problems. The method's efficiency is demonstrated based on a three-dimensional quarter-core problem, where responses are sought on the pin cell level. The SUBSPACE method is compared to the FW-CADIS method and is found to be more efficient for the utilized test problem because of the reason that the FW-CADIS method solves a forward eigenvalue problem and an adjoint fixed-source problem while the SUBSPACE method only solves an adjoint fixed-source problem. Based on the favorable results obtained here, we are confident that the applicability of Monte Carlo for large scale reactor analysis could be realized in the near future. (authors)

Propagators in magnetic string background and the problem of self-adjoint extensions

International Nuclear Information System (INIS)

Kaiser, H.J.

1993-01-01

Ghost and gluon propagators of a non-Abelian gauge theory in the background of a magnetic string are calculated. A simple technique to derive the ghost propagator is presented which makes use of the fact that the presence of a magnetic string of strength β shifts the differential operators ∂/∂φ to ∂/∂φ - iβ. In the case of a gluon propagator in the magnetic string background a difficulty arises from the presence of the magnetic field strength term involving a δ function. Here the ambiguities of a self-adjoint extension of the differential operator must be met. A proper treatment demands the specification of a limiting process starting from a string of finite thickness and well-defined structure and leading to the δ function string. Without this additional structure information about the background string the gauge field propagator is undetermined. (orig.)

New Quasi-Newton Method for Solving Systems of Nonlinear Equations

Czech Academy of Sciences Publication Activity Database

Lukšan, Ladislav; Vlček, Jan

2017-01-01

Roč. 62, č. 2 (2017), s. 121-134 ISSN 0862-7940 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : nonlinear equations * systems of equations * trust-region methods * quasi-Newton methods * adjoint Broyden methods * numerical algorithms * numerical experiments Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.618, year: 2016 http://hdl.handle.net/10338.dmlcz/146699

Discrete Adjoint-Based Design for Unsteady Turbulent Flows On Dynamic Overset Unstructured Grids

Science.gov (United States)

Nielsen, Eric J.; Diskin, Boris

2012-01-01

A discrete adjoint-based design methodology for unsteady turbulent flows on three-dimensional dynamic overset unstructured grids is formulated, implemented, and verified. The methodology supports both compressible and incompressible flows and is amenable to massively parallel computing environments. The approach provides a general framework for performing highly efficient and discretely consistent sensitivity analysis for problems involving arbitrary combinations of overset unstructured grids which may be static, undergoing rigid or deforming motions, or any combination thereof. General parent-child motions are also accommodated, and the accuracy of the implementation is established using an independent verification based on a complex-variable approach. The methodology is used to demonstrate aerodynamic optimizations of a wind turbine geometry, a biologically-inspired flapping wing, and a complex helicopter configuration subject to trimming constraints. The objective function for each problem is successfully reduced and all specified constraints are satisfied.

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.

Sensitivity technologies for large scale simulation

International Nuclear Information System (INIS)

Collis, Samuel Scott; Bartlett, Roscoe Ainsworth; Smith, Thomas Michael; Heinkenschloss, Matthias; Wilcox, Lucas C.; Hill, Judith C.; Ghattas, Omar; Berggren, Martin Olof; Akcelik, Volkan; Ober, Curtis Curry; van Bloemen Waanders, Bart Gustaaf; Keiter, Eric Richard

2005-01-01

order approximation of the Euler equations and used as a preconditioner. In comparison to other methods, the AD preconditioner showed better convergence behavior. Our ultimate target is to perform shape optimization and hp adaptivity using adjoint formulations in the Premo compressible fluid flow simulator. A mathematical formulation for mixed-level simulation algorithms has been developed where different physics interact at potentially different spatial resolutions in a single domain. To minimize the implementation effort, explicit solution methods can be considered, however, implicit methods are preferred if computational efficiency is of high priority. We present the use of a partial elimination nonlinear solver technique to solve these mixed level problems and show how these formulation are closely coupled to intrusive optimization approaches and sensitivity analyses. Production codes are typically not designed for sensitivity analysis or large scale optimization. The implementation of our optimization libraries into multiple production simulation codes in which each code has their own linear algebra interface becomes an intractable problem. In an attempt to streamline this task, we have developed a standard interface between the numerical algorithm (such as optimization) and the underlying linear algebra. These interfaces (TSFCore and TSFCoreNonlin) have been adopted by the Trilinos framework and the goal is to promote the use of these interfaces especially with new developments. Finally, an adjoint based a posteriori error estimator has been developed for discontinuous Galerkin discretization of Poisson's equation. The goal is to investigate other ways to leverage the adjoint calculations and we show how the convergence of the forward problem can be improved by adapting the grid using adjoint-based error estimates. Error estimation is usually conducted with continuous adjoints but if discrete adjoints are available it may be possible to reuse the discrete version

On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators

Czech Academy of Sciences Publication Activity Database

Krejčiřík, David; Siegl, Petr; Železný, Jakub

2014-01-01

Roč. 8, č. 1 (2014), s. 255-281 ISSN 1661-8254 R&D Projects: GA MŠk LC06002; GA MŠk LC527; GA ČR GAP203/11/0701 Grant - others:GA ČR(CZ) GD202/08/H072 Institutional support: RVO:61389005 Keywords : Sturm-Liouville operators * non-symmetric Robin boundary conditions * similarity to normal or self-adjoint operators * discrete spectral operator * complex symmetric operator * PT-symmetry * metric operator * C operator * Hilbert- Schmidt operators Subject RIV: BE - Theoretical Physics Impact factor: 0.545, year: 2014

AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION

Science.gov (United States)

Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...

Construction of the seismic wave-speed model by adjoint tomography beneath the Japanese metropolitan area

Science.gov (United States)

Miyoshi, Takayuki

2017-04-01

The Japanese metropolitan area has high risks of earthquakes and volcanoes associated with convergent tectonic plates. It is important to clarify detail three-dimensional structure for understanding tectonics and predicting strong motion. Classical tomographic studies based on ray theory have revealed seismotectonics and volcanic tectonics in the region, however it is unknown whether their models reproduce observed seismograms. In the present study, we construct new seismic wave-speed model by using waveform inversion. Adjoint tomography and the spectral element method (SEM) were used in the inversion (e.g. Tape et al. 2009; Peter et al. 2011). We used broadband seismograms obtained at NIED F-net stations for 140 earthquakes occurred beneath the Kanto district. We selected four frequency bands between 5 and 30 sec and used from the seismograms of longer period bands for the inversion. Tomographic iteration was conducted until obtaining the minimized misfit between data and synthetics. Our SEM model has 16 million grid points that covers the metropolitan area of the Kanto district. The model parameters were the Vp and Vs of the grid points, and density and attenuation were updated to new values depending on new Vs in each iteration. The initial model was assumed the tomographic model (Matsubara and Obara 2011) based on ray theory. The source parameters were basically used from F-net catalog, while the centroid times were inferred from comparison between data and synthetics. We simulated the forward and adjoint wavefields of each event and obtained Vp and Vs misfit kernels from their interaction. Large computation was conducted on K computer, RIKEN. We obtained final model (m16) after 16 iterations in the present study. For the waveform improvement, it is clearly shown that m16 is better than the initial model, and the seismograms especially improved in the frequency bands of longer than 8 sec and changed better for seismograms of the events occurred at deeper than a

Adjoint sensitivity analysis of dynamic reliability models based on Markov chains - I: Theory

International Nuclear Information System (INIS)

Cacuci, D. G.; Cacuci, D. G.; Ionescu-Bujor, M.

2008-01-01

The development of the adjoint sensitivity analysis procedure (ASAP) for generic dynamic reliability models based on Markov chains is presented, together with applications of this procedure to the analysis of several systems of increasing complexity. The general theory is presented in Part I of this work and is accompanied by a paradigm application to the dynamic reliability analysis of a simple binary component, namely a pump functioning on an 'up/down' cycle until it fails irreparably. This paradigm example admits a closed form analytical solution, which permits a clear illustration of the main characteristics of the ASAP for Markov chains. In particular, it is shown that the ASAP for Markov chains presents outstanding computational advantages over other procedures currently in use for sensitivity and uncertainty analysis of the dynamic reliability of large-scale systems. This conclusion is further underscored by the large-scale applications presented in Part II. (authors)

Adjoint sensitivity analysis of dynamic reliability models based on Markov chains - I: Theory

Energy Technology Data Exchange (ETDEWEB)

Cacuci, D. G. [Commiss Energy Atom, Direct Energy Nucl, Saclay, (France); Cacuci, D. G. [Univ Karlsruhe, Inst Nucl Technol and Reactor Safety, D-76021 Karlsruhe, (Germany); Ionescu-Bujor, M. [Forschungszentrum Karlsruhe, Fus Program, D-76021 Karlsruhe, (Germany)

2008-07-01

The development of the adjoint sensitivity analysis procedure (ASAP) for generic dynamic reliability models based on Markov chains is presented, together with applications of this procedure to the analysis of several systems of increasing complexity. The general theory is presented in Part I of this work and is accompanied by a paradigm application to the dynamic reliability analysis of a simple binary component, namely a pump functioning on an 'up/down' cycle until it fails irreparably. This paradigm example admits a closed form analytical solution, which permits a clear illustration of the main characteristics of the ASAP for Markov chains. In particular, it is shown that the ASAP for Markov chains presents outstanding computational advantages over other procedures currently in use for sensitivity and uncertainty analysis of the dynamic reliability of large-scale systems. This conclusion is further underscored by the large-scale applications presented in Part II. (authors)

''Use of perturbative methods to break down the variation of reactivity between two systems''

International Nuclear Information System (INIS)

Perruchot-Triboulet, S.; Sanchez, R.

1997-01-01

The modification of the isotopic composition, the temperature or even accounting for across section uncertainties in one part of a nuclear reactor core, affects the value of the effective multiplication factor. A new tool allows the analysis of the reactivity effect generated by the modification of the system. With the help of the direct and adjoint fluxes, a detailed balance of reactivity, between the compared systems, is done for each isotopic cross section. After the presentation of the direct and adjoint transport equations in the context of the multigroup code transport APOLLO2, this note describes the method, based on perturbation theory, for the analysis of the reactivity variation. An example application is also given. (author)

Calculation of neutron importance function in fissionable assemblies using Monte Carlo method

International Nuclear Information System (INIS)

Feghhi, S.A.H.; Shahriari, M.; Afarideh, H.

2007-01-01

The purpose of the present work is to develop an efficient solution method for the calculation of neutron importance function in fissionable assemblies for all criticality conditions, based on Monte Carlo calculations. The neutron importance function has an important role in perturbation theory and reactor dynamic calculations. Usually this function can be determined by calculating the adjoint flux while solving the adjoint weighted transport equation based on deterministic methods. However, in complex geometries these calculations are very complicated. In this article, considering the capabilities of MCNP code in solving problems with complex geometries and its closeness to physical concepts, a comprehensive method based on the physical concept of neutron importance has been introduced for calculating the neutron importance function in sub-critical, critical and super-critical conditions. For this propose a computer program has been developed. The results of the method have been benchmarked with ANISN code calculations in 1 and 2 group modes for simple geometries. The correctness of these results has been confirmed for all three criticality conditions. Finally, the efficiency of the method for complex geometries has been shown by the calculation of neutron importance in Miniature Neutron Source Reactor (MNSR) research reactor

Nonperturbative volume reduction of large-N QCD with adjoint fermions

International Nuclear Information System (INIS)

Bringoltz, Barak; Sharpe, Stephen R.

2009-01-01

We use nonperturbative lattice techniques to study the volume-reduced 'Eguchi-Kawai' version of four-dimensional large-N QCD with a single adjoint Dirac fermion. We explore the phase diagram of this single-site theory in the space of quark mass and gauge coupling using Wilson fermions for a number of colors in the range 8≤N≤15. Our evidence suggests that these values of N are large enough to determine the nature of the phase diagram for N→∞. We identify the region in the parameter space where the (Z N ) 4 center symmetry is intact. According to previous theoretical work using the orbifolding paradigm, and assuming that translation invariance is not spontaneously broken in the infinite-volume theory, in this region volume reduction holds: the single-site and infinite-volume theories become equivalent when N→∞. We find strong evidence that this region includes both light and heavy quarks (with masses that are at the cutoff scale), and our results are consistent with this region extending toward the continuum limit. We also compare the action density and the eigenvalue density of the overlap Dirac operator in the fundamental representation with those obtained in large-N pure-gauge theory.

Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

International Nuclear Information System (INIS)

Rozanov, Vladimir V.; Vountas, Marco

2014-01-01

Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes–Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently. -- Highlights: • We derived the radiative transfer equation accounting for rotational Raman scattering. • Different approximate radiative transfer approaches with first order scattering were used. • Rigorous and approximate approaches are shown to derive particular integrals. • An alternative forward-adjoint technique is suggested as well. • An additional spectral binning scheme which speeds up the calculations is presented

Adjoint sensitivity analysis of the RELAPS/MOD3.2 two-fluid thermal-hydraulic code system

International Nuclear Information System (INIS)

Ionescu-Bujor, M.

2000-10-01

This work presents the implementation of the Adjoint Sensitivity Analysis Procedure (ASAP) for the non-equilibrium, non-homogeneous two-fluid model, including boron concentration and non-condensable gases, of the RELAP5/MOD3.2 code. The end-product of this implementation is the Adjoint Sensitivity Model (ASM-REL/TF), which is derived for both the differential and discretized equations underlying the two-fluid model with non-condensable(s). The consistency requirements between these two representations are also highlighted. The validation of the ASM-REL/TF has been carried out by using sample problems involving: (i) liquid-phase only, (ii) gas-phase only, and (iii) two-phase mixture (of water and steam). Thus the 'Two-Loops with Pumps' sample problem supplied with RELAP5/MOD3.2 has been used to verify the accuracy and stability of the numerical solution of the ASM-REL/TF when only the liquid-phase is present. Furthermore, the 'Edwards Pipe' sample problem, also supplied with RELAP5/MOD3.2, has been used to verify the accuracy and stability of the numerical solution of the ASM-REL/TF when both (i.e., liquid and gas) phases are present. In addition, the accuracy and stability of the numerical solution of the ASM-REL/TF have been verified when only the gas-phase is present by using modified 'Two-Loops with Pumps' and the 'Edwards Pipe' sample problems in which the liquid and two-phase fluids, respectively, were replaced by pure steam. The results obtained for these sample problems depict typical sensitivities of junction velocities and volume-averaged pressures to perturbations in initial conditions, and indicate that the numerical solution of the ASM-REL/TF is as robust, stable, and accurate as the original RELAP5/MOD3.2 calculations. In addition, the solution of the ASM-REL/TF has been used to calculate sample sensitivities of volume-averaged pressures to variations in the pump head. (orig.) [de

Aerosol Health Impact Source Attribution Studies with the CMAQ Adjoint Air Quality Model

Science.gov (United States)

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

Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone

Directory of Open Access Journals (Sweden)

Yuan Wang

2015-01-01

Full Text Available Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.

Variational Multi-Scale method with spectral approximation of the sub-scales.

KAUST Repository

Dia, Ben Mansour

2015-01-07

A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a nite number of modes.

Calculational model based on influence function method for power distribution and control rod worth in fast reactors

International Nuclear Information System (INIS)

Sanda, T.; Azekura, K.

1983-01-01

A model for calculating the power distribution and the control rod worth in fast reactors has been developed. This model is based on the influence function method. The characteristics of the model are as follows: Influence functions for any changes in the control rod insertion ratio are expressed by using an influence function for an appropriate control rod insertion in order to reduce the computer memory size required for the method. A control rod worth is calculated on the basis of a one-group approximation in which cross sections are generated by bilinear (flux-adjoint) weighting, not the usual flux weighting, in order to reduce the collapse error. An effective neutron multiplication factor is calculated by adjoint weighting in order to reduce the effect of the error in the one-group flux distribution. The results obtained in numerical examinations of a prototype fast reactor indicate that this method is suitable for on-line core performance evaluation because of a short computing time and a small memory size

Time-domain least-squares migration using the Gaussian beam summation method

Science.gov (United States)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

International Nuclear Information System (INIS)

Gerstl, S.A.W.; Zardecki, A.

1985-01-01

Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered

Neutron transport and Montecarlo method: analysis and revision

International Nuclear Information System (INIS)

Perlado, J.M.

1982-01-01

The resolution of the neutron transport equation by the Montecarlo method is presented. Coming from an extensive discussion on the best formulation of that equation in order to be treated through the mentioned method, the theoretical bases of the estimator and random-walk generation is extensively explained. The most general expression for the estimators in different physical situations, each with a diverse random-walk, is included in this basical theoretical part. Furthemore, a large revision on the variance reduction methods is made. Its theoretical presentation is claimed to be in connection with the need for each one of them. The use of the adjoint equation, as a part of the importance sampling, Russian Roulette, splitting, exponential transform, conditional and correlated Montecarlo, and one-collision and next-event extimators, are discussed. Finally, come comments in the presentation of the last works on the theoretical prediction of errors in the generation of estimators-random walks are made. (author)

Toward the Development of a Coupled COAMPS-ROMS Ensemble Kalman Filter and Adjoint with a focus on the Indian Ocean and the Intraseasonal Oscillation

Science.gov (United States)

2015-09-30

1 Approved for public release; distribution is unlimited. Toward the Development of a Coupled COAMPS-ROMS Ensemble Kalman Filter and Adjoint...system at NCAR. (2) Compare the performance of the Ensemble Kalman Filter (EnKF) using the Data Assimilation Research Testbed (DART) and 4...undercurrent is clearly visible. Figure 2 shows the horizontal temperature structure and circulation at a depth of 50 m within the surface mixed layer

Application of finite element method in the solution of transport equation

International Nuclear Information System (INIS)

Maiorino, J.R.; Vieira, W.J.

1985-01-01

It is presented the application of finite element method in the solution of second order transport equation (self-adjoint) for the even parity flux. The angular component is treated by expansion in Legendre polinomials uncoupled of the spatial component, which is approached by an expansion in base functions, interpolated in each spatial element. (M.C.K.) [pt

Adjoint sensitivity analysis procedure of Markov chains with applications on reliability of IFMIF accelerator-system facilities

Energy Technology Data Exchange (ETDEWEB)

Balan, I.

2005-05-01

This work presents the implementation of the Adjoint Sensitivity Analysis Procedure (ASAP) for the Continuous Time, Discrete Space Markov chains (CTMC), as an alternative to the other computational expensive methods. In order to develop this procedure as an end product in reliability studies, the reliability of the physical systems is analyzed using a coupled Fault-Tree - Markov chain technique, i.e. the abstraction of the physical system is performed using as the high level interface the Fault-Tree and afterwards this one is automatically converted into a Markov chain. The resulting differential equations based on the Markov chain model are solved in order to evaluate the system reliability. Further sensitivity analyses using ASAP applied to CTMC equations are performed to study the influence of uncertainties in input data to the reliability measures and to get the confidence in the final reliability results. The methods to generate the Markov chain and the ASAP for the Markov chain equations have been implemented into the new computer code system QUEFT/MARKOMAGS/MCADJSEN for reliability and sensitivity analysis of physical systems. The validation of this code system has been carried out by using simple problems for which analytical solutions can be obtained. Typical sensitivity results show that the numerical solution using ASAP is robust, stable and accurate. The method and the code system developed during this work can be used further as an efficient and flexible tool to evaluate the sensitivities of reliability measures for any physical system analyzed using the Markov chain. Reliability and sensitivity analyses using these methods have been performed during this work for the IFMIF Accelerator System Facilities. The reliability studies using Markov chain have been concentrated around the availability of the main subsystems of this complex physical system for a typical mission time. The sensitivity studies for two typical responses using ASAP have been

Global estimates of CO sources with high resolution by adjoint inversion of multiple satellite datasets (MOPITT, AIRS, SCIAMACHY, TES

Directory of Open Access Journals (Sweden)

M. Kopacz

2010-02-01

Full Text Available We combine CO column measurements from the MOPITT, AIRS, SCIAMACHY, and TES satellite instruments in a full-year (May 2004–April 2005 global inversion of CO sources at 4°×5° spatial resolution and monthly temporal resolution. The inversion uses the GEOS-Chem chemical transport model (CTM and its adjoint applied to MOPITT, AIRS, and SCIAMACHY. Observations from TES, surface sites (NOAA/GMD, and aircraft (MOZAIC are used for evaluation of the a posteriori solution. Using GEOS-Chem as a common intercomparison platform shows global consistency between the different satellite datasets and with the in situ data. Differences can be largely explained by different averaging kernels and a priori information. The global CO emission from combustion as constrained in the inversion is 1350 Tg a⁻¹. This is much higher than current bottom-up emission inventories. A large fraction of the correction results from a seasonal underestimate of CO sources at northern mid-latitudes in winter and suggests a larger-than-expected CO source from vehicle cold starts and residential heating. Implementing this seasonal variation of emissions solves the long-standing problem of models underestimating CO in the northern extratropics in winter-spring. A posteriori emissions also indicate a general underestimation of biomass burning in the GFED2 inventory. However, the tropical biomass burning constraints are not quantitatively consistent across the different datasets.

Trotter-Kato product formula and fractional powers of self-adjoint generators

CERN Document Server

Ichinose, I; Zagrebnov, Z

2002-01-01

Let $A$ and $B$ be non-negative self-adjoint operators in a Hilbert space such that their densely defined form sum $H = A \\stackrel{\\cdot}{+} B$ obeys $\\dom(H^\\ga) \\subseteq \\dom(A^\\ga) \\cap \\dom(B^\\ga)$ for some $\\ga \\in (1/2,1)$. It is proved that if, in addition, $A$ and $B$ satisfy $\\dom(A^{1/2}) \\subseteq \\dom(B^{1/2})$, then the symmetric and non-symmetric Trotter-Kato product formula converges in the operator norm: % % \\bed \\ba{c} \\left\\|\\left(e^{-tB/2n}e^{-tA/n}e^{-tB/2n}\\right)^n - e^{-tH}\\right\\| = O(n^{-(2\\ga-1)}), \\\\[2mm] \\left\\|\\left(e^{-tA/n}e^{-tB/n}\\right)^n - e^{-tH}\\right\\| = O(n^{-(2\\ga-1)}) \\ea \\eed % % uniformly in $t \\in [0,T]$, $0 < T < \\infty$, as $n \\to \\infty$, both with the same optimal error bound. The same is valid if one replaces the exponential function in the product by functions of the Kato class, that is, by real-valued Borel measurable functions $f(\\cdot)$ defined on the non-negative real axis obeying $0 \\le f(x) \\le 1$, $f(0) = 1$ and $f'(+0) = -1$, with some addition...

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

Science.gov (United States)

Jakeman, J. D.; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

International Nuclear Information System (INIS)

Jakeman, J.D.; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation

A loading pattern optimization method for nuclear fuel management

International Nuclear Information System (INIS)

Argaud, J.P.

1997-01-01

Nuclear fuel reload of PWR core leads to the search of an optimal nuclear fuel assemblies distribution, namely of loading pattern. This large discrete optimization problem is here expressed as a cost function minimization. To deal with this problem, an approach based on gradient information is used to direct the search in the patterns discrete space. A method using an adjoint state formulation is then developed, and final results of complete patterns search tests by this method are presented. (author)

FOCUS, Neutron Transport System for Complex Geometry Reactor Core and Shielding Problems by Monte-Carlo

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1980-01-01

1 - Description of problem or function: FOCUS enables the calculation of any quantity related to neutron transport in reactor or shielding problems, but was especially designed to calculate differential quantities, such as point values at one or more of the space, energy, direction and time variables of quantities like neutron flux, detector response, reaction rate, etc. or averages of such quantities over a small volume of the phase space. Different types of problems can be treated: systems with a fixed neutron source which may be a mono-directional source located out- side the system, and Eigen function problems in which the neutron source distribution is given by the (unknown) fundamental mode Eigen function distribution. Using Monte Carlo methods complex 3- dimensional geometries and detailed cross section information can be treated. Cross section data are derived from ENDF/B, with anisotropic scattering and discrete or continuous inelastic scattering taken into account. Energy is treated as a continuous variable and time dependence may also be included. 2 - Method of solution: A transformed form of the adjoint Boltzmann equation in integral representation is solved for the space, energy, direction and time variables by Monte Carlo methods. Adjoint particles are defined with properties in some respects contrary to those of neutrons. Adjoint particle histories are constructed from which estimates are obtained of the desired quantity. Adjoint cross sections are defined with which the nuclide and reaction type are selected in a collision. The energy after a collision is selected from adjoint energy distributions calculated together with the adjoint cross sections in advance of the actual Monte Carlo calculation. For multiplying systems successive generations of adjoint particles are obtained which will die out for subcritical systems with a fixed neutron source and will be kept approximately stationary for Eigen function problems. Completely arbitrary problems can

A method for including external feed in depletion calculations with CRAM and implementation into ORIGEN

International Nuclear Information System (INIS)

Isotalo, A.E.; Wieselquist, W.A.

2015-01-01

Highlights: • A method for handling external feed in depletion calculations with CRAM. • Source term can have polynomial or exponentially decaying time-dependence. • CRAM with source term and adjoint capability implemented to ORIGEN in SCALE. • The new solver is faster and more accurate than the original solver of ORIGEN. - Abstract: A method for including external feed with polynomial time dependence in depletion calculations with the Chebyshev Rational Approximation Method (CRAM) is presented and the implementation of CRAM to the ORIGEN module of the SCALE suite is described. In addition to being able to handle time-dependent feed rates, the new solver also adds the capability to perform adjoint calculations. Results obtained with the new CRAM solver and the original depletion solver of ORIGEN are compared to high precision reference calculations, which shows the new solver to be orders of magnitude more accurate. Furthermore, in most cases, the new solver is up to several times faster due to not requiring similar substepping as the original one

Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods

Directory of Open Access Journals (Sweden)

W. Castaings

2009-04-01

Full Text Available Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised with respect to model inputs.

In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thoré basin and used as a relatively simple (synthetic observations but didactic application case.

It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (~6 times the computing time of a single model run and the singular value decomposition (SVD of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation.

For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers is adopted.

Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting.

Analysis of inconsistent source sampling in monte carlo weight-window variance reduction methods

Directory of Open Access Journals (Sweden)

David P. Griesheimer

2017-09-01

Full Text Available The application of Monte Carlo (MC to large-scale fixed-source problems has recently become possible with new hybrid methods that automate generation of parameters for variance reduction techniques. Two common variance reduction techniques, weight windows and source biasing, have been automated and popularized by the consistent adjoint-driven importance sampling (CADIS method. This method uses the adjoint solution from an inexpensive deterministic calculation to define a consistent set of weight windows and source particles for a subsequent MC calculation. One of the motivations for source consistency is to avoid the splitting or rouletting of particles at birth, which requires computational resources. However, it is not always possible or desirable to implement such consistency, which results in inconsistent source biasing. This paper develops an original framework that mathematically expresses the coupling of the weight window and source biasing techniques, allowing the authors to explore the impact of inconsistent source sampling on the variance of MC results. A numerical experiment supports this new framework and suggests that certain classes of problems may be relatively insensitive to inconsistent source sampling schemes with moderate levels of splitting and rouletting.

Calculational model based on influence function method for power distribution and control rod worth in fast reactors

International Nuclear Information System (INIS)

Toshio, S.; Kazuo, A.

1983-01-01

A model for calculating the power distribution and the control rod worth in fast reactors has been developed. This model is based on the influence function method. The characteristics of the model are as follows: 1. Influence functions for any changes in the control rod insertion ratio are expressed by using an influence function for an appropriate control rod insertion in order to reduce the computer memory size required for the method. 2. A control rod worth is calculated on the basis of a one-group approximation in which cross sections are generated by bilinear (flux-adjoint) weighting, not the usual flux weighting, in order to reduce the collapse error. 3. An effective neutron multiplication factor is calculated by adjoint weighting in order to reduce the effect of the error in the one-group flux distribution. The results obtained in numerical examinations of a prototype fast reactor indicate that this method is suitable for on-line core performance evaluation because of a short computing time and a small memory size

Different protein-protein interface patterns predicted by different machine learning methods.

Science.gov (United States)

Wang, Wei; Yang, Yongxiao; Yin, Jianxin; Gong, Xinqi

2017-11-22

Different types of protein-protein interactions make different protein-protein interface patterns. Different machine learning methods are suitable to deal with different types of data. Then, is it the same situation that different interface patterns are preferred for prediction by different machine learning methods? Here, four different machine learning methods were employed to predict protein-protein interface residue pairs on different interface patterns. The performances of the methods for different types of proteins are different, which suggest that different machine learning methods tend to predict different protein-protein interface patterns. We made use of ANOVA and variable selection to prove our result. Our proposed methods taking advantages of different single methods also got a good prediction result compared to single methods. In addition to the prediction of protein-protein interactions, this idea can be extended to other research areas such as protein structure prediction and design.

Adjoint optimization scheme for lower hybrid current rampup and profile control in Tokamak

International Nuclear Information System (INIS)

Litaudon, X.; Moreau, D.; Bizarro, J.P.; Hoang, G.T.; Kupfer, K.; Peysson, Y.; Shkarofsky, I.P.; Bonoli, P.

1992-12-01

The purpose of this work is to take into account and study the effect of the electric field profiles on the Lower Hybrid (LH) current drive efficiency during transient phases such as rampup. As a complement to the full ray-tracing / Fokker Planck studies, and for the purpose of optimization studies, we developed a simplified 1-D model based on the adjoint Karney-Fisch numerical results. This approach allows us to estimate the LH power deposition profile which would be required for ramping the current with prescribed rate, total current density profile (q-profile) and surface loop voltage. For rampup optimization studies, we can therefore scan the whole parameter space and eliminate a posteriori those scenarios which correspond to unrealistic deposition profiles. We thus obtain the time evolution of the LH power, minor radius of the plasma, volt-second consumption and total energy dissipated. Optimization can thus be performed with respect to any of those criteria. This scheme is illustrated by some numerical simulations performed with TORE-SUPRA and NET/ITER parameters. We conclude with a derivation of a simple and general scaling law for the flux consumption during the rampup phase

Thermal boundary condition effects on forced convection heat transfer. Application of a numerical solution of an adjoint problem; Kyosei tairyu netsudentatsu mondai ni okeru netsuteki kyokai joken no eikyo. Zuihan mondai no suchi kai wo mochiita kosatsu

Energy Technology Data Exchange (ETDEWEB)

Momose, K.; Saso, K.; Kimoto, H. [Osaka University, Osaka (Japan). Faculty of Engineering Science

1997-11-25

We propose a numerical solution for the adjoint operator of a forced convection heat transfer problem to evaluate mean heat transfer characteristics under arbitrary thermal conditions. Using the numerical solutions of the adjoint problems under Dirichlet and Neumann conditions, both of which can be computed using a conventional CFD code, the influence function of the local surface temperature on the total heat transfer and that of the local surface heat flux on the mean surface temperature are obtained. As a result, the total heat fluxes for arbitrary surface temperature distributions and the mean surface temperatures for arbitrary surface heat flux distributions can be calculated using these influence functions. The influence functions for a circular cylinder and for an in-line square rod array are presented. 14 refs., 9 figs., 1 tab.

Seismic structure of the European upper mantle based on adjoint tomography

Science.gov (United States)

Zhu, Hejun; Bozdağ, Ebru; Tromp, Jeroen

2015-04-01

We use adjoint tomography to iteratively determine seismic models of the crust and upper mantle beneath the European continent and the North Atlantic Ocean. Three-component seismograms from 190 earthquakes recorded by 745 seismographic stations are employed in the inversion. Crustal model EPcrust combined with mantle model S362ANI comprise the 3-D starting model, EU00. Before the structural inversion, earthquake source parameters, for example, centroid moment tensors and locations, are reinverted based on global 3-D Green's functions and Fréchet derivatives. This study consists of three stages. In stage one, frequency-dependent phase differences between observed and simulated seismograms are used to constrain radially anisotropic wave speed variations. In stage two, frequency-dependent phase and amplitude measurements are combined to simultaneously constrain elastic wave speeds and anelastic attenuation. In these two stages, long-period surface waves and short-period body waves 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 simultaneously constrain radial and azimuthal anisotropy. After this three-stage inversion, we obtain a new seismic model of the European curst and upper mantle, named EU60. Improvements in misfits and histograms in both phase and amplitude help us to validate this three-stage inversion strategy. Long-wavelength elastic wave speed variations in model EU60 compare favourably with previous body- and surface wave tomographic models. Some hitherto unidentified features, such as the Adria microplate, naturally emerge from the smooth starting model. Subducting slabs, slab detachments, ancient suture zones, continental rifts and backarc basins are well resolved in model EU60. We find an anticorrelation between shear wave speed and anelastic attenuation at depths agreement with previous global attenuation studies

Forward and adjoint spectral-element simulations of seismic wave propagation using hardware accelerators

Science.gov (United States)

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.

Prediction of the neutrons subcritical multiplication using the diffusion hybrid equation with external neutron sources

Energy Technology Data Exchange (ETDEWEB)

Costa da Silva, Adilson; Carvalho da Silva, Fernando [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-914, Rio de Janeiro (Brazil); Senra Martinez, Aquilino, E-mail: aquilino@lmp.ufrj.br [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-914, Rio de Janeiro (Brazil)

2011-07-15

Highlights: > We proposed a new neutron diffusion hybrid equation with external neutron source. > A coarse mesh finite difference method for the adjoint flux and reactivity calculation was developed. > 1/M curve to predict the criticality condition is used. - Abstract: We used the neutron diffusion hybrid equation, in cartesian geometry with external neutron sources to predict the subcritical multiplication of neutrons in a pressurized water reactor, using a 1/M curve to predict the criticality condition. A Coarse Mesh Finite Difference Method was developed for the adjoint flux calculation and to obtain the reactivity values of the reactor. The results obtained were compared with benchmark values in order to validate the methodology presented in this paper.

Prediction of the neutrons subcritical multiplication using the diffusion hybrid equation with external neutron sources

International Nuclear Information System (INIS)

Costa da Silva, Adilson; Carvalho da Silva, Fernando; Senra Martinez, Aquilino

2011-01-01

Highlights: → We proposed a new neutron diffusion hybrid equation with external neutron source. → A coarse mesh finite difference method for the adjoint flux and reactivity calculation was developed. → 1/M curve to predict the criticality condition is used. - Abstract: We used the neutron diffusion hybrid equation, in cartesian geometry with external neutron sources to predict the subcritical multiplication of neutrons in a pressurized water reactor, using a 1/M curve to predict the criticality condition. A Coarse Mesh Finite Difference Method was developed for the adjoint flux calculation and to obtain the reactivity values of the reactor. The results obtained were compared with benchmark values in order to validate the methodology presented in this paper.

A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians

KAUST Repository

Cagnetti, Filippo; Gomes, Diogo A.; Mitake, Hiroyoshi; Tran, Hung V.

2015-01-01

We investigate large-time asymptotics for viscous Hamilton-Jacobi equations with possibly degenerate diffusion terms. We establish new results on the convergence, which are the first general ones concerning equations which are neither uniformly parabolic nor first order. Our method is based on the nonlinear adjoint method and the derivation of new estimates on long time averaging effects. It also extends to the case of weakly coupled systems.

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

Energy Technology Data Exchange (ETDEWEB)

Slattery, S. R.; Wilson, P. P. H. [Engineering Physics Department, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Evans, T. M. [Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830 (United States)

2013-07-01

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

International Nuclear Information System (INIS)

Slattery, S. R.; Wilson, P. P. H.; Evans, T. M.

2013-01-01

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

Generalized perturbation theory (GPT) methods. A heuristic approach

International Nuclear Information System (INIS)

Gandini, A.

1987-01-01

Wigner first proposed a perturbation theory as early as 1945 to study fundamental quantities such as the reactivity worths of different materials. The first formulation, CPT, for conventional perturbation theory is based on universal quantum mechanics concepts. Since that early conception, significant contributions have been made to CPT, in particular, Soodak, who rendered a heuristic interpretation of the adjoint function, (referred to as the GPT method for generalized perturbation theory). The author illustrates the GPT methodology in a variety of linear and nonlinear domains encountered in nuclear reactor analysis. The author begins with the familiar linear neutron field and then generalizes the methodology to other linear and nonlinear fields, using heuristic arguments. The author believes that the inherent simplicity and elegance of the heuristic derivation, although intended here for reactor physics problems might be usefully adopted in collateral fields and includes such examples

Deterministic Local Sensitivity Analysis of Augmented Systems - I: Theory

International Nuclear Information System (INIS)

Cacuci, Dan G.; Ionescu-Bujor, Mihaela

2005-01-01

This work provides the theoretical foundation for the modular implementation of the Adjoint Sensitivity Analysis Procedure (ASAP) for large-scale simulation systems. The implementation of the ASAP commences with a selected code module and then proceeds by augmenting the size of the adjoint sensitivity system, module by module, until the entire system is completed. Notably, the adjoint sensitivity system for the augmented system can often be solved by using the same numerical methods used for solving the original, nonaugmented adjoint system, particularly when the matrix representation of the adjoint operator for the augmented system can be inverted by partitioning

Zero modes and the vacuum problem: A study of scalar adjoint matter in two-dimensional Yang-Mills theory via light-cone quantization

International Nuclear Information System (INIS)

Kalloniatis, A.C.

1996-01-01

SU(2) Yang-Mills theory coupled to massive adjoint scalar matter is studied in 1+1 dimensions using discretized light-cone quantization. This theory can be obtained from pure Yang-Mills theory in 2+1 dimensions via dimensional reduction. On the light cone, the vacuum structure of this theory is encoded in the dynamical zero mode of a gluon and a constrained mode of the scalar field. The latter satisfies a linear constraint, suggesting no nontrivial vacua in the present paradigm for symmetry breaking on the light cone. I develop a diagrammatic method to solve the constraint equation. In the adiabatic approximation I compute the quantum-mechanical potential governing the dynamical gauge mode. Because of a condensation of the lowest momentum modes of the dynamical gluons, a centrifugal barrier is generated in the adiabatic potential. In the present theory, however, the barrier height appears too small to make any impact in this model. Although the theory is superrenormalizable on naive power-counting grounds, the removal of ultraviolet divergences is nontrivial when the constrained mode is taken into account. The solution of this problem is discussed. copyright 1996 The American Physical Society

Support Operators Method for the Diffusion Equation in Multiple Materials

Energy Technology Data Exchange (ETDEWEB)

Winters, Andrew R. [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory

2012-08-14

A second-order finite difference scheme for the solution of the diffusion equation on non-uniform meshes is implemented. The method allows the heat conductivity to be discontinuous. The algorithm is formulated on a one dimensional mesh and is derived using the support operators method. A key component of the derivation is that the discrete analog of the flux operator is constructed to be the negative adjoint of the discrete divergence, in an inner product that is a discrete analog of the continuum inner product. The resultant discrete operators in the fully discretized diffusion equation are symmetric and positive definite. The algorithm is generalized to operate on meshes with cells which have mixed material properties. A mechanism to recover intermediate temperature values in mixed cells using a limited linear reconstruction is introduced. The implementation of the algorithm is verified and the linear reconstruction mechanism is compared to previous results for obtaining new material temperatures.

Detector placement optimization for cargo containers using deterministic adjoint transport examination for SNM detection

International Nuclear Information System (INIS)

McLaughlin, Trevor D.; Sjoden, Glenn E.; Manalo, Kevin L.

2011-01-01

With growing concerns over port security and the potential for illicit trafficking of SNM through portable cargo shipping containers, efforts are ongoing to reduce the threat via container monitoring. This paper focuses on answering an important question of how many detectors are necessary for adequate coverage of a cargo container considering the detection of neutrons and gamma rays. Deterministic adjoint transport calculations are performed with compressed helium- 3 polyethylene moderated neutron detectors and sodium activated cesium-iodide gamma-ray scintillation detectors on partial and full container models. Results indicate that the detector capability is dependent on source strength and potential shielding. Using a surrogate weapons grade plutonium leakage source, it was determined that for a 20 foot ISO container, five neutron detectors and three gamma detectors are necessary for adequate coverage. While a large CsI(Na) gamma detector has the potential to monitor the entire height of the container for SNM, the He-3 neutron detector is limited to roughly 1.25 m in depth. Detector blind spots are unavoidable inside the container volume unless additional measures are taken for adequate coverage. (author)

Adjoint-based optimization of mechanical performance in polycrystalline materials and structures through texture control

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.

An inverse method for radiation transport

Energy Technology Data Exchange (ETDEWEB)

Favorite, J. A. (Jeffrey A.); Sanchez, R. (Richard)

2004-01-01

Adjoint functions have been used with forward functions to compute gradients in implicit (iterative) solution methods for inverse problems in optical tomography, geoscience, thermal science, and other fields, but only once has this approach been used for inverse solutions to the Boltzmann transport equation. In this paper, this approach is used to develop an inverse method that requires only angle-independent flux measurements, rather than angle-dependent measurements as was done previously. The method is applied to a simplified form of the transport equation that does not include scattering. The resulting procedure uses measured values of gamma-ray fluxes of discrete, characteristic energies to determine interface locations in a multilayer shield. The method was implemented with a Newton-Raphson optimization algorithm, and it worked very well in numerical one-dimensional spherical test cases. A more sophisticated optimization method would better exploit the potential of the inverse method.

Research on Monte Carlo improved quasi-static method for reactor space-time dynamics

International Nuclear Information System (INIS)

Xu Qi; Wang Kan; Li Shirui; Yu Ganglin

2013-01-01

With large time steps, improved quasi-static (IQS) method can improve the calculation speed for reactor dynamic simulations. The Monte Carlo IQS method was proposed in this paper, combining the advantages of both the IQS method and MC method. Thus, the Monte Carlo IQS method is beneficial for solving space-time dynamics problems of new concept reactors. Based on the theory of IQS, Monte Carlo algorithms for calculating adjoint neutron flux, reactor kinetic parameters and shape function were designed and realized. A simple Monte Carlo IQS code and a corresponding diffusion IQS code were developed, which were used for verification of the Monte Carlo IQS method. (authors)

Influence of the external neutron sources in the criticality prediction using 1/M curve

Energy Technology Data Exchange (ETDEWEB)

Pereira, Valmir [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-972 Rio de Janeiro (Brazil); Carvalho da Silva, Fernando [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-972 Rio de Janeiro (Brazil); Martinez, Aquilino Senra [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-972 Rio de Janeiro (Brazil)]. E-mail: aquilino@lmp.ufrj.br

2005-11-15

The influence of external neutron sources in the process to obtain the criticality condition is estimated. To reach this objective, the three-dimensional neutron diffusion equation in two groups of energy is solved, for a subcritical PWR reactor core with external neutron sources. The results are compared with the solution of the corresponding problem without external neutron sources, that is an eigenvalue problem. The method developed for this purposes it makes use of both the nodal method (for calculation of the neutron flux) and the finite differences method (for calculation of the adjoint flux). A coarse mesh finite difference method was developed for the adjoint flux calculation, which uses the output of the nodal expansion method. The results regarding the influence of the external neutron source presence for attaining criticality have shown that far from criticality it is necessary to calculate the reactivity values of the system.

Influence of the external neutron sources in the criticality prediction using 1/M curve

International Nuclear Information System (INIS)

Pereira, Valmir; Carvalho da Silva, Fernando; Martinez, Aquilino Senra

2005-01-01

The influence of external neutron sources in the process to obtain the criticality condition is estimated. To reach this objective, the three-dimensional neutron diffusion equation in two groups of energy is solved, for a subcritical PWR reactor core with external neutron sources. The results are compared with the solution of the corresponding problem without external neutron sources, that is an eigenvalue problem. The method developed for this purposes it makes use of both the nodal method (for calculation of the neutron flux) and the finite differences method (for calculation of the adjoint flux). A coarse mesh finite difference method was developed for the adjoint flux calculation, which uses the output of the nodal expansion method. The results regarding the influence of the external neutron source presence for attaining criticality have shown that far from criticality it is necessary to calculate the reactivity values of the system

Interpretation of incore noise measurements in BWR's

International Nuclear Information System (INIS)

Dam, H. van

1982-01-01

A survey is given of the main incentives for power reactor noise research and the differences and similarities of noise in power and zero power systems are touched on. The basic characteristics of the adjoint method in reactor noise theory are treated. The detector adjoint functions describe the transfer functions between spatially distributed noise sources and a (neutron or gamma) detector. In particular, the spatial dependence of these functions explains the 'local' and 'global' effects in BWR noise measurements. By including thermal hydraulic feedback effects in the adjoint analysis, it is shown that the common idea of a dominant global effect at low frequencies which should result in point kinetic behaviour, is erroneous. The same analysis provides a method for nonperturbing on-line measurement of the reactor transfer function, which is demonstrated by results from measurements on a BWR in the Netherlands. In the final part of the paper some ideas are given for further research in the field of BWR noise. (author)

Interpretation of incore noise measurements in BWR's

International Nuclear Information System (INIS)

Dam, H. van

1983-01-01

A survey is given of the main incentives for power reactor noise research, and the differences and similarities of noise in power and zero power systems are shown. After a short outline of historical developments the basic characteristics of the adjoint method in reactor noise theory are dealt with. The detector adjoint functions describe the transfer functions between spatially distributed noise sources and a (neutron or gamma) detector. In particular, the spatial dependence of these functions explains the 'local' and 'global' effects in BWR noise measurements. By including thermal hydraulic feedback effects in the adjoint analysis, it is shown that the common idea of a dominant global effect at low frequencies, which should result in point kinetic behaviour, is erroneous. The same analysis provides a method for nonperturbing on-line measurements on a BWR in The Netherlands. In the final part of the paper some ideas are given for further research in the field of BWR noise. (author)

Uncertainty analysis

International Nuclear Information System (INIS)

Thomas, R.E.

1982-03-01

An evaluation is made of the suitability of analytical and statistical sampling methods for making uncertainty analyses. The adjoint method is found to be well-suited for obtaining sensitivity coefficients for computer programs involving large numbers of equations and input parameters. For this purpose the Latin Hypercube Sampling method is found to be inferior to conventional experimental designs. The Latin hypercube method can be used to estimate output probability density functions, but requires supplementary rank transformations followed by stepwise regression to obtain uncertainty information on individual input parameters. A simple Cork and Bottle problem is used to illustrate the efficiency of the adjoint method relative to certain statistical sampling methods. For linear models of the form Ax=b it is shown that a complete adjoint sensitivity analysis can be made without formulating and solving the adjoint problem. This can be done either by using a special type of statistical sampling or by reformulating the primal problem and using suitable linear programming software

Adaptive finite element method for shape optimization

KAUST Repository

Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco

2012-01-01

We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.

Adaptive finite element method for shape optimization

KAUST Repository

Morin, Pedro

2012-01-16

We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.

Error estimation for goal-oriented spatial adaptivity for the SN equations on triangular meshes

International Nuclear Information System (INIS)

Lathouwers, D.

2011-01-01

In this paper we investigate different error estimation procedures for use within a goal oriented adaptive algorithm for the S N equations on unstructured meshes. The method is based on a dual-weighted residual approach where an appropriate adjoint problem is formulated and solved in order to obtain the importance of residual errors in the forward problem on the specific goal of interest. The forward residuals and the adjoint function are combined to obtain both economical finite element meshes tailored to the solution of the target functional as well as providing error estimates. Various approximations made to make the calculation of the adjoint angular flux more economically attractive are evaluated by comparing the performance of the resulting adaptive algorithm and the quality of the error estimators when applied to two shielding-type test problems. (author)

A method of the sensitivity analysis of build-up and decay of actinides

International Nuclear Information System (INIS)

Mitani, Hiroshi; Koyama, Kinji; Kuroi, Hideo

1977-07-01

To make sensitivity analysis of build-up and decay of actinides, mathematical methods related to this problem have been investigated in detail. Application of time-dependent perturbation technique and Bateman method to sensitivity analysis is mainly studied. For the purpose, a basic equation and its adjoint equation for build-up and decay of actinides are systematically solved by introducing Laplace and modified Laplace transforms and their convolution theorems. Then, the mathematical method of sensitivity analyses is formulated by the above technique; its physical significance is also discussed. Finally, application of eigenvalue-method is investigated. Sensitivity coefficients can be directly calculated by this method. (auth.)

Efficient transfer of sensitivity information in multi-component models

International Nuclear Information System (INIS)

Abdel-Khalik, Hany S.; Rabiti, Cristian

2011-01-01

In support of adjoint-based sensitivity analysis, this manuscript presents a new method to efficiently transfer adjoint information between components in a multi-component model, whereas the output of one component is passed as input to the next component. Often, one is interested in evaluating the sensitivities of the responses calculated by the last component to the inputs of the first component in the overall model. The presented method has two advantages over existing methods which may be classified into two broad categories: brute force-type methods and amalgamated-type methods. First, the presented method determines the minimum number of adjoint evaluations for each component as opposed to the brute force-type methods which require full evaluation of all sensitivities for all responses calculated by each component in the overall model, which proves computationally prohibitive for realistic problems. Second, the new method treats each component as a black-box as opposed to amalgamated-type methods which requires explicit knowledge of the system of equations associated with each component in order to reach the minimum number of adjoint evaluations. (author)

GRASP [GRound-Water Adjunct Sensitivity Program]: A computer code to perform post-SWENT [simulator for water, energy, and nuclide transport] adjoint sensitivity analysis of steady-state ground-water flow: Technical report

International Nuclear Information System (INIS)

Wilson, J.L.; RamaRao, B.S.; McNeish, J.A.

1986-11-01

GRASP (GRound-Water Adjunct Senstivity Program) computes measures of the behavior of a ground-water system and the system's performance for waste isolation, and estimates the sensitivities of these measures to system parameters. The computed measures are referred to as ''performance measures'' and include weighted squared deviations of computed and observed pressures or heads, local Darcy velocity components and magnitudes, boundary fluxes, and travel distance and time along travel paths. The sensitivities are computed by the adjoint method and are exact derivatives of the performance measures with respect to the parameters for the modeled system, taken about the assumed parameter values. GRASP presumes steady-state, saturated grondwater flow, and post-processes the results of a multidimensional (1-D, 2-D, 3-D) finite-difference flow code. This document describes the mathematical basis for the model, the algorithms and solution techniques used, and the computer code design. The implementation of GRASP is verified with simple one- and two-dimensional flow problems, for which analytical expressions of performance measures and sensitivities are derived. The linkage between GRASP and multidimensional finite-difference flow codes is described. This document also contains a detailed user's manual. The use of GRASP to evaluate nuclear waste disposal issues has been emphasized throughout the report. The performance measures and their sensitivities can be employed to assist in directing data collection programs, expedite model calibration, and objectively determine the sensitivity of projected system performance to parameters

Adjoint sensitivity analysis applied on a model of irradiation assisted degradation of metals in aqueous systems

International Nuclear Information System (INIS)

Simonson, S.A.; Ballinger, R.G.; Christensen, R.A.

1990-01-01

Irradiation of an aqueous environment results, in general, in a steady state concentration of oxidizing chemical species in solution. Although the effect may be beneficial to the metal in contact with the solution in some cases, say by producing a more protective film, it is generally believed to be detrimental. The ability to predict the concentrations of the oxidizing species and from this begin to analyze the detrimental behavior on the metals requires computer codes that model the chemical reactions, production rates, and diffusion characteristics of the species being produced by irradiation. The large number of parameters and the complexity of the interactions involved in the predictions of irradiation effects on metals degradation requires a more sophisticated approach to determining the sensitivities of the final results. Monte Carlo techniques are too computationally intensive for practical use in determining sensitivities. The paper presents an approach, adjoint sensitivity analysis, that is more practical, i.e., three computer runs versus thousands, and also a more accurate measure of the sensitivities of the model

An Adjoint State Method for Three-Dimensional Transmission Traveltime Tomography Using First-Arrivals

Science.gov (United States)

2006-01-30

detail next. 3.2 Fast Sweeping Method for Equation (1) The fast sweeping method was originated in Boue and Dupis [5], its first PDE formulation was in...Geophysics, 50:903–923, 1985. [5] M. Boue and P. Dupuis. Markov chain approximations for deterministic control prob- lems with affine dynamics and

BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N=4 SUSY

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.

A conjecture for the effective condition of Jimbo's method

International Nuclear Information System (INIS)

Ma Zhongqi

1992-01-01

The method for constructing the spectrum-dependent solutions to the Yang-Baxter equation, according to Jimbo's theorem, is based on the existence of the representation matrix of e 0 , corresponding to the lowest negative root, in an irreducible representation of a quantum enveloping algebra. In this paper a conjecture for the existent condition of the representation matrix of e 0 is made. As an example, the adjoint representation of U q C 2 is discussed where the representation matrix e 0 does not exist because the existent condition is violated

Adjoint acceleration of Monte Carlo simulations using TORT/MCNP coupling approach: A case study on the shielding improvement for the cyclotron room of the Buddhist Tzu Chi General Hospital

International Nuclear Information System (INIS)

Sheu, R. J.; Sheu, R. D.; Jiang, S. H.; Kao, C. H.

2005-01-01

Full-scale Monte Carlo simulations of the cyclotron room of the Buddhist Tzu Chi General Hospital were carried out to improve the original inadequate maze design. Variance reduction techniques are indispensable in this study to facilitate the simulations for testing a variety of configurations of shielding modification. The TORT/MCNP manual coupling approach based on the Consistent Adjoint Driven Importance Sampling (CADIS) methodology has been used throughout this study. The CADIS utilises the source and transport biasing in a consistent manner. With this method, the computational efficiency was increased significantly by more than two orders of magnitude and the statistical convergence was also improved compared to the unbiased Monte Carlo run. This paper describes the shielding problem encountered, the procedure for coupling the TORT and MCNP codes to accelerate the calculations and the calculation results for the original and improved shielding designs. In order to verify the calculation results and seek additional accelerations, sensitivity studies on the space-dependent and energy-dependent parameters were also conducted. (authors)

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

Science.gov (United States)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the

3D CSEM inversion based on goal-oriented adaptive finite element method

Science.gov (United States)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

Droplet number uncertainties associated with CCN: an assessment using observations and a global model adjoint

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.

Nuclear methods in medical physics

International Nuclear Information System (INIS)

Jeraj, R.

2003-01-01

A common ground for both, reactor and medical physics is a demand for high accuracy of particle transport calculations. In reactor physics, safe operation of nuclear power plants has been asking for high accuracy of calculation methods. Similarly, dose calculation in radiation therapy for cancer has been requesting high accuracy of transport methods to ensure adequate dosimetry. Common to both problems has always been a compromise between achievable accuracy and available computer power leading into a variety of calculation methods developed over the decades. On the other hand, differences of subjects (nuclear reactor vs. humans) and radiation types (neutron/photon vs. photon/electron or ions) are calling for very field-specific approach. Nevertheless, it is not uncommon to see drift of researches from one field to another. Several examples from both fields will be given with the aim to compare the problems, indicating their similarities and discussing their differences. As examples of reactor physics applications, both deterministic and Monte Carlo calculations will be presented for flux distributions of the VENUS and TRIGA Mark II benchmark. These problems will be paralleled to medical physics applications in linear accelerator radiation field determination and dose distribution calculations. Applicability of the adjoint/forward transport will be discussed in the light of both transport problems. Boron neutron capture therapy (BNCT) as an example of the close collaboration between the fields will be presented. At last, several other examples from medical physics, which can and cannot find corresponding problems in reactor physics, will be discussed (e.g., beam optimisation in inverse treatment planning, imaging applications). (author)

Efficient estimation of feedback effects with application to climate models

International Nuclear Information System (INIS)

Cacugi, D.G.; Hall, M.C.G.

1984-01-01

This work presents an efficient method for calculating the sensitivity of a mathematical model's result to feedback. Feedback is defined in terms of an operator acting on the model's dependent variables. The sensitivity to feedback is defined as a functional derivative, and a method is presented to evaluate this derivative using adjoint functions. Typically, this method allows the individual effect of many different feedbacks to be estimated with a total additional computing time comparable to only one recalculation. The effects on a CO 2 -doubling experiment of actually incorporating surface albedo and water vapor feedbacks in radiative-convective model are compared with sensivities calculated using adjoint functions. These sensitivities predict the actual effects of feedback with at least the correct sign and order of magnitude. It is anticipated that this method of estimation the effect of feedback will be useful for more complex models where extensive recalculations for each of a variety of different feedbacks is impractical

On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar N=4 SYM

Energy Technology Data Exchange (ETDEWEB)

Bondarenko, Sergey; Prygarin, Alex [Physics Department, Ariel University,Ariel 40700, territories administered by (Israel)

2016-07-15

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. http://arxiv.org/abs/1510.00589 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.

Atmospheric weighting functions and surface partial derivatives for remote sensing of scattering planetary atmospheres in thermal spectral region: general adjoint approach

International Nuclear Information System (INIS)

Ustinov, Eugene A.

2005-01-01

An approach to formulation of inversion algorithms for remote sensing in the thermal spectral region in the case of a scattering planetary atmosphere, based on the adjoint equation of radiative transfer (Ustinov (JQSRT 68 (2001) 195; JQSRT 73 (2002) 29); referred to as Papers 1 and 2, respectively, in the main text), is applied to the general case of retrievals of atmospheric and surface parameters for the scattering atmosphere with nadir viewing geometry. Analytic expressions for corresponding weighting functions for atmospheric parameters and partial derivatives for surface parameters are derived. The case of pure atmospheric absorption with a scattering underlying surface is considered and convergence to results obtained for the non-scattering atmospheres (Ustinov (JQSRT 74 (2002) 683), referred to as Paper 3 in the main text) is demonstrated

Inverse analysis of a rectangular fin using the lattice Boltzmann method

International Nuclear Information System (INIS)

Bamdad, Keivan; Ashorynejad, Hamid Reza

2015-01-01

Highlights: • Lattice Boltzmann method is used to study a transient conductive-convective fin. • LBM and Conjugate Gradient Method (CGM) are used to solve an inverse problem in fins. • LBM–ACGM estimates the unknown boundary conditions of fins accurately. • The accuracy and CPU time of LBM–ACGM are compared to IFDM–ACGM. • LBM–ACGM could be a good alternative for the conventional inverse methods. - Abstract: Inverse methods have many applications in determining unknown variables in heat transfer problems when direct measurements are impossible. As most common inverse methods are iterative and time consuming especially for complex geometries, developing more efficient methods seems necessary. In this paper, a direct transient conduction–convection heat transfer problem (fin) under several boundary conditions was solved by using lattice Boltzmann method (LBM), and then the results were successfully validated against both the finite difference method and analytical solution. Then, in the inverse problem both unknown base temperatures and heat fluxes in the rectangular fin were estimated by combining the adjoint conjugate gradient method (ACGM) and LBM. A close agreement between the exact values and estimated results confirmed the validity and accuracy of the ACGM–LBM. To compare the calculation time of ACGM–LBM, the inverse problem was solved by implicit finite difference methods as well. This comparison proved that the ACGM–LBM was an accurate and fast method to determine unknown thermal boundary conditions in transient conduction–convection heat transfer problems. The findings can efficiently determine the unknown variables in fins when a desired temperature distribution is available

Predictor-Corrector Quasi-Static Method Applied to Nonoverlapping Local/Global Iterations with 2-D/1-D Fusion Transport Kernel and p-CMFD Wrapper for Transient Reactor Analysis

International Nuclear Information System (INIS)

Cho, Bumhee; Cho, Nam Zin

2015-01-01

In this study, the steady-state p-CMFD adjoint flux is used as the weighting function to obtain PK parameters instead of the computationally expensive transport adjoint angular flux. Several numerical problems are investigated to see the capability of the PCQS method applied to the NLG iteration. CRX-2K adopts the nonoverlapping local/global (NLG) iterative method with the 2-D/1-D fusion transport kernel and the global p-CMFD wrapper. The parallelization of the NLG iteration has been recently implemented in CRX-2K and several numerical results are reported in a companion paper. However, the direct time discretization leads to a fine time step size to acquire an accurate transient solution, and the step size involved in the transport transient calculations is millisecond-order. Therefore, the transient calculations need much longer computing time than the steady-state calculation. To increase the time step size, Predictor-Corrector Quasi-Static (PCQS) method can be one option to apply to the NLG iteration. The PCQS method is a linear algorithm, so the shape function does not need to be updated more than once at a specific time step like a conventional quasi-static (QS) family such as Improved Quasi-Static (IQS) method. Moreover, the shape function in the PCQS method directly comes from the direct transport calculation (with a large time step), so one can easily implement the PCQS method in an existing transient transport code. Any QS method needs to solve the amplitude function in the form of the point kinetics (PK) equations, and accurate PK parameters can be obtained by the transport steady-state adjoint angular flux as a weighting function. The PCQS method is applied to the transient NLG iteration with the 2-D/1-D fusion transport kernel and the global p-CMFD wrapper, and has been implemented in CRX-2K. In the numerical problems, the PCQS method with the NLG iteration shows more accurate solutions compared to the direct transient calculations with large time step

Analytical approximations for wide and narrow resonances

International Nuclear Information System (INIS)

Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2005-01-01

This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U 238 were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author)

Analytical approximations for wide and narrow resonances

Energy Technology Data Exchange (ETDEWEB)

Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br

2005-07-01

This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U{sup 238} were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author)

Optimal design method for magnetization directions of a permanent magnet array

Energy Technology Data Exchange (ETDEWEB)

Choi, Jae Seok [Center for Information Storage Device, Yonsei University, 262 Seongsanno, Seodaemun-gu, Seoul 120-749 (Korea, Republic of); Yoo, Jeonghoon, E-mail: yoojh@yonsei.ac.k [School of Mechanical Engineering, Yonsei University, 262 Seongsanno, Seodaemun-gu, Seoul 120-749 (Korea, Republic of)

2010-08-15

In many magnetic systems, the permanent magnet (PM) pattern has a great influence on their performance. This study proposes a systematic optimization method for designing discrete magnetization directions. While previous works have been mostly dependent on researchers' intuition, the developed method is systematic and can be applied to a two-dimensional PM-type eddy current brake model. The effectiveness of the method is confirmed, where the design's aim is to maximize the braking force on a moving conductor. The sensitivity analysis is accomplished by the adjoint variable method and the sequential linear programming is used as an optimizer. Several optimization results for various conditions through the proposed design method are compared to each other and the optimal magnet configuration for an eddy current brake is suggested.

Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling

KAUST Repository

Liu, Shaolin

2017-09-28

The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.

Comparison of Thermal Properties Measured by Different Methods

International Nuclear Information System (INIS)

Sundberg, Jan; Kukkonen, Ilmo; Haelldahl, Lars

2003-04-01

A strategy for a thermal site descriptive model of bedrock is under development at SKB. In the model different kinds of uncertainties exist. Some of these uncertainties are related to the potential errors in the methods used for determining thermal properties of rock. In two earlier investigations thermal properties of rock samples were analysed according to the TPS method (transient plane source). Thermal conductivity and thermal diffusivity were determined using the TPS method. For a comparison, the same samples have been measured at the Geological Survey of Finland (GSF), using different laboratory methods. In this later investigation, the thermal conductivity was determined using the divided-bar method and the specific heat capacity using a calorimetric method. The mean differences between the results of different methods are relatively low but the results of individual samples show large variations. The thermal conductivity measured by the divided bar method gives for most samples slightly higher values, in average about 3%, than the TPS method. The specific heat capacity measured by the calorimetric method gives lower values, in average about 2%, than the TPS method. Consequently, the thermal diffusivity calculated from thermal conductivity and specific heat capacity gives higher values, in average about 6%, than the TPS method. Reasons for the differences are estimated mainly to be dependent on differences between the samples, errors in the temperature dependence of specific heat and in the transformation from volumetric to specific heat. The TPS measurements are performed using two pieces (sub-samples) of rock. Only one of these two sub-samples was measured using the divided bar method and the calorimetric method. Further, sample preparation involved changes in the size of some of the samples. The mean differences between the results of different methods are within the margins of error reported by the measuring laboratories. However, systematic errors in

Comparison of Thermal Properties Measured by Different Methods

Energy Technology Data Exchange (ETDEWEB)

Sundberg, Jan [Geo Innova AB, Linkoeping (Sweden); Kukkonen, Ilmo [Geological Survey of Finland, Helsinki (Finland); Haelldahl, Lars [Hot Disk AB, Uppsala (Sweden)

2003-04-01

A strategy for a thermal site descriptive model of bedrock is under development at SKB. In the model different kinds of uncertainties exist. Some of these uncertainties are related to the potential errors in the methods used for determining thermal properties of rock. In two earlier investigations thermal properties of rock samples were analysed according to the TPS method (transient plane source). Thermal conductivity and thermal diffusivity were determined using the TPS method. For a comparison, the same samples have been measured at the Geological Survey of Finland (GSF), using different laboratory methods. In this later investigation, the thermal conductivity was determined using the divided-bar method and the specific heat capacity using a calorimetric method. The mean differences between the results of different methods are relatively low but the results of individual samples show large variations. The thermal conductivity measured by the divided bar method gives for most samples slightly higher values, in average about 3%, than the TPS method. The specific heat capacity measured by the calorimetric method gives lower values, in average about 2%, than the TPS method. Consequently, the thermal diffusivity calculated from thermal conductivity and specific heat capacity gives higher values, in average about 6%, than the TPS method. Reasons for the differences are estimated mainly to be dependent on differences between the samples, errors in the temperature dependence of specific heat and in the transformation from volumetric to specific heat. The TPS measurements are performed using two pieces (sub-samples) of rock. Only one of these two sub-samples was measured using the divided bar method and the calorimetric method. Further, sample preparation involved changes in the size of some of the samples. The mean differences between the results of different methods are within the margins of error reported by the measuring laboratories. However, systematic errors in

Solution of axisymmetric transient inverse heat conduction problems using parameter estimation and multi block methods

International Nuclear Information System (INIS)

Azimi, A.; Hannani, S.K.; Farhanieh, B.

2005-01-01

In this article, a comparison between two iterative inverse techniques to solve simultaneously two unknown functions of axisymmetric transient inverse heat conduction problems in semi complex geometries is presented. The multi-block structured grid together with blocked-interface nodes is implemented for geometric decomposition of physical domain. Numerical scheme for solution of transient heat conduction equation is the finite element method with frontal technique to solve algebraic system of discrete equations. The inverse heat conduction problem involves simultaneous unknown time varying heat generation and time-space varying boundary condition estimation. Two parameter-estimation techniques are considered, Levenberg-Marquardt scheme and conjugate gradient method with adjoint problem. Numerically computed exact and noisy data are used for the measured transient temperature data needed in the inverse solution. The results of the present study for a configuration including two joined disks with different heights are compared to those of exact heat source and temperature boundary condition, and show good agreement. (author)

Ethiopian Journal of Education and Sciences - Vol 13, No 1 (2017)

African Journals Online (AJOL)

Sixth order stable central difference method for self-adjoint singularly perturbed two-point boundary value problems · EMAIL FREE FULL TEXT EMAIL FREE FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT. Yitbarek Zeslassie, Gemechis File, Tesfaye Aga, 23-41 ...

Radial anisotropy of the North American upper mantle based on adjoint tomography with USArray

Science.gov (United States)

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

SPEED POWER AFTER DIFFERENT TRAINING METHODS

Directory of Open Access Journals (Sweden)

Milan Gužvica

2011-09-01

Full Text Available As the strength is a very important capability, with which are more or less, related and all other motor skills relevant to the successful conduct of sports fight in karate, we were interested in what extent the ability of the speed of force development changes under the influence of different types of loads. For this purpose we used two different methods: the development of speed power with weights and plyometric method. Research is organized on a sample of 20 subjects (first year students of the College of Internal Affairs in Banja Luka, divided into two groups, of which only 12 students responded to the demands of research. The program was implemented during the period of six weeks for two hours per week. Before beginning and three days after the training process, we also tested levels of speed power using eight specific motor tests. After completion of the initial and final measurements, data were analyzed by appropriate statistical procedures, where all respondents, across the various tests, achieved better results. However, statistically significant differences were not obtained in both groups. Specifically, statistically significant differences were obtained in the group T across the various tests, while in group P, statistically significant differences were not obtained in three tests conducted. Given results allowed us that, with caution, we conclude that the method of working with weights, in a limited period of time, when it comes to beginners, is still more efficient than the plyometric method of work. Therefore recommendation for increasing the speed power, in a limited period of time, is to use a method of working with weights.

An inverse method for non linear ablative thermics with experimentation of automatic differentiation

Energy Technology Data Exchange (ETDEWEB)

Alestra, S [Simulation Information Technology and Systems Engineering, EADS IW Toulouse (France); Collinet, J [Re-entry Systems and Technologies, EADS ASTRIUM ST, Les Mureaux (France); Dubois, F [Professor of Applied Mathematics, Conservatoire National des Arts et Metiers Paris (France)], E-mail: stephane.alestra@eads.net, E-mail: jean.collinet@astrium.eads.net, E-mail: fdubois@cnam.fr

2008-11-01

Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.

Track 4: basic nuclear science variance reduction for Monte Carlo criticality simulations. 6. Variational Variance Reduction for Monte Carlo Criticality Calculations

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Larsen, Edward W.

2001-01-01

. We present results from a class of criticality calculations. These problems consist of alternating arrays of fuel and moderator regions, each region being 3.0 cm thick. Forward Monte Carlo calculations were run with (a) traditional Monte Carlo using a track-length estimate of k and survival biasing (SB); (b) the new VVR method without the linear spatial term (VVR1); (c) the new VVR method without the linear spatial term, but with SB (VVR1/SB); (d) the new VVR method with the linear spatial term (VVR2); and (e) the new VVR method with the linear spatial term and with SB (VVR2/SB). The traditional Monte Carlo calculation was performed with SB since this resulted in a higher FOM than using analog Monte Carlo. We performed the adjoint calculation using a finite difference diffusion code with a fine-mesh size of Δx = 0.1 cm. The time required to perform the deterministic adjoint calculation was much less than the time required for the Monte Carlo calculation and evaluation of the variational functional and is not included in the FOM. For each problem, the new VVR method outperforms the traditional Monte Carlo method, and the VVR method with the linear spatial term performs slightly better. For the largest problem, the two VVR methods without survival biasing (SB) outperformed the traditional Monte Carlo method by a factor of 36. We note that the use of SB decreases the efficiency of the VVR method. This decrease in FOM is due to the extra cost per history of the VVR method and the longer history length incurred by using SB. However, the new VVR method still outperforms the traditional Monte Carlo calculation even when (non-optimally) used with SB. In conclusion, we have developed a new VVR method for Monte Carlo criticality calculations. This method employs (a) a variational functional that is more accurate than the standard direct functional, (b) a representation of the deterministically obtained adjoint flux that is especially accurate for optically thick problems with

Topology optimization using the improved element-free Galerkin method for elasticity*

International Nuclear Information System (INIS)

Wu Yi; Ma Yong-Qi; Feng Wei; Cheng Yu-Min

2017-01-01

The improved element-free Galerkin (IEFG) method of elasticity is used to solve the topology optimization problems. In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin (EFG) method. The central processing unit (CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown. (paper)

Adjoint sensitivity analysis of dynamic reliability models based on Markov chains - II: Application to IFMIF reliability assessment

Energy Technology Data Exchange (ETDEWEB)

Cacuci, D. G. [Commiss Energy Atom, Direct Energy Nucl, Saclay, (France); Cacuci, D. G.; Balan, I. [Univ Karlsruhe, Inst Nucl Technol and Reactor Safetly, Karlsruhe, (Germany); Ionescu-Bujor, M. [Forschungszentrum Karlsruhe, Fus Program, D-76021 Karlsruhe, (Germany)

2008-07-01

In Part II of this work, the adjoint sensitivity analysis procedure developed in Part I is applied to perform sensitivity analysis of several dynamic reliability models of systems of increasing complexity, culminating with the consideration of the International Fusion Materials Irradiation Facility (IFMIF) accelerator system. Section II presents the main steps of a procedure for the automated generation of Markov chains for reliability analysis, including the abstraction of the physical system, construction of the Markov chain, and the generation and solution of the ensuing set of differential equations; all of these steps have been implemented in a stand-alone computer code system called QUEFT/MARKOMAG-S/MCADJSEN. This code system has been applied to sensitivity analysis of dynamic reliability measures for a paradigm '2-out-of-3' system comprising five components and also to a comprehensive dynamic reliability analysis of the IFMIF accelerator system facilities for the average availability and, respectively, the system's availability at the final mission time. The QUEFT/MARKOMAG-S/MCADJSEN has been used to efficiently compute sensitivities to 186 failure and repair rates characterizing components and subsystems of the first-level fault tree of the IFMIF accelerator system. (authors)

Adjoint sensitivity analysis of dynamic reliability models based on Markov chains - II: Application to IFMIF reliability assessment

International Nuclear Information System (INIS)

Cacuci, D. G.; Cacuci, D. G.; Balan, I.; Ionescu-Bujor, M.

2008-01-01

In Part II of this work, the adjoint sensitivity analysis procedure developed in Part I is applied to perform sensitivity analysis of several dynamic reliability models of systems of increasing complexity, culminating with the consideration of the International Fusion Materials Irradiation Facility (IFMIF) accelerator system. Section II presents the main steps of a procedure for the automated generation of Markov chains for reliability analysis, including the abstraction of the physical system, construction of the Markov chain, and the generation and solution of the ensuing set of differential equations; all of these steps have been implemented in a stand-alone computer code system called QUEFT/MARKOMAG-S/MCADJSEN. This code system has been applied to sensitivity analysis of dynamic reliability measures for a paradigm '2-out-of-3' system comprising five components and also to a comprehensive dynamic reliability analysis of the IFMIF accelerator system facilities for the average availability and, respectively, the system's availability at the final mission time. The QUEFT/MARKOMAG-S/MCADJSEN has been used to efficiently compute sensitivities to 186 failure and repair rates characterizing components and subsystems of the first-level fault tree of the IFMIF accelerator system. (authors)

Implicit and fully implicit exponential finite difference methods

Indian Academy of Sciences (India)

Burgers' equation; exponential finite difference method; implicit exponential finite difference method; ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. ... Current Issue

Monte Carlo techniques for analyzing deep-penetration problems

International Nuclear Information System (INIS)

Cramer, S.N.; Gonnord, J.; Hendricks, J.S.

1986-01-01

Current methods and difficulties in Monte Carlo deep-penetration calculations are reviewed, including statistical uncertainty and recent adjoint optimization of splitting, Russian roulette, and exponential transformation biasing. Other aspects of the random walk and estimation processes are covered, including the relatively new DXANG angular biasing technique. Specific items summarized are albedo scattering, Monte Carlo coupling techniques with discrete ordinates and other methods, adjoint solutions, and multigroup Monte Carlo. The topic of code-generated biasing parameters is presented, including the creation of adjoint importance functions from forward calculations. Finally, current and future work in the area of computer learning and artificial intelligence is discussed in connection with Monte Carlo applications

The exhibition"La France au CERN" was inaugurated by Danièle Hulin, Directrice adjointe Secteur Physique, Chimie, Sciences pour l'Ingénieur (PCSI), Ministère délégué à l'Enseignement supérieur et à la recherche.

CERN Document Server

Patrice Loïez

2005-01-01

The exhibition"La France au CERN" was inaugurated by Danièle Hulin, Directrice adjointe Secteur Physique, Chimie, Sciences pour l'Ingénieur (PCSI), Ministère délégué à l'Enseignement supérieur et à la recherche.

Time-dependent problems and difference methods

CERN Document Server

Gustafsson, Bertil; Oliger, Joseph

2013-01-01

Praise for the First Edition "". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations."" -SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-de

Radiation Source Mapping with Bayesian Inverse Methods

Science.gov (United States)

Hykes, Joshua Michael

We present a method to map the spectral and spatial distributions of radioactive sources using a small number of detectors. Locating and identifying radioactive materials is important for border monitoring, accounting for special nuclear material in processing facilities, and in clean-up operations. Most methods to analyze these problems make restrictive assumptions about the distribution of the source. In contrast, the source-mapping method presented here allows an arbitrary three-dimensional distribution in space and a flexible group and gamma peak distribution in energy. To apply the method, the system's geometry and materials must be known. A probabilistic Bayesian approach is used to solve the resulting inverse problem (IP) since the system of equations is ill-posed. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint flux, discrete ordinates solutions, obtained in this work by the Denovo code, are required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes are then used to form the linear model to map the state space to the response space. The test for the method is simultaneously locating a set of 137Cs and 60Co gamma sources in an empty room. This test problem is solved using synthetic measurements generated by a Monte Carlo (MCNP) model and using experimental measurements that we collected for this purpose. With the synthetic data, the predicted source distributions identified the locations of the sources to within tens of centimeters, in a room with an approximately four-by-four meter floor plan. Most of the predicted source intensities were within a factor of ten of their true value. The chi-square value of the predicted source was within a factor of five from the expected value based on the number of measurements employed. With a favorable uniform initial guess, the predicted source map was nearly identical to the true distribution

A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions

KAUST Repository

Butler, T.; Dawson, C.; Wildey, T.

2011-01-01

We develop computable a posteriori error estimates for linear functionals of a solution to a general nonlinear stochastic differential equation with random model/source parameters. These error estimates are based on a variational analysis applied to stochastic Galerkin methods for forward and adjoint problems. The result is a representation for the error estimate as a polynomial in the random model/source parameter. The advantage of this method is that we use polynomial chaos representations for the forward and adjoint systems to cheaply produce error estimates by simple evaluation of a polynomial. By comparison, the typical method of producing such estimates requires repeated forward/adjoint solves for each new choice of random parameter. We present numerical examples showing that there is excellent agreement between these methods. © 2011 Society for Industrial and Applied Mathematics.

Nonlinear Model Predictive Control for Oil Reservoirs Management

DEFF Research Database (Denmark)

Capolei, Andrea

expensive gradient computation by using high-order ESDIRK (Explicit Singly Diagonally Implicit Runge-Kutta) temporal integration methods and continuous adjoints. The high order integration scheme allows larger time steps and therefore faster solution times. We compare gradient computation by the continuous...... gradient-based optimization and the required gradients are computed by the adjoint method. We propose the use of efficient high order implicit time integration methods for the solution of the forward and the adjoint equations of the dynamical model. The Ensemble Kalman filter is used for data assimilation...... equivalent strategy is not justified for the particular case studied in this paper. The third contribution of this thesis is a mean-variance method for risk mitigation in production optimization of oil reservoirs. We introduce a return-risk bicriterion objective function for the profit-risk tradeoff...

Simultaneous Optimization of Tallies in Difficult Shielding Problems

International Nuclear Information System (INIS)

Peplow, Douglas E.; Evans, Thomas M.; Wagner, John C.

2008-01-01

Monte Carlo is quite useful for calculating specific quantities in complex transport problems. Many variance reduction strategies have been developed that accelerate Monte Carlo calculations for specific tallies. However, when trying to calculate multiple tallies or a mesh tally, users have had to accept different levels of relative uncertainty among the tallies or run separate calculations optimized for each individual tally. To address this limitation, an extension of the CADIS (Consistent Adjoint Driven Importance Sampling) method, which is used for difficult source/detector problems, has been developed to optimize several tallies or the cells of a mesh tally simultaneously. The basis for this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. This method utilizes the results of a forward discrete ordinates solution, which may be based on a quick, coarse-mesh calculation, to develop a forward-weighted source for the adjoint calculation. The importance map and the biased source computed from the adjoint flux are then used in the forward Monte Carlo calculation to obtain approximately uniform relative uncertainties for the desired tallies. This extension is called forward-weighted CADIS, or FW-CADIS