Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
Cirpka, Olaf A.; Kitanidis, Peter K.
Including tracer data into geostatistically based methods of inverse modeling is computationally very costly when all concentration measurements are used and the sensitivities of many observations are calculated by the direct differentiation approach. Harvey and Gorelick (Water Resour Res 1995;31(7):1615-26) have suggested the use of the first temporal moment instead of the complete concentration record at a point. We derive a computationally efficient adjoint-state method for the sensitivities of the temporal moments that require the solution of the steady-state flow equation and two steady-state transport equations for the forward problem and the same number of equations for each first-moment measurement. The efficiency of the method makes it feasible to evaluate the sensitivity matrix many times in large domains. We incorporate our approach for the calculation of sensitivities in the quasi-linear geostatistical method of inversing ("iterative cokriging"). The application to an artificial example of a tracer introduced into an injection well shows good convergence behavior when both head and first-moment data are used for inversing, whereas inversing of arrival times alone is less stable.
Mesh-free adjoint methods for nonlinear filters
NASA Astrophysics Data System (ADS)
Daum, Fred
2005-09-01
We apply a new industrial strength numerical approximation, called the "mesh-free adjoint method", to solve the nonlinear filtering problem. This algorithm exploits the smoothness of the problem, unlike particle filters, and hence we expect that mesh-free adjoints are superior to particle filters for many practical applications. The nonlinear filter problem is equivalent to solving the Fokker-Planck equation in real time. The key idea is to use a good adaptive non-uniform quantization of state space to approximate the solution of the Fokker-Planck equation. In particular, the adjoint method computes the location of the nodes in state space to minimize errors in the final answer. This use of an adjoint is analogous to optimal control algorithms, but it is more interesting. The adjoint method is also analogous to importance sampling in particle filters, but it is better for four reasons: (1) it exploits the smoothness of the problem; (2) it explicitly minimizes the errors in the relevant functional; (3) it explicitly models the dynamics in state space; and (4) it can be used to compute a corrected value for the desired functional using the residuals. We will attempt to make this paper accessible to normal engineers who do not have PDEs for breakfast.
Hekmat, Mohamad Hamed; Mirzaei, Masoud
2015-01-01
In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced. PMID:25679735
NASA Astrophysics Data System (ADS)
Anis, Fatima; Lou, Yang; Conjusteau, André; Su, Richard; Oruganti, Tanmayi; Ermilov, Sergey A.; Oraevsky, Alexander A.; Anastasio, Mark A.
2014-03-01
In this work, we investigate a novel reconstruction method for laser-induced ultrasound computed tomography (USCT) breast imaging that circumvents limitations of existing methods that rely on ray-tracing. There is currently great interest in developing hybrid imaging systems that combine optoacoustic tomography (OAT) and USCT. There are two primary motivations for this: (1) the speed-of-sound (SOS) distribution reconstructed by USCT can provide complementary diagnostic information; and (2) the reconstructed SOS distribution can be incorporated in the OAT reconstruction algorithm to improve OAT image quality. However, image reconstruction in USCT remains challenging. The majority of existing approaches for USCT breast imaging involve ray-tracing to establish the imaging operator. This process is cumbersome and can lead to inaccuracies in the reconstructed SOS images in the presence of multiple ray-paths and/or shadow zones. To circumvent these problems, we implemented a partial differential equation-based Eulerian approach to USCT that was proposed in the mathematics literature but never investigated for medical imaging applications. This method operates by directly inverting the Eikonal equation without ray-tracing. A numerical implementation of this method was developed and compared to existing reconstruction methods for USCT breast imaging. We demonstrated the ability of the new method to reconstruct SOS maps from TOF data obtained by a hybrid OAT/USCT imager built by our team.
Wing planform optimization via an adjoint method
NASA Astrophysics Data System (ADS)
Leoviriyakit, Kasidit
This dissertation focuses on the problem of wing planform optimization for transonic aircraft based on flow simulation using Computational Fluid Dynamics (CFD) combined with an adjoint-gradient based numerical optimization procedure. The adjoint method, traditionally used for wing section design has been extended to cover planform variations and to compute the sensitivities of the structural weight of both the wing section and planform variations. The two relevant disciplines accounted for are the aerodynamics and structural weight. A simplified structural weight model is used for the optimization. Results of a variety of long range transports indicate that significant improvement in both aerodynamics and structures can be achieved simultaneously. The proof-of-concept optimal results indicate large improvements for both drag and structural weight. The work is an "enabling step" towards a realistic automated wing designed by a computer.
NASA Astrophysics Data System (ADS)
Virieux, J.; Bretaudeau, F.; Metivier, L.; Brossier, R.
2013-12-01
Simultaneous inversion of seismic velocities and source parameters have been a long standing challenge in seismology since the first attempts to mitigate trade-off between very different parameters influencing travel-times (Spencer and Gubbins 1980, Pavlis and Booker 1980) since the early development in the 1970s (Aki et al 1976, Aki and Lee 1976, Crosson 1976). There is a strong trade-off between earthquake source positions, initial times and velocities during the tomographic inversion: mitigating these trade-offs is usually carried empirically (Lemeur et al 1997). This procedure is not optimal and may lead to errors in the velocity reconstruction as well as in the source localization. For a better simultaneous estimation of such multi-parametric reconstruction problem, one may take benefit of improved local optimization such as full Newton method where the Hessian influence helps balancing between different physical parameter quantities and improving the coverage at the point of reconstruction. Unfortunately, the computation of the full Hessian operator is not easily computed in large models and with large datasets. Truncated Newton (TCN) is an alternative optimization approach (Métivier et al. 2012) that allows resolution of the normal equation H Δm = - g using a matrix-free conjugate gradient algorithm. It only requires to be able to compute the gradient of the misfit function and Hessian-vector products. Traveltime maps can be computed in the whole domain by numerical modeling (Vidale 1998, Zhao 2004). The gradient and the Hessian-vector products for velocities can be computed without ray-tracing using 1st and 2nd order adjoint-state methods for the cost of 1 and 2 additional modeling step (Plessix 2006, Métivier et al. 2012). Reciprocity allows to compute accurately the gradient and the full Hessian for each coordinates of the sources and for their initial times. Then the resolution of the problem is done through two nested loops. The model update Δm is
Adjoint methods for external beam inverse treatment planning
NASA Astrophysics Data System (ADS)
Kowalok, Michael E.
Forward and adjoint radiation transport methods may both be used to determine the dosimetric relationship between source parameters and voxel elements of a phantom. Forward methods consider one specific tuple of source parameters and calculate the response in all voxels of interest. This response is often cast as the dose delivered per unit source-weight. Adjoint transport methods, conversely, consider one particular voxel and calculate the response of that voxel in relation to all possible source parameters. In this regard, adjoint methods provide an "adjoint function" in addition to a dose value. Although the dose is for a single voxel only, the adjoint function illustrates the source parameters, (e.g. beam positions and directions) that are most important to delivering the dose to that voxel. In this regard, adjoint methods of analysis lend themselves in a natural way to optimization problems and perturbation studies. This work investigates the utility of adjoint analytic methods for treatment planning and for Monte Carlo dose calculations. Various methods for implementing this approach are discussed, along with their strengths and weaknesses. The complementary nature of adjoint and forward techniques is illustrated and exploited. Also, several features of the Monte Carlo codes MCNP and MCNPX are reviewed for treatment planning applications.
Aerodynamic design optimization by using a continuous adjoint method
NASA Astrophysics Data System (ADS)
Luo, JiaQi; Xiong, JunTao; Liu, Feng
2014-07-01
This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows. General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived. With the adjoint method, the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function, regardless of the number of design parameters. An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method. Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil, wing, and wing-body configuration, and the aerodynamic performance improvement of turbine and compressor blade rows. The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.
Sensitivity of Lumped Constraints Using the Adjoint Method
NASA Technical Reports Server (NTRS)
Akgun, Mehmet A.; Haftka, Raphael T.; Wu, K. Chauncey; Walsh, Joanne L.
1999-01-01
Adjoint sensitivity calculation of stress, buckling and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. Adjoint stress and displacement sensitivities are available in the literature. Expressions for local buckling sensitivity of isotropic plate elements are derived in this study. Computational efficiency of the adjoint method is sensitive to the number of constraints and, therefore, the method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser (KS) function is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a simple HSCT wing model, and a large HSCT model. These sensitivity derivatives are then used in optimization.
Adjoint sensitivity analysis of plasmonic structures using the FDTD method.
Zhang, Yu; Ahmed, Osman S; Bakr, Mohamed H
2014-05-15
We present an adjoint variable method for estimating the sensitivities of arbitrary responses with respect to the parameters of dispersive discontinuities in nanoplasmonic devices. Our theory is formulated in terms of the electric field components at the vicinity of perturbed discontinuities. The adjoint sensitivities are computed using at most one extra finite-difference time-domain (FDTD) simulation regardless of the number of parameters. Our approach is illustrated through the sensitivity analysis of an add-drop coupler consisting of a square ring resonator between two parallel waveguides. The computed adjoint sensitivities of the scattering parameters are compared with those obtained using the accurate but computationally expensive central finite difference approach. PMID:24978258
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
NASA Astrophysics Data System (ADS)
Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.
2015-03-01
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space-time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge-Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.
2015-03-15
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that
Adjoint Formulation for an Embedded-Boundary Cartesian Method
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.
2004-01-01
Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code
Comparison of the Monte Carlo adjoint-weighted and differential operator perturbation methods
Kiedrowski, Brian C; Brown, Forrest B
2010-01-01
Two perturbation theory methodologies are implemented for k-eigenvalue calculations in the continuous-energy Monte Carlo code, MCNP6. A comparison of the accuracy of these techniques, the differential operator and adjoint-weighted methods, is performed numerically and analytically. Typically, the adjoint-weighted method shows better performance over a larger range; however, there are exceptions.
Use of adjoint methods in the probabilistic finite element approach to fracture mechanics
NASA Technical Reports Server (NTRS)
Liu, Wing Kam; Besterfield, Glen; Lawrence, Mark; Belytschko, Ted
1988-01-01
The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.
NASA Technical Reports Server (NTRS)
Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe
2013-01-01
This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.
Multigrid methods for bifurcation problems: The self adjoint case
NASA Technical Reports Server (NTRS)
Taasan, Shlomo
1987-01-01
This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.
Introduction to Adjoint Models
NASA Technical Reports Server (NTRS)
Errico, Ronald M.
2015-01-01
In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.
Adjoint-Based Methods for Estimating CO2 Sources and Sinks from Atmospheric Concentration Data
NASA Technical Reports Server (NTRS)
Andrews, Arlyn E.
2003-01-01
Work to develop adjoint-based methods for estimating CO2 sources and sinks from atmospheric concentration data was initiated in preparation for last year's summer institute on Carbon Data Assimilation (CDAS) at the National Center for Atmospheric Research in Boulder, CO. The workshop exercises used the GSFC Parameterized Chemistry and Transport Model and its adjoint. Since the workshop, a number of simulations have been run to evaluate the performance of the model adjoint. Results from these simulations will be presented, along with an outline of challenges associated with incorporating a variety of disparate data sources, from sparse, but highly precise, surface in situ observations to less accurate, global future satellite observations.
NASA Astrophysics Data System (ADS)
Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark
2005-09-01
Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.
Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.
2004-01-01
Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented
Reconstruction of ocean circulation from sparse data using the adjoint method: LGM and the present
NASA Astrophysics Data System (ADS)
Kurahashi-Nakamura, T.; Losch, M. J.; Paul, A.; Mulitza, S.; Schulz, M.
2010-12-01
Understanding the behavior of the Earth's climate system under different conditions in the past is the basis for more robust projections of future climate. It is thought that the ocean circulation plays a very important role in the climate system, because it can greatly affect climate by dynamic-thermodynamic (as a medium of heat transport) and biogeochemical processes (by affecting the global carbon cycle). In this context, studying the period of the Last Glacial Maximum (LGM) is particularly promising, as it represents a climate state that is very different from today. Furthermore the LGM, compared to other paleoperiods, is characterized by a relatively good paleo-data coverage. Unfortunately, the ocean circulation during the LGM is still uncertain, with a range of climate models estimating both a stronger and a weaker formation rate of North Atlantic Deep Water (NADW) as compared to the present rate. Here, we present a project aiming at reducing this uncertainty by combining proxy data with a numerical ocean model using variational techniques. Our approach, the so-called adjoint method, employs a quadratic cost function of model-data differences weighted by their prior error estimates. We seek an optimal state estimate at the global minimum of the cost function by varying the independent control variables such as initial conditions (e.g. temperature), boundary conditions (e.g. surface winds, heat flux), or internal parameters (e.g. vertical diffusivity). The adjoint or dual model computes the gradient of the cost function with respect to these control variables and thus provides the information required by gradient descent algorithms. The gradients themselves provide valuable information about the sensitivity of the system to perturbations in the control variables. We use the Massachusetts Institute of Technology ocean general circulation model (MITgcm) with a cubed-sphere grid system that avoids converging grid lines and pole singularities. This model code is
Sensitivity analysis of numerically-simulated convective storms using direct and adjoint methods
Park, S.K.; Droegemeier, K.K.; Bischof, C.; Knauff, T.
1994-06-01
The goal of this project is to evaluate the sensitivity of numerically modeled convective storms to control parameters such as the initial conditions, boundary conditions, environment, and various physical and computational parameters. In other words, the authors seek the gradient of the solution vector with respect to specified parameters. One can use two approaches to accomplish this task. In the first or so-called brute force method, one uses a fully nonlinear model to generate a control forecast starting from a specified initial state. Then, a number of other forecasts are made in which chosen parameters (e.g., initial conditions) are systematically varied. The obvious drawback is that a large number of full model predictions are needed to examine the effects of only a single parameter. The authors describe herein an alternative, essentially automated method (ADIFOR, or Automatic DIfferentiation of FORtran) for obtaining the solution gradient that bypasses the adjoint altogether yet provides even more information about the gradient. (ADIFOR, like the adjoint technique, is constrained by the linearity assumption.) Applied to a 1-D moist cloud model, the authors assess the utility of ADIFOR relative to the brute force approach and evaluate the validity of the tangent linear approximation in the context of deep convection.
NASA Astrophysics Data System (ADS)
Clemo, T. M.; Ramarao, B.; Kelly, V. A.; Lavenue, M.
2011-12-01
Capture is a measure of the impact of groundwater pumping upon groundwater and surface water systems. The computation of capture through analytical or numerical methods has been the subject of articles in the literature for several decades (Bredehoeft et al., 1982). Most recently Leake et al. (2010) described a systematic way to produce capture maps in three-dimensional systems using a numerical perturbation approach in which capture from streams was computed using unit rate pumping at many locations within a MODFLOW model. The Leake et al. (2010) method advances the current state of computing capture. A limitation stems from the computational demand required by the perturbation approach wherein days or weeks of computational time might be required to obtain a robust measure of capture. In this paper, we present an efficient method to compute capture in three-dimensional systems based upon adjoint states. The efficiency of the adjoint method will enable uncertainty analysis to be conducted on capture calculations. The USGS and INTERA have collaborated to extend the MODFLOW Adjoint code (Clemo, 2007) to include stream-aquifer interaction and have applied it to one of the examples used in Leake et al. (2010), the San Pedro Basin MODFLOW model. With five layers and 140,800 grid blocks per layer, the San Pedro Basin model, provided an ideal example data set to compare the capture computed from the perturbation and the adjoint methods. The capture fraction map produced from the perturbation method for the San Pedro Basin model required significant computational time to compute and therefore the locations for the pumping wells were limited to 1530 locations in layer 4. The 1530 direct simulations of capture require approximately 76 CPU hours. Had capture been simulated in each grid block in each layer, as is done in the adjoint method, the CPU time would have been on the order of 4 years. The MODFLOW-Adjoint produced the capture fraction map of the San Pedro Basin model
Adaptive mesh refinement and adjoint methods in geophysics simulations
NASA Astrophysics Data System (ADS)
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.
Martien, Philip T; Harley, Robert A; Cacuci, Dan G
2006-04-15
Photochemical air pollution forms when emissions of nitrogen oxides (NO(x)) and volatile organic compounds (VOC) react in the atmosphere in the presence of sunlight. The goal of applying three-dimensional photochemical air quality models is usually to conduct sensitivity analysis: for example, to predict changes in an ozone response due to changes in NO(x) and VOC emissions or other model data. Forward sensitivity analysis methods are best suited to investigating sensitivities of many model responses to changes in a few inputs or parameters. Here we develop a continuous adjoint model and demonstrate an adjoint sensitivity analysis procedure that is well-suited to the complementary case of determining sensitivity of a small number of model responses to many parameters. Sensitivities generated using the adjoint method agree with those generated using other methods. Compared to the forward method, the adjoint method had large disk storage requirements but was more efficient in terms of computer processor time for receptor-based investigations focused on a single response at a specified site and time. The adjoint method also generates sensitivity apportionment fields, which reveal when and where model data are important to the target response. PMID:16683606
NASA Technical Reports Server (NTRS)
Pulliam, T. H.; Nemec, M.; Holst, T.; Zingg, D. W.; Kwak, Dochan (Technical Monitor)
2002-01-01
A comparison between an Evolutionary Algorithm (EA) and an Adjoint-Gradient (AG) Method applied to a two-dimensional Navier-Stokes code for airfoil design is presented. Both approaches use a common function evaluation code, the steady-state explicit part of the code,ARC2D. The parameterization of the design space is a common B-spline approach for an airfoil surface, which together with a common griding approach, restricts the AG and EA to the same design space. Results are presented for a class of viscous transonic airfoils in which the optimization tradeoff between drag minimization as one objective and lift maximization as another, produces the multi-objective design space. Comparisons are made for efficiency, accuracy and design consistency.
Assessing the Impact of Observations on Numerical Weather Forecasts Using the Adjoint Method
NASA Technical Reports Server (NTRS)
Gelaro, Ronald
2012-01-01
The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. This talk provides a general overview of the adjoint method, including the theoretical basis and practical implementation of the technique. Results are presented from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. When performed in conjunction with standard observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies may be important for optimizing the use of the current observational network and defining requirements for future observing systems
Pappin, Amanda Joy
2013-01-01
Background: Decision making regarding air pollution can be better informed if air quality impacts are traced back to individual emission sources. Adjoint or backward sensitivity analysis is a modeling tool that can achieve this goal by allowing for quantification of how emissions from sources in different locations influence human health metrics. Objectives: We attributed short-term mortality (valuated as an overall “health benefit”) in Canada and the United States to anthropogenic nitrogen oxides (NOx) and volatile organic compound (VOC) emissions across North America. Methods: We integrated epidemiological data derived from Canadian and U.S. time-series studies with the adjoint of an air quality model and also estimated influences of anthropogenic emissions at each location on nationwide health benefits. Results: We found significant spatiotemporal variability in estimated health benefit influences of NOx and VOC emission reductions on Canada and U.S. mortality. The largest estimated influences on Canada (up to $250,000/day) were from emissions originating in the Quebec City–Windsor Corridor, where population centers are concentrated. Estimated influences on the United States tend to be widespread and more substantial owing to both larger emissions and larger populations. The health benefit influences calculated using 24-hr average ozone (O3) concentrations are lower in magnitude than estimates calculated using daily 1-hr maximum O3 concentrations. Conclusions: Source specificity of the adjoint approach provides valuable information for guiding air quality decision making. Adjoint results suggest that the health benefits of reducing NOx and VOC emissions are substantial and highly variable across North America. PMID:23434744
NASA Technical Reports Server (NTRS)
Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.
2009-01-01
.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.
Eulerian-Lagrangian localized adjoint methods for reactive transport in groundwater
Ewing, R.E.; Wang, Hong
1996-12-31
In this paper, we present Eulerian-Lagrangian localized adjoint methods (ELLAM) to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through an adsorbing porous medium. These ELLAM schemes can treat various combinations of boundary conditions and conserve mass. Numerical results are presented to demonstrate the strong potential of ELLAM schemes.
NASA Astrophysics Data System (ADS)
Ren, L.; Liu, Q.
2012-12-01
We present multiple moment-tensor solution of the December 26, 2004 Sumatra earthquake based upon adjoint methods. An objective function Φ that measures the goodness of waveform fit between data and synthetics is minimized. Synthetics are calculated by spectral-element simulations (SPECFEM3D_GLOBE) in a 3D global earth model S362ANI to reduce the effect of heterogeneous structures. The Fréchet derivatives of Φ in the form δΦ = ∫T ∫VI(ɛ †ij)(x,T-t) δ(m_dot)ij(x,t)d3xdt, where δmij is the perturbation of moment density function and I(ɛ†ij)(x,T-t) denotes the time-integrated adjoint strain tensor, are calculated based upon adjoint methods implemented in SPECFEM3D_GLOBE. Our initial source model is obtained by monitoring the time-integrated adjoint strain tensors in the vicinity of the presumed source region. Source model parameters are iteratively updated by a preconditioned conjugate-gradient method to iteratively utilizing the calculated Φ and δΦ values. Our final inversion results show both similarities to and differences from previous source inversion results based on 1D background models.
NASA Astrophysics Data System (ADS)
Ren, L.; Liu, Q.; Hjörleifsdóttir, V.
2010-12-01
We present multiple moment-tensor solution of the Dec 26, 2004 Sumatra earthquake based upon the adjoint methods. An objective function Φ(m), where m is the multiple source model, measures the goodness of waveform fit between data and synthetics. The Fréchet derivatives of Φ in the form δΦ = ∫∫I(ɛ†)(x,T-t)δmij_dot(x,t)dVdt, where δmij is the source model perturbation and I(ɛ†)(x,T-t) denotes the time-integrated adjoint strain tensor, are calculated based upon adjoint methods and spectral-element simulations (SPECFEM3D_GLOBE) in a 3D global earth model S362ANI. Our initial source model is obtained independently by monitoring the time-integrated adjoint strain tensors around the presumed source region. We then utilize the Φ and δΦ calculations in a conjugate-gradient method to iteratively invert for the source model. Our final inversion results show both similarities with and differences to previous source inversion results based on 1D earth models.
NASA Astrophysics Data System (ADS)
Sikarwar, Nidhi
multiple experiments or numerical simulations. Alternatively an inverse design method can be used. An adjoint optimization method can be used to achieve the optimum blowing rate. It is shown that the method works for both geometry optimization and active control of the flow in order to deflect the flow in desirable ways. An adjoint optimization method is described. It is used to determine the blowing distribution in the diverging section of a convergent-divergent nozzle that gives a desired pressure distribution in the nozzle. Both the direct and adjoint problems and their associated boundary conditions are developed. The adjoint method is used to determine the blowing distribution required to minimize the shock strength in the nozzle to achieve a known target pressure and to achieve close to an ideally expanded flow pressure. A multi-block structured solver is developed to calculate the flow solution and associated adjoint variables. Two and three-dimensional calculations are performed for internal and external of the nozzle domains. A two step MacCormack scheme based on predictor- corrector technique is was used for some calculations. The four and five stage Runge-Kutta schemes are also used to artificially march in time. A modified Runge-Kutta scheme is used to accelerate the convergence to a steady state. Second order artificial dissipation has been added to stabilize the calculations. The steepest decent method has been used for the optimization of the blowing velocity after the gradients of the cost function with respect to the blowing velocity are calculated using adjoint method. Several examples are given of the optimization of blowing using the adjoint method.
Sensitivity analysis of a model of CO2 exchange in tundra ecosystems by the adjoint method
NASA Technical Reports Server (NTRS)
Waelbroek, C.; Louis, J.-F.
1995-01-01
A model of net primary production (NPP), decomposition, and nitrogen cycling in tundra ecosystems has been developed. The adjoint technique is used to study the sensitivity of the computed annual net CO2 flux to perturbation in initial conditions, climatic inputs, and model's main parameters describing current seasonal CO2 exchange in wet sedge tundra at Barrow, Alaska. The results show that net CO2 flux is most sensitive to parameters characterizing litter chemical composition and more sensitive to decomposition parameters than to NPP parameters. This underlines the fact that in nutrient-limited ecosystems, decomposition drives net CO2 exchange by controlling mineralization of main nutrients. The results also indicate that the short-term (1 year) response of wet sedge tundra to CO2-induced warming is a significant increase in CO2 emission, creating a positive feedback to atmosphreic CO2 accumulation. However, a cloudiness increase during the same year can severely alter this response and lead to either a slight decrease or a strong increase in emitted CO2, depending on its exact timing. These results demonstrate that the adjoint method is well suited to study systems encountering regime changes, as a single run of the adjoint model provides sensitivities of the net CO2 flux to perturbations in all parameters and variables at any time of the year. Moreover, it is shown that large errors due to the presence of thresholds can be avoided by first delimiting the range of applicability of the adjoint results.
On the proper treatment of grid sensitivities in continuous adjoint methods for shape optimization
NASA Astrophysics Data System (ADS)
Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Giannakoglou, K. C.
2015-11-01
The continuous adjoint method for shape optimization problems, in flows governed by the Navier-Stokes equations, can be formulated in two different ways, each of which leads to a different expression for the sensitivity derivatives of the objective function with respect to the control variables. The first formulation leads to an expression including only boundary integrals; it, thus, has low computational cost but, when used with coarse grids, its accuracy becomes questionable. The second formulation comprises a sum of boundary and field integrals; due to the field integrals, it has noticeably higher computational cost, obtaining though higher accuracy. In this paper, the equivalence of the two formulations is revisited from the mathematical and, particularly, the numerical point of view. Internal and external aerodynamics cases, in which the objective function is either the total pressure losses or the force exerted on a solid body, are examined and differences in the computed gradients are discussed. After identifying the reason behind these discrepancies, the adjoint formulation is enhanced by the adjoint to a (hypothetical) grid displacement model and the new approach is proved to reproduce the accuracy of the second adjoint formulation while maintaining the low cost of the first one.
NASA Astrophysics Data System (ADS)
Edwards, S.; Reuther, J.; Chattot, J. J.
The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjoint approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to a target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speeds.
Active adjoint modeling method in microwave induced thermoacoustic tomography for breast tumor.
Zhu, Xiaozhang; Zhao, Zhiqin; Wang, Jinguo; Chen, Guoping; Liu, Qing Huo
2014-07-01
To improve the model-based inversion performance of microwave induced thermoacoustic tomography for breast tumor imaging, an active adjoint modeling (AAM) method is proposed. It aims to provide a more realistic breast acoustic model used for tumor inversion as the background by actively measuring and reconstructing the structural heterogeneity of human breast environment. It utilizes the reciprocity of acoustic sensors, and adapts the adjoint tomography method from seismic exploration. With the reconstructed acoustic model of breast environment, the performance of model-based inversion method such as time reversal mirror is improved significantly both in contrast and accuracy. To prove the advantage of AAM, a checkerboard pattern model and anatomical realistic breast models have been used in full wave numerical simulations. PMID:24956614
NASA Astrophysics Data System (ADS)
Shi, Lei; Wang, Z. J.
2015-08-01
Adjoint-based mesh adaptive methods are capable of distributing computational resources to areas which are important for predicting an engineering output. In this paper, we develop an adjoint-based h-adaptation approach based on the high-order correction procedure via reconstruction formulation (CPR) to minimize the output or functional error. A dual-consistent CPR formulation of hyperbolic conservation laws is developed and its dual consistency is analyzed. Super-convergent functional and error estimate for the output with the CPR method are obtained. Factors affecting the dual consistency, such as the solution point distribution, correction functions, boundary conditions and the discretization approach for the non-linear flux divergence term, are studied. The presented method is then used to perform simulations for the 2D Euler and Navier-Stokes equations with mesh adaptation driven by the adjoint-based error estimate. Several numerical examples demonstrate the ability of the presented method to dramatically reduce the computational cost comparing with uniform grid refinement.
NASA Astrophysics Data System (ADS)
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.
An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.
2003-01-01
An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.
NASA Technical Reports Server (NTRS)
Andrews, A.
2002-01-01
A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future COS levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an "inverse problem," where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from long-term surface monitoring stations with data from intensive field campaigns and with proposed future satellite observations. A major advantage of the adjoint approach is that meteorological and surface data, as well as data for other atmospheric constituents and pollutants can be efficiently included in addition to observations of CO2 mixing ratios. This presentation will provide an overview of potentially useful datasets for carbon cycle research in general with an emphasis on planning for the North American Carbon Project. Areas of overlap with ongoing and proposed work on air quality/air pollution issues will be highlighted.
Adjoint-based deviational Monte Carlo methods for phonon transport calculations
NASA Astrophysics Data System (ADS)
Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.
2015-06-01
In the field of linear transport, adjoint formulations exploit linearity to derive powerful reciprocity relations between a variety of quantities of interest. In this paper, we develop an adjoint formulation of the linearized Boltzmann transport equation for phonon transport. We use this formulation for accelerating deviational Monte Carlo simulations of complex, multiscale problems. Benefits include significant computational savings via direct variance reduction, or by enabling formulations which allow more efficient use of computational resources, such as formulations which provide high resolution in a particular phase-space dimension (e.g., spectral). We show that the proposed adjoint-based methods are particularly well suited to problems involving a wide range of length scales (e.g., nanometers to hundreds of microns) and lead to computational methods that can calculate quantities of interest with a cost that is independent of the system characteristic length scale, thus removing the traditional stiffness of kinetic descriptions. Applications to problems of current interest, such as simulation of transient thermoreflectance experiments or spectrally resolved calculation of the effective thermal conductivity of nanostructured materials, are presented and discussed in detail.
Source attribution of particulate matter pollution over North China with the adjoint method
NASA Astrophysics Data System (ADS)
Zhang, Lin; Liu, Licheng; Zhao, Yuanhong; Gong, Sunling; Zhang, Xiaoye; Henze, Daven K.; Capps, Shannon L.; Fu, Tzung-May; Zhang, Qiang; Wang, Yuxuan
2015-08-01
We quantify the source contributions to surface PM2.5 (fine particulate matter) pollution over North China from January 2013 to 2015 using the GEOS-Chem chemical transport model and its adjoint with improved model horizontal resolution (1/4° × 5/16°) and aqueous-phase chemistry for sulfate production. The adjoint method attributes the PM2.5 pollution to emissions from different source sectors and chemical species at the model resolution. Wintertime surface PM2.5 over Beijing is contributed by emissions of organic carbon (27% of the total source contribution), anthropogenic fine dust (27%), and SO2 (14%), which are mainly from residential and industrial sources, followed by NH3 (13%) primarily from agricultural activities. About half of the Beijing pollution originates from sources outside of the city municipality. Adjoint analyses for other cities in North China all show significant regional pollution transport, supporting a joint regional control policy for effectively mitigating the PM2.5 air pollution.
Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.
2006-01-01
A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design
Imaging the slab beneath central Chile using the Spectral Elements Method and adjoint techniques
NASA Astrophysics Data System (ADS)
Mercerat, E. D.; Nolet, G.; Marot, M.; Deshayes, P.; Monfret, T.
2010-12-01
This work focuses on imaging the subducting slab beneath Central Chile using novel inversion techniques based on the adjoint method and accurate wave propagation simulations using the Spectral Elements Method. The study area comprises the flat slab portion of the Nazca plate between 29 S and 34 S subducting beneath South America. We will use a database of regional seismicity consisting of both crustal and deep slab earthquakes with magnitude 3 < Mw < 6 recorded by different temporary and permanent seismological networks. Our main goal is to determine both the kinematics and the geometry of the subducting slab in order to help the geodynamical interpretation of such particular active margin. The Spectral Elements Method (SPECFEM3D code) is used to generate the synthetic seismograms and it will be applied for the iterative minimization based on adjoint techniques. The numerical mesh is 600 km x 600 km in horizontal coordinates and 220 km depth. As a first step, we are faced to well-known issues concerning mesh generation (resolution, quality, absorbing boundary conditions). In particular, we must evaluate the influence of free surface topography, as well as the MOHO and other geological interfaces in the synthetic seismograms. The initial velocity model from a previous travel-time tomography study, is linearly interpolated to the Gauss-Lobatto-Legendre grid. The comparison between the first forward simulations (up to 4 seconds minimum period) validate the initial velocity model of the study area, although many features not reproduced by the initial model have already been identified. Next step will concentrate in the comparison between finite-frequency kernels calculated by travel-time methods with ones based on adjoint methods, in order to highlight advantages and disadvantages in terms of resolution, accuracy, but also computational cost.
Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis,Michael J.
2006-01-01
Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach
NASA Astrophysics Data System (ADS)
Gopalakrishnan, Ganesh; Cornuelle, Bruce D.; Hoteit, Ibrahim; Rudnick, Daniel L.; Owens, W. Brechner
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 1˜2 months.
Pricing of American style options with an adjoint process correction method
NASA Astrophysics Data System (ADS)
Jaekel, Uwe
2005-07-01
Pricing of American options is a more complicated problem than pricing of European options. In this work a formula is derived that allows the computation of the early exercise premium, i.e. the price difference between these two option types in terms of an adjoint process evolving in the reversed time direction of the original process determining the evolution of the European price. We show how this equation can be utilised to improve option price estimates from numerical schemes like finite difference or Monte Carlo methods.
Source attribution of PM2.5 pollution over North China using the adjoint method
NASA Astrophysics Data System (ADS)
Zhang, L.; Liu, L.; Zhao, Y.; Gong, S.; Henze, D. K.
2014-12-01
Conventional methods for source attribution of air pollution are based on measurement statistics (such as Positive Matrix Factorization) or sensitivity simulations with a chemical transport model (CTM). These methods generally ignore the nonlinear chemistry associated with the pollution formation or require unaffordable computational time. Here we use the adjoint of GEOS-Chem CTM at 0.25x0.3125 degree resolution to examine the sources contributing to the PM2.5 pollution over North China in winter 2013. We improved the model sulfate simulation by implementing the aqueous-phase oxidation of S(IV) by nitrogen dioxide. The adjoint results provide detailed source information at the model underlying grid resolution including source types and sectors. We show that PM2.5 pollution over Beijing and Baoding (Hebei) in winter was largely contributed by the large-scale residential and industrial burnings, and ammonia (NH3) emissions from agriculture activities. Nearly half of pollution was transported from outside of the city domains, and accumulated over 2-3 days. We also show under the current emission conditions, the PM2.5 concentrations over North China are more sensitive to NH3 emissions than NOx and SO2 emissions.
Ocean acoustic tomography from different receiver geometries using the adjoint method.
Zhao, Xiaofeng; Wang, Dongxiao
2015-12-01
In this paper, an ocean acoustic tomography inversion using the adjoint method in a shallow water environment is presented. The propagation model used is an implicit Crank-Nicolson finite difference parabolic equation solver with a non-local boundary condition. Unlike previous matched-field processing works using the complex pressure fields as the observations, here, the observed signals are the transmission losses. Based on the code tests of the tangent linear model, the adjoint model, and the gradient, the optimization problem is solved by a gradient-based minimization algorithm. The inversions are performed in numerical simulations for two geometries: one in which hydrophones are sparsely distributed in the horizontal direction, and another in which the hydrophones are distributed vertically. The spacing in both cases is well beyond the half-wavelength threshold at which beamforming could be used. To deal with the ill-posedness of the inverse problem, a linear differential regularization operator of the sound-speed profile is used to smooth the inversion results. The L-curve criterion is adopted to select the regularization parameter, and the optimal value can be easily determined at the elbow of the logarithms of the residual norm of the measured-predicted fields and the norm of the penalty function. PMID:26723329
Using Adjoint Methods to Improve 3-D Velocity Models of Southern California
NASA Astrophysics Data System (ADS)
Liu, Q.; Tape, C.; Maggi, A.; Tromp, J.
2006-12-01
We use adjoint methods popular in climate and ocean dynamics to calculate Fréchet derivatives for tomographic inversions in southern California. The Fréchet derivative of an objective function χ(m), where m denotes the Earth model, may be written in the generic form δχ=int Km(x) δln m(x) d3x, where δln m=δ m/m denotes the relative model perturbation. For illustrative purposes, we construct the 3-D finite-frequency banana-doughnut kernel Km, corresponding to the misfit of a single traveltime measurement, by simultaneously computing the 'adjoint' wave field s† forward in time and reconstructing the regular wave field s backward in time. The adjoint wave field is produced by using the time-reversed velocity at the receiver as a fictitious source, while the regular wave field is reconstructed on the fly by propagating the last frame of the wave field saved by a previous forward simulation backward in time. The approach is based upon the spectral-element method, and only two simulations are needed to produce density, shear-wave, and compressional-wave sensitivity kernels. This method is applied to the SCEC southern California velocity model. Various density, shear-wave, and compressional-wave sensitivity kernels are presented for different phases in the seismograms. We also generate 'event' kernels for Pnl, S and surface waves, which are the Fréchet kernels of misfit functions that measure the P, S or surface wave traveltime residuals at all the receivers simultaneously for one particular event. Effectively, an event kernel is a sum of weighted Fréchet kernels, with weights determined by the associated traveltime anomalies. By the nature of the 3-D simulation, every event kernel is also computed based upon just two simulations, i.e., its construction costs the same amount of computation time as an individual banana-doughnut kernel. One can think of the sum of the event kernels for all available earthquakes, called the 'misfit' kernel, as a graphical
Full waveform seismic tomography of the Vrancea region using the adjoint method
NASA Astrophysics Data System (ADS)
Baron, J.; Danecek, P.; Morelli, A.; Tondi, R.
2013-12-01
constrained by the quantity of usable seismic data as well as a poor signal-to-noise ratio, which imposes to carry out the analysis in a frequency band of relatively high frequencies. The adjoint tomographic inversion is implemented with the SPECFEM3D solver (a community code applying the spectral element method) to generate synthetic data and traveltime misfit kernels in a fine computational mesh that satisfies the data frequency band requirements. The computation is run on a BlueGene/Q massively parallel computer available at the CINECA supercomputing centre. We show what information can be retrieved about the tomographic model applying the full-waveform inversion and adjoint methods even applied to a modest-quality, mostly high-frequency content, regional dataset.
NASA Astrophysics Data System (ADS)
Truchet, G.; Leconte, P.; Peneliau, Y.; Santamarina, A.; Malvagi, F.
2014-06-01
Pile-oscillation experiments are performed in the MINERVE reactor at the CEA Cadarache to improve nuclear data accuracy. In order to precisely calculate small reactivity variations (<10 pcm) obtained in these experiments, a reference calculation need to be achieved. This calculation may be accomplished using the continuous-energy Monte Carlo code TRIPOLI-4® by using the eigenvalue difference method. This "direct" method has shown limitations in the evaluation of very small reactivity effects because it needs to reach a very small variance associated to the reactivity in both states. To answer this problem, it has been decided to implement the exact perturbation theory in TRIPOLI-4® and, consequently, to calculate a continuous-energy adjoint flux. The Iterated Fission Probability (IFP) method was chosen because it has shown great results in some other Monte Carlo codes. The IFP method uses a forward calculation to compute the adjoint flux, and consequently, it does not rely on complex code modifications but on the physical definition of the adjoint flux as a phase-space neutron importance. In the first part of this paper, the IFP method implemented in TRIPOLI-4® is described. To illustrate the effciency of the method, several adjoint fluxes are calculated and compared with their equivalent obtained by the deterministic code APOLLO-2. The new implementation can calculate angular adjoint flux. In the second part, a procedure to carry out an exact perturbation calculation is described. A single cell benchmark has been used to test the accuracy of the method, compared with the "direct" estimation of the perturbation. Once again the method based on the IFP shows good agreement for a calculation time far more inferior to the "direct" method. The main advantage of the method is that the relative accuracy of the reactivity variation does not depend on the magnitude of the variation itself, which allows us to calculate very small reactivity perturbations with high
Comparison of adjoint and nudging methods to initialise ice sheet model basal conditions
NASA Astrophysics Data System (ADS)
Mosbeux, Cyrille; Gillet-Chaulet, Fabien; Gagliardini, Olivier
2016-07-01
Ice flow models are now routinely used to forecast the ice sheets' contribution to 21st century sea-level rise. For such short term simulations, the model response is greatly affected by the initial conditions. Data assimilation algorithms have been developed to invert for the friction of the ice on its bedrock using observed surface velocities. A drawback of these methods is that remaining uncertainties, especially in the bedrock elevation, lead to non-physical ice flux divergence anomalies resulting in undesirable transient effects. In this study, we compare two different assimilation algorithms based on adjoints and nudging to constrain both bedrock friction and elevation. Using synthetic twin experiments with realistic observation errors, we show that the two algorithms lead to similar performances in reconstructing both variables and allow the flux divergence anomalies to be significantly reduced.
NASA Technical Reports Server (NTRS)
Rozvany, G. I. N.; Sobieszczanski-Sobieski, J.
1992-01-01
In new, iterative continuum-based optimality criteria (COC) methods, the strain in the adjoint structure becomes non-unique if the number of active local constraints is greater than the number of design variables for an element. This brief note discusses the use of smooth envelope functions (SEFs) in overcoming economically computational problems caused by the above non-uniqueness.
NASA Astrophysics Data System (ADS)
Kocaogul, Ibrahim; Hu, Fang; Li, Xiaodong
2014-03-01
Radiation of acoustic waves at all frequencies can be obtained by Time Domain Wave Packet (TDWP) method in a single time domain computation. Other benefit of the TDWP method is that it makes possible the separation of acoustic and instability wave in the shear flow. The TDWP method is also particularly useful for computations in the ducted or waveguide environments where incident wave modes can be imposed cleanly without a potentially long transient period. The adjoint equations for the linearized Euler equations are formulated for the Cartesian coordinates. Analytical solution for adjoint equations is derived by using Green's function in 2D and 3D. The derivation of reciprocal relations is presented for closed and open ducts. The adjoint equations are then solved numerically in reversed time by the TDWP method. Reciprocal relation between the duct mode amplitudes and far field point sources in the presence of the exhaust shear flow is computed and confirmed numerically. Applications of the adjoint problem to closed and open ducts are also presented.
Seismic Imaging of VTI, HTI and TTI based on Adjoint Methods
NASA Astrophysics Data System (ADS)
Rusmanugroho, H.; Tromp, J.
2014-12-01
Recent studies show that isotropic seismic imaging based on adjoint method reduces low-frequency artifact caused by diving waves, which commonly occur in two-wave wave-equation migration, such as Reverse Time Migration (RTM). Here, we derive new expressions of sensitivity kernels for Vertical Transverse Isotropy (VTI) using the Thomsen parameters (ɛ, δ, γ) plus the P-, and S-wave speeds (α, β) as well as via the Chen & Tromp (GJI 2005) parameters (A, C, N, L, F). For Horizontal Transverse Isotropy (HTI), these parameters depend on an azimuthal angle φ, where the tilt angle θ is equivalent to 90°, and for Tilted Transverse Isotropy (TTI), these parameters depend on both the azimuth and tilt angles. We calculate sensitivity kernels for each of these two approaches. Individual kernels ("images") are numerically constructed based on the interaction between the regular and adjoint wavefields in smoothed models which are in practice estimated through Full-Waveform Inversion (FWI). The final image is obtained as a result of summing all shots, which are well distributed to sample the target model properly. The impedance kernel, which is a sum of sensitivity kernels of density and the Thomsen or Chen & Tromp parameters, looks crisp and promising for seismic imaging. The other kernels suffer from low-frequency artifacts, similar to traditional seismic imaging conditions. However, all sensitivity kernels are important for estimating the gradient of the misfit function, which, in combination with a standard gradient-based inversion algorithm, is used to minimize the objective function in FWI.
NASA Astrophysics Data System (ADS)
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.
MCNP: Multigroup/adjoint capabilities
Wagner, J.C.; Redmond, E.L. II; Palmtag, S.P.; Hendricks, J.S.
1994-04-01
This report discusses various aspects related to the use and validity of the general purpose Monte Carlo code MCNP for multigroup/adjoint calculations. The increased desire to perform comparisons between Monte Carlo and deterministic codes, along with the ever-present desire to increase the efficiency of large MCNP calculations has produced a greater user demand for the multigroup/adjoint capabilities. To more fully utilize these capabilities, we review the applications of the Monte Carlo multigroup/adjoint method, describe how to generate multigroup cross sections for MCNP with the auxiliary CRSRD code, describe how to use the multigroup/adjoint capability in MCNP, and provide examples and results indicating the effectiveness and validity of the MCNP multigroup/adjoint treatment. This information should assist users in taking advantage of the MCNP multigroup/adjoint capabilities.
High-resolution array imaging using teleseismic converted waves based on adjoint methods
NASA Astrophysics Data System (ADS)
Liu, Q.; Chen, C.
2011-12-01
Seismic coda waves and converted phases have been used extensively to image detailed subsurface structures underneath seismic arrays, based on methods such as receiver functions, Kirchhoff migration and generalized Radon transform (GRT). Utilizing the same coda and converted waves, we propose to image both discontinuity interfaces and 3D velocity anomalies by combining full numerical simulations of wave propagation with adjoint methods recently adopted in global and regional tomography inversions. The `sensitivities' of these coda/converted waves to density, P and S velocities are calculated based on the interaction of the forward wave field that produces the main P phase, and the adjoint wave field generated by injecting the coda/converted phases at array stations as virtual sources, similar to the computation of isochrons in previous techniques. The density kernels generally highlight discontinuity interfaces and sharp velocity contrasts, while P and S velocity kernels provide hints to the update of volumetric velocity structures. The application of numerical solvers also allows the incorporation of 3D regional tomography models as background velocity models, providing better focusing of velocity anomalies. We show the feasibility of this technique on a synthetic case built based on the imaging geometry for Slave craton in the northwestern Canadian Shield by the POLARIS broadband seismic network. The main challenge of this technique lies in reproducing the forward wave field generated by tele-seismic sources in a limited simulation domain encompassing only local heterogeneous structures underneath array receivers. For simple homogeneous and layer-over-half-space background models, this can be solved by setting the incoming plane waves as initial conditions based on analytical formulae. For more sophisticated background models, a hybrid spectral-element solver is implemented by defining a fictitious boundary encompassing all local heterogeneities within the
NASA Astrophysics Data System (ADS)
Hagedoorn, J. M.; Martinec, Z.
2012-12-01
Recent models of the Earth's geomagnetic field at the core-mantle boundary (CMB) are based on satellite measurements and/or observatory data, which are mostly harmonically downward continued to the CMB. One aim of the upcoming satellite mission Swarm is to determine the three-dimensional distribution of electric conductivity of the Earth's mantle. On this background, we developed an adjoint sensitivity downward continuation approach that is capable to consider three-dimensional electric conductivity distributions. Martinec (Geophys. J. Int., 136, 1999) developed a time-domain spectral-finite element approach for the forward modelling of vector electromagnetic induction data as measured on ground-based magnetic observatory or by satellites. We design a new method to compute the sensitivity of the magnetic induction data to a magnetic field prescribed at the core-mantle boundary, which we term the adjoint sensitivity method. The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the specification of prescribed boundary conditions. The respective boundary-value data are the measured X magnetic component for the forward method and the difference between the measured and predicted Z magnetic component for the adjoint method. The squares of the differences in Z magnetic component summed up over the time of observation and all spatial positions of observations determine the misfit. Then the sensitivities of observed data, i.e. the partial derivatives of the misfit with respect to the parameters characterizing the magnetic field at the core-mantle boundary, are obtained by the surface integral over the core-mantle boundary of the product of the adjoint solution multiplied by the time-dependent functions describing the time variability of magnetic field at the core-mantle boundary, and integrated over the time of observation. The time variability of boundary data is represented in terms of locally supported B
Estimates of black carbon emissions in the western United States using the GEOS-Chem adjoint model
NASA Astrophysics Data System (ADS)
Mao, Y. H.; Li, Q. B.; Henze, D. K.; Jiang, Z.; Jones, D. B. A.; Kopacz, M.; He, C.; Qi, L.; Gao, M.; Hao, W.-M.; Liou, K.-N.
2015-07-01
We estimate black carbon (BC) emissions in the western United States for July-September 2006 by inverting surface BC concentrations from the Interagency Monitoring of Protected Visual Environments (IMPROVE) network using a global chemical transport model (GEOS-Chem) and its adjoint. Our best estimate of the BC emissions is 49.9 Gg at 2° × 2.5° (a factor of 2.1 increase) and 47.3 Gg at 0.5° × 0.667° (1.9 times increase). Model results now capture the observed major fire episodes with substantial bias reductions ( 35 % at 2° × 2.5° and 15 % at 0.5° × 0.667°). The emissions are 20-50 % larger than those from our earlier analytical inversions (Mao et al., 2014). The discrepancy is especially drastic in the partitioning of anthropogenic versus biomass burning emissions. The August biomass burning BC emissions are 4.6-6.5 Gg and anthropogenic BC emissions 8.6-12.8 Gg, varying with the model resolution, error specifications, and subsets of observations used. On average both anthropogenic and biomass burning emissions in the adjoint inversions increase 2-fold relative to the respective {a priori} emissions, in distinct contrast to the halving of the anthropogenic and tripling of the biomass burning emissions in the analytical inversions. We attribute these discrepancies to the inability of the adjoint inversion system, with limited spatiotemporal coverage of the IMPROVE observations, to effectively distinguish collocated anthropogenic and biomass burning emissions on model grid scales. This calls for concurrent measurements of other tracers of biomass burning and fossil fuel combustion (e.g., carbon monoxide and carbon isotopes). We find that the adjoint inversion system as is has sufficient information content to constrain the total emissions of BC on the model grid scales.
Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method
Dekeyser, W.; Reiter, D.; Baelmans, M.
2014-12-01
As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation of the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry.
Hep, J.; Konecna, A.; Krysl, V.; Smutny, V.
2011-07-01
This paper describes the application of effective source in forward calculations and the adjoint method to the solution of fast neutron fluence and activation detector activities in the reactor pressure vessel (RPV) and RPV cavity of a VVER-440 reactor. Its objective is the demonstration of both methods on a practical task. The effective source method applies the Boltzmann transport operator to time integrated source data in order to obtain neutron fluence and detector activities. By weighting the source data by time dependent decay of the detector activity, the result of the calculation is the detector activity. Alternatively, if the weighting is uniform with respect to time, the result is the fluence. The approach works because of the inherent linearity of radiation transport in non-multiplying time-invariant media. Integrated in this way, the source data are referred to as the effective source. The effective source in the forward calculations method thereby enables the analyst to replace numerous intensive transport calculations with a single transport calculation in which the time dependence and magnitude of the source are correctly represented. In this work, the effective source method has been expanded slightly in the following way: neutron source data were performed with few group method calculation using the active core calculation code MOBY-DICK. The follow-up neutron transport calculation was performed using the neutron transport code TORT to perform multigroup calculations. For comparison, an alternative method of calculation has been used based upon adjoint functions of the Boltzmann transport equation. Calculation of the three-dimensional (3-D) adjoint function for each required computational outcome has been obtained using the deterministic code TORT and the cross section library BGL440. Adjoint functions appropriate to the required fast neutron flux density and neutron reaction rates have been calculated for several significant points within the RPV
Comparison of Observation Impacts in Two Forecast Systems using Adjoint Methods
NASA Technical Reports Server (NTRS)
Gelaro, Ronald; Langland, Rolf; Todling, Ricardo
2009-01-01
An experiment is being conducted to compare directly the impact of all assimilated observations on short-range forecast errors in different operational forecast systems. We use the adjoint-based method developed by Langland and Baker (2004), which allows these impacts to be efficiently calculated. This presentation describes preliminary results for a "baseline" set of observations, including both satellite radiances and conventional observations, used by the Navy/NOGAPS and NASA/GEOS-5 forecast systems for the month of January 2007. In each system, about 65% of the total reduction in 24-h forecast error is provided by satellite observations, although the impact of rawinsonde, aircraft, land, and ship-based observations remains significant. Only a small majority (50- 55%) of all observations assimilated improves the forecast, while the rest degrade it. It is found that most of the total forecast error reduction comes from observations with moderate-size innovations providing small to moderate impacts, not from outliers with very large positive or negative innovations. In a global context, the relative impacts of the major observation types are fairly similar in each system, although regional differences in observation impact can be significant. Of particular interest is the fact that while satellite radiances have a large positive impact overall, they degrade the forecast in certain locations common to both systems, especially over land and ice surfaces. Ongoing comparisons of this type, with results expected from other operational centers, should lead to more robust conclusions about the impacts of the various components of the observing system as well as about the strengths and weaknesses of the methodologies used to assimilate them.
The adjoint method of data assimilation used operationally for shelf circulation
NASA Astrophysics Data System (ADS)
Griffin, David A.; Thompson, Keith R.
1996-02-01
A real-time shelf circulation model with data assimilation has been successfully used, possibly for the first time, on the outer Nova Scotian Shelf. The adjoint method was used to infer the time histories of flows across the four open boundaries of a 60 km × 60 km shallow-water equation model of Western Bank. The aim was to hindcast and nowcast currents over the bank so that a patch of water (initially 15 km in diameter) could be resampled over a 3-week period as part of a study of the early life history of Atlantic cod. Observations available in near real time for assimilation were from 14 drifting buoys, 2 telemetering moored current meters, the ship's acoustic Doppler current profiler and the local wind. For the postcruise hindcasts presented here, data from two bottom pressure gauges and two more current meters are also available. The experiment was successful, and the patch was sampled over a 19-day period that included two intense storms. In this paper we (1) document the model and how the data are assimilated, (2) present and discuss the observations, (3) demonstrate that the interpolative skill of the model exceeds that of simpler schemes that use just the current velocity data, and (4) provide examples of how particle tracking with the model enables asynoptically acquired data to be displayed as synoptic maps, greatly facilitating both underway cruise planning and postcruise data analysis. An interesting feature of the circulation on the bank was a nearly stationary eddy atop the bank crest. Larvae within the eddy were retained on the bank in a favorable environment until the onset of the storms. The variable integrity of the eddy may contribute to fluctuations of year-class success.
NASA Astrophysics Data System (ADS)
Morency, C.; Tromp, J.
2008-12-01
successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.
Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel
NASA Technical Reports Server (NTRS)
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
Healy, R.W.; Russell, T.F.
1993-01-01
Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors
NASA Astrophysics Data System (ADS)
Wang, Brian; Goldstein, Moshe; Xu, X. George; Sahoo, Narayan
2005-03-01
Recently, the theoretical framework of the adjoint Monte Carlo (AMC) method has been developed using a simplified patient geometry. In this study, we extended our previous work by applying the AMC framework to a 3D anatomical model called VIP-Man constructed from the Visible Human images. First, the adjoint fluxes for the prostate (PTV) and rectum and bladder (organs at risk (OARs)) were calculated on a spherical surface of 1 m radius, centred at the centre of gravity of PTV. An importance ratio, defined as the PTV dose divided by the weighted OAR doses, was calculated for each of the available beamlets to select the beam angles. Finally, the detailed doses in PTV and OAR were calculated using a forward Monte Carlo simulation to include the electron transport. The dose information was then used to generate dose volume histograms (DVHs). The Pinnacle treatment planning system was also used to generate DVHs for the 3D plans with beam angles obtained from the AMC (3D-AMC) and a standard six-field conformal radiation therapy plan (3D-CRT). Results show that the DVHs for prostate from 3D-AMC and the standard 3D-CRT are very similar, showing that both methods can deliver prescribed dose to the PTV. A substantial improvement in the DVHs for bladder and rectum was found for the 3D-AMC method in comparison to those obtained from 3D-CRT. However, the 3D-AMC plan is less conformal than the 3D-CRT plan because only bladder, rectum and PTV are considered for calculating the importance ratios. Nevertheless, this study clearly demonstrated the feasibility of the AMC in selecting the beam directions as a part of a treatment planning based on the anatomical information in a 3D and realistic patient anatomy.
NASA Astrophysics Data System (ADS)
Chen, H.; Li, K.
2012-12-01
We applied a wave-equation based adjoint wavefield method for seismic illumination/resolution analyses and full waveform inversion. A two-way wave-equation is used to calculate directional and diffracted energy fluxes for waves propagating between sources and receivers to the subsurface target. The first-order staggered-grid pressure-velocity formulation, which lacks the characteristic of being self-adjoint is further validated and corrected to render the modeling operator before its practical application. Despite most published papers on synthetic kernel research, realistic applications to two field experiments are demonstrated and emphasize its practical needs. The Fréchet sensitivity kernels are used to quantify the target illumination conditions. For realistic illumination measurements and resolution analyses, two completely different survey geometries and nontrivial pre-conditioning strategies based on seismic data type are demonstrated and compared. From illumination studies, particle velocity responses are more sensitive to lateral velocity variations than pressure records. For waveform inversion, the more accurately estimated velocity model obtained the deeper the depth of investigation would be reached. To achieve better resolution and illumination, closely spaced OBS receiver interval is preferred. Based on the results, waveform inversion is applied for a gas hydrate site in Taiwan for shallow structure and BSR detection. Full waveform approach potentially provides better depth resolution than ray approach. The quantitative analyses, a by-product of full waveform inversion, are useful for quantifying seismic processing and depth migration strategies.llumination/resolution analysis for a 3D MCS/OBS survey in 2008. Analysis of OBS data shows that pressure (top), horizontal (middle) and vertical (bottom) velocity records produce different resolving power for gas hydrate exploration. ull waveform inversion of 8 OBS data along Yuan-An Ridge in SW Taiwan
NASA Astrophysics Data System (ADS)
Kopacz, Monika; Jacob, Daniel J.; Henze, Daven K.; Heald, Colette L.; Streets, David G.; Zhang, Qiang
2008-04-01
We apply the adjoint of an atmospheric chemical transport model (GEOS-Chem CTM) to constrain Asian sources of carbon monoxide (CO) with 2° × 2.5° spatial resolution using Measurement of Pollution in the Troposphere (MOPITT) satellite observations of CO columns in February-April 2001. Results are compared to the more common analytical method for solving the same Bayesian inverse problem and applied to the same data set. The analytical method is more exact but because of computational limitations it can only constrain emissions over coarse regions. We find that the correction factors to the a priori CO emission inventory from the adjoint inversion are consistent with those of the analytical inversion when averaged over the large regions of the latter. Unlike the analytical solution, the adjoint correction factors are not subject to compensating errors between adjacent regions (error anticorrelation). The adjoint solution also reveals fine-scale variability that the analytical inversion cannot resolve. For example, India shows both large emissions underestimates in the densely populated Ganges Valley and large overestimates in the eastern part of the country where springtime emissions are dominated by biomass burning. Correction factors to Chinese emissions are largest in central and eastern China, consistent with a recent bottom-up inventory though there are disagreements in the fine structure. Correction factors for biomass burning are consistent with a recent bottom-up inventory based on MODIS satellite fire data.
NASA Astrophysics Data System (ADS)
Al-Attar, D.; Woodhouse, J. H.
2011-12-01
Normal mode spectra provide a valuable data set for global seismic tomography, and, notably, are amongst the few geophysical observables that are sensitive to lateral variations in density structure within the Earth. Nonetheless, the effects of lateral density variations on mode spectra are rather subtle. In order, therefore, to reliably determine density variations with in the earth, it is necessary to make use of sufficiently accurate methods for calculating synthetic mode spectra. In particular, recent work has highlighted the need to perform 'full-coupling calculations' that take into account the interaction of large numbers of spherical earth multiplets. However, present methods for performing such full-coupling calculations require diagonalization of large coupling matrices, and so become computationally inefficient as the number of coupled modes is increased. In order to perform full-coupling calculations more efficiently, we describe a new implementation of the direct solution method for calculating synthetic spectra in laterally heterogeneous earth models. This approach is based on the solution of the inhomogeneous mode coupling equations in the frequency domain, and does not require the diagonalization of large matrices. Early implementations of the direct solution method used LU-decomposition to solve the mode coupling equations. However, as the number of coupled modes is increased, this method becomes impractically slow. To circumvent this problem, we solve the mode coupling equations iteratively using the preconditioned biconjugate gradient algorithm. We present a number of numerical tests to display the accuracy and efficiency of this method for performing large full-coupling calculations. In addition, we describe a frequency-domain formulation of the adjoint method for the calculation of Frechet kernels that show the sensitivity of normal mode observations to variations in earth structure. The calculation of such Frechet kernels involves one solution
Healy, R.W.; Russell, T.F.
1992-01-01
A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.
Wang, H.; Man, S.; Ewing, R.E.; Qin, G.; Lyons, S.L.; Al-Lawatia, M.
1999-06-10
Many difficult problems arise in the numerical simulation of fluid flow processes within porous media in petroleum reservoir simulation and in subsurface contaminant transport and remediation. The authors develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for first-order advection-reaction equations on general multi-dimensional domains. Different tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes, which are full mass conservative, naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary conditions. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices, which can be efficiently solved by the conjugate gradient method in an optimal order number of iterations without any preconditioning needed. Numerical results are presented to compare the performance of the ELLAM schemes with many well studied and widely used methods, including the upwind finite difference method, the Galerkin and the Petrov-Galerkin finite element methods with backward-Euler or Crank-Nicolson temporal discretization, the streamline diffusion finite element methods, the monotonic upstream-centered scheme for conservation laws (MUSCL), and the Minmod scheme.
Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology
NASA Technical Reports Server (NTRS)
Rallabhandi, Siriam K.; Diskin, Boris; Nielsen, Eric J.
2012-01-01
This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.
Adjoint Error Estimation for Linear Advection
Connors, J M; Banks, J W; Hittinger, J A; Woodward, C S
2011-03-30
An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.
Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.
2000-01-01
This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.
Ayyoubzadeh, Seyed Mohsen; Vosoughi, Naser
2011-09-14
Obtaining the set of algebraic equations that directly correspond to a physical phenomenon has been viable in the recent direct discrete method (DDM). Although this method may find its roots in physical and geometrical considerations, there are still some degrees of freedom that one may suspect optimize-able. Here we have used the information embedded in the corresponding adjoint equation to form a local functional, which in turn by its minimization, yield suitable dual mesh positioning.
D.L. Henderson; S. Yoo; M. Kowalok; T.R. Mackie; B.R. Thomadsen
2001-10-30
The goal of this project is to investigate the use of the adjoint method, commonly used in the reactor physics community, for the optimization of radiation therapy patient treatment plans. Two different types of radiation therapy are being examined, interstitial brachytherapy and radiotherapy. In brachytherapy radioactive sources are surgically implanted within the diseased organ such as the prostate to treat the cancerous tissue. With radiotherapy, the x-ray source is usually located at a distance of about 1-metere from the patient and focused on the treatment area. For brachytherapy the optimization phase of the treatment plan consists of determining the optimal placement of the radioactive sources, which delivers the prescribed dose to the disease tissue while simultaneously sparing (reducing) the dose to sensitive tissue and organs. For external beam radiation therapy the optimization phase of the treatment plan consists of determining the optimal direction and intensity of beam, which provides complete coverage of the tumor region with the prescribed dose while simultaneously avoiding sensitive tissue areas. For both therapy methods, the optimal treatment plan is one in which the diseased tissue has been treated with the prescribed dose and dose to the sensitive tissue and organs has been kept to a minimum.
Arnal, B; Pinton, G; Garapon, P; Pernot, M; Fink, M; Tanter, M
2013-10-01
Shear wave imaging (SWI) maps soft tissue elasticity by measuring shear wave propagation with ultrafast ultrasound acquisitions (10 000 frames s(-1)). This spatiotemporal data can be used as an input for an inverse problem that determines a shear modulus map. Common inversion methods are local: the shear modulus at each point is calculated based on the values of its neighbour (e.g. time-of-flight, wave equation inversion). However, these approaches are sensitive to the information loss such as noise or the lack of the backscattered signal. In this paper, we evaluate the benefits of a global approach for elasticity inversion using a least-squares formulation, which is derived from full waveform inversion in geophysics known as the adjoint method. We simulate an acoustic waveform in a medium with a soft and a hard lesion. For this initial application, full elastic propagation and viscosity are ignored. We demonstrate that the reconstruction of the shear modulus map is robust with a non-uniform background or in the presence of noise with regularization. Compared to regular local inversions, the global approach leads to an increase of contrast (∼+3 dB) and a decrease of the quantification error (∼+2%). We demonstrate that the inversion is reliable in the case when there is no signal measured within the inclusions like hypoechoic lesions which could have an impact on medical diagnosis. PMID:24018867
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
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...
EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. uch characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. eneralization of characteristic...
NASA Astrophysics Data System (ADS)
Martinec, Zdenek; Sasgen, Ingo; Velimsky, Jakub
2014-05-01
In this study, two new methods for computing the sensitivity of the glacial isostatic adjustment (GIA) forward solution with respect to the Earth's mantle viscosity are presented: the forward sensitivity method (FSM) and the adjoint sensitivity method (ASM). These advanced formal methods are based on the time-domain,spectral-finite element method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec (2000). There are many similarities between the forward method and the FSM and ASM for a general physical system. However, in the case of GIA, there are also important differences between the forward and sensitivity methods. The analysis carried out in this study results in the following findings. First, the forward method of GIA is unconditionally solvable, regardless of whether or not a combined ice and ocean-water load contains the first-degree spherical harmonics. This is also the case for the FSM, however, the ASM must in addition be supplemented by nine conditions on the misfit between the given GIA-related data and the forward model predictions to guarantee the existence of a solution. This constrains the definition of data least-squares misfit. Second, the forward method of GIA implements an ocean load as a free boundary-value function over an ocean area with a free geometry. That is, an ocean load and the shape of ocean, the so-called ocean function, are being sought, in addition to deformation and gravity-increment fields, by solving the forward method. The FSM and ASM also apply the adjoint ocean load as a free boundary-value function, but instead over an ocean area with the fixed geometry given by the ocean function determined by the forward method. In other words, a boundary-value problem for the forward method of GIA is free with respect to determining (i) the boundary-value data over an ocean area and (ii) the ocean function itself, while the boundary-value problems for the FSM and ASM are free only with respect to
Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.
2006-01-01
Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.
NASA Astrophysics Data System (ADS)
Masson, Y.; Pierre, C.; Romanowicz, B. A.; French, S. W.; Yuan, H.
2014-12-01
Yuan et al. (2013) developed a 3D radially anisotropic shear wave model of North America (NA) upper mantle based on full waveform tomography, combining teleseismic and regional distance data sampling the NA. In this model, synthetic seismograms associated with regional events (i.e. events located inside in the region imaged NA) were computed exactly using the Spectral Element method (Cupillard et al., 2012), while, synthetic seismograms associated with teleseismic events were performed approximately using non-linear asymptotic coupling theory (NACT, Li and Romanowicz, 1995). Both the regional and the teleseismic dataset have been inverted using approximate sensitivity kernels based upon normal mode theory. Our objective is to improve our current model and to build the next generation model of NA by introducing new methodological developments (Masson et al., 2014) that allow us to compute exact synthetic seismograms as well as adjoint sensitivity kernels associated with teleseismic events, using mostly regional computations of wave propagation. The principle of the method is to substitute a teleseismic source (i.e. an earthquake) by an "equivalent" set of seismic sources acting on the boundaries of the region to be imaged that is producing exactly the same wavefield. Computing the equivalent set of sources associated with each one of the teleseismic events requires a few global simulations of the seismic wavefield that can be done once for all, prior to the regional inversion. Then, the regional full waveform inversion can be preformed using regional simulations only. We present a 3D model of NA demonstrating the advantages of the proposed method.
NASA Technical Reports Server (NTRS)
Edwards, S.; Reuther, J.; Chattot, J. J.
1997-01-01
The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjunct approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speed.
Design sensitivity analysis with Applicon IFAD using the adjoint variable method
NASA Technical Reports Server (NTRS)
Frederick, Marjorie C.; Choi, Kyung K.
1984-01-01
A numerical method is presented to implement structural design sensitivity analysis using the versatility and convenience of existing finite element structural analysis program and the theoretical foundation in structural design sensitivity analysis. Conventional design variables, such as thickness and cross-sectional areas, are considered. Structural performance functionals considered include compliance, displacement, and stress. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. That is, design sensitivity analysis software does not have to be imbedded in an existing finite element code. The finite element structural analysis program used in the implementation presented is IFAD. Feasibility of the method is shown through analysis of several problems, including built-up structures. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of a finite difference perturbation.
NASA Astrophysics Data System (ADS)
Yaremchuk, Max; Martin, Paul; Koch, Andrey; Beattie, Christopher
2016-01-01
Performance of the adjoint and adjoint-free 4-dimensional variational (4dVar) data assimilation techniques is compared in application to the hydrographic surveys and velocity observations collected in the Adriatic Sea in 2006. Assimilating the data into the Navy Coastal Ocean Model (NCOM) has shown that both methods deliver similar reduction of the cost function and demonstrate comparable forecast skill at approximately the same computational expense. The obtained optimal states were, however, significantly different in terms of distance from the background state: application of the adjoint method resulted in a 30-40% larger departure, mostly due to the excessive level of ageostrophic motions in the southern basin of the Sea that was not covered by observations.
Shape optimization governed by the Euler equations using an adjoint method
NASA Technical Reports Server (NTRS)
Iollo, Angelo; Salas, Manuel D.; Taasan, Shlomo
1993-01-01
A numerical approach for the treatment of optimal shape problems governed by the Euler equations is discussed. Focus is on flows with embedded shocks. A very simple problem is considered: the design of a quasi-one-dimensional Laval nozzle. A cost function and a set of Lagrange multipliers are introduced to achieve the minimum. The nature of the resulting costate equations is discussed. A theoretical difficulty that arises for cases with embedded shocks is pointed out and solved. Finally, some results are given to illustrate the effectiveness of the method.
NASA Astrophysics Data System (ADS)
Bozdag, Ebru; Lefebvre, Matthieu; Lei, Wenjie; Peter, Daniel; Smith, James; Komatitsch, Dimitri; Tromp, Jeroen
2015-04-01
We will present our initial results of global adjoint tomography based on 3D seismic wave simulations which is one of the most challenging examples in seismology in terms of intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. Using a spectral-element method, we incorporate full 3D wave propagation in seismic tomography by running synthetic seismograms and adjoint simulations to compute exact sensitivity kernels in realistic 3D background models. We run our global simulations on the Oak Ridge National Laboratory's Cray XK7 "Titan" system taking advantage of the GPU version of the SPECFEM3D_GLOBE package. We have started iterations with initially selected 253 earthquakes within the magnitude range of 5.5 < Mw < 7.0 and numerical simulations having resolution down to ~27 s to invert for a transversely isotropic crust and mantle model using a non-linear conjugate gradient algorithm. The measurements are currently based on frequency-dependent traveltime misfits. We use both minor- and major-arc body and surface waves by running 200 min simulations where inversions are performed with more than 2.6 million measurements. Our initial results after 12 iterations already indicate several prominent features such as enhanced slab (e.g., Hellenic, Japan, Bismarck, Sandwich), plume/hotspot (e.g., the Pacific superplume, Caroline, Yellowstone, Hawaii) images, etc. To improve the resolution and ray coverage, particularly in the lower mantle, our aim is to increase the resolution of numerical simulations first going down to ~17 s and then to ~9 s to incorporate high-frequency body waves in inversions. While keeping track of the progress and illumination of features in our models with a limited data set, we work towards to assimilate all available data in inversions from all seismic networks and earthquakes in the global CMT catalogue.
NASA Technical Reports Server (NTRS)
Gelaro, Ron; Liu, Emily; Sienkiewicz, Meta
2011-01-01
The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. In this talk, we present results from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. The tool has been running in various off-line configurations for some time, and is scheduled to run as a regular part of the real-time forecast suite beginning in autumn 20 I O. We focus on the impacts of the newest components of the satellite observing system, including AIRS, IASI and GPS. For AIRS and IASI, it is shown that the vast majority of the channels assimilated have systematic positive impacts (of varying magnitudes), although some channels degrade the forecast. Of the latter, most are moisture-sensitive or near-surface channels. The impact of GPS observations in the southern hemisphere is found to be a considerable overall benefit to the system. In addition, the spatial variability of observation impacts reveals coherent patterns of positive and negative impacts that may point to deficiencies in the use of certain observations over, for example, specific surface types. When performed in conjunction with selected observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies appears to pose a major challenge for optimizing the use of the current observational network and
NASA Technical Reports Server (NTRS)
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.
Towards Global Adjoint Tomography
NASA Astrophysics Data System (ADS)
Bozdag, E.; Zhu, H.; Peter, D. B.; Tromp, J.
2012-12-01
Seismic tomography is at a stage where we can harness entire seismograms using the opportunities offered by advances in numerical wave propagation solvers and high-performance computing. Adjoint methods provide an efficient way for incorporating full nonlinearity of wave propagation and 3D Fréchet kernels in iterative seismic inversions which have so far given promising results at continental and regional scales. Our goal is to take adjoint tomography forward to image the entire planet. Using an iterative conjugate gradient scheme, we initially set the aim to obtain a global crustal and mantle model with confined transverse isotropy in the upper mantle. We have started with around 255 global CMT events having moment magnitudes between 5.8 and 7, and used GSN stations as well as some local networks such as USArray, European stations etc. Prior to the structure inversion, we reinvert global CMT solutions by computing Green functions in our 3D reference model to take into account effects of crustal variations on source parameters. Using the advantages of numerical simulations, our strategy is to invert crustal and mantle structure together to avoid any bias introduced into upper-mantle images due to "crustal corrections", which are commonly used in classical tomography. 3D simulations dramatically increase the usable amount of data so that, with the current earthquake-station setup, we perform each iteration with more than two million measurements. Multi-resolution smoothing based on ray density is applied to the gradient to better deal with the imperfect source-station distribution on the globe and extract more information underneath regions with dense ray coverage and vice versa. Similar to frequency domain approach, we reduce nonlinearities by starting from long periods and gradually increase the frequency content of data after successive model updates. To simplify the problem, we primarily focus on the elastic structure and therefore our measurements are based on
Improved Adjoint-Operator Learning For A Neural Network
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad; Barhen, Jacob
1995-01-01
Improved method of adjoint-operator learning reduces amount of computation and associated computational memory needed to make electronic neural network learn temporally varying pattern (e.g., to recognize moving object in image) in real time. Method extension of method described in "Adjoint-Operator Learning for a Neural Network" (NPO-18352).
Diagnositcs With Adjoint Modelling
NASA Astrophysics Data System (ADS)
Blessing, S.; Fraedrich, K.; Kirk, E.; Lunkeit, F.
The potential usefulness of an adjoint primitive equations global atmospheric circu- lation model for climate diagnostics is demonstrated in a feasibility study. A daily NAO-type index is calculated as one-point correlation of the 300 hPa streamfunction anomaly. By application of the adjoint model we diagnose its temperature forcing on short timescales in terms of spatial temperature sensitivity patterns at different time lags, which, in a first order approximation, induce growth of the index. The dynamical relevance of these sensitivity patterns is confirmed by lag-correlating the index time series and the projection time series of the model temperature on these sensitivity patterns.
NASA Astrophysics Data System (ADS)
Kano, Masayuki; Miyazaki, Shin'ichi; Ishikawa, Yoichi; Hiyoshi, Yoshihisa; Ito, Kosuke; Hirahara, Kazuro
2015-10-01
Data assimilation is a technique that optimizes the parameters used in a numerical model with a constraint of model dynamics achieving the better fit to observations. Optimized parameters can be utilized for the subsequent prediction with a numerical model and predicted physical variables are presumably closer to observations that will be available in the future, at least, comparing to those obtained without the optimization through data assimilation. In this work, an adjoint data assimilation system is developed for optimizing a relatively large number of spatially inhomogeneous frictional parameters during the afterslip period in which the physical constraints are a quasi-dynamic equation of motion and a laboratory derived rate and state dependent friction law that describe the temporal evolution of slip velocity at subduction zones. The observed variable is estimated slip velocity on the plate interface. Before applying this method to the real data assimilation for the afterslip of the 2003 Tokachi-oki earthquake, a synthetic data assimilation experiment is conducted to examine the feasibility of optimizing the frictional parameters in the afterslip area. It is confirmed that the current system is capable of optimizing the frictional parameters A-B, A and L by adopting the physical constraint based on a numerical model if observations capture the acceleration and decaying phases of slip on the plate interface. On the other hand, it is unlikely to constrain the frictional parameters in the region where the amplitude of afterslip is less than 1.0 cm d-1. Next, real data assimilation for the 2003 Tokachi-oki earthquake is conducted to incorporate slip velocity data inferred from time dependent inversion of Global Navigation Satellite System time-series. The optimized values of A-B, A and L are O(10 kPa), O(102 kPa) and O(10 mm), respectively. The optimized frictional parameters yield the better fit to the observations and the better prediction skill of slip
Adjoint affine fusion and tadpoles
NASA Astrophysics Data System (ADS)
Urichuk, Andrew; Walton, Mark A.
2016-06-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Double-difference adjoint seismic tomography
NASA Astrophysics Data System (ADS)
Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen
2016-06-01
We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher-resolution) structural variations in areas close to the stations. Whereas in conventional tomography a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.
The compressible adjoint equations in geodynamics: equations and numerical assessment
NASA Astrophysics Data System (ADS)
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
ADGEN: ADjoint GENerator for computer models
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.
NASA Astrophysics Data System (ADS)
Galanti, Eli; Kaspi, Yohai
2016-04-01
During 2016-17, the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. These data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus only allowing the calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model is developed to relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for the examination of various scenarios, simulating cases in which the depth of the wind depends on latitude. We show that it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn, also taking into account measurement errors. Calculating the solution uncertainties, we show that the wind depth can be determined more precisely in the low-to-mid-latitudes. In addition, the gravitational moments are found to be particularly sensitive to flows at the equatorial intermediate depths. Therefore, we expect that if deep winds exist on these planets they will have a measurable signature by Juno and Cassini.
2004-04-21
Version 04 NESTLE solves the few-group neutron diffusion equation utilizing the NEM. The NESTLE code can solve the eigenvalue (criticality), eigenvalue adjoint, external fixed-source steady-state, and external fixed-source or eigenvalue initiated transient problems. 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- ormore » four-energy groups can be utilized, with all energy groups being thermal groups (i.e., upscatter exits) if desired. Core geometries modeled include Cartesian and hexagonal. Three-, two-, and one-dimensional models can be utilized with various symmetries. The thermal conditions predicted by the thermal-hydraulic model of the core are used to correct cross sections for temperature and density effects. Cross sections are parameterized by color, control rod state (i.e., in or out), and burnup, allowing fuel depletion to be modeled. Either a macroscopic or microscopic model may be employed.« less
NASA Astrophysics Data System (ADS)
Galanti, E.; Finocchiaro, S.; Kaspi, Y.; Iess, L.
2013-12-01
The upcoming high precision measurements of the Juno flybys around Jupiter, have the potential of improving the estimation of Jupiter's gravity field. The analysis of the Juno Doppler data will provide a very accurate reconstruction of spacial gravity variations, but these measurements will be over a limited latitudinal and longitudinal range. In order to deduce the full gravity field of Jupiter, additional information needs to be incorporated into the analysis, especially with regards to the Jovian wind structure and its depth at high latitudes. In this work we propose a new iterative method for the estimation of the Jupiter gravity field, using the Juno expected measurements, a trajectory estimation model, and an adjoint based inverse thermal wind model. Beginning with an artificial gravitational field, the trajectory estimation model together with an optimization procedure is used to obtain an initial solution of the gravitational moments. As upper limit constraints, the model applies the gravity harmonics obtained from a thermal wind model in which the winds are assumed to penetrate barotropicaly along the direction of the spin axis. The solution from the trajectory model is then used as an initial guess for the thermal wind model, and together with an adjoint optimization method, the optimal penetration depth of the winds is computed. As a final step, the gravity harmonics solution from the thermal wind model is given back to the trajectory model, along with an uncertainties estimate, to be used as constraints for a new calculation of the gravity field. We test this method for several cases, some with zonal harmonics only, and some with the full gravity field including longitudinal variations that include the tesseral harmonics as well. The results show that using this method some of the gravitational moments are fitted better to the 'observed' ones, mainly due to the fact that the thermal wind model is taking into consideration the wind structure and depth
Healy, R.W.; Russell, T.F.
1998-01-01
We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.
Southern California Adjoint Source Inversions
NASA Astrophysics Data System (ADS)
Tromp, J.; Kim, Y.
2007-12-01
Southern California Centroid-Moment Tensor (CMT) solutions with 9 components (6 moment tensor elements, latitude, longitude, and depth) are sought to minimize a misfit function computed from waveform differences. The gradient of a misfit function is obtained based upon two numerical simulations for each earthquake: one forward calculation for the southern California model, and an adjoint calculation that uses time-reversed signals at the receivers. Conjugate gradient and square-root variable metric methods are used to iteratively improve the earthquake source model while reducing the misfit function. The square-root variable metric algorithm has the advantage of providing a direct approximation to the posterior covariance operator. We test the inversion procedure by perturbing each component of the CMT solution, and see how the algorithm converges. Finally, we demonstrate full inversion capabilities using data for real Southern California earthquakes.
Adjoint Function: Physical Basis of Variational & Perturbation Theory in Transport
2009-07-27
Version 00 Dr. J.D. Lewins has now released the following legacy book for free distribution: Importance: The Adjoint Function: The Physical Basis of Variational and Perturbation Theory in Transport and Diffusion Problems, North-Holland Publishing Company - Amsterdam, 582 pages, 1966 Introduction: Continuous Systems and the Variational Principle 1. The Fundamental Variational Principle 2. The Importance Function 3. Adjoint Equations 4. Variational Methods 5. Perturbation and Iterative Methods 6. Non-Linear Theory
NASA Astrophysics Data System (ADS)
Lee, E.; Chen, P.; Jordan, T. H.; Maechling, P. J.; Denolle, M.; Beroza, G. C.
2013-12-01
We apply a unified methodology for seismic waveform analysis and inversions to Southern California. To automate the waveform selection processes, we developed a semi-automatic seismic waveform analysis algorithm for full-wave earthquake source parameters and tomographic inversions. The algorithm is based on continuous wavelet transforms, a topological watershed method, and a set of user-adjustable criteria to select usable waveform windows for full-wave inversions. The algorithm takes advantages of time-frequency representations of seismograms and is able to separate seismic phases in both time and frequency domains. The selected wave packet pairs between observed and synthetic waveforms are then used for extracting frequency-dependent phase and amplitude misfit measurements, which are used in our seismic source and structural inversions. Our full-wave waveform tomography uses the 3D SCEC Community Velocity Model Version 4.0 as initial model, a staggered-grid finite-difference code to simulate seismic wave propagations. The sensitivity (Fréchet) kernels are calculated based on the scattering integral and adjoint methods to iteratively improve the model. We use both earthquake recordings and ambient noise Green's functions, stacking of station-to-station correlations of ambient seismic noise, in our full-3D waveform tomographic inversions. To reduce errors of earthquake sources, the epicenters and source parameters of earthquakes used in our tomographic inversion are inverted by our full-wave CMT inversion method. Our current model shows many features that relate to the geological structures at shallow depth and contrasting velocity values across faults. The velocity perturbations could up to 45% with respect to the initial model in some regions and relate to some structures that do not exist in the initial model, such as southern Great Valley. The earthquake waveform misfits reduce over 70% and the ambient noise Green's function group velocity delay time variance
Surface wave sensitivity: mode summation versus adjoint SEM
NASA Astrophysics Data System (ADS)
Zhou, Ying; Liu, Qinya; Tromp, Jeroen
2011-12-01
We compare finite-frequency phase and amplitude sensitivity kernels calculated based on frequency-domain surface wave mode summation and a time-domain adjoint method. The adjoint calculations involve a forward wavefield generated by an earthquake and an adjoint wavefield generated at a seismic receiver. We determine adjoint sources corresponding to frequency-dependent phase and amplitude measurements made using a multitaper technique, which may be applied to any single-taper measurement, including box car windowing. We calculate phase and amplitude sensitivity kernels using an adjoint method based on wave propagation simulations using a spectral element method (SEM). Sensitivity kernels calculated using the adjoint SEM are in good agreement with kernels calculated based on mode summation. In general, the adjoint SEM is more computationally expensive than mode summation in global studies. The advantage of the adjoint SEM lies in the calculation of sensitivity kernels in 3-D earth models. We compare surface wave sensitivity kernels computed in 1-D and 3-D reference earth models and show that (1) lateral wave speed heterogeneities may affect the geometry and amplitude of surface wave sensitivity; (2) sensitivity kernels of long-period surface waves calculated in 1-D model PREM and 3-D models S20RTS+CRUST2.0 and FFSW1+CRUST2.0 do not show significant differences, indicating that the use of a 1-D reference model is adequate in global inversions of long-period surface waves (periods of 50 s and longer); and (3) the differences become significant for short-period Love waves when mode coupling is sensitive to large differences in reference crustal structure. Finally, we show that sensitivity kernels in anelastic earth models may be calculated in purely elastic earth models provided physical dispersion is properly accounted for.
A new mathematical adjoint for the modified SAAF_{-SN} equations
Schunert, Sebastian; Wang, Yaqi; Martineau, Richard; DeHart, Mark D.
2015-01-01
We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF_{-SN}) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF_{-SN} method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF_{-SN} . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both for fixed source and eigenvalue problems.
Nonlinear self-adjointness and conservation laws of Klein-Gordon-Fock equation with central symmetry
NASA Astrophysics Data System (ADS)
Abdulwahhab, Muhammad Alim
2015-05-01
The concept of nonlinear self-adjointness, introduced by Ibragimov, has significantly extends approaches to constructing conservation laws associated with symmetries since it incorporates the strict self-adjointness, the quasi self-adjointness as well as the usual linear self-adjointness. Using this concept, the nonlinear self-adjointness condition for the Klein-Gordon-Fock equation was established and subsequently used to construct simplified but infinitely many nontrivial and independent conserved vectors. The Noether's theorem was further applied to the Klein-Gordon-Fock equation to explore more distinct first integrals, result shows that conservation laws constructed through this approach are exactly the same as those obtained under strict self-adjointness of Ibragimov's method.
Adjoint-Based Methodology for Time-Dependent Optimization
NASA Technical Reports Server (NTRS)
Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.
2008-01-01
This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.
NASA Astrophysics Data System (ADS)
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
Adjoint sensitivity analysis of an ultrawideband antenna
Stephanson, M B; White, D A
2011-07-28
The frequency domain finite element method using H(curl)-conforming finite elements is a robust technique for full-wave analysis of antennas. As computers become more powerful, it is becoming feasible to not only predict antenna performance, but also to compute sensitivity of antenna performance with respect to multiple parameters. This sensitivity information can then be used for optimization of the design or specification of manufacturing tolerances. In this paper we review the Adjoint Method for sensitivity calculation, and apply it to the problem of optimizing a Ultrawideband antenna.
Probability density adjoint for sensitivity analysis of the Mean of Chaos
Blonigan, Patrick J. Wang, Qiqi
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 simulation of stream depletion due to aquifer pumping.
Neupauer, Roseanna M; Griebling, Scott A
2012-01-01
If an aquifer is hydraulically connected to an adjacent stream, a pumping well operating in the aquifer will draw some water from aquifer storage and some water from the stream, causing stream depletion. Several analytical, semi-analytical, and numerical approaches have been developed to estimate stream depletion due to pumping. These approaches are effective if the well location is known. If a new well is to be installed, it may be desirable to install the well at a location where stream depletion is minimal. If several possible locations are considered for the location of a new well, stream depletion would have to be estimated for all possible well locations, which can be computationally inefficient. The adjoint approach for estimating stream depletion is a more efficient alternative because with one simulation of the adjoint model, stream depletion can be estimated for pumping at a well at any location. We derive the adjoint equations for a coupled system with a confined aquifer, an overlying unconfined aquifer, and a river that is hydraulically connected to the unconfined aquifer. We assume that the stage in the river is known, and is independent of the stream depletion, consistent with the assumptions of the MODFLOW river package. We describe how the adjoint equations can be solved using MODFLOW. In an illustrative example, we show that for this scenario, the adjoint approach is as accurate as standard forward numerical simulation methods, and requires substantially less computational effort. PMID:22182421
Kim, Min-Geun; Jang, Hong-Lae; Cho, Seonho
2013-05-01
An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.
Adjoints and Low-rank Covariance Representation
NASA Technical Reports Server (NTRS)
Tippett, Michael K.; Cohn, Stephen E.
2000-01-01
Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.
RamaRao, B.S.; Reeves, M. )
1990-10-01
Calibration of a numerical model of the regional ground-water flow in the Culebra dolomite at the Waste Isolation Pilot Plant in southeastern New Mexico, has been performed by an interative parameter-fitting procedure. Parameterization has been secured by choosing to assign the transmissivity values at a limited number of selected locations, designated as pilot points. The transmissivity distribution in the model is derived by kriging the combined pool of measured and pilot-plant transmissivities. Iterating on the twin steps of sequentially adding additional pilot point(s) and kriging leads to the model of required accuracy, as judged by a weighted least-square-error objective function. At the end of calibration, it must be ensured that the correlation structure of the measured transmissivities is broadly preserved by the pilot-plant transmissivities. Adjoint-sensitivity analysis of the model has been coupled with kriging to provide objectively the optimal location of the pilot points during an iteration. The pilot-point transmissivities have been adjusted by modeler's judgement incorporating information, where available, on local geologic conditions and large-scale hydraulic interference tests, in order to minimize the objective function. 43 refs., 5 figs., 5 tabs.
Self-adjointness of deformed unbounded operators
Much, Albert
2015-09-15
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
Adjoint Based Data Assimilation for an Ionospheric Model
NASA Astrophysics Data System (ADS)
Rosen, I. G.; Hajj, G. A.; Hajj, G. A.; Pi, X.; Pi, X.; Wang, C.; Wilson, B. D.
2001-05-01
The success of ionospheric modeling depends primarily on accurate knowledge of the forces (drivers) which enter into the collisional plasma hydrodynamic equations for the ionosphere and control the ionization as well as other dynamical and chemical processes. These include solar EUV and UV radiation, magnetospheric electric fields, particle precipitation, dynamo electric fields, thermospheric winds, neutral densities, and temperature. The determination of these model parameters from observational data is known as data assimilation. The data assimilation problem is formulated as a problem of minimizing a nonlinear functional, J (typically least squares) under a system of constraints consisting primarily of the underlying model equations. The performance index, J, can, in principle, be minimized using standard techniques such as the Newton's steepest decent method. There are however major technical challenges in practice. Since J is highly nonlinear and each evaluation of the functional requires the integration of the ionospheric model equations, computing the gradient vector of J with respect to the unknown parameters is time consuming. This problem is solved by use of the adjoint method. The ionospheric model used in this effort is for mid- and low-latitudes and consists of solving the continuity and momentum partial differential equations in four dimensional (three spatial dimensions and time) to compute the O+ density in the ionosphere and plasmasphere. We have developed codes for solving the forward model on a fixed grid. This makes it relatively straight forward to apply the adjoint method for computing gradients when doing nonlinear least squares based data assimilation. Because of the significant cost (in computational effort and CPU time) involved in performing a forward integration of the underlying 3-D model at any reasonable grid resolution, the use of the adjoint method for computing the gradients is indispensable. The adjoint method provides an elegant
MS S4.03.002 - Adjoint-Based Design for Configuration Shaping
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.
2009-01-01
This slide presentation discusses a method of inverse design for low sonic boom using adjoint-based gradient computations. It outlines a method for shaping a configuration in order to match a prescribed near-field signature.
Adjoint operator approach to shape design for internal incompressible flows
NASA Technical Reports Server (NTRS)
Cabuk, H.; Sung, C.-H.; Modi, V.
1991-01-01
The problem of determining the profile of a channel or duct that provides the maximum static pressure rise is solved. Incompressible, laminar flow governed by the steady state Navier-Stokes equations is assumed. Recent advances in computational resources and algorithms have made it possible to solve the direct problem of determining such a flow through a body of known geometry. It is possible to obtain a set of adjoint equations, the solution to which permits the calculation of the direction and relative magnitude of change in the diffuser profile that leads to a higher pressure rise. The solution to the adjoint problem can be shown to represent an artificially constructed flow. This interpretation provides a means to construct numerical solutions to the adjoint equations that do not compromise the fully viscous nature of the problem. The algorithmic and computational aspects of solving the adjoint equations are addressed. The form of these set of equations is similar but not identical to the Navier-Stokes equations. In particular some issues related to boundary conditions and stability are discussed.
Numerical Computation of Sensitivities and the Adjoint Approach
NASA Technical Reports Server (NTRS)
Lewis, Robert Michael
1997-01-01
We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.
NASA Astrophysics Data System (ADS)
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.
Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.
2010-01-01
Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.
Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.
2009-01-01
Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.
Adjoint active surfaces for localization and imaging.
Cook, Daniel A; Mueller, Martin Fritz; Fedele, Francesco; Yezzi, Anthony J
2015-01-01
This paper addresses the problem of localizing and segmenting regions embedded within a surrounding medium by characterizing their boundaries, as opposed to imaging the entirety of the volume. Active surfaces are used to directly reconstruct the shape of the region of interest. We describe the procedure for finding the optimal surface, which is computed iteratively via gradient descent that exploits the sensitivity of an error minimization functional to changes of the active surface. In doing so, we introduce the adjoint model to compute the sensitivity, and in this respect, the method shares common ground with several other disciplines, such as optimal control. Finally, we illustrate the proposed active surface technique in the framework of wave propagation governed by the scalar Helmholtz equation. Potential applications include electromagnetics, acoustics, geophysics, nondestructive testing, and medical imaging. PMID:25438311
Adjoint tomography of the southern California crust.
Tape, Carl; Liu, Qinya; Maggi, Alessia; Tromp, Jeroen
2009-08-21
Using an inversion strategy based on adjoint methods, we developed a three-dimensional seismological model of the southern California crust. The resulting model involved 16 tomographic iterations, which required 6800 wavefield simulations and a total of 0.8 million central processing unit hours. The new crustal model reveals strong heterogeneity, including local changes of +/-30% with respect to the initial three-dimensional model provided by the Southern California Earthquake Center. The model illuminates shallow features such as sedimentary basins and compositional contrasts across faults. It also reveals crustal features at depth that aid in the tectonic reconstruction of southern California, such as subduction-captured oceanic crustal fragments. The new model enables more realistic and accurate assessments of seismic hazard. PMID:19696349
The Θ-KMS adjoint and time reversed quantum Markov semigroups
NASA Astrophysics Data System (ADS)
Bolaños-Servin, Jorge R.; Quezada, Roberto
2015-08-01
We introduce the notion of Θ-KMS adjoint of a quantum Markov semigroup, which is identified with the time reversed semigroup. The break of Θ-KMS symmetry, or Θ-standard quantum detailed balance in the sense of Fagnola-Umanità,11 is measured by means of the von Neumann relative entropy of states associated with the semigroup and its Θ-KMS adjoint.
Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle
Peplow, Douglas E.; Mosher, Scott W; Evans, Thomas M
2012-08-01
For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.
GPU-accelerated adjoint algorithmic differentiation
NASA Astrophysics Data System (ADS)
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.
GPU-Accelerated Adjoint Algorithmic Differentiation
Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe
2015-01-01
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
A comparison of adjoint and data-centric verification techniques.
Wildey, Timothy Michael; Cyr, Eric Christopher; Shadid, John Nicolas; Pawlowski, Roger Patrick; Smith, Thomas Michael
2013-03-01
This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. We compare the adjoint-based a posteriori error estimation approach with a recent variant of a data-centric verification technique. We provide a brief overview of each technique and then we discuss their relative advantages and disadvantages. We use Drekar::CFD to produce numerical results for steady-state Navier Stokes and SARANS approximations. 3
A Generalized Adjoint Approach for Quantifying Reflector Assembly Discontinuity Factor Uncertainties
Yankov, Artem; Collins, Benjamin; Jessee, Matthew Anderson; Downar, Thomas
2012-01-01
Sensitivity-based uncertainty analysis of assembly discontinuity factors (ADFs) can be readily performed using adjoint methods for infinite lattice models. However, there is currently no adjoint-based methodology to obtain uncertainties for ADFs along an interface between a fuel and reflector region. To accommodate leakage effects in a reflector region, a 1D approximation is usually made in order to obtain the homogeneous interface flux required to calculate the ADF. Within this 1D framework an adjoint-based method is proposed that is capable of efficiently calculating ADF uncertainties. In the proposed method the sandwich rule is utilized to relate the covariance of the input parameters of 1D diffusion theory in the reflector region to the covariance of the interface ADFs. The input parameters covariance matrix can be readily obtained using sampling-based codes such as XSUSA or adjoint-based codes such as TSUNAMI. The sensitivity matrix is constructed using a fixed-source adjoint approach for inputs characterizing the reflector region. An analytic approach is then used to determine the sensitivity of the ADFs to fuel parameters using the neutron balance equation. A stochastic approach is used to validate the proposed adjoint-based method.
NASA Astrophysics Data System (ADS)
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
Accurate adjoint design sensitivities for nano metal optics.
Hansen, Paul; Hesselink, Lambertus
2015-09-01
We present a method for obtaining accurate numerical design sensitivities for metal-optical nanostructures. Adjoint design sensitivity analysis, long used in fluid mechanics and mechanical engineering for both optimization and structural analysis, is beginning to be used for nano-optics design, but it fails for sharp-cornered metal structures because the numerical error in electromagnetic simulations of metal structures is highest at sharp corners. These locations feature strong field enhancement and contribute strongly to design sensitivities. By using high-accuracy FEM calculations and rounding sharp features to a finite radius of curvature we obtain highly-accurate design sensitivities for 3D metal devices. To provide a bridge to the existing literature on adjoint methods in other fields, we derive the sensitivity equations for Maxwell's equations in the PDE framework widely used in fluid mechanics. PMID:26368483
Application of Adjoint Methodology in Various Aspects of Sonic Boom Design
NASA Technical Reports Server (NTRS)
Rallabhandi, Sriram K.
2014-01-01
One of the advances in computational design has been the development of adjoint methods allowing efficient calculation of sensitivities in gradient-based shape optimization. This paper discusses two new applications of adjoint methodology that have been developed to aid in sonic boom mitigation exercises. In the first, equivalent area targets are generated using adjoint sensitivities of selected boom metrics. These targets may then be used to drive the vehicle shape during optimization. The second application is the computation of adjoint sensitivities of boom metrics on the ground with respect to parameters such as flight conditions, propagation sampling rate, and selected inputs to the propagation algorithms. These sensitivities enable the designer to make more informed selections of flight conditions at which the chosen cost functionals are less sensitive.
On improving storm surge forecasting using an adjoint optimal technique
NASA Astrophysics Data System (ADS)
Li, Yineng; Peng, Shiqiu; Yan, Jing; Xie, Lian
2013-12-01
A three-dimensional ocean model and its adjoint model are used to simultaneously optimize the initial conditions (IC) and the wind stress drag coefficient (Cd) for improving storm surge forecasting. To demonstrate the effect of this proposed method, a number of identical twin experiments (ITEs) with a prescription of different error sources and two real data assimilation experiments are performed. Results from both the idealized and real data assimilation experiments show that adjusting IC and Cd simultaneously can achieve much more improvements in storm surge forecasting than adjusting IC or Cd only. A diagnosis on the dynamical balance indicates that adjusting IC only may introduce unrealistic oscillations out of the assimilation window, which can be suppressed by the adjustment of the wind stress when simultaneously adjusting IC and Cd. Therefore, it is recommended to simultaneously adjust IC and Cd to improve storm surge forecasting using an adjoint technique.
Adjoint-Based Sensitivity Maps for the Nearshore
NASA Astrophysics Data System (ADS)
Orzech, Mark; Veeramony, Jay; Ngodock, Hans
2013-04-01
The wave model SWAN (Booij et al., 1999) solves the spectral action balance equation to produce nearshore wave forecasts and climatologies. It is widely used by the coastal modeling community and is part of a variety of coupled ocean-wave-atmosphere model systems. A variational data assimilation system (Orzech et al., 2013) has recently been developed for SWAN and is presently being transitioned to operational use by the U.S. Naval Oceanographic Office. This system is built around a numerical adjoint to the fully nonlinear, nonstationary SWAN code. When provided with measured or artificial "observed" spectral wave data at a location of interest on a given nearshore bathymetry, the adjoint can compute the degree to which spectral energy levels at other locations are correlated with - or "sensitive" to - variations in the observed spectrum. Adjoint output may be used to construct a sensitivity map for the entire domain, tracking correlations of spectral energy throughout the grid. When access is denied to the actual locations of interest, sensitivity maps can be used to determine optimal alternate locations for data collection by identifying regions of greatest sensitivity in the mapped domain. The present study investigates the properties of adjoint-generated sensitivity maps for nearshore wave spectra. The adjoint and forward SWAN models are first used in an idealized test case at Duck, NC, USA, to demonstrate the system's effectiveness at optimizing forecasts of shallow water wave spectra for an inaccessible surf-zone location. Then a series of simulations is conducted for a variety of different initializing conditions, to examine the effects of seasonal changes in wave climate, errors in bathymetry, and variations in size and shape of the inaccessible region of interest. Model skill is quantified using two methods: (1) a more traditional correlation of observed and modeled spectral statistics such as significant wave height, and (2) a recently developed RMS
Constructing parent Hamiltonians for SU(N) ALKT states - a diagrammatic method
NASA Astrophysics Data System (ADS)
Roy, Abhishek; Quella, Thomas
Over the last decade, there has been increasing experimental interest in alkaline cold atom systems which exhibit SU (N) symmmetry. Theoretical work has shown that a one-dimensional SU (N) chain can have N - 1 symmetric protected states distinguished by fractionalized boundary spins. We introduce a new method for constructing SU (N) invariant Hamiltonians for Haldane phases in one dimension. Working at the AKLT point where the ground state is known exactly, we show a universal form of the Hamiltonian for any appropriate choice of physical and boundary spins. We apply our method to the case where the physical spin is in the adjoint representation and obtain a general expression for the Hamiltonian as well the Transfer Matrix for any N. Finally we comment on the relevance of our results to the generalized Haldane conjecture.
FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations
NASA Astrophysics Data System (ADS)
Ibragimov, N. H.; Torrisi, M.; Tracinà, R.
2010-11-01
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.
Wronskian Method for Bound States
ERIC Educational Resources Information Center
Fernandez, Francisco M.
2011-01-01
We propose a simple and straightforward method based on Wronskians for the calculation of bound-state energies and wavefunctions of one-dimensional quantum-mechanical problems. We explicitly discuss the asymptotic behaviour of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider…
Adjoint-Based Uncertainty Quantification with MCNP
Seifried, Jeffrey E.
2011-09-01
This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence in the simulation is acquired.
Application of adjoint operators to neural learning
NASA Technical Reports Server (NTRS)
Barhen, J.; Toomarian, N.; Gulati, S.
1990-01-01
A technique for the efficient analytical computation of such parameters of the neural architecture as synaptic weights and neural gain is presented as a single solution of a set of adjoint equations. The learning model discussed concentrates on the adiabatic approximation only. A problem of interest is represented by a system of N coupled equations, and then adjoint operators are introduced. A neural network is formalized as an adaptive dynamical system whose temporal evolution is governed by a set of coupled nonlinear differential equations. An approach based on the minimization of a constrained neuromorphic energylike function is applied, and the complete learning dynamics are obtained as a result of the calculations.
Uematsu, Mikio; Kurosawa, Masahiko
2005-01-01
A generalised and convenient skyshine dose analysis method has been developed based on forward-adjoint folding technique. In the method, the air penetration data were prepared by performing an adjoint DOT3.5 calculation with cylindrical air-over-ground geometry having an adjoint point source (importance of unit flux to dose rate at detection point) in the centre. The accuracy of the present method was certified by comparing with DOT3.5 forward calculation. The adjoint flux data can be used as generalised radiation skyshine data for all sorts of nuclear facilities. Moreover, the present method supplies plenty of energy-angular dependent contribution flux data, which will be useful for detailed shielding design of facilities. PMID:16604693
A self-adjoint decomposition of the radial momentum operator
NASA Astrophysics Data System (ADS)
Liu, Q. H.; Xiao, S. F.
2015-12-01
With acceptance of the Dirac's observation that the canonical quantization entails using Cartesian coordinates, we examine the operator erPr rather than Pr itself and demonstrate that there is a decomposition of erPr into a difference of two self-adjoint but noncommutative operators, in which one is the total momentum and another is the transverse one. This study renders the operator Pr indirectly measurable and physically meaningful, offering an explanation of why the mean value of Pr over a quantum mechanical state makes sense and supporting Dirac's claim that Pr "is real and is the true momentum conjugate to r".
NASA Astrophysics Data System (ADS)
Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Dimitrakopoulos, G.; Giannakoglou, K. C.
2015-11-01
In this article, the gradient of aerodynamic objective functions with respect to design variables, in problems governed by the incompressible Navier-Stokes equations coupled with the k-ω SST turbulence model, is computed using the continuous adjoint method, for the first time. Shape optimization problems for minimizing drag, in external aerodynamics (flows around isolated airfoils), or viscous losses in internal aerodynamics (duct flows) are considered. Sensitivity derivatives computed with the proposed adjoint method are compared to those computed with finite differences or a continuous adjoint variant based on the frequently used assumption of frozen turbulence; the latter proves the need for differentiating the turbulence model. Geometries produced by optimization runs performed with sensitivities computed by the proposed method and the 'frozen turbulence' assumption are also compared to quantify the gain from formulating and solving the adjoint to the turbulence model equations.
Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions
NASA Technical Reports Server (NTRS)
Akgun, Mehmet A.; Haftka, Raphael T.
2000-01-01
The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local
Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Park, Michael A.
2006-01-01
An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.
Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Park, Michael A.
2005-01-01
An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.
Examining Tropical Cyclone - Kelvin Wave Interactions using Adjoint Diagnostics
NASA Astrophysics Data System (ADS)
Reynolds, C. A.; Doyle, J. D.; Hong, X.
2015-12-01
Adjoint-based tools can provide valuable insight into the mechanisms that influence the evolution and predictability of atmospheric phenomena, as they allow for the efficient and rigorous computation of forecast sensitivity to changes in the initial state. We apply adjoint-based tools from the non-hydrostatic Coupled Atmosphere/Ocean Mesoscale Prediction System (COAMPS) to explore the initial-state sensitivity and interactions between a tropical cyclone and atmospheric equatorial waves associated with the Madden Julian Oscillation (MJO) in the Indian Ocean during the DYNAMO field campaign. The development of Tropical Cyclone 5 (TC05) coincided with the passage of an equatorial Kelvin wave and westerly wind burst associated with an MJO that developed in the Indian Ocean in late November 2011, but it was unclear if and how one affected the other. COAMPS 24-h and 36-h adjoint sensitivities are analyzed for both TC05 and the equatorial waves to understand how the evolution of each system is sensitive to the other. The sensitivity of equatorial westerlies in the western Indian Ocean on 23 November shares characteristics with the classic Gill (1980) Rossby and Kelvin wave response to symmetric heating about the equator, including symmetric cyclonic circulations to the north and south of the westerlies, and enhanced heating in the area of convergence between the equatorial westerlies and easterlies. In addition, there is sensitivity in the Bay of Bengal associated with the cyclonic circulation that eventually develops into TC05. At the same time, the developing TC05 system shows strongest sensitivity to local wind and heating perturbations, but sensitivity to the equatorial westerlies is also clear. On 24 November, when the Kelvin wave is immediately south of the developing tropical cyclone, both phenomena are sensitive to each other. On 25 November TC05 no longer shows sensitivity to the Kelvin wave, while the Kelvin Wave still exhibits some weak sensitivity to TC05. In
Adjoint tomography of the Middle East
NASA Astrophysics Data System (ADS)
Peter, D. B.; Savage, B.; Rodgers, A. J.; Tromp, J.
2010-12-01
Improvements in nuclear explosion monitoring require refined seismic models of the target region. In our study, we focus on the Middle East, spanning a region from Turkey to the west and West India to the east. This area represents a complex geologic and tectonic setting with sparse seismic data coverage. This has lead to diverging interpretations of crustal and underlying upper-mantle structure by different research groups, complicating seismic monitoring of the Middle East at regional distances. We evaluated an initial 3D seismic model of this region by computing full waveforms for several regional earthquakes by a spectral-element method. We measure traveltime and multitaper phase shifts between observed broadband data and synthetic seismograms for distinct seismic phases within selected time windows using a recently developed automated measurement algorithm. Based on the remaining misfits, we setup an iterative inversion procedure for a fully numerical 3D seismic tomography approach. In order to improve the initial 3D seismic model, the sensitivity to seismic structure of the traveltime and multitaper phase measurements for all available seismic network recordings is computed. As this represents a computationally very intensive task, we take advantage of a fully numerical adjoint approach by using the efficient software package SPECFEM3D_GLOBE on a dedicated cluster. We show examples of such sensitivity kernels for different seismic events and use them in a steepest descent approach to update the 3D seismic model, starting at longer periods between 60 s and up to 200 s and moving towards shorter periods of 11 s. We highlight various improvements in the initial seismic structure during the iterations in order to better fit regional seismic waveforms in the Middle East.
Adjoint tomography of the Middle East
NASA Astrophysics Data System (ADS)
Peter, D. B.; Savage, B.; Rodgers, A.; Morency, C.; Tromp, J.
2011-12-01
Improvements in nuclear explosion monitoring require refined seismic models of the target region. In our study, we focus on the Middle East, spanning a region from Turkey to the west and West India to the east. This area represents a complex geologic and tectonic setting with sparse seismic data coverage. This has lead to diverging interpretations of crustal and underlying upper-mantle structure by different research groups, complicating seismic monitoring of the Middle East at regional distances. We evaluated an initial 3D seismic model of this region by computing full waveforms for several regional earthquakes based on a spectral-element method. We measure traveltime and multitaper phase differences between observed broadband data and synthetic seismograms for distinct seismic phases within selected time windows using a recently developed automated measurement algorithm. Based on the remaining misfits, we setup an iterative inversion procedure for a fully numerical 3D seismic tomography approach. In order to improve the initial 3D seismic model, sensitivity to seismic structures of traveltime and multitaper phase measurements for all available seismic network recordings is computed. As this represents a computationally very intensive task, we take advantage of a fully numerical adjoint approach by using the efficient software package SPECFEM3D_GLOBE on a dedicated cluster. We show examples of such sensitivity kernels for different seismic events. All these `event kernels' are then summed, smoothed and further used in a preconditioned conjugate-gradient approach. Thus we iteratively update the 3D seismic model, starting at longer periods between 60~s and up to 150~s and moving towards shorter periods of 11~s. We highlight various improvements in the initial seismic structure during the iterations in order to better fit regional seismic waveforms in the Middle East.
Fully automatic adjoints: a robust and efficient mechanism for generating adjoint ocean models
NASA Astrophysics Data System (ADS)
Ham, D. A.; Farrell, P. E.; Funke, S. W.; Rognes, M. E.
2012-04-01
The problem of generating and maintaining adjoint models is sufficiently difficult that typically only the most advanced and well-resourced community ocean models achieve it. There are two current technologies which each suffer from their own limitations. Algorithmic differentiation, also called automatic differentiation, is employed by models such as the MITGCM [2] and the Alfred Wegener Institute model FESOM [3]. This technique is very difficult to apply to existing code, and requires a major initial investment to prepare the code for automatic adjoint generation. AD tools may also have difficulty with code employing modern software constructs such as derived data types. An alternative is to formulate the adjoint differential equation and to discretise this separately. This approach, known as the continuous adjoint and employed in ROMS [4], has the disadvantage that two different model code bases must be maintained and manually kept synchronised as the model develops. The discretisation of the continuous adjoint is not automatically consistent with that of the forward model, producing an additional source of error. The alternative presented here is to formulate the flow model in the high level language UFL (Unified Form Language) and to automatically generate the model using the software of the FEniCS project. In this approach it is the high level code specification which is differentiated, a task very similar to the formulation of the continuous adjoint [5]. However since the forward and adjoint models are generated automatically, the difficulty of maintaining them vanishes and the software engineering process is therefore robust. The scheduling and execution of the adjoint model, including the application of an appropriate checkpointing strategy is managed by libadjoint [1]. In contrast to the conventional algorithmic differentiation description of a model as a series of primitive mathematical operations, libadjoint employs a new abstraction of the simulation
Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico
NASA Astrophysics Data System (ADS)
Gopalakrishnan, Ganesh; Cornuelle, Bruce D.; Hoteit, Ibrahim
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
Advances in Global Adjoint Tomography -- Massive Data Assimilation
NASA Astrophysics Data System (ADS)
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
Instantons and the 5D U(1) gauge theory with extra adjoint
NASA Astrophysics Data System (ADS)
Poghossian, Rubik; Samsonyan, Marine
2009-07-01
In this paper, we compute the partition function of 5D supersymmetric U(1) gauge theory with extra adjoint matter in general Ω background. It is well known that such partition functions encode very rich topological information. We show in particular that unlike the case with no extra matter, the partition function with extra adjoint at some special values of the parameters directly reproduces the generating function for the Poincare polynomial of the moduli space of instantons. We compare our results with those recently obtained by Iqbal et al (Refined topological vertex, cylindric partitions and the U(1) adjoint theory, arXiv:0803.2260), who used the so-called refined topological vertex method.
Adjoint-based sensitivity analysis for reactor safety applications
Parks, C.V.
1986-08-01
The application and usefulness of an adjoint-based methodology for performing sensitivity analysis on reactor safety computer codes is investigated. The adjoint-based methodology, referred to as differential sensitivity theory (DST), provides first-order derivatives of the calculated quantities of interest (responses) with respect to the input parameters. The basic theoretical development of DST is presented along with the needed general extensions for consideration of model discontinuities and a variety of useful response definitions. A simple analytic problem is used to highlight the general DST procedures. finally, DST procedures presented in this work are applied to two highly nonlinear reactor accident analysis codes: (1) FASTGAS, a relatively small code for analysis of a loss-of-decay-heat-removal accident in a gas-cooled fast reactor, and (2) an existing code called VENUS-II which has been employed for analyzing the core disassembly phase of a hypothetical fast reactor accident. The two codes are different both in terms of complexity and in terms of the facets of DST which can be illustrated. Sensitivity results from the adjoint codes ADJGAS and VENUS-ADJ are verified with direct recalcualtions using perturbed input parameters. The effectiveness of the DST results for parameter ranking, prediction of response changes, and uncertainty analysis are illustrated. The conclusion drawn from this study is that DST is a viable, cost-effective methodology for accurate sensitivity analysis. In addition, a useful sensitivity tool for use in the fast reactor safety area has been developed in VENUS-ADJ. Future work needs to concentrate on combining the accurate first-order derivatives/results from DST with existing methods (based solely on direct recalculations) for higher-order response surfaces.
Adjoint optimization of natural convection problems: differentially heated cavity
NASA Astrophysics Data System (ADS)
Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.
2016-06-01
Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here
NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO
NASA Astrophysics Data System (ADS)
Vidard, A.; Bouttier, P.-A.; Vigilant, F.
2014-10-01
The tangent linear and adjoint model (TAM) are efficient tools to analyse and to control dynamical systems such as NEMO. They can be involved in a large range of applications such as sensitivity analysis, parameter estimation or the computation of characteristics vectors. TAM is also required by the 4-D-VAR algorithm which is one of the major method in Data Assimilation. This paper describes the development and the validation of the Tangent linear and Adjoint Model for the NEMO ocean modelling platform (NEMOTAM). The diagnostic tools that are available alongside NEMOTAM are detailed and discussed and several applications are also presented.
Dual of QCD with one adjoint fermion
Mojaza, Matin; Nardecchia, Marco; Pica, Claudio; Sannino, Francesco
2011-03-15
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling, and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the anomalous dimension of the Dirac fermion mass operator to be less than one in the conformal window.
NASA Astrophysics Data System (ADS)
Ito, Shin-Ichi; Nagao, Hiromichi; Yamanaka, Akinori; Tsukada, Yuhki; Koyama, Toshiyuki; Inoue, Junya
Phase field (PF) method, which phenomenologically describes dynamics of microstructure evolutions during solidification and phase transformation, has progressed in the fields of hydromechanics and materials engineering. How to determine, based on observation data, an initial state and model parameters involved in a PF model is one of important issues since previous estimation methods require too much computational cost. We propose data assimilation (DA), which enables us to estimate the parameters and states by integrating the PF model and observation data on the basis of the Bayesian statistics. The adjoint method implemented on DA not only finds an optimum solution by maximizing a posterior distribution but also evaluates the uncertainty in the estimations by utilizing the second order information of the posterior distribution. We carried out an estimation test using synthetic data generated by the two-dimensional Kobayashi's PF model. The proposed method is confirmed to reproduce the true initial state and model parameters we assume in advance, and simultaneously estimate their uncertainties due to quality and quantity of the data. This result indicates that the proposed method is capable of suggesting the experimental design to achieve the required accuracy.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
NASA Astrophysics Data System (ADS)
Al-Hashimi, M. H.; Salman, M.; Shalaby, A.; Wiese, U.-J.
2013-10-01
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.
Limitations of Adjoint-Based Optimization for Separated Flows
NASA Astrophysics Data System (ADS)
Otero, J. Javier; Sharma, Ati; Sandberg, Richard
2015-11-01
Cabin noise is generated by the transmission of turbulent pressure fluctuations through a vibrating panel and can lead to fatigue. In the present study, we model this problem by using DNS to simulate the flow separating off a backward facing step and interacting with a plate downstream of the step. An adjoint formulation of the full compressible Navier-Stokes equations with varying viscosity is used to calculate the optimal control required to minimize the fluid-structure-acoustic interaction with the plate. To achieve noise reduction, a cost function in wavenumber space is chosen to minimize the excitation of the lower structural modes of the structure. To ensure the validity of time-averaged cost functions, it is essential that the time horizon is long enough to be a representative sample of the statistical behaviour of the flow field. The results from the current study show how this scenario is not always feasible for separated flows, because the chaotic behaviour of turbulence surpasses the ability of adjoint-based methods to compute time-dependent sensitivities of the flow.
Nievaart, V. A.; Legrady, D.; Moss, R. L.; Kloosterman, J. L.; Hagen, T. H. J. J. van der; Dam, H. van
2007-04-15
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
Generalized uncertainty principle and self-adjoint operators
Balasubramanian, Venkat; Das, Saurya; Vagenas, Elias C.
2015-09-15
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Coupling of Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences
Slater, C.O.; Lillie, R.A.; Johnson, J.O.; Simpson, D.B.
1998-04-01
A computer code, DRC3, has been developed for coupling Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences in order to solve a special category of geometrically-complex deep penetration shielding problems. The code extends the capabilities of earlier methods that coupled Monte Carlo adjoint leakages with two-dimensional discrete ordinates forward fluences. The problems involve the calculation of fluences and responses in a perturbation to an otherwise simple two- or three-dimensional radiation field. In general, the perturbation complicates the geometry such that it cannot be modeled exactly using any of the discrete ordinates geometry options and thus a direct discrete ordinates solution is not possible. Also, the calculation of radiation transport from the source to the perturbation involves deep penetration. One approach to solving such problems is to perform the calculations in three steps: (1) a forward discrete ordinates calculation, (2) a localized adjoint Monte Carlo calculation, and (3) a coupling of forward fluences from the first calculation with adjoint leakages from the second calculation to obtain the response of interest (fluence, dose, etc.). A description of this approach is presented along with results from test problems used to verify the method. The test problems that were selected could also be solved directly by the discrete ordinates method. The good agreement between the DRC3 results and the direct-solution results verify the correctness of DRC3.
NASA Astrophysics Data System (ADS)
Smith, J. A.; Peter, D. B.; Tromp, J.; Komatitsch, D.; Lefebvre, M. P.
2015-12-01
We present both SPECFEM3D_Cartesian and SPECFEM3D_GLOBE open-source codes, representing high-performance numerical wave solvers simulating seismic wave propagation for local-, regional-, and global-scale application. These codes are suitable for both forward propagation in complex media and tomographic imaging. Both solvers compute highly accurate seismic wave fields using the continuous Galerkin spectral-element method on unstructured meshes. Lateral variations in compressional- and shear-wave speeds, density, as well as 3D attenuation Q models, topography and fluid-solid coupling are all readily included in both codes. For global simulations, effects due to rotation, ellipticity, the oceans, 3D crustal models, and self-gravitation are additionally included. Both packages provide forward and adjoint functionality suitable for adjoint tomography on high-performance computing architectures. We highlight the most recent release of the global version which includes improved performance, simultaneous MPI runs, OpenCL and CUDA support via an automatic source-to-source transformation library (BOAST), parallel I/O readers and writers for databases using ADIOS and seismograms using the recently developed Adaptable Seismic Data Format (ASDF) with built-in provenance. This makes our spectral-element solvers current state-of-the-art, open-source community codes for high-performance seismic wave propagation on arbitrarily complex 3D models. Together with these solvers, we provide full-waveform inversion tools to image the Earth's interior at unprecedented resolution.
Estimation of ex-core detector responses by adjoint Monte Carlo
Hoogenboom, J. E.
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)
Development of CO2 inversion system based on the adjoint of the global coupled transport model
NASA Astrophysics Data System (ADS)
Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon
2014-05-01
We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) Eulerian transport model (TM) and the Lagrangian plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the Lagrangian model FLEXPART. The Lagrangian component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the Lagrangian part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to Eulerian part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of Lagrangian model is required, making it applicable to combination of global NIES TM and any Lagrangian model; 2. Once run, the Lagrangian output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over
NASA Astrophysics Data System (ADS)
Heimbach, Patick; Menemenlis, Dimitris; Losch, Martin; Campin, Jean-Michel; Hill, Chris
The adjoint of an ocean general circulation model is at the heart of the ocean state estimation system of the Estimating the Circulation and Climate of the Ocean (ECCO) project. As part of an ongoing effort to extend ECCO to a coupled ocean/sea-ice estimation system, a dynamic and thermodynamic sea-ice model has been developed for the Massachusetts Institute of Technology general circulation model (MITgcm). One key requirement is the ability to generate, by means of automatic differentiation (AD), tangent linear (TLM) and adjoint (ADM) model code for the coupled MITgcm ocean/sea-ice system. This second part of a two-part paper describes aspects of the adjoint model. The adjoint ocean and sea-ice model is used to calculate transient sensitivities of solid (ice and snow) freshwater export through Lancaster Sound in the Canadian Arctic Archipelago (CAA). The adjoint state provides a complementary view of the dynamics. In particular, the transient, multi-year sensitivity patterns reflect dominant pathways and propagation timescales through the CAA as resolved by the model, thus shedding light on causal relationships, in the model, across the Archipelago. The computational cost of inferring such causal relationships from forward model diagnostics alone would be prohibitive. The role of the exact model trajectory around which the adjoint is calculated (and therefore of the exactness of the adjoint) is exposed through calculations using free-slip vs no-slip lateral boundary conditions. Effective ice thickness, sea surface temperature, and precipitation sensitivities, are discussed in detail as examples of the coupled sea-ice/ocean and atmospheric forcing control space. To test the reliability of the adjoint, finite-difference perturbation experiments were performed for each of these elements and the cost perturbations were compared to those "predicted" by the adjoint. Overall, remarkable qualitative and quantitative agreement is found. In particular, the adjoint correctly
Using adjoint-based optimization to study wing flexibility in flapping flight
NASA Astrophysics Data System (ADS)
Wei, Mingjun; Xu, Min; Dong, Haibo
2014-11-01
In the study of flapping-wing flight of birds and insects, it is important to understand the impact of wing flexibility/deformation on aerodynamic performance. However, the large control space from the complexity of wing deformation and kinematics makes usual parametric study very difficult or sometimes impossible. Since the adjoint-based approach for sensitivity study and optimization strategy is a process with its cost independent of the number of input parameters, it becomes an attractive approach in our study. Traditionally, adjoint equation and sensitivity are derived in a fluid domain with fixed solid boundaries. Moving boundary is only allowed when its motion is not part of control effort. Otherwise, the derivation becomes either problematic or too complex to be feasible. Using non-cylindrical calculus to deal with boundary deformation solves this problem in a very simple and still mathematically rigorous manner. Thus, it allows to apply adjoint-based optimization in the study of flapping wing flexibility. We applied the ``improved'' adjoint-based method to study the flexibility of both two-dimensional and three-dimensional flapping wings, where the flapping trajectory and deformation are described by either model functions or real data from the flight of dragonflies. Supported by AFOSR.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
Al-Hashimi, M.H.; Salman, M.; Shalaby, A.; Wiese, U.-J.
2013-10-15
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
NASA Technical Reports Server (NTRS)
Ustinov, Eugene A.; Sunseri, Richard F.
2005-01-01
An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.
Adjoint-based optimal control of an airfoil in gusting flows
NASA Astrophysics Data System (ADS)
Choi, Jeesoon; Colonius, Tim; California Institute of Technology Team
2015-11-01
In this study, we apply optimal control to an airfoil in gusting flow to investigate the possibility of extracting energy. The gradients of an objective function are obtained via the adjoint method and used to minimize the cost. The immersed boundary projection method is used for our forward solver, and the relevant adjoint equations are derived by the discrete-then-differentiate approach. Translational gusts are generated by a body force in the computational domain upstream to the body, and the method finds the optimal angles of the airfoil that exploits the greatest amount of energy. The influence of a vortex traversing an airfoil is also investigated and optimized to reduce the fluctuating lift.
Self-adjointness and conservation laws of difference equations
NASA Astrophysics Data System (ADS)
Peng, Linyu
2015-06-01
A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.
Adjoint tomography of crust and upper-mantle structure beneath Continental China
NASA Astrophysics Data System (ADS)
Chen, M.; Niu, F.; Liu, Q.; Tromp, J.
2013-12-01
Four years of regional earthquake recordings from 1,869 seismic stations are used for high-resolution and high-fidelity seismic imaging of the crust and upper-mantle structure beneath Continental China. This unprecedented high-density dataset is comprised of seismograms recorded by the China Earthquake Administration Array (CEArray), NorthEast China Extended SeiSmic Array (NECESSArray), INDEPTH-IV Array, F-net and other global and regional seismic networks, and involves 1,326,384 frequency-dependent phase measurements. Adjoint tomography is applied to this unprecedented dataset, aiming to resolve detailed 3D maps of compressional and shear wavespeeds, and radial anisotropy. Contrary to traditional ray-theory based tomography, adjoint tomography takes into account full 3D wave propagation effects and off-ray-path sensitivity. In our implementation, it utilizes a spectral-element method for precise wave propagation simulations. The tomographic method starts with a 3D initial model that combines smooth radially anisotropic mantle model S362ANI and 3D crustal model Crust2.0. Traveltime and amplitude misfits are minimized iteratively based on a conjugate gradient method, harnessing 3D finite-frequency kernels computed for each updated 3D model. After 17 iterations, our inversion reveals strong correlations of 3D wavespeed heterogeneities in the crust and upper mantle with surface tectonic units, such as the Himalaya Block, the Tibetan Plateau, the Tarim Basin, the Ordos Block, and the South China Block. Narrow slab features emerge from the smooth initial model above the transition zone beneath the Japan, Ryukyu, Philippine, Izu-Bonin, Mariana and Andaman arcs. 3D wavespeed variations appear comparable to or much sharper than in high-frequency P-and S-wave models from previous studies. Moreover our results include new information, such as 3D variations of radial anisotropy and the Vp/Vs ratio, which are expected to shed new light to the composition, thermal state, flow
Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Kleb, William L.
2005-01-01
A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Kleb, William L.
2005-01-01
A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.
Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization
NASA Technical Reports Server (NTRS)
Green, Lawrence; Carle, Alan; Fagan, Mike
1999-01-01
Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop
Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation
NASA Astrophysics Data System (ADS)
Yaşar, Emrullah; San, Sait; Özkan, Yeşim Sağlam
2016-01-01
In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.
Universal Racah matrices and adjoint knot polynomials: Arborescent knots
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.
2016-04-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.
Unsteady adjoint of a gas turbine inlet guide vane
NASA Astrophysics Data System (ADS)
Talnikar, Chaitanya; Wang, Qiqi
2015-11-01
Unsteady fluid flow simulations like large eddy simulation have been shown to be crucial in accurately predicting heat transfer in turbomachinery applications like transonic flow over an inlet guide vane. To compute sensitivities of aerothermal objectives for a vane with respect to design parameters an unsteady adjoint is required. In this talk we present unsteady adjoint solutions for a vane from VKI using pressure loss and heat transfer over the vane surface as the objectives. The boundary layer on the suction side near the trailing edge of the vane is turbulent and this poses a challenge for an adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially to infinity from that region when simulated backwards in time. The prospect of adding artificial viscosity to the adjoint equations to dampen the adjoint fields is investigated. Results for the vane from simulations performed on the Titan supercomputer will be shown and the effect of the additional viscosity on the accuracy of the sensitivities will be discussed.
Neural network training by integration of adjoint systems of equations forward in time
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)
1992-01-01
A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically, it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved, but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. The trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.
Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)
1999-01-01
A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.
Seismic wave-speed structure beneath the metropolitan area of Japan based on adjoint tomography
NASA Astrophysics Data System (ADS)
Miyoshi, T.; Obayashi, M.; Tono, Y.; Tsuboi, S.
2015-12-01
We have obtained a three-dimensional (3D) model of seismic wave-speed structure beneath the metropolitan area of Japan. We applied the spectral-element method (e.g. Komatitsch and Tromp 1999) and adjoint method (Liu and Tromp 2006) to the broadband seismograms in order to infer the 3D model. We used the travel-time tomography result (Matsubara and Obara 2011) as an initial 3D model and used broadband waveforms recorded at the NIED F-net stations. We selected 147 earthquakes with magnitude of larger than 4.5 from the F-net earthquake catalog and used their bandpass filtered seismograms between 5 and 20 second with a high S/N ratio. The 3D model used for the forward and adjoint simulations is represented as a region of approximately 500 by 450 km in horizontal and 120 km in depth. Minimum period of theoretical waveforms was 4.35 second. For the adjoint inversion, we picked up the windows of the body waves from the observed and theoretical seismograms. We used SPECFEM3D_Cartesian code (e.g. Peter et al. 2011) for the forward and adjoint simulations, and their simulations were implemented by K-computer in RIKEN. Each iteration required about 0.1 million CPU hours at least. The model parameters of Vp and Vs were updated by using the steepest descent method. We obtained the fourth iterative model (M04), which reproduced observed waveforms better than the initial model. The shear wave-speed of M04 was significantly smaller than the initial model at any depth. The model of compressional wave-speed was not improved by inversion because of small alpha kernel values. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We thank to the NIED for providing seismological data.
NASA Astrophysics Data System (ADS)
Zhao, Xiao-Feng; Huang, Si-Xun; Du, Hua-Dong
2011-02-01
This paper puts forward possibilities of refractive index profile retrieval using field measurements at an array of radio receivers in terms of variational adjoint approach. The derivation of the adjoint model begins with the parabolic wave equation for a smooth, perfectly conducting surface and horizontal polarization conditions. To deal with the ill-posed difficulties of the inversion, the regularization ideas are introduced into the establishment of the cost function. Based on steepest descent iterations, the optimal value of refractivity could be retrieved quickly at each point over height. Numerical experiments demonstrate that the method works well for low-distance signals, while it is not accurate enough for long-distance propagations. Through curve fitting processing, however, giving a good initial refractivity profile could generally improve the inversions.
Adjoint equations and analysis of complex systems: Application to virus infection modelling
NASA Astrophysics Data System (ADS)
Marchuk, G. I.; Shutyaev, V.; Bocharov, G.
2005-12-01
Recent development of applied mathematics is characterized by ever increasing attempts to apply the modelling and computational approaches across various areas of the life sciences. The need for a rigorous analysis of the complex system dynamics in immunology has been recognized since more than three decades ago. The aim of the present paper is to draw attention to the method of adjoint equations. The methodology enables to obtain information about physical processes and examine the sensitivity of complex dynamical systems. This provides a basis for a better understanding of the causal relationships between the immune system's performance and its parameters and helps to improve the experimental design in the solution of applied problems. We show how the adjoint equations can be used to explain the changes in hepatitis B virus infection dynamics between individual patients.
Towards efficient backward-in-time adjoint computations using data compression techniques
Cyr, E. C.; Shadid, J. N.; Wildey, T.
2014-12-16
In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for themore » difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.« less
Towards efficient backward-in-time adjoint computations using data compression techniques
Cyr, E. C.; Shadid, J. N.; Wildey, T.
2014-12-16
In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for the difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.
Baryogenesis via leptogenesis in adjoint SU(5)
Blanchet, Steve; Fileviez Perez, Pavel E-mail: fileviez@physics.wisc.edu
2008-08-15
The possibility of explaining the baryon asymmetry in the Universe through the leptogenesis mechanism in the context of adjoint SU(5) is investigated. In this model neutrino masses are generated through the type I and type III seesaw mechanisms, and the field responsible for the type III seesaw, called {rho}{sub 3}, generates the B-L asymmetry needed to satisfy the observed value of the baryon asymmetry in the Universe. We find that the CP asymmetry originates only from the vertex correction, since the self-energy contribution is not present. When neutrino masses have a normal hierarchy, successful leptogenesis is possible for 10{sup 11} GeV{approx}
A variational level set method for the topology optimization of steady-state Navier Stokes flow
NASA Astrophysics Data System (ADS)
Zhou, Shiwei; Li, Qing
2008-12-01
The smoothness of topological interfaces often largely affects the fluid optimization and sometimes makes the density-based approaches, though well established in structural designs, inadequate. This paper presents a level-set method for topology optimization of steady-state Navier-Stokes flow subject to a specific fluid volume constraint. The solid-fluid interface is implicitly characterized by a zero-level contour of a higher-order scalar level set function and can be naturally transformed to other configurations as its host moves. A variational form of the cost function is constructed based upon the adjoint variable and Lagrangian multiplier techniques. To satisfy the volume constraint effectively, the Lagrangian multiplier derived from the first-order approximation of the cost function is amended by the bisection algorithm. The procedure allows evolving initial design to an optimal shape and/or topology by solving the Hamilton-Jacobi equation. Two classes of benchmarking examples are presented in this paper: (1) periodic microstructural material design for the maximum permeability; and (2) topology optimization of flow channels for minimizing energy dissipation. A number of 2D and 3D examples well demonstrated the feasibility and advantage of the level-set method in solving fluid-solid shape and topology optimization problems.
Automatic verification methods for finite state systems
Sifakis, J. )
1990-01-01
This volume contains the proceedings of a workshop devoted to the verification of finite state systems. The workshop focused on the development and use of methods, tools and theories for automatic verification of finite state systems. The goal at the workshop was to compare verification methods and tools to assist the applications designer. The papers review verification techniques for finite state systems and evaluate their relative advantages. The techniques considered cover various specification formalisms such as process algebras, automata and logics. Most of the papers focus on exploitation of existing results in three application areas: hardware design, communication protocols and real-time systems.
Big Data Challenges in Global Seismic 'Adjoint Tomography' (Invited)
NASA Astrophysics Data System (ADS)
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
Conformal versus confining scenario in SU(2) with adjoint fermions
Del Debbio, L.; Pica, C.; Lucini, B.; Patella, A.; Rago, A.
2009-10-01
The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling {beta}=4/g{sub 0}{sup 2}=2.25 for values of the bare fermion mass m{sub 0} that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near-)conformal and the confining scenario is outlined.
Strong Adjoint Sensitivities in Tropical Eddy-Permitting Variational Data Assimilation
NASA Astrophysics Data System (ADS)
Cornuelle, B.; Hoteit, I.; Koehl, A.; Stammer, D.
2007-05-01
A variational data assimilation system has been implemented for the tropical Pacific Ocean for an eddy-permitting regional implementation of the MIT general circulation model (MITgcm). The model uses realistic topography with parameterizations for the surface boundary layer (KPP) and open boundaries at the south and north, as well as in the Indonesian throughflow. The adjoint method is used to adjust the model to observations in the tropical Pacific region using control parameters which include initial temperature and salinity, temperature, salinity and horizontal velocities at the open boundaries, and twice-daily surface fluxes of momentum, heat and freshwater. The model is constrained with most of the available datasets in the tropical Pacific, including climatologies, TAO, ARGO, XBT, and satellite SST and SSH data. The forward model runs exhibit strongly growing flow instabilities in the regions of high kinetic energy and low planetary potential vorticity gradient. The growth of these perturbations is limited by nonlinearities once they reach finite size, meaning that the high linear growth rates do not apply for long time periods. This poses a technical problem for adjoint-based assimilation, which depends on the linearized sensitivities to adjust the controls. Relative to the forward model runs, increased viscosity and diffusivity terms are used in the adjoint model runs to avoid large sensitivities related to the flow instabilities present in the high-resolution model. This talk will discuss some of the technical aspects and show results for 1 year assimilation period.
Global adjoint tomography: Perspectives, initial results and future directions
NASA Astrophysics Data System (ADS)
Bozdag, Ebru; Zhu, Hejun; Peter, Daniel; Tromp, Jeroen
2013-04-01
Adjoint methods provide an efficient way for incorporating the full nonlinearity of wave propagation and 3D Fréchet kernels in iterative seismic inversions. Our goal is to take adjoint tomography forward to image the entire planet using the opportunities offered by advances in numerical wave propagation solvers and high-performance computing. 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. Our strategy is to invert crustal and mantle structure together to avoid any bias introduced into upper-mantle images due to "crustal corrections", which are commonly used in classical tomography. We have started with 255 global CMT events (5.8 ≤ Mw ≤ 7) and used GSN stations as well as some local networks such as USArray, European stations, etc. We have demonstrated the feasibility of global scale inversions by performing two iterations based on numerical simulations accurate down to ~27 s. To simplify the problem, we primarily focus on elastic structure, and therefore our measurements are based on multitaper traveltime differences between observed and synthetic seismograms. We compute 3D sensitivity kernels for the selected events combining long-period surface waves (initially T > 60 s), where it is easier to handle nonlinearities due to the crust, with shorter-period body waves (initially T > 27 s), which are more sensitive to deeper parts of the mantle. 3D simulations dramatically increase the usable amount of data so that, with the current earthquake-station setup, we perform each iteration with more than two million measurements. Our initial results are promising to improve images from the upper mantle all the way down to the core-mantle boundary. 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
Determining scaling laws from geodynamic simulations using adjoint gradients.
NASA Astrophysics Data System (ADS)
Reuber, Georg; Kaus, Boris; Popov, Anton
2016-04-01
Whereas significant progress has been made in modelling of lithospheric and crustal scale processes in recent years, it often remains a challenge to understand which of the many model parameters is of key importance for a particular simulation. Determining this is usually done by manually changing the model input parameters and performing new simulations. For a few cases, such as for crustal-scale folding instabilities (with viscous rheologies, e.g. [1]) or for Rayleigh-Taylor instabilities, one can use existing scaling laws to obtain such insights. Yet, for a more general case, it is not straightforward to do this (apart from running many simulations). Here, we test a different approach which computes gradients of the model parameters using adjoint based methods, which has the advantage that we can test the influence of an independent number of parameters on the system by computing and analysing the covariance matrix and the gradient of the parameter space. This method might give us the chance to get insights on which parameters affect for example subduction processes and how strong the system depends on their influence. [1] Fernandez, N., & Kaus, B. J. (2014). Fold interaction and wavelength selection in 3D models of multilayer detachment folding. Tectonophysics, 632, 199-217.
Receptivity in parallel flows: An adjoint approach
NASA Technical Reports Server (NTRS)
Hill, D. Christopher
1993-01-01
Linear receptivity studies in parallel flows are aimed at understanding how external forcing couples to the natural unstable motions which a flow can support. The vibrating ribbon problem models the original Schubauer and Skramstad boundary layer experiment and represents the classic boundary layer receptivity problem. The process by which disturbances are initiated in convectively-unstable jets and shear layers has also received attention. Gaster was the first to handle the boundary layer analysis with the recognition that spatial modes, rather than temporal modes, were relevant when studying convectively-unstable flows that are driven by a time-harmonic source. The amplitude of the least stable spatial mode, far downstream of the source, is related to the source strength by a coupling coefficient. The determination of this coefficient is at the heart of this type of linear receptivity study. The first objective of the present study was to determine whether the various wave number derivative factors, appearing in the coupling coefficients for linear receptivity problems, could be reexpressed in a simpler form involving adjoint eigensolutions. Secondly, it was hoped that the general nature of this simplification could be shown; indeed, a rather elegant characterization of the receptivity properties of spatial instabilities does emerge. The analysis is quite distinct from the usual Fourier-inversion procedures, although a detailed knowledge of the spectrum of the Orr-Sommerfeld equation is still required. Since the cylinder wake analysis proved very useful in addressing control considerations, the final objective was to provide a foundation upon which boundary layer control theory may be developed.
A Posteriori Analysis for Hydrodynamic Simulations Using Adjoint Methodologies
Woodward, C S; Estep, D; Sandelin, J; Wang, H
2009-02-26
This report contains results of analysis done during an FY08 feasibility study investigating the use of adjoint methodologies for a posteriori error estimation for hydrodynamics simulations. We developed an approach to adjoint analysis for these systems through use of modified equations and viscosity solutions. Targeting first the 1D Burgers equation, we include a verification of the adjoint operator for the modified equation for the Lax-Friedrichs scheme, then derivations of an a posteriori error analysis for a finite difference scheme and a discontinuous Galerkin scheme applied to this problem. We include some numerical results showing the use of the error estimate. Lastly, we develop a computable a posteriori error estimate for the MAC scheme applied to stationary Navier-Stokes.
Learning a trajectory using adjoint functions and teacher forcing
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad B.; Barhen, Jacob
1992-01-01
A new methodology for faster supervised temporal learning in nonlinear neural networks is presented which builds upon the concept of adjoint operators to allow fast computation of the gradients of an error functional with respect to all parameters of the neural architecture, and exploits the concept of teacher forcing to incorporate information on the desired output into the activation dynamics. The importance of the initial or final time conditions for the adjoint equations is discussed. A new algorithm is presented in which the adjoint equations are solved simultaneously (i.e., forward in time) with the activation dynamics of the neural network. We also indicate how teacher forcing can be modulated in time as learning proceeds. The results obtained show that the learning time is reduced by one to two orders of magnitude with respect to previously published results, while trajectory tracking is significantly improved. The proposed methodology makes hardware implementation of temporal learning attractive for real-time applications.
A method of enciphering quantum states
NASA Astrophysics Data System (ADS)
Azuma, Hiroo; Ban, Masashi
2001-04-01
In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with only a certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the intercept/resend attack), the probability that Alice and Bob do not notice Eve's action is equal to (3/4)m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack using entanglement. This remains to be solved in the future.
Diffusion Acceleration Schemes for Self-Adjoint Angular Flux Formulation with a Void Treatment
Yaqi Wang; Hongbin Zhang; Richard C. Martineau
2014-02-01
A Galerkin weak form for the monoenergetic neutron transport equation with a continuous finite element method and discrete ordinate method is developed based on self-adjoint angular flux formulation. This weak form is modified for treating void regions. A consistent diffusion scheme is developed with projection. Correction terms of the diffusion scheme are derived to reproduce the transport scalar flux. A source iteration that decouples the solution of all directions with both linear and nonlinear diffusion accelerations is developed and demonstrated. One-dimensional Fourier analysis is conducted to demonstrate the stability of the linear and nonlinear diffusion accelerations. Numerical results of these schemes are presented.
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony; Alonso, Juan Jose; Rimlinger, Mark J.; Saunders, David
1997-01-01
An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat
ANISORROPIA: the adjoint of the aerosol thermodynamic model ISORROPIA
NASA Astrophysics Data System (ADS)
Capps, S. L.; Henze, D. K.; Hakami, A.; Russell, A. G.; Nenes, A.
2011-08-01
We present the development of ANISORROPIA, the discrete adjoint of the ISORROPIA thermodynamic equilibrium model that treats the Na+-SO42--HSO4--NH4+-NO3--Cl--H2O aerosol system, and we demonstrate its sensitivity analysis capabilities. ANISORROPIA calculates sensitivities of an inorganic species in aerosol or gas phase with respect to the total concentrations of each species present with only a two-fold increase in computational time over the forward model execution. Due to the highly nonlinear and discontinuous solution surface of ISORROPIA, evaluation of the adjoint required a new, complex-variable version of the the model, which determines first-order sensitivities with machine precision and avoids cancellation errors arising from finite difference calculations. The adjoint is verified over an atmospherically relevant range of concentrations, temperature, and relative humidity. We apply ANISORROPIA to recent field campaign results from Atlanta, GA, USA, and Mexico City, Mexico, to characterize the inorganic aerosol sensitivities of these distinct urban air masses. The variability in the relationship between PM2.5 mass and precursor concentrations shown has important implications for air quality and climate. ANISORROPIA enables efficient elucidation of aerosol concentration dependence on aerosol precursor emissions in the context of atmospheric chemical transport model adjoints.
Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"
Ammonia emissions parameters in North America can be refined in order to improve the evaluation of modeled concentrations against observations. Here, we seek to do so by developing and applying the GEOS-Chem adjoint nested over North America to conductassimilation of observations...
Adjoint-Operator Learning For A Neural Network
NASA Technical Reports Server (NTRS)
Barhen, Jacob; Toomarian, Nikzad
1993-01-01
Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.
Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David
1996-01-01
This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.
NASA Astrophysics Data System (ADS)
Zheng, Xiangyang; Mayerle, Roberto; Xing, Qianguo; Fernández Jaramillo, José Manuel
2016-08-01
In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.
NASA Astrophysics Data System (ADS)
Zheng, Xiangyang; Mayerle, Roberto; Xing, Qianguo; Fernández Jaramillo, José Manuel
2016-06-01
In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.
Solid oxide fuel cell simulation and design optimization with numerical adjoint techniques
NASA Astrophysics Data System (ADS)
Elliott, Louie C.
This dissertation reports on the application of numerical optimization techniques as applied to fuel cell simulation and design. Due to the "multi-physics" inherent in a fuel cell, which results in a highly coupled and non-linear behavior, an experimental program to analyze and improve the performance of fuel cells is extremely difficult. This program applies new optimization techniques with computational methods from the field of aerospace engineering to the fuel cell design problem. After an overview of fuel cell history, importance, and classification, a mathematical model of solid oxide fuel cells (SOFC) is presented. The governing equations are discretized and solved with computational fluid dynamics (CFD) techniques including unstructured meshes, non-linear solution methods, numerical derivatives with complex variables, and sensitivity analysis with adjoint methods. Following the validation of the fuel cell model in 2-D and 3-D, the results of the sensitivity analysis are presented. The sensitivity derivative for a cost function with respect to a design variable is found with three increasingly sophisticated techniques: finite difference, direct differentiation, and adjoint. A design cycle is performed using a simple optimization method to improve the value of the implemented cost function. The results from this program could improve fuel cell performance and lessen the world's dependence on fossil fuels.
Gardner, Adam R; Hayakawa, Carole K; Venugopalan, Vasan
2014-06-01
We present a coupled forward-adjoint Monte Carlo (cFAMC) method to determine the spatially resolved sensitivity distributions produced by optical interrogation of three-dimensional (3-D) tissue volumes. We develop a general computational framework that computes the spatial and angular distributions of the forward-adjoint light fields to provide accurate computations in mesoscopic tissue volumes. We provide full computational details of the cFAMC method and provide results for low- and high-scattering tissues probed using a single pair of optical fibers. We examine the effects of source-detector separation and orientation on the sensitivity distributions and consider how the degree of angular discretization used in the 3-D tissue model impacts the accuracy of the resulting absorption sensitivity profiles. We discuss the value of such computations for optical imaging and the design of optical measurements. PMID:24972356
Gardner, Adam R.; Hayakawa, Carole K.; Venugopalan, Vasan
2014-01-01
Abstract. We present a coupled forward-adjoint Monte Carlo (cFAMC) method to determine the spatially resolved sensitivity distributions produced by optical interrogation of three-dimensional (3-D) tissue volumes. We develop a general computational framework that computes the spatial and angular distributions of the forward-adjoint light fields to provide accurate computations in mesoscopic tissue volumes. We provide full computational details of the cFAMC method and provide results for low- and high-scattering tissues probed using a single pair of optical fibers. We examine the effects of source-detector separation and orientation on the sensitivity distributions and consider how the degree of angular discretization used in the 3-D tissue model impacts the accuracy of the resulting absorption sensitivity profiles. We discuss the value of such computations for optical imaging and the design of optical measurements. PMID:24972356
Mapping Emissions that Contribute to Air Pollution Using Adjoint Sensitivity Analysis
NASA Astrophysics Data System (ADS)
Bastien, L. A. J.; Mcdonald, B. C.; Brown, N. J.; Harley, R.
2014-12-01
The adjoint of the Community Multiscale Air Quality model (CMAQ) is used to map emissions that contribute to air pollution at receptors of interest. Adjoint tools provide an efficient way to calculate the sensitivity of a model response to a large number of model inputs, a task that would require thousands of simulations using a more traditional forward sensitivity approach. Initial applications of this technique, demonstrated here, are to benzene and directly-emitted diesel particulate matter, for which atmospheric reactions are neglected. Emissions of these pollutants are strongly influenced by light-duty gasoline vehicles and heavy-duty diesel trucks, respectively. We study air quality responses in three receptor areas where populations have been identified as especially susceptible to, and adversely affected by air pollution. Population-weighted air basin-wide responses for each pollutant are also evaluated for the entire San Francisco Bay area. High-resolution (1 km horizontal grid) emission inventories have been developed for on-road motor vehicle emission sources, based on observed traffic count data. Emission estimates represent diurnal, day of week, and seasonal variations of on-road vehicle activity, with separate descriptions for gasoline and diesel sources. Emissions that contribute to air pollution at each receptor have been mapped in space and time using the adjoint method. Effects on air quality of both relative (multiplicative) and absolute (additive) perturbations to underlying emission inventories are analyzed. The contributions of local versus upwind sources to air quality in each receptor area are quantified, and weekday/weekend and seasonal variations in the influence of emissions from upwind areas are investigated. The contribution of local sources to the total air pollution burden within the receptor areas increases from about 40% in the summer to about 50% in the winter due to increased atmospheric stagnation. The effectiveness of control
The basis spline method and associated techniques
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.
Examination of Observation Impacts derived from OSEs and Adjoint Models
NASA Technical Reports Server (NTRS)
Gelaro, Ronald
2008-01-01
With the adjoint of a data assimilation system, the impact of any or all assimilated observations on measures of forecast skill can be estimated accurately and efficiently. The approach allows aggregation of results in terms of individual data types, channels or locations, all computed simultaneously. In this study, adjoint-based estimates of observation impact are compared with results from standard observing system experiments (OSEs) in the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) GEOS-5 system. The two approaches are shown to provide unique, but complimentary, information. Used together, they reveal both redundancies and dependencies between observing system impacts as observations are added or removed. Understanding these dependencies poses a major challenge for optimizing the use of the current observational network and defining requirements for future observing systems.
Three-Dimensional Turbulent RANS Adjoint-Based Error Correction
NASA Technical Reports Server (NTRS)
Park, Michael A.
2003-01-01
Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.
Seismic Window Selection and Misfit Measurements for Global Adjoint Tomography
NASA Astrophysics Data System (ADS)
Lei, W.; Bozdag, E.; Lefebvre, M.; Podhorszki, N.; Smith, J. A.; Tromp, J.
2013-12-01
Global Adjoint Tomography requires fast parallel processing of large datasets. After obtaing the preprocessed observed and synthetic seismograms, we use the open source software packages FLEXWIN (Maggi et al. 2007) to select time windows and MEASURE_ADJ to make measurements. These measurements define adjoint sources for data assimilation. Previous versions of these tools work on a pair of SAC files---observed and synthetic seismic data for the same component and station, and loop over all seismic records associated with one earthquake. Given the large number of stations and earthquakes, the frequent read and write operations create severe I/O bottlenecks on modern computing platforms. We present new versions of these tools utilizing a new seismic data format, namely the Adaptive Seismic Data Format(ASDF). This new format shows superior scalability for applications on high-performance computers and accommodates various types of data, including earthquake, industry and seismic interferometry datasets. ASDF also provides user-friendly APIs, which can be easily integrated into the adjoint tomography workflow and combined with other data processing tools. In addition to solving the I/O bottleneck, we are making several improvements to these tools. For example, FLEXWIN is tuned to select windows for different types of earthquakes. To capture their distinct features, we categorize earthquakes by their depths and frequency bands. Moreover, instead of only picking phases between the first P arrival and the surface-wave arrivals, our aim is to select and assimilate many other later prominent phases in adjoint tomography. For example, in the body-wave band (17 s - 60 s), we include SKS, sSKS and their multiple, while in the surface-wave band (60 s - 120 s) we incorporate major-arc surface waves.
Adjoint calculations for multiple scattering of Compton and Rayleigh effects
NASA Astrophysics Data System (ADS)
Fernández, J. E.; Sumini, M.
1992-08-01
As is well known, the experimental determination of the Compton profile requires a particular geometry with a scattering angle close to π. That situation involves a narrow multiple-scattering spectrum that overlaps the Compton peak, making it difficult to analyze the different contributions to the profile. We show how the solution of the adjoint problem can help in devising more useful experimental configurations, giving, through its classical "importance" meaning, a formally clear picture of the whole problem.
Forward and adjoint sensitivity computation of chaotic dynamical systems
Wang, Qiqi
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.
Monopole condensation in two-flavor adjoint QCD
Cossu, Guido; D'Elia, Massimo; Di Giacomo, Adriano; Lacagnina, Giuseppe; Pica, Claudio
2008-04-01
In QCD with adjoint fermions, the deconfining transition takes place at a lower temperature than the chiral transition. We study the two transitions by use of the Polyakov loop, the monopole order parameter, and the chiral condensate. The deconfining transition is first order, the chiral is a crossover. The order parameters for confinement are not affected by the chiral transition. We conclude that the degrees of freedom relevant to confinement are different from those describing chiral symmetry.
Adjoint Tomography of Taiwan Region: From Travel-Time Toward Waveform Inversion
NASA Astrophysics Data System (ADS)
Huang, H. H.; Lee, S. J.; Tromp, J.
2014-12-01
The complicated tectonic environment such as Taiwan region can modulate the seismic waveform severely and hamper the discrimination and the utilization of later phases. Restricted to the use of only first arrivals of P- and S-wave, the travel-time tomographic models of Taiwan can simulate the seismic waveform barely to a frequency of 0.2 Hz to date. While it has been sufficient for long-period studies, e.g. source inversion, this frequency band is still far from the applications to the community and high-resolution studies. To achieve a higher-frequency simulation, more data and the considerations of off-path and finite-frequency effects are necessary. Based on the spectral-element and the adjoint method recently developed, we prepared 94 MW 3.5-6.0 earthquakes with well-defined location and focal mechanism solutions from Real-Time Moment Tensor Monitoring System (RMT), and preformed an iterative gradient-based inversion employing waveform modeling and finite-frequency measurements of adjoint method. By which the 3-D sensitivity kernels are taken into account realistically and the full waveform information are naturally sought, without a need of any phase pick. A preliminary model m003 using 10-50 sec data was demonstrated and compared with previous travel-time models. The primary difference appears in the mountainous area, where the previous travel-time model may underestimate the S-wave speed in the upper crust, but overestimates in the lower crust.
NASA Astrophysics Data System (ADS)
Yu, Jia; Ji, Lucheng; Li, Weiwei; Yi, Weilin
2016-06-01
Adjoint method is an important tool for design refinement of multistage compressors. However, the radial static pressure distribution deviates during the optimization procedure and deteriorates the overall performance, producing final designs that are not well suited for realistic engineering applications. In previous development work on multistage turbomachinery blade optimization using adjoint method and thin shear-layer N-S equations, the entropy production is selected as the objective function with given mass flow rate and total pressure ratio as imposed constraints. The radial static pressure distribution at the interfaces between rows is introduced as a new constraint in the present paper. The approach is applied to the redesign of a five-stage axial compressor, and the results obtained with and without the constraint on the radial static pressure distribution at the interfaces between rows are discussed in detail. The results show that the redesign without the radial static pressure distribution constraint (RSPDC) gives an optimal solution that shows deviations on radial static pressure distribution, especially at rotor exit tip region. On the other hand, the redesign with the RSPDC successfully keeps the radial static pressure distribution at the interfaces between rows and make sure that the optimization results are applicable in a practical engineering design.
Coupling of MASH-MORSE Adjoint Leakages with Space- and Time-Dependent Plume Radiation Sources
Slater, C.O.
2001-04-20
In the past, forward-adjoint coupling procedures in air-over-ground geometry have typically involved forward fluences arising from a point source a great distance from a target or vehicle system. Various processing codes were used to create localized forward fluence files that could be used to couple with the MASH-MORSE adjoint leakages. In recent years, radiation plumes that result from reactor accidents or similar incidents have been modeled by others, and the source space and energy distributions as a function of time have been calculated. Additionally, with the point kernel method, they were able to calculate in relatively quick fashion free-field radiation doses for targets moving within the fluence field or for stationary targets within the field, the time dependence for the latter case coming from the changes in position, shape, source strength, and spectra of the plume with time. The work described herein applies the plume source to the MASH-MORSE coupling procedure. The plume source replaces the point source for generating the forward fluences that are folded with MASH-MORSE adjoint leakages. Two types of source calculations are described. The first is a ''rigorous'' calculation using the TORT code and a spatially large air-over-ground geometry. For each time step desired, directional fluences are calculated and are saved over a predetermined region that encompasses a structure within which it is desired to calculate dose rates. Processing codes then create the surface fluences (which may include contributions from radiation sources that deposit on the roof or plateout) that will be coupled with the MASH-MORSE adjoint leakages. Unlike the point kernel calculations of the free-field dose rates, the TORT calculations in practice include the effects of ground scatter on dose rates and directional fluences, although the effects may be underestimated or overestimated because of the use of necessarily coarse mesh and quadrature in order to reduce computational
Spectral monodromy of non-self-adjoint operators
NASA Astrophysics Data System (ADS)
Phan, Quang Sang
2014-01-01
In the present paper, we build a combinatorial invariant, called the "spectral monodromy" from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc ["Quantum monodromy in integrable systems," Commun. Math. Phys. 203(2), 465-479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat ["On global action-angle coordinates," Commun. Pure Appl. Math. 33(6), 687-706 (1980)].
Adjoint-based sensitivity analysis for reactor-safety applications
Parks, C.V.
1985-01-01
The application and usefulness of an adjoint-based methodology for performing sensitivity analysis on reactor safety computer codes is investigated. The adjoint-based methodology, referred to as differential sensitivity theory (DST), provides first-order derivatives of the calculated quantities of interest (responses) with respect to the input parameters. The basic theoretical development of DST is presented along with the needed general extensions for consideration of model discontinuities and a variety of useful response definitions. A simple analytic problem is used to highlight the general DST procedures. Finally, DST procedures presented in this work are applied to two highly nonlinear reactor accident analysis codes: (1) FASTGAS, a relatively small code for analysis of loss-of-decay-heat-removal accident in a gas-cooled fast reactor, and (2) an existing code called VENUS-II which is typically employed for analyzing the core disassembly phase of a hypothetical fast reactor accident. The two codes are different both in terms of complexity and in terms of the facets of DST which can be illustrated. Sensitivity results from the adjoint codes ADJGAS and VENUS-ADJ are verified with direct recalculations using perturbed input parameters. The effectiveness of the DST results for parameter ranking, prediction of response changes, and uncertainty analysis are illustrated. The conclusion drawn from this study is that DST is a viable, cost-effective methodology for accurate sensitivity analysis.
ANISORROPIA: the adjoint of the aerosol thermodynamic model ISORROPIA
NASA Astrophysics Data System (ADS)
Capps, S. L.; Henze, D. K.; Hakami, A.; Russell, A. G.; Nenes, A.
2012-01-01
We present the development of ANISORROPIA, the discrete adjoint of the ISORROPIA thermodynamic equilibrium model that treats the Na+-SO42-- HSO4--NH4+ -NO3--Cl--H2O aerosol system, and we demonstrate its sensitivity analysis capabilities. ANISORROPIA calculates sensitivities of an inorganic species in aerosol or gas phase with respect to the total concentrations of each species present with less than a two-fold increase in computational time over the concentration calculations. Due to the highly nonlinear and discontinuous solution surface of ISORROPIA, evaluation of the adjoint required a new, complex-variable version of the model, which determines first-order sensitivities with machine precision and avoids cancellation errors arising from finite difference calculations. The adjoint is verified over an atmospherically relevant range of concentrations, temperature, and relative humidity. We apply ANISORROPIA to recent field campaign results from Atlanta, GA, USA, and Mexico City, Mexico, to characterize the inorganic aerosol sensitivities of these distinct urban air masses. The variability in the relationship between fine mode inorganic aerosol mass and precursor concentrations shown has important implications for air quality and climate.
Self-adjoint time operators and invariant subspaces
NASA Astrophysics Data System (ADS)
Gómez, Fernando
2008-02-01
The question of existence of self-adjoint time operators for unitary evolutions in classical and quantum mechanics is revisited on the basis of Halmos-Helson theory of invariant subspaces, Sz.-Nagy-Foiaş dilation theory and Misra-Prigogine-Courbage theory of irreversibility. It is shown that the existence of self-adjoint time operators is equivalent to the intertwining property of the evolution plus the existence of simply invariant subspaces or rigid operator-valued functions for its Sz.-Nagy-Foiaş functional model. Similar equivalent conditions are given in terms of intrinsic randomness in the context of statistical mechanics. The rest of the contents are mainly a unifying review of the subject scattered throughout an unconnected literature. A well-known extensive set of equivalent conditions is derived from the above results; such conditions are written in terms of Schrrdinger couples, the Weyl commutation relation, incoming and outgoing subspaces, innovation processes, Lax-Phillips scattering, translation and spectral representations, and spectral properties. Also the natural procedure dealing with symmetric time operators in standard quantum mechanics involving their self-adjoint extensions is illustrated by considering the quantum Aharonov-Bohm time-of-arrival operator.
Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils
NASA Technical Reports Server (NTRS)
Lee, Byung Joon; Liou, Meng-Sing
2012-01-01
This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.
Spectral monodromy of non-self-adjoint operators
Phan, Quang Sang
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)].
On a Time-Space Operator (and other Non-Self-Adjoint Operators) for Observables in QM and QFT
NASA Astrophysics Data System (ADS)
Recami, Erasmo; Zamboni-Rached, Michel; Licata, Ignazio
The aim of this paper is to show the possible significance, and usefulness, of various non-self-adjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics (QM), and in quantum electrodynamics. More specifically, this work deals with: (i) the Hermitian (but not self-adjoint) Time operator in non-relativistic QM and in quantum electrodynamics; (ii) idem, the introduction of Time and Space operators; and (iii) the problem of the four-position and four-momentum operators, each one with its Hermitian and anti-Hermitian parts, for relativistic spin-zero particles. Afterwards, other physical applications of non-self-adjoint (and even non-Hermitian) operators are briefly discussed. We mention how non-Hermitian operators can indeed be used in physics [as it was done, elsewhere, for describing Unstable States]; and some considerations are added on the cases of the nuclear optical potential, of quantum dissipation, and in particular of an approach to the measurement problem in QM in terms of a chronon. This paper is largely based on work developed, along the years, in collaboration with V.S. Olkhovsky, and, in smaller parts, with P. Smrz, with R.H.A. Farias, and with S.P. Maydanyuk.
NASA Astrophysics Data System (ADS)
Holdaway, D.; Coy, L.
2015-12-01
In September 2002 a major sudden stratospheric warming (SSW) occurred in the southern hemisphere. Although numerous SSWs have been observed in the northern hemisphere, this remains the only recorded major SSW in the southern hemisphere. Much debate has focused on this unique event and the causes, even resulting in a special issue of the Journal of Atmospheric Science. In this work we use the adjoint of NASA's Goddard Earth Observing System version 5 (GEOS-5) to investigate sensitivity to initial conditions during the onset of the 2002 SSW. The adjoint model provides a framework for propagating gradients with respect to the model state backwards in time. As such it is used to reveal aspects of the model initial conditions that have the biggest impact on the temperature in the stratosphere during the warming. The adjoint model reveals a large sensitivity over the southern Atlantic ocean and in the troposphere. This reinforces previous studies that attributed the SSW to a blocking ridge in this region. By converting sensitivity to perturbations it is shown that relatively small localized tropospheric perturbations to winds and temperature can be transported to the stratosphere and have a large impact on the SSW.
NASA Astrophysics Data System (ADS)
Holdaway, D. R.; Errico, R.
2011-12-01
Inherent in the minimization process in the 4D-Var data assimilation system is the need for the model's adjoint. It is straightforward to obtain the exact adjoint by linearizing the code in a line by line sense; however it only provides an accurate overall representation of the physical processes if the model behaviour is linear. Moist processes in the atmosphere, and thus the models that represent them, are intrinsically highly non-linear and can contain discrete switches. The adjoint that is required in the data assimilation system needs to provide an accurate representation of the physical behaviour for perturbation sizes of the order of the analysis error, so an exact adjoint of the moist physics model is likely to be inaccurate. Instead a non-exact adjoint model, which is accurate for large enough perturbations, must be developed. The constraint on the development is that the simplified adjoint be consistent with the actual trajectory of the model. Previous attempts to include the moist physics in the 4D-Var have emphasized the need for redevelopment of the actual moist scheme to a simpler version. These schemes are designed to be linear in the limit of realistic perturbation size but also capture the essence of the physical behaviour, making the adjoint version of the scheme suitable for use in the 4D-Var. A downside to this approach is that it can result in an over simplification of the physics and represent a larger departure from the true model trajectory than necessary. The adjoint is just the transpose of the tangent linear model, which is the differential of the model operator. This differential of the operator can be constructed from Jacobian matrices. Examining the structures of the Jacobians as perturbations of varying size are added to the state vector can help determine whether the adjoint model - be it of actual or simplified physics - will be suitable for use in the assimilation algorithm. If Jacobian structures change considerably when the
Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes
NASA Astrophysics Data System (ADS)
Peter, Daniel; Komatitsch, Dimitri; Luo, Yang; Martin, Roland; Le Goff, Nicolas; Casarotti, Emanuele; Le Loher, Pieyre; Magnoni, Federica; Liu, Qinya; Blitz, Céline; Nissen-Meyer, Tarje; Basini, Piero; Tromp, Jeroen
2011-08-01
We present forward and adjoint spectral-element simulations of coupled acoustic and (an)elastic seismic wave propagation on fully unstructured hexahedral meshes. Simulations benefit from recent advances in hexahedral meshing, load balancing and software optimization. Meshing may be accomplished using a mesh generation tool kit such as CUBIT, and load balancing is facilitated by graph partitioning based on the SCOTCH library. Coupling between fluid and solid regions is incorporated in a straightforward fashion using domain decomposition. Topography, bathymetry and Moho undulations may be readily included in the mesh, and physical dispersion and attenuation associated with anelasticity are accounted for using a series of standard linear solids. Finite-frequency Fréchet derivatives are calculated using adjoint methods in both fluid and solid domains. The software is benchmarked for a layercake model. We present various examples of fully unstructured meshes, snapshots of wavefields and finite-frequency kernels generated by Version 2.0 'Sesame' of our widely used open source spectral-element package SPECFEM3D.
Global Adjoint Tomography: Combining Big Data with HPC Simulations
NASA Astrophysics Data System (ADS)
Bozdag, E.; Lefebvre, M. P.; Lei, W.; Peter, D. B.; Smith, J. A.; Komatitsch, D.; Tromp, J.
2014-12-01
The steady increase in data quality and the number of global seismographic stations have substantially grown the amount of data available for construction of Earth models. Meanwhile, developments in the theory of wave propagation, numerical methods and HPC systems have enabled unprecedented simulations of seismic wave propagation in realistic 3D Earth models which lead the extraction of more information from data, ultimately culminating in the use of entire three-component seismograms.Our aim is to take adjoint tomography further to image the entire planet which is one of the extreme cases in seismology due to its intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. We have started low resolution (T > 27 s, soon will be > 17 s) global inversions with 253 earthquakes for a transversely isotropic crust and mantle model on Oak Ridge National Laboratory's Cray XK7 "Titan" system. Recent improvements in our 3D solvers, such as the GPU version of the SPECFEM3D_GLOBE package, will allow us perform higher-resolution (T > 9 s) and longer-duration (~180 m) simulations to take the advantage of high-frequency body waves and major-arc surface waves to improve imbalanced ray coverage as a result of uneven distribution of sources and receivers on the globe. Our initial results after 10 iterations already indicate several prominent features reported in high-resolution continental studies, such as major slabs (Hellenic, Japan, Bismarck, Sandwich, etc.) and enhancement in plume structures (the Pacific superplume, the Hawaii hot spot, etc.). Our ultimate goal is to assimilate seismic data from more than 6,000 earthquakes within the magnitude range 5.5 ≤ Mw ≤ 7.0. To take full advantage of this data set on ORNL's computational resources, we need a solid framework for managing big data sets during pre-processing (e.g., data requests and quality checks), gradient calculations, and post-processing (e
NASA Astrophysics Data System (ADS)
Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland; Matzen, René
2014-09-01
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 an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D 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 the auxiliary differential equation (ADE) form of CFS-UPML, which allows for extension to higher order time schemes and is easier to implement. Secondly, we rigorously derive the CFS-UPML formulation for time-domain adjoint elastic wave problems, which to our knowledge has never been done before. Thirdly, in the case of classical low-order FE methods, we show numerically that we achieve long-time stability for both forward and adjoint problems both for the convolution and the ADE formulations. In the case of higher order Legendre spectral-element methods, we show that weak numerical instabilities can appear in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and
Bastien, Lucas A J; McDonald, Brian C; Brown, Nancy J; Harley, Robert A
2015-06-16
The adjoint of the Community Multiscale Air Quality (CMAQ) model at 1 km horizontal resolution is used to map emissions that contribute to ambient concentrations of benzene and diesel black carbon (BC) in the San Francisco Bay area. Model responses of interest include population-weighted average concentrations for three highly polluted receptor areas and the entire air basin. We consider both summer (July) and winter (December) conditions. We introduce a novel approach to evaluate adjoint sensitivity calculations that complements existing methods. Adjoint sensitivities to emissions are found to be accurate to within a few percent, except at some locations associated with large sensitivities to emissions. Sensitivity of model responses to emissions is larger in winter, reflecting weaker atmospheric transport and mixing. The contribution of sources located within each receptor area to the same receptor's air pollution burden increases from 38-74% in summer to 56-85% in winter. The contribution of local sources is higher for diesel BC (62-85%) than for benzene (38-71%), reflecting the difference in these pollutants' atmospheric lifetimes. Morning (6-9am) and afternoon (4-7 pm) commuting-related emissions dominate region-wide benzene levels in winter (14 and 25% of the total response, respectively). In contrast, afternoon rush hour emissions do not contribute significantly in summer. Similar morning and afternoon peaks in sensitivity to emissions are observed for the BC response; these peaks are shifted toward midday because most diesel truck traffic occurs during off-peak hours. PMID:26001097
Andrade, F.M.; Silva, E.O.; Pereira, M.
2013-12-15
In this work the bound state and scattering problems for a spin- 1/2 particle undergone to an Aharonov–Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin- 1/2 Aharonov–Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator. -- Highlights: •Planar dynamics of a spin- 1/2 neutral particle. •Bound state for Aharonov–Bohm systems. •Aharonov–Bohm scattering. •Helicity nonconservation. •Determination of the self-adjoint extension parameter.
42 CFR 455.452 - Other State screening methods.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 4 2011-10-01 2011-10-01 false Other State screening methods. 455.452 Section 455....452 Other State screening methods. Nothing in this subpart must restrict the State Medicaid agency from establishing provider screening methods in addition to or more stringent than those required...
42 CFR 455.452 - Other State screening methods.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 4 2013-10-01 2013-10-01 false Other State screening methods. 455.452 Section 455....452 Other State screening methods. Nothing in this subpart must restrict the State Medicaid agency from establishing provider screening methods in addition to or more stringent than those required...
NASA Technical Reports Server (NTRS)
Andrews, Arlyn; Kawa, Randy; Zhu, Zhengxin; Burris, John; Abshire, Jim
2004-01-01
A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.
Adjoint-based optimization for understanding and suppressing jet noise
NASA Astrophysics Data System (ADS)
Freund, Jonathan B.
2011-08-01
Advanced simulation tools, particularly large-eddy simulation techniques, are becoming capable of making quality predictions of jet noise for realistic nozzle geometries and at engineering relevant flow conditions. Increasing computer resources will be a key factor in improving these predictions still further. Quality prediction, however, is only a necessary condition for the use of such simulations in design optimization. Predictions do not themselves lead to quieter designs. They must be interpreted or harnessed in some way that leads to design improvements. As yet, such simulations have not yielded any simplifying principals that offer general design guidance. The turbulence mechanisms leading to jet noise remain poorly described in their complexity. In this light, we have implemented and demonstrated an aeroacoustic adjoint-based optimization technique that automatically calculates gradients that point the direction in which to adjust controls in order to improve designs. This is done with only a single flow solutions and a solution of an adjoint system, which is solved at computational cost comparable to that for the flow. Optimization requires iterations, but having the gradient information provided via the adjoint accelerates convergence in a manner that is insensitive to the number of parameters to be optimized. This paper, which follows from a presentation at the 2010 IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction, reviews recent and ongoing efforts by the author and co-workers. It provides a new formulation of the basic approach and demonstrates the approach on a series of model flows, culminating with a preliminary result for a turbulent jet.
Adjoint-Based Methodology for Time-Dependent Optimal Control (AMTOC)
NASA Technical Reports Server (NTRS)
Yamaleev, Nail; Diskin, boris; Nishikawa, Hiroaki
2012-01-01
During the five years of this project, the AMTOC team developed an adjoint-based methodology for design and optimization of complex time-dependent flows, implemented AMTOC in a testbed environment, directly assisted in implementation of this methodology in the state-of-the-art NASA's unstructured CFD code FUN3D, and successfully demonstrated applications of this methodology to large-scale optimization of several supersonic and other aerodynamic systems, such as fighter jet, subsonic aircraft, rotorcraft, high-lift, wind-turbine, and flapping-wing configurations. In the course of this project, the AMTOC team has published 13 refereed journal articles, 21 refereed conference papers, and 2 NIA reports. The AMTOC team presented the results of this research at 36 international and national conferences, meeting and seminars, including International Conference on CFD, and numerous AIAA conferences and meetings. Selected publications that include the major results of the AMTOC project are enclosed in this report.
Spectral Solutions of Self-adjoint Elliptic Problems with Immersed Interfaces
Auchmuty, G.; Kloucek, P.
2011-12-15
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{sub {Gamma}}({Omega}) 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.
Supersonic wing and wing-body shape optimization using an adjoint formulation
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony
1995-01-01
This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used toeviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.
A Note About HARP's State Trimming Method
NASA Technical Reports Server (NTRS)
Butler, Ricky W.; Hayhurst, Kelly J.; Johnson, Sally C.
1998-01-01
This short note provides some additional insight into how the HARP program works. In some cases, it is possible for HARP to tdm away too many states and obtain an optimistic result. The HARP Version 7.0 manual warns the user that 'Unlike the ALL model, the SAME model can automatically drop failure modes for certain system models. The user is cautioned to insure that no important failure modes are dropped; otherwise, a non-conservative result can be given.' This note provides an example of where this occurs and a pointer to further documentation that gives a means of bounding the error associated with trimming these states.
7 CFR 215.5 - Method of payment to States.
Code of Federal Regulations, 2011 CFR
2011-01-01
... AGRICULTURE CHILD NUTRITION PROGRAMS SPECIAL MILK PROGRAM FOR CHILDREN § 215.5 Method of payment to States. (a... 7 Agriculture 4 2011-01-01 2011-01-01 false Method of payment to States. 215.5 Section 215.5... Authorities and child-care institutions through presentation by designated State officials of a...
7 CFR 215.5 - Method of payment to States.
Code of Federal Regulations, 2010 CFR
2010-01-01
... AGRICULTURE CHILD NUTRITION PROGRAMS SPECIAL MILK PROGRAM FOR CHILDREN § 215.5 Method of payment to States. (a... 7 Agriculture 4 2010-01-01 2010-01-01 false Method of payment to States. 215.5 Section 215.5... Authorities and child-care institutions through presentation by designated State officials of a...
Method for numerical simulations of metastable states
Heller, U.M.; Seiberg, N.
1983-06-15
We present a numerical simulation of metastable states near a first-order phase transition in the example of a U(1) lattice gauge theory with a generalized action. In order to make measurements in these states possible their decay has to be prevented. We achieve this by using a microcanonical simulation for a finite system. We then obtain the coupling constant (inverse temperature) as a function of the action density. It turns out to be nonmonotonic and hence not uniquely invertible. From it we derive the effective potential for the action density. This effective potential is not always convex, a property that seems to be in contradiction with the standard lore about its convexity. This apparent ''paradox'' is resolved in a discussion about different definitions of the effective potential.
Towards Multi-resolution Adjoint Tomography of the European Crust and Upper Mantle
NASA Astrophysics Data System (ADS)
Basini, P.; Nissen-Meyer, T.; Boschi, L.; Schenk, O.; Verbeke, J.; Hanasoge, S.; Giardini, D.
2010-12-01
Thanks to continuously improved instrument coverage, and the growth of high-performance computational infrastructure, it is now possible to enhance the resolution at which seismologists image the Earth's interior. While most algorithms in global seismic tomography today are grounded on the ray-theory approximation, however, resolution and model complexity can effectively be enhanced only through the application of more advanced techniques accounting for the many complexities of the partial derivatives relating seismic data and Earth structure. These include full-wave forward modelling methods and adjoint algorithms, which together set a framework for iterative, nonlinear inversion upon complex 3D structures. We take advantage of these methodological improvements using a newly developed, flexible spectral-element method (SPECFEM3D) with embedded adjoint capabilities to devise new tomographic models of the European crust and upper mantle. We chose a two-scale strategy, in which we use global surface wave data to first constrain the large-scale structures, and simultaneously invert for high-resolution, regional structures based on measurements of ambient noise in central and southern Europe. By its very nature, and as a result of the dense station coverage over the continent, the ambient-noise method affords us a particularly uniform seismic coverage. To define surface-wave sensitivity kernels, we construct a flexible, global mesh of the upper mantle only (i.e., a spherical shell) honoring all global discontinuities, and include 3D starting models down to periods of 30 seconds. The noise data are cross-correlated to obtain station-to-station Green's functions. We will present examples of sensitivity kernels computed for these noise-based Green's functions and discuss the data-specific validity of the underlying assumptions to extract Green's functions. The local setup, which is constructed using the same software as in the global case, needs to honor internal and
Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow
NASA Astrophysics Data System (ADS)
Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar
2014-09-01
We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the
7 CFR 220.5 - Method of payment to States.
Code of Federal Regulations, 2013 CFR
2013-01-01
... AGRICULTURE CHILD NUTRITION PROGRAMS SCHOOL BREAKFAST PROGRAM § 220.5 Method of payment to States. Funds to be paid to any State for the School Breakfast Program shall be made available by means of Letters...
7 CFR 220.5 - Method of payment to States.
Code of Federal Regulations, 2012 CFR
2012-01-01
... AGRICULTURE CHILD NUTRITION PROGRAMS SCHOOL BREAKFAST PROGRAM § 220.5 Method of payment to States. Funds to be paid to any State for the School Breakfast Program shall be made available by means of Letters...
7 CFR 220.5 - Method of payment to States.
Code of Federal Regulations, 2010 CFR
2010-01-01
... AGRICULTURE CHILD NUTRITION PROGRAMS SCHOOL BREAKFAST PROGRAM § 220.5 Method of payment to States. Funds to be paid to any State for the School Breakfast Program shall be made available by means of Letters...
7 CFR 220.5 - Method of payment to States.
Code of Federal Regulations, 2011 CFR
2011-01-01
... AGRICULTURE CHILD NUTRITION PROGRAMS SCHOOL BREAKFAST PROGRAM § 220.5 Method of payment to States. Funds to be paid to any State for the School Breakfast Program shall be made available by means of Letters...
7 CFR 220.5 - Method of payment to States.
Code of Federal Regulations, 2014 CFR
2014-01-01
... AGRICULTURE CHILD NUTRITION PROGRAMS SCHOOL BREAKFAST PROGRAM § 220.5 Method of payment to States. Funds to be paid to any State for the School Breakfast Program shall be made available by means of Letters...
Solution of the self-adjoint radiative transfer equation on hybrid computer systems
NASA Astrophysics Data System (ADS)
Gasilov, V. A.; Kuchugov, P. A.; Olkhovskaya, O. G.; Chetverushkin, B. N.
2016-06-01
A new technique for simulating three-dimensional radiative energy transfer for the use in the software designed for the predictive simulation of plasma with high energy density on parallel computers is proposed. A highly scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is developed based on the solution of a second-order equation with a self-adjoint operator. A distinctive feature of this algorithm is a preliminary transformation of rotation to eliminate mixed derivatives with respect to the spatial variables, simplify the structure of the difference operator, and accelerate the convergence of the iterative solution of the equation. It is shown that the proposed method correctly reproduces the limiting cases—isotropic radiation and the directed radiation with a δ-shaped angular distribution.
Method for solid state crystal growth
Nolas, George S.; Beekman, Matthew K.
2013-04-09
A novel method for high quality crystal growth of intermetallic clathrates is presented. The synthesis of high quality pure phase crystals has been complicated by the simultaneous formation of both clathrate type-I and clathrate type-II structures. It was found that selective, phase pure, single-crystal growth of type-I and type-II clathrates can be achieved by maintaining sufficient partial pressure of a chemical constituent during slow, controlled deprivation of the chemical constituent from the primary reactant. The chemical constituent is slowly removed from the primary reactant by the reaction of the chemical constituent vapor with a secondary reactant, spatially separated from the primary reactant, in a closed volume under uniaxial pressure and heat to form the single phase pure crystals.
7 CFR 215.5 - Method of payment to States.
Code of Federal Regulations, 2013 CFR
2013-01-01
... favor of the State agency. The State agency shall: (1) Obtain funds needed to reimburse School Food... 7 Agriculture 4 2013-01-01 2013-01-01 false Method of payment to States. 215.5 Section 215.5 Agriculture Regulations of the Department of Agriculture (Continued) FOOD AND NUTRITION SERVICE, DEPARTMENT...
7 CFR 215.5 - Method of payment to States.
Code of Federal Regulations, 2012 CFR
2012-01-01
... favor of the State agency. The State agency shall: (1) Obtain funds needed to reimburse School Food... 7 Agriculture 4 2012-01-01 2012-01-01 false Method of payment to States. 215.5 Section 215.5 Agriculture Regulations of the Department of Agriculture (Continued) FOOD AND NUTRITION SERVICE, DEPARTMENT...
Mass anomalous dimension in SU(2) with two adjoint fermions
Bursa, Francis; Del Debbio, Luigi; Keegan, Liam; Pica, Claudio; Pickup, Thomas
2010-01-01
We study SU(2) lattice gauge theory with two flavors of Dirac fermions in the adjoint representation. We measure the running of the coupling in the Schroedinger functional scheme and find it is consistent with existing results. We discuss how systematic errors affect the evidence for an infrared fixed point (IRFP). We present the first measurement of the running of the mass in the Schroedinger functional scheme. The anomalous dimension of the chiral condensate, which is relevant for phenomenological applications, can be easily extracted from the running of the mass, under the assumption that the theory has an IRFP. At the current level of accuracy, we can estimate 0.05<{gamma}<0.56 at the IRFP.
Infrared regime of SU(2) with one adjoint Dirac flavor
NASA Astrophysics Data System (ADS)
Athenodorou, Andreas; Bennett, Ed; Bergner, Georg; Lucini, Biagio
2015-06-01
SU(2) gauge theory with one Dirac flavor in the adjoint representation is investigated on a lattice. Initial results for the gluonic and mesonic spectrum, static potential from Wilson and Polyakov loops, and the anomalous dimension of the fermionic condensate from the Dirac mode number are presented. The results found are not consistent with conventional confining behavior, pointing instead tentatively towards a theory lying within or very near the onset of the conformal window, with the anomalous dimension of the fermionic condensate in the range 0.9 ≲γ*≲0.95 . The implications of our work for building a viable theory of strongly interacting dynamics beyond the standard model are discussed.
7 CFR 215.5 - Method of payment to States.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 4 2014-01-01 2014-01-01 false Method of payment to States. 215.5 Section 215.5 Agriculture Regulations of the Department of Agriculture (Continued) FOOD AND NUTRITION SERVICE, DEPARTMENT OF AGRICULTURE CHILD NUTRITION PROGRAMS SPECIAL MILK PROGRAM FOR CHILDREN § 215.5 Method of payment to States. (a) Funds to be paid to any...
Optimizing spectral wave estimates with adjoint-based sensitivity maps
NASA Astrophysics Data System (ADS)
Orzech, Mark; Veeramony, Jay; Flampouris, Stylianos
2014-04-01
A discrete numerical adjoint has recently been developed for the stochastic wave model SWAN. In the present study, this adjoint code is used to construct spectral sensitivity maps for two nearshore domains. The maps display the correlations of spectral energy levels throughout the domain with the observed energy levels at a selected location or region of interest (LOI/ROI), providing a full spectrum of values at all locations in the domain. We investigate the effectiveness of sensitivity maps based on significant wave height ( H s ) in determining alternate offshore instrument deployment sites when a chosen nearshore location or region is inaccessible. Wave and bathymetry datasets are employed from one shallower, small-scale domain (Duck, NC) and one deeper, larger-scale domain (San Diego, CA). The effects of seasonal changes in wave climate, errors in bathymetry, and multiple assimilation points on sensitivity map shapes and model performance are investigated. Model accuracy is evaluated by comparing spectral statistics as well as with an RMS skill score, which estimates a mean model-data error across all spectral bins. Results indicate that data assimilation from identified high-sensitivity alternate locations consistently improves model performance at nearshore LOIs, while assimilation from low-sensitivity locations results in lesser or no improvement. Use of sub-sampled or alongshore-averaged bathymetry has a domain-specific effect on model performance when assimilating from a high-sensitivity alternate location. When multiple alternate assimilation locations are used from areas of lower sensitivity, model performance may be worse than with a single, high-sensitivity assimilation point.
NASA Technical Reports Server (NTRS)
Arian, Eyal; Salas, Manuel D.
1997-01-01
We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.
Time domain adjoint sensitivity analysis of electromagnetic problems with nonlinear media.
Bakr, Mohamed H; Ahmed, Osman S; El Sherif, Mohamed H; Nomura, Tsuyoshi
2014-05-01
In this paper, we propose a theory for wideband adjoint sensitivity analysis of problems with nonlinear media. We show that the sensitivities of the desired response with respect to all shape and material parameters are obtained through one extra adjoint simulation. Unlike linear problems, the system matrices of this adjoint simulation are time varying. Their values are determined during the original simulation. The proposed theory exploits the time-domain transmission line modeling (TLM) and provides an efficient AVM approach for sensitivity analysis of general time domain objective functions. The theory has been illustrated through a number of examples. PMID:24921783
On basic conditions to generate multi-adjoint concept lattices via Galois connections
NASA Astrophysics Data System (ADS)
Díaz-Moreno, J. C.; Medina, J.; Ojeda-Aciego, M.
2014-02-01
This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multi-adjoint sufficiency, possibility, and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined using the same syntactical form than the extension and intension operators of multi-adjoint concept lattices) form a Galois connection. As a consequence, given a relational database, we have much more possibilities to construct concept lattices associated with it, so that we can choose the specific version which better suits the situation.
A flexible transition state searching method for atmospheric reaction systems
NASA Astrophysics Data System (ADS)
Lin, Xiao-Xiao; Liu, Yi-Rong; Huang, Teng; Chen, Jiao; Jiang, Shuai; Huang, Wei
2015-04-01
The precise and rapid exploration of transition states (TSs) is a major challenge when studying atmospheric reactions due to their complexity. In this work, a Monte Carlo Transition State Search Method (MCTSSM), which integrates Monte Carlo sampling technique with transition state optimization methods using an efficient computer script, has been developed for transition state searches. The efficiency and the potential application in atmospheric reactions of this method have been demonstrated by three types of test suits related to the reactions of atmospheric volatile organic compounds (VOCs): (1) OH addition, (2) OH hydrogen-abstraction, and (3) the other reactive group (e.g. Cl, O3, NO3), especially for the reaction of β-pinene-sCI (stabilized Criegee Intermediates) with water. It was shown that the application of this method with effective restricted parameters has greatly simplified the time-consuming and tedious manual search procedure for transition state (TS) of the bimolecular reaction systems.
A Flexible Transition State Searching Method for Atmospheric Reaction Systems
Lin, Xiao-Xiao; Liu, Yi-Rong; Huang, Teng; Chen, Jiao; Jiang, Shuai; Huang, Wei
2015-04-01
The precise and rapid exploration of transition states (TSs) is a major challenge when studying atmospheric reactions due to their complexity. In this work, a Monte Carlo Transition State Search Method (MCTSSM), which integrates Monte Carlo sampling technique with transition state optimization methods using an efficient computer script, has been developed for transition state searches. The efficiency and the potential application in atmospheric reactions of this method have been demonstrated by three types of test suits related to the reactions of atmospheric volatile organic compounds (VOCs): (1) OH addition, (2) OH hydrogen-abstraction, and (3) the other reactive group (e.g. Cl, O3, NO3), especially for the reaction of β-pinene-sCI (stabilized Criegee Intermediates) with water. It was shown that the application of this method with effective restricted parameters has greatly simplified the time-consuming and tedious manual search procedure for transition state (TS) of the bimolecular reaction systems.
Methods for thermodynamic evaluation of battery state of health
Yazami, Rachid; McMenamin, Joseph; Reynier, Yvan; Fultz, Brent T
2013-05-21
Described are systems and methods for accurately characterizing thermodynamic and materials properties of electrodes and battery systems and for characterizing the state of health of electrodes and battery systems. Measurement of physical attributes of electrodes and batteries corresponding to thermodynamically stabilized electrode conditions permit determination of thermodynamic parameters, including state functions such as the Gibbs free energy, enthalpy and entropy of electrode/electrochemical cell reactions, that enable prediction of important performance attributes of electrode materials and battery systems, such as energy, power density, current rate, cycle life and state of health. Also provided are systems and methods for charging a battery according to its state of health.
Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.
2009-01-01
An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.
Preliminary Results from the Application of Automated Adjoint Code Generation to CFL3D
NASA Technical Reports Server (NTRS)
Carle, Alan; Fagan, Mike; Green, Lawrence L.
1998-01-01
This report describes preliminary results obtained using an automated adjoint code generator for Fortran to augment a widely-used computational fluid dynamics flow solver to compute derivatives. These preliminary results with this augmented code suggest that, even in its infancy, the automated adjoint code generator can accurately and efficiently deliver derivatives for use in transonic Euler-based aerodynamic shape optimization problems with hundreds to thousands of independent design variables.
NASA Technical Reports Server (NTRS)
Lee-Rausch, E. M.; Park, M. A.; Jones, W. T.; Hammond, D. P.; Nielsen, E. J.
2005-01-01
This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge
Adjoint Data Assimilative Model Study of the Gulf of Maine Coastal Circulation
NASA Astrophysics Data System (ADS)
He, R.; McGillicuddy, D. J.; Lynch, D. R.
2004-12-01
Data assimilation (DA) in the coastal ocean can be divided into category of either sequential estimation or variational adjoint. Sequential estimation techniques blend models with observations directly, using a variety of algorithms with which the relative weights of data and model are calculated. Variational adjoint techniques infer model control variables (e.g. parameters, forcing functions, boundary conditions, etc.) that minimize the misfit between observations and predictions. The advantage of the latter techniques over the former is that the resulting model solutions obey model dynamics. In this study, the Gulf of Maine coastal circulation and the material property transport are investigated with the Dartmouth variational adjoint DA modeling system, which assimilates in-situ data via inversion for the unknown sea level elevation at open boundaries. In-situ observations include ADCP currents and coastal sea levels. The adjoint DA model skill is evaluated by the inter-comparisons between modeled and observed drifter trajectories. Excellent model skill is found, demonstrating the utility and effectiveness of the adjoint DA modeling system in bridging in-situ observations with coastal ocean model simulations. Implications of the adjoint DA strategy on the emergent coastal ocean observing systems are discussed.
A New Method for Incremental Testing of Finite State Machines
NASA Technical Reports Server (NTRS)
Pedrosa, Lehilton Lelis Chaves; Moura, Arnaldo Vieira
2010-01-01
The automatic generation of test cases is an important issue for conformance testing of several critical systems. We present a new method for the derivation of test suites when the specification is modeled as a combined Finite State Machine (FSM). A combined FSM is obtained conjoining previously tested submachines with newly added states. This new concept is used to describe a fault model suitable for incremental testing of new systems, or for retesting modified implementations. For this fault model, only the newly added or modified states need to be tested, thereby considerably reducing the size of the test suites. The new method is a generalization of the well-known W-method and the G-method, but is scalable, and so it can be used to test FSMs with an arbitrarily large number of states.
General finite state machine reasoning method for digital forensics
NASA Astrophysics Data System (ADS)
Chen, Long; Wang, Guoyin
2008-04-01
Digital forensics investigator faces the challenge of reliability of forensic conclusions. Formal automatic analysis method is helpful to deal with the challenge. The finite state machine analysis method tries to determine all possible sequences of events that could have happened in a digital system during an incident. Its basic idea is to model the target system using a finite state machine and then explore its all possible states on the condition of available evidence. Timed mealy finite state machine is introduced to model the target system, and the formalization of system running process and evidence is presented to match the system running with possible source evidence automatically. Based on Gladyshev's basic reasoning method, general reasoning algorithms with multi strategies are developed to find the possible real scenarios. Case study and experimental results show that our method is feasible and adaptable to possible cases and takes a further step to practical formal reasoning for digital forensics.
NASA Astrophysics Data System (ADS)
Galanti, E.; Kaspi, Y.
2014-12-01
In approximately two years Juno will perform close flybys of Jupiter, obtaining a high precision gravity spectrum for the planet. This data can potentially be used to estimate the depth of the observed flows on the Jupiter. Here, we propose a new methodology for the inversion of the gravity data into into the full three-dimensional flow on Jupiter. Using the adjoint method we construct an inverse model for a dynamical model in which the gravity field is calculated from the observed surface wind, thus allowing its backward integration, from the gravity field to the wind. Given a gravity field, the adjoint based model finds the atmospheric dynamics that can explain best the gravity field (minimum difference). The dynamical model is set up to allow either zonal flow only, or a full horizontal flow in both zonal and meridional directions based on the observed cloud-level wind. In addition, dynamical perturbations resulting from the the non-spherical shape of the planet are accounted for. The dynamical model, together with its adjoint counterpart, are used for examination of various scenarios, including cases in which the depth of the wind depend on latitudinal position.We show that given the expected sensitivities of Juno, it is possible to use the gravity measurements to derive the depth of the wind on Jupiter. This holds for a large range of zonal wind possible penetration depths, from 100km to 10,000km, and for winds depth that vary with latitude. This method proves to be useful also when incorporating the full horizontal flow, and thus taking into account gravity perturbations that vary with longitude. We show that our adjoint based inversion method allows not only to estimate the depth of the circulation, but allows via iterations with the spacecraft trajectory estimation model to improve the inferred gravity field.
A comparison of ancestral state reconstruction methods for quantitative characters.
Royer-Carenzi, Manuela; Didier, Gilles
2016-09-01
Choosing an ancestral state reconstruction method among the alternatives available for quantitative characters may be puzzling. We present here a comparison of seven of them, namely the maximum likelihood, restricted maximum likelihood, generalized least squares under Brownian, Brownian-with-trend and Ornstein-Uhlenbeck models, phylogenetic independent contrasts and squared parsimony methods. A review of the relations between these methods shows that the maximum likelihood, the restricted maximum likelihood and the generalized least squares under Brownian model infer the same ancestral states and can only be distinguished by the distributions accounting for the reconstruction uncertainty which they provide. The respective accuracy of the methods is assessed over character evolution simulated under a Brownian motion with (and without) directional or stabilizing selection. We give the general form of ancestral state distributions conditioned on leaf states under the simulation models. Ancestral distributions are used first, to give a theoretical lower bound of the expected reconstruction error, and second, to develop an original evaluation scheme which is more efficient than comparing the reconstructed and the simulated states. Our simulations show that: (i) the distributions of the reconstruction uncertainty provided by the methods generally make sense (some more than others); (ii) it is essential to detect the presence of an evolutionary trend and to choose a reconstruction method accordingly; (iii) all the methods show good performances on characters under stabilizing selection; (iv) without trend or stabilizing selection, the maximum likelihood method is generally the most accurate. PMID:27234644
Plumes, Hotspot & Slabs Imaged by Global Adjoint Tomography
NASA Astrophysics Data System (ADS)
Bozdag, E.; Lefebvre, M. P.; Lei, W.; Peter, D. B.; Smith, J. A.; Komatitsch, D.; Tromp, J.
2015-12-01
We present the "first generation" global adjoint tomography model based on 3D wave simulations, which is the result of 15 conjugate-gradient iterations with confined transverse isotropy to the upper mantle. Our starting model is the 3D mantle and crustal models S362ANI (Kustowski et al. 2008) and Crust2.0 (Bassin et al. 2000), respectively. We take into account the full nonlinearity of wave propagation in numerical simulations including attenuation (both in forward and adjoint simulations), topography/bathymetry, etc., using the GPU version of the SPECFEM3D_GLOBE package. We invert for crust and mantle together without crustal corrections to avoid any bias in mantle structure. We started with an initial selection of 253 global CMT events within the magnitude range 5.8 ≤ Mw ≤ 7.0 with numerical simulations having resolution down to 27 s combining 30-s body and 60-s surface waves. After the 12th iteration we increased the resolution to 17 s, including higher-frequency body waves as well as going down to 45 s in surface-wave measurements. We run 180-min seismograms and assimilate all minor- and major-arc body and surface waves. Our 15th iteration model update shows a tantalisingly enhanced image of the Tahiti plume as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone, Erebus, etc. 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 initial model. Point-spread function tests (Fichtner & Trampert 2011) suggest that we are close to the resolution of continental-scale studies in our global inversions and able to confidently map features, for instance, at the scale of the Yellowstone hotspot. This is a clear consequence of our multi-scale smoothing strategy, in which we define our smoothing operator as a function of the approximate Hessian kernel and smooth our gradients less wherever we have good ray coverage
Adjoint-based optimal control for black-box simulators enabled by model calibration
NASA Astrophysics Data System (ADS)
Chen, Han; Wang, Qiqi; Klie, Hector
2013-11-01
Many simulations are performed using legacy code that are difficult to modify, or commercial software without available source code. Such ``black-box'' simulator often solves a partial differential equation involving some unknown parameters, functions or discretization methods. Optimal control for black-box simulators can be performed using gradient-free methods, but these methods can be computationally expensive when the controls are high dimensional. We aim at developing a more efficient optimization methodology for black-box simulations by first inferring and calibrating a ``twin model'' of the black-box simulator. The twin model is an open-box model that mirrors the behavior of the black-box simulation using data assimilation techniques. We then apply adjoint-based optimal control to the calibrated twin model. This method is applied to a 1D Buckley-Leverett equation solver, and a black-box multi-phase porous media flow solver PSIM. Special thanks to the support from the subsurface technology group of ConocoPhillips.
Adjoint sensitivity analysis of hydrodynamic stability in cyclonic flows
NASA Astrophysics Data System (ADS)
Guzman Inigo, Juan; Juniper, Matthew
2015-11-01
Cyclonic separators are used in a variety of industries to efficiently separate mixtures of fluid and solid phases by means of centrifugal forces and gravity. In certain circumstances, the vortex core of cyclonic flows is known to precess due to the instability of the flow, which leads to performance reductions. We aim to characterize the unsteadiness using linear stability analysis of the Reynolds Averaged Navier-Stokes (RANS) equations in a global framework. The system of equations, including the turbulence model, is linearised to obtain an eigenvalue problem. Unstable modes corresponding to the dynamics of the large structures of the turbulent flow are extracted. The analysis shows that the most unstable mode is a helical motion which develops around the axis of the flow. This result is in good agreement with LES and experimental analysis, suggesting the validity of the approach. Finally, an adjoint-based sensitivity analysis is performed to determine the regions of the flow that, when altered, have most influence on the frequency and growth-rate of the unstable eigenvalues.
Periodic differential equations with self-adjoint monodromy operator
NASA Astrophysics Data System (ADS)
Yudovich, V. I.
2001-04-01
A linear differential equation \\dot u=A(t)u with p-periodic (generally speaking, unbounded) operator coefficient in a Euclidean or a Hilbert space \\mathbb H is considered. It is proved under natural constraints that the monodromy operator U_p is self-adjoint and strictly positive if A^*(-t)=A(t) for all t\\in\\mathbb R.It is shown that Hamiltonian systems in the class under consideration are usually unstable and, if they are stable, then the operator U_p reduces to the identity and all solutions are p-periodic.For higher frequencies averaged equations are derived. Remarkably, high-frequency modulation may double the number of critical values.General results are applied to rotational flows with cylindrical components of the velocity a_r=a_z=0, a_\\theta=\\lambda c(t)r^\\beta, \\beta<-1, c(t) is an even p-periodic function, and also to several problems of free gravitational convection of fluids in periodic fields.
Multireference state-specific coupled-cluster methods. State-of-the-art and perspectives.
Ivanov, Vladimir V; Lyakh, Dmitry I; Adamowicz, Ludwik
2009-04-14
This work reviews the state-specific multireference coupled-cluster (CC) approaches which have been developed as approximate methods for performing high-level quantum mechanical calculations on quasidegenerate ground and excited states of atomic and molecular systems. The term "quasidegenerate" refers to a state that cannot be described even in the first approximation by a single-determinant wavefunction (a Slater determinant), but requires two or more determinants for this purpose. The main challenge with applying the coupled-cluster theory to such states is in describing the electron correlation effects in the wavefunctions representing these states in a manner that is size-extensive, yet accurate and simple enough so the method can be routinely applied to small and medium-size molecular systems. We are describing how this can be accomplished within a theory that focuses on only one state of the system in a single CC calculation (the state-specific theory). PMID:19325966
Methods for determining the physiological state of a plant
Kramer, David M.; Sacksteder, Colette
2003-09-23
The present invention provides methods for measuring a photosynthetic parameter. The methods of the invention include the steps of: (a) illuminating a plant leaf until steady-state photosynthesis is achieved; (b) subjecting the illuminated plant leaf to a period of darkness; (c) using a kinetic spectrophotometer or kinetic spectrophotometer/fluorimeter to collect spectral data from the plant leaf treated in accordance with steps (a) and (b); and (d) determining a photosynthetic parameter from the spectral data. In another aspect, the invention provides methods for determining the physiological state of a plant.
NASA Astrophysics Data System (ADS)
Chen, M.; Masy, J.; Niu, F.; Levander, A.
2014-12-01
We present a high-resolution 3D crustal model of Eastern Venezuela from a full waveform inversion adjoint tomography technique, based on the spectral-element method. Empirical Green's functions (EGFs) of Rayleigh waves from ambient noise interferometry serve as the observed waveforms. Rayleigh wave signals in the period range of 10 - 50 s were extracted by cross-correlations of 48 stations from both Venezuelan national seismic network and the BOLIVAR project array. The synthetic Green's functions (SGFs) are calculated with an initial regional 3D shear wave model determined from ballistic Rayleigh wave tomography from earthquake records with periods longer than 20 s. The frequency-dependent traveltime time misfits between the SGFs and EGFs are minimized iteratively using adjoint tomography = to refine 3D crustal structure [Chen et al. 2014]. The final 3D model shows lateral shear wave velocity variations that are well correlated with the geological terranes within the continental interior. In particular, the final model reveals low velocities distributed along the axis of the Espino Graben, indicating that the graben has a substantially different crustal structure than the rest of the Eastern Venezuela Basin. We also observe high shear velocities in the lower crust beneath some of the subterranes of the Proterozoic-Archean Guayana Shield.
Design methods for fault-tolerant finite state machines
NASA Technical Reports Server (NTRS)
Niranjan, Shailesh; Frenzel, James F.
1993-01-01
VLSI electronic circuits are increasingly being used in space-borne applications where high levels of radiation may induce faults, known as single event upsets. In this paper we review the classical methods of designing fault tolerant digital systems, with an emphasis on those methods which are particularly suitable for VLSI-implementation of finite state machines. Four methods are presented and will be compared in terms of design complexity, circuit size, and estimated circuit delay.
Note: Excited State Studies of Ozone using State-Specific Multireference Coupled Cluster Methods
Bhaskaran-Nair, Kiran; Kowalski, Karol
2012-12-07
Vertical excitation energies obtained with state-specific multi-reference coupled cluster (MRCC) methods are reported for the ozone molecule. Using state-specific MRCC non-iterative methods with singles, doubles, and non-iterative triples (MRCCSD(T)) we obtain 4.40 eV for the challenging doubly excited 21A1 state when using a reliable model space. This estimate is in good agreement with experiment (4.5 eV). We also compare our MRCC results with the excitation energies obtained with high-order equation-of-motion coupled cluster methods
Comparison of Ensemble and Adjoint Approaches to Variational Optimization of Observational Arrays
NASA Astrophysics Data System (ADS)
Nechaev, D.; Panteleev, G.; Yaremchuk, M.
2015-12-01
Comprehensive monitoring of the circulation in the Chukchi Sea and Bering Strait is one of the key prerequisites of the successful long-term forecast of the Arctic Ocean state. Since the number of continuously maintained observational platforms is restricted by logistical and political constraints, the configuration of such an observing system should be guided by an objective strategy that optimizes the observing system coverage, design, and the expenses of monitoring. The presented study addresses optimization of system consisting of a limited number of observational platforms with respect to reduction of the uncertainties in monitoring the volume/freshwater/heat transports through a set of key sections in the Chukchi Sea and Bering Strait. Variational algorithms for optimization of observational arrays are verified in the test bed of the set of 4Dvar optimized summer-fall circulations in the Pacific sector of the Arctic Ocean. The results of an optimization approach based on low-dimensional ensemble of model solutions is compared against a more conventional algorithm involving application of the tangent linear and adjoint models. Special attention is paid to the computational efficiency and portability of the optimization procedure.
Haydock’s recursive solution of self-adjoint problems. Discrete spectrum
Moroz, Alexander
2014-12-15
Haydock’s recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber’s quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock’s recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials (p{sub n}(E)) in energy variable E. The polynomials (p{sub n}(E)) are orthonormal with respect to the density of states n{sub 0}(E) and energy eigenstate |E〉 is the generating function of (p{sub n}(E)). The generality of Haydock’s recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.
Optimal ozone reduction policy design using adjoint-based NOx marginal damage information.
Mesbah, S Morteza; Hakami, Amir; Schott, Stephan
2013-01-01
Despite substantial reductions in nitrogen oxide (NOx) emissions in the United States, the success of emission control programs in optimal ozone reduction is disputable because they do not consider the spatial and temporal differences in health and environmental damages caused by NOx emissions. This shortcoming in the current U.S. NOx control policy is explored, and various methodologies for identifying optimal NOx emission control strategies are evaluated. The proposed approach combines an optimization platform with an adjoint (or backward) sensitivity analysis model and is able to examine the environmental performance of the current cap-and-trade policy and two damage-based emissions-differentiated policies. Using the proposed methodology, a 2007 case study of 218 U.S. electricity generation units participating in the NOx trading program is examined. The results indicate that inclusion of damage information can significantly enhance public health performance of an economic instrument. The net benefit under the policy that minimizes the social cost (i.e., health costs plus abatement costs) is six times larger than that of an exchange rate cap-and-trade policy. PMID:24144173
Multi-point Adjoint-Based Design of Tilt-Rotors in a Noninertial Reference Frame
NASA Technical Reports Server (NTRS)
Jones, William T.; Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Acree, Cecil W.
2014-01-01
Optimization of tilt-rotor systems requires the consideration of performance at multiple design points. In the current study, an adjoint-based optimization of a tilt-rotor blade is considered. The optimization seeks to simultaneously maximize the rotorcraft figure of merit in hover and the propulsive efficiency in airplane-mode for a tilt-rotor system. The design is subject to minimum thrust constraints imposed at each design point. The rotor flowfields at each design point are cast as steady-state problems in a noninertial reference frame. Geometric design variables used in the study to control blade shape include: thickness, camber, twist, and taper represented by as many as 123 separate design variables. Performance weighting of each operational mode is considered in the formulation of the composite objective function, and a build up of increasing geometric degrees of freedom is used to isolate the impact of selected design variables. In all cases considered, the resulting designs successfully increase both the hover figure of merit and the airplane-mode propulsive efficiency for a rotor designed with classical techniques.
Finn, John M.
2015-03-01
Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a 'special divergence-free' property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. 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 Ref. [11], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Ref. [35], appears to work very well.
NASA Astrophysics Data System (ADS)
Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.
2016-09-01
A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.
A simple method for labeling CT images with respiratory states
Berlinger, Kajetan; Sauer, Otto; Vences, Lucia; Roth, Michael
2006-09-15
A method is described for labeling CT images with their respiratory state by a needle, connected to the patient's chest/abdomen. By means of a leverage the needle follows the abdominal respiratory motion. The needle is visible as a blurred spot in every CT slice. The method was tested with nine patients. A series of volume scans during free breathing was performed. The detected positions of the moving needle in every single slice were compared to each other thus enabling respiratory state assignment. The tool is an inexpensive alternative to complex respiratory measuring tools for four dimensional (4D) CT and was greatly accepted in the clinic due to its simplicity.
Adjoint-based airfoil shape optimization in transonic flow
NASA Astrophysics Data System (ADS)
Gramanzini, Joe-Ray
The primary focus of this work is efficient aerodynamic shape optimization in transonic flow. Adjoint-based optimization techniques are employed on airfoil sections and evaluated in terms of computational accuracy as well as efficiency. This study examines two test cases proposed by the AIAA Aerodynamic Design Optimization Discussion Group. The first is a two-dimensional, transonic, inviscid, non-lifting optimization of a Modified-NACA 0012 airfoil. The second is a two-dimensional, transonic, viscous optimization problem using a RAE 2822 airfoil. The FUN3D CFD code of NASA Langley Research Center is used as the ow solver for the gradient-based optimization cases. Two shape parameterization techniques are employed to study their effect and the number of design variables on the final optimized shape: Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD) and the BandAids free-form deformation technique. For the two airfoil cases, angle of attack is treated as a global design variable. The thickness and camber distributions are the local design variables for MASSOUD, and selected airfoil surface grid points are the local design variables for BandAids. Using the MASSOUD technique, a drag reduction of 72.14% is achieved for the NACA 0012 case, reducing the total number of drag counts from 473.91 to 130.59. Employing the BandAids technique yields a 78.67% drag reduction, from 473.91 to 99.98. The RAE 2822 case exhibited a drag reduction from 217.79 to 132.79 counts, a 39.05% decrease using BandAids.
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
NASA Astrophysics Data System (ADS)
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
Self-adjoint Operators as Functions I. Lattices, Galois Connections, and the Spectral Order
NASA Astrophysics Data System (ADS)
Döring, Andreas; Dewitt, Barry
2014-06-01
Observables of a quantum system, described by self-adjoint operators in a von Neumann algebra or affiliated with it in the unbounded case, form a conditionally complete lattice when equipped with the spectral order. Using this order-theoretic structure, we develop a new perspective on quantum observables. In this first paper (of two), we show that self-adjoint operators affiliated with a von Neumann algebra can equivalently be described as certain real-valued functions on the projection lattice of the algebra, which we call q-observable functions. Bounded self-adjoint operators correspond to q-observable functions with compact image on non-zero projections. These functions, originally defined in a similar form by de Groote (Observables II: quantum observables, 2005), are most naturally seen as adjoints (in the categorical sense) of spectral families. We show how they relate to the daseinisation mapping from the topos approach to quantum theory (Döring and Isham , New Structures for Physics, Springer, Heidelberg, 2011). Moreover, the q-observable functions form a conditionally complete lattice which is shown to be order-isomorphic to the lattice of self-adjoint operators with respect to the spectral order. In a subsequent paper (Döring and Dewitt, 2012, preprint), we will give an interpretation of q-observable functions in terms of quantum probability theory, and using results from the topos approach to quantum theory, we will provide a joint sample space for all quantum observables.
Low-Lying ππ* States of Heteroaromatic Molecules: A Challenge for Excited State Methods.
Prlj, Antonio; Sandoval-Salinas, María Eugenia; Casanova, David; Jacquemin, Denis; Corminboeuf, Clémence
2016-06-14
The description of low-lying ππ* states of linear acenes by standard electronic structure methods is known to be challenging. Here, we broaden the framework of this problem by considering a set of fused heteroaromatic rings and demonstrate that standard electronic structure methods do not provide a balanced description of the two (typically) lowest singlet state (La and Lb) excitations. While the Lb state is highly sensitive to correlation effects, La suffers from the same drawbacks as charge transfer excitations. We show that the comparison between CIS/CIS(D) can serve as a diagnostic for detecting the two problematic excited states. Standard TD-DFT and even its spin-flip variant lead to inaccurate excitation energies and interstate gaps, with only a double hybrid functional performing somewhat better. The complication inherent to a balanced description of these states is so important that even CC2 and ADC(2) do not necessarily match the ADC(3) reference. PMID:27144975
An Extended Equation of State Modeling Method II. Mixtures
NASA Astrophysics Data System (ADS)
Scalabrin, G.; Marchi, P.; Stringari, P.; Richon, D.
2006-09-01
This work is the extension of previous work dedicated to pure fluids. The same method is extended to the representation of thermodynamic properties of a mixture through a fundamental equation of state in terms of the Helmholtz energy. The proposed technique exploits the extended corresponding-states concept of distorting the independent variables of a dedicated equation of state for a reference fluid using suitable scale factor functions to adapt the equation to experimental data of a target system. An existing equation of state for the target mixture is used instead of an equation for the reference fluid, completely avoiding the need for a reference fluid. In particular, a Soave-Redlich-Kwong cubic equation with van der Waals mixing rules is chosen. The scale factors, which are functions of temperature, density, and mole fraction of the target mixture, are expressed in the form of a multilayer feedforward neural network, whose coefficients are regressed by minimizing a suitable objective function involving different kinds of mixture thermodynamic data. As a preliminary test, the model is applied to five binary and two ternary haloalkane mixtures, using data generated from existing dedicated equations of state for the selected mixtures. The results show that the method is robust and straightforward for the effective development of a mixture- specific equation of state directly from experimental data.
NASA Astrophysics Data System (ADS)
Komatitsch, Dimitri; Xie, Zhinan; Bozdağ, Ebru; Sales de Andrade, Elliott; Peter, Daniel; Liu, Qinya; Tromp, Jeroen
2016-06-01
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.
One-loop test of free SU( N ) adjoint model holography
NASA Astrophysics Data System (ADS)
Bae, Jin-Beom; Joung, Euihun; Lal, Shailesh
2016-04-01
We consider the holographic duality where the CFT side is given by SU( N ) adjoint free scalar field theory. Compared to the vector models, the set of single trace operators is immensely extended so that the corresponding AdS theory also contains infinitely many massive higher spin fields on top of the massless ones. We compute the one-loop vacuum energy of these AdS fields to test this duality at the subleading order in large N expansion. The determination of the bulk vacuum energy requires a proper scheme to sum up the infinitely many contributions. For that, we develop a new method and apply it first to calculate the vacuum energies for the first few `Regge trajectories' in AdS4 and AdS5 . In considering the full vacuum energy of AdS theory dual to a matrix model CFT, we find that there exist more than one available prescriptions for the one-loop vacuum energy. Taking a particular prescription, we determine the full vacuum energy of the AdS5 theory, whereas the AdS4 calculation still remains technically prohibitive. This result shows that the full vacuum energy of the AdS5 theory coincides with minus of the free energy of a single scalar field on the boundary. This is analogous to the O( N ) vector model case, hence suggests an interpretation of the positive shift of the bulk coupling constant, i.e. from N 2 - 1 to N 2.
Adjoint sensitivity analysis of thermoacoustic instability in a nonlinear Helmholtz solver
NASA Astrophysics Data System (ADS)
Juniper, Matthew; Magri, Luca
2014-11-01
Thermoacoustic instability is a persistent problem in aircraft and rocket engines. It occurs when heat release in the combustion chamber synchronizes with acoustic oscillations. It is always noisy and can sometimes result in catastrophic failure of the engine. Typically, the heat release from the flame is assumed to equal the acoustic velocity at a reference point multiplied by a spatially-varying function (the flame envelope) subject to a spatially-varying time delay. This models hydrodynamic perturbations convecting down the flame causing subsequent heat release perturbations. This creates an eigenvalue problem that is linear in the acoustic pressure but nonlinear in the complex frequency, omega. This can be solved as a sequence of linear eigenvalue problems in which the operators are updated with a new value of omega after each iteration. Adjoint methods find the sensitivity of each eigenmode to all the parameters simultaneously and are well suited to thermoacoustic problems because there are a few interesting eigenmodes but many influential parameters. The challenge here is to express the sensitivity of the eigenvalue at the final iteration to an arbitrary change in the parameters of the first iteration. This is a promising new technique for the control of thermoacoustics. European Research Council Grant Number 2590620.
Comparison of double-ended transition state search methods
NASA Astrophysics Data System (ADS)
Koslover, Elena F.; Wales, David J.
2007-10-01
While a variety of double-ended transition state search methods have been developed, their relative performance in characterizing complex multistep pathways between structurally disparate molecular conformations remains unclear. Three such methods (doubly-nudged elastic band, a string method, and a growing string method) are compared for a series of benchmarks ranging from permutational isomerizations of the seven-atom Lennard-Jones cluster (LJ7) to highly cooperative LJ38 and LJ75 rearrangements, and the folding pathways of two peptides. A database of short paths between LJ13 local minima is used to explore the effects of parameters and suggest reasonable default values. Each double-ended method was employed within the framework of a missing connection network flow algorithm to construct more complicated multistep pathways. We find that in our implementation none of the three methods definitively outperforms the others, and that their relative effectiveness is strongly system and parameter dependent.
Comparison of double-ended transition state search methods.
Koslover, Elena F; Wales, David J
2007-10-01
While a variety of double-ended transition state search methods have been developed, their relative performance in characterizing complex multistep pathways between structurally disparate molecular conformations remains unclear. Three such methods (doubly-nudged elastic band, a string method, and a growing string method) are compared for a series of benchmarks ranging from permutational isomerizations of the seven-atom Lennard-Jones cluster (LJ(7)) to highly cooperative LJ(38) and LJ(75) rearrangements, and the folding pathways of two peptides. A database of short paths between LJ(13) local minima is used to explore the effects of parameters and suggest reasonable default values. Each double-ended method was employed within the framework of a missing connection network flow algorithm to construct more complicated multistep pathways. We find that in our implementation none of the three methods definitively outperforms the others, and that their relative effectiveness is strongly system and parameter dependent. PMID:17919006
State-recycling method for testing quantum contextuality
NASA Astrophysics Data System (ADS)
Wajs, Marek; Lee, Su-Yong; Kurzyński, Paweł; Kaszlikowski, Dagomir
2016-05-01
We introduce a method to test the state-independent contextuality using a single copy of a system and without a state preparation. It can be implemented in realistic setups, like ion traps, or in other scenarios in which measurements are nondestructive. In particular, we show how to apply our idea to the Peres-Mermin state-independent contextuality test designed for nine observables of two spin-1 /2 particles. Each measurement round is performed on a postmeasurement state from the previous round. The sequence of measurements can be described as a Markov chain, and we observe that after a few rounds the system arrives at a stationary state to which the contextuality of the system can be attributed. However, it has to be noted that it does not depend on the initial state of the system and therefore it is not a property of a particular state preparation. Finally, we show that our approach to test contextuality admits noisy measurements as it implies the self-correction of possible detection errors present in any real experiments.
NASA Technical Reports Server (NTRS)
Lewis, Robert Michael
1997-01-01
This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.
A matrix product state method for solving combinatorial optimization problems
NASA Astrophysics Data System (ADS)
Pelton, S. S.; Chamon, C.; Mucciolo, E. R.
2015-03-01
We present a method based on a matrix product state representation to solve combinatorial optimization problems. All constraints are met by mapping Boolean gates into projection operators and applying operators sequentially. The method provides exact solutions with high success probability, even in the case of frustrated systems. The computational cost of the method is controlled by the maximum relative entropy of the system. Results of numerical simulations for several types of problems will be shown and discussed. NSF Grants CCF-1116590 and CCF-1117241.
Characterizing Awake and Anesthetized States Using a Dimensionality Reduction Method.
Mirsadeghi, M; Behnam, H; Shalbaf, R; Jelveh Moghadam, H
2016-01-01
Distinguishing between awake and anesthetized states is one of the important problems in surgery. Vital signals contain valuable information that can be used in prediction of different levels of anesthesia. Some monitors based on electroencephalogram (EEG) such as the Bispectral (BIS) index have been proposed in recent years. This study proposes a new method for characterizing between awake and anesthetized states. We validated our method by obtaining data from 25 patients during the cardiac surgery that requires cardiopulmonary bypass. At first, some linear and non-linear features are extracted from EEG signals. Then a method called "LLE"(Locally Linear Embedding) is used to map high-dimensional features in a three-dimensional output space. Finally, low dimensional data are used as an input to a quadratic discriminant analyzer (QDA). The experimental results indicate that an overall accuracy of 88.4 % can be obtained using this method for classifying the EEG signal into conscious and unconscious states for all patients. Considering the reliability of this method, we can develop a new EEG monitoring system that could assist the anesthesiologists to estimate the depth of anesthesia accurately. PMID:26573650
Engineering applications of a dynamical state feedback chaotification method
NASA Astrophysics Data System (ADS)
Şahin, Savaş; Güzeliş, Cüneyt
2012-09-01
This paper presents two engineering applications of a chaotification method which can be applied to any inputstate linearizable (nonlinear) system including linear controllable ones as special cases. In the used chaotification method, a reference chaotic and linear system can be combined into a special form by a dynamical state feedback increasing the order of the open loop system to have the same chaotic dynamics with the reference chaotic system. Promising dc motor applications of the method are implemented by the proposed dynamical state feedback which is based on matching the closed loop dynamics to the well known Chua and also Lorenz chaotic systems. The first application, which is the chaotified dc motor used for mixing a corn syrup added acid-base mixture, is implemented via a personal computer and a microcontroller based circuit. As a second application, a chaotified dc motor with a taco-generator used in the feedback is realized by using fully analog circuit elements.
Fault detection in electromagnetic suspension systems with state estimation methods
Sinha, P.K.; Zhou, F.B.; Kutiyal, R.S. . Dept. of Engineering)
1993-11-01
High-speed maglev vehicles need a high level of safety that depends on the whole vehicle system's reliability. There are many ways of attaining high reliability for the system. Conventional method uses redundant hardware with majority vote logic circuits. Hardware redundancy costs more, weigh more and occupy more space than that of analytically redundant methods. Analytically redundant systems use parameter identification and state estimation methods based on the system models to detect and isolate the fault of instruments (sensors), actuator and components. In this paper the authors use the Luenberger observer to estimate three state variables of the electromagnetic suspension system: position (airgap), vehicle velocity, and vertical acceleration. These estimates are compared with the corresponding sensor outputs for fault detection. In this paper, they consider FDI of the accelerometer, the sensor which provides the ride quality.
NASA Technical Reports Server (NTRS)
Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony
1996-01-01
This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.
NASA Technical Reports Server (NTRS)
Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony
1996-01-01
This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that this basic methodology could be ported to distributed memory parallel computing architectures. In this paper, our concern will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.
An Extended Equation of State Modeling Method I. Pure Fluids
NASA Astrophysics Data System (ADS)
Scalabrin, G.; Bettio, L.; Marchi, P.; Piazza, L.; Richon, D.
2006-09-01
A new technique is proposed here to represent the thermodynamic surface of a pure fluid in the fundamental Helmholtz energy form. The peculiarity of the present method is the extension of a generic equation of state for the target fluid, which is assumed as the basic equation, through the distortion of its independent variables by individual shape functions, which are represented by a neural network used as function approximator. The basic equation of state for the target fluid can have the simple functional form of a cubic equation, as, for instance, the Soave-Redlich-Kwong equation assumed in the present study. A set of nine fluids including hydrocarbons, haloalkane refrigerants, and strongly polar substances has been considered. For each of them the model has been regressed and then validated against volumetric and caloric properties generated in the vapor, liquid, and supercritical regions from highly accurate dedicated equations of state. In comparison with the underlying cubic equation of state, the prediction accuracy is improved by a factor between 10 and 100, depending on the property and on the region. It has been verified that about 100 density experimental points, together with from 10 to 20 coexistence data, are sufficient to guarantee high prediction accuracy for different thermodynamic properties. The method is a promising modeling technique for the heuristic development of multiparameter dedicated equations of state from experimental data.
Tracking influential haze source areas in North China using an adjoint model, GRAPES-CUACE
NASA Astrophysics Data System (ADS)
An, X. Q.; Zhai, S. X.; Jin, M.; Gong, S. L.; Wang, Y.
2015-08-01
Based upon the adjoint theory, the adjoint of the aerosol module in the atmospheric chemical modeling system GRAPES-CUACE (Global/Regional Assimilation and PrEdiction System coupled with the CMA Unified Atmospheric Chemistry Environment) was developed and tested for its correctness. Through statistic comparison, BC (black carbon aerosol) concentrations simulated by GRAPES-CUACE were generally consistent with observations from Nanjiao (one urban observation station) and Shangdianzi (one rural observation station) stations. To track the most influential emission-sources regions and the most influential time intervals for the high BC concentration during the simulation period, the adjoint model was adopted to simulate the sensitivity of average BC concentration over Beijing at the highest concentration time point (referred to as the Objective Function) with respect to BC emission amount over Beijing-Tianjin-Hebei region. Four types of regions were selected based on administrative division and sensitivity coefficient distribution. The adjoint model was used to quantify the effects of emission-sources reduction in different time intervals over different regions by one independent simulation. Effects of different emission reduction strategies based on adjoint sensitivity information show that the more influential regions (regions with relatively larger sensitivity coefficients) do not necessarily correspond to the administrative regions, and the influence effectiveness of sensitivity-oriented regions was greater than the administrative divisions. The influence of emissions on the objective function decreases sharply approximately for the pollutants emitted 17-18 h ago in this episode. Therefore, controlling critical emission regions during critical time intervals on the basis of adjoint sensitivity analysis is much more efficient than controlling administrative specified regions during an experiential time period.
Constrained Path Quantum Monte Carlo Method for Fermion Ground States
NASA Astrophysics Data System (ADS)
Zhang, Shiwei; Carlson, J.; Gubernatis, J. E.
1995-05-01
We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wave function by a branching random walk in an over-complete basis space of Slater determinants. By constraining the determinants according to a trial wave function \\|ΨT>, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if \\|ΨT> is exact. We report results on the two-dimensional Hubbard model up to size 16×16, for various electron fillings and interaction strengths.
Stratospheric Water Vapor and the Asian Monsoon: An Adjoint Model Investigation
NASA Technical Reports Server (NTRS)
Olsen, Mark A.; Andrews, Arlyn E.
2003-01-01
A new adjoint model of the Goddard Parameterized Chemistry and Transport Model is used to investigate the role that the Asian monsoon plays in transporting water to the stratosphere. The adjoint model provides a unique perspective compared to non-diffusive and non-mixing Lagrangian trajectory analysis. The quantity of water vapor transported from the monsoon and the pathways into the stratosphere are examined. The emphasis is on the amount of water originating from the monsoon that contributes to the tropical tape recorder signal. The cross-tropopause flux of water from the monsoon to the midlatitude lower stratosphere will also be discussed.
Constrained path Monte Carlo method for fermion ground states
Zhang, S. |; Carlson, J.; Gubernatis, J.E.
1997-03-01
We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an overcomplete basis of Slater determinants. By constraining the determinants according to a trial wave function {vert_bar}{psi}{sub T}{r_angle}, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if {vert_bar}{psi}{sub T}{r_angle} is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to 16{times}16 and for various electron fillings and interaction strengths. With simple single-determinant wave functions as {vert_bar}{psi}{sub T}{r_angle}, the method yields accurate (often to within a few percent) estimates of the ground-state energy as well as correlation functions, such as those for electron pairing. We conclude by discussing possible extensions of the algorithm. {copyright} {ital 1997} {ital The American Physical Society}
Constrained path Monte Carlo method for fermion ground states
NASA Astrophysics Data System (ADS)
Zhang, Shiwei; Carlson, J.; Gubernatis, J. E.
1997-03-01
We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an overcomplete basis of Slater determinants. By constraining the determinants according to a trial wave function \\|ψT>, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if \\|ψT> is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to 16×16 and for various electron fillings and interaction strengths. With simple single-determinant wave functions as \\|ψT>, the method yields accurate (often to within a few percent) estimates of the ground-state energy as well as correlation functions, such as those for electron pairing. We conclude by discussing possible extensions of the algorithm.
Demographic estimation methods for plants with unobservable life-states
Kery, M.; Gregg, K.B.; Schaub, M.
2005-01-01
Demographic estimation of vital parameters in plants with an unobservable dormant state is complicated, because time of death is not known. Conventional methods assume that death occurs at a particular time after a plant has last been seen aboveground but the consequences of assuming a particular duration of dormancy have never been tested. Capture-recapture methods do not make assumptions about time of death; however, problems with parameter estimability have not yet been resolved. To date, a critical comparative assessment of these methods is lacking. We analysed data from a 10 year study of Cleistes bifaria, a terrestrial orchid with frequent dormancy, and compared demographic estimates obtained by five varieties of the conventional methods, and two capture-recapture methods. All conventional methods produced spurious unity survival estimates for some years or for some states, and estimates of demographic rates sensitive to the time of death assumption. In contrast, capture-recapture methods are more parsimonious in terms of assumptions, are based on well founded theory and did not produce spurious estimates. In Cleistes, dormant episodes lasted for 1-4 years (mean 1.4, SD 0.74). The capture-recapture models estimated ramet survival rate at 0.86 (SE~ 0.01), ranging from 0.77-0.94 (SEs # 0.1) in anyone year. The average fraction dormant was estimated at 30% (SE 1.5), ranging 16 -47% (SEs # 5.1) in anyone year. Multistate capture-recapture models showed that survival rates were positively related to precipitation in the current year, but transition rates were more strongly related to precipitation in the previous than in the current year, with more ramets going dormant following dry years. Not all capture-recapture models of interest have estimable parameters; for instance, without excavating plants in years when they do not appear aboveground, it is not possible to obtain independent timespecific survival estimates for dormant plants. We introduce rigorous
NASA Astrophysics Data System (ADS)
Galanti, Eli; Kaspi, Yohai
2015-11-01
, the flexibility of the adjoint method allows for a wide range of dynamical setups, so that when new observations and physical understanding will arise, these constraints could be easily implemented and used to better decipher Jupiter flow dynamics.
NASA Astrophysics Data System (ADS)
Xu, X.; Wang, J.; Henze, D. K.; Qu, W.; Kopacz, M.
2012-12-01
The knowledge of aerosol emissions from both natural and anthropogenic sources are needed to study the impacts of tropospheric aerosol on atmospheric composition, climate, and human health, but large uncertainties persist in quantifying the aerosol sources with the current bottom-up methods. This study presents a new top-down approach that spatially constrains the amount of aerosol emissions from satellite (MODIS) observed reflectance with the adjoint of a chemistry transport model (GEOS-Chem). We apply this technique with a one-month case study (April 2008) over the East Asia. The bottom-up estimated sulfate-nitrate-ammonium precursors, such as sulfur dioxide (SO2), ammonia (NH3), and nitrogen oxides (NOx), all from INTEX-B 2006 inventory, emissions of black carbon (BC), organic carbon (OC) from Bond-2007 inventory, and mineral dust simulated from DEAD dust mobilization scheme, are spatially optimized from the GEOS-Chem model and its adjoint constrained by the aerosol optical depth (AOD) that are derived from MODIS reflectance with the GEOS-Chem aerosol single scattering properties. The adjoint inverse modeling for the study period yields notable decreases in anthropogenic aerosol emissions over China: 436 Gg (33.5%) for SO2, 378 Gg (34.5%) for NH3, 319 (18.8%) for NOx, 10 Gg (9.1%) for BC, and 30 Gg (15.0%) for OC. The total amount of the mineral dust emission is reduced by 56.4% from the DEAD mobilization module which simulates dust production of 19020 Gg. Sub-regional adjustments are significant and directions of changes are spatially different. The model simulation with optimized aerosol emissions shows much better agreement with independent observations from sun-spectrophotometer observed AOD from AERONET, MISR (Multi-angle Imaging SpectroRadiometer) AOD, OMI (Ozone Monitoring Instrument) NO2 and SO2 columns, and surface aerosol concentrations measured over both anthropogenic pollution and dust source regions. Assuming the used bottom-up anthropogenic
Ashton, C.J.; Muckerman, J.T.; Schubert, F.E.
1984-12-15
A systematic scheme is developed for the incorporation into quasiclassical trajectory (QCT) methodology of recent advances in the understanding of vibrationally adiabatic barriers in collinear atom + diatom reactions. The resulting hybrid QCT method centers on a definite set of rules for optimally combining the results of forward and reverse trajectory calculations. It is argued, and demonstrated by practical examples, that the hybrid method will give a more consistently reliable account of the threshold behavior of collinear reaction cross sections than the conventional QCT method. Extension of the method to the three dimensional F+H/sub 2/ reaction gives similarly encouraging results, both for state to state reaction cross sections and for rate constants.
Ashton, C.J.; Muckerman, J.T.; Schubert, F.E.
1984-12-15
A systematic scheme is developed for the incorporation into quasiclassical trajectory (QCT) methodology of recent advances in the understanding of vibrationally adiabatic barriers in collinear atom + diatom reactions. The resulting hybrid QCT method centers on a definite set of rules for optimally combining the results of forward and reverse trajectory calculations. It is argued, and demonstrated by practical examples, that the hybrid method will give a more consistently reliable account of the threshold behavior of collinear reaction cross sections than the conventional QCT method. Extension of the method to the three dimensional F + H/sub 2/ reaction gives similarly encouraging results, both for state to state reaction cross sections and for rate constants. 43 references, 15 figures, 4 tables.
NASA Astrophysics Data System (ADS)
Ng, Cheuk-Yiu
2014-04-01
Recent advances in high-resolution photoionization, photoelectron, and photodissociation studies based on single-photon vacuum ultraviolet (VUV) and two-color infrared (IR)-VUV, visible (Vis)-ultraviolet (UV), and VUV-VUV laser excitations are illustrated with selected examples. VUV laser photoionization coupled with velocity-map-imaging threshold photoelectron (VMI-TPE) detection can achieve comparable energy resolution but has higher-detection sensitivities than those observed in VUV laser pulsed field ionization photoelectron (PFI-PE) measurements. For molecules with known intermediate states, IR-VUV and Vis-UV excitation schemes are highly sensitive for rovibronically selected and resolved PFI-PE studies. The successful applications of the VUV-PFI-PE, VUV-VMI-TPE, and Vis-UV-PFI-PE methods to state-resolved and state-to-state photoelectron studies of transient radicals and transitional metal-containing molecules are highlighted. The most recently established VUV-VUV pump-probe time-slice VMI photoion method is shown to be promising for state-to-state photodissociation studies of small molecules relevant to planetary atmospheres and for the fundamental understanding of photodissociation dynamics.
Electron excitation from ground state to first excited state: Bohmian mechanics method
NASA Astrophysics Data System (ADS)
Yang, Song; Shuang, Zhao; Fu-Ming, Guo; Yu-Jun, Yang; Su-Yu, Li
2016-03-01
The excitation process of electrons from the ground state to the first excited state via the resonant laser pulse is investigated by the Bohmian mechanics method. It is found that the Bohmian particles far away from the nucleus are easier to be excited and are excited firstly, while the Bohmian particles in the ground state is subject to a strong quantum force at a certain moment, being excited to the first excited state instantaneously. A detailed analysis for one of the trajectories is made, and finally we present the space and energy distribution of 2000 Bohmian particles at several typical instants and analyze their dynamical process at these moments. Project supported by the Doctoral Research Start-up Funding of Northeast Dianli University, China (Grant No. BSJXM-201332), the National Natural Science Foundation of China (Grant Nos. 11547114, 11534004, 11474129, 11274141, 11447192, and 11304116), and the Graduate Innovation Fund of Jilin University, China (Grant No. 2015091).
NASA Astrophysics Data System (ADS)
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.
Accelerating forward and adjoint simulations of seismic wave propagation on large GPU-clusters
NASA Astrophysics Data System (ADS)
Peter, D. B.; Rietmann, M.; Charles, J.; Messmer, P.; Komatitsch, D.; Schenk, O.; Tromp, J.
2012-12-01
In seismic tomography, waveform inversions require accurate simulations of seismic wave propagation in complex media.The current versions of our spectral-element method (SEM) packages, the local-scale code SPECFEM3D and the global-scale code SPECFEM3D_GLOBE, are widely used open-source community codes which simulate seismic wave propagation for local-, regional- and global-scale applications. These numerical simulations compute highly accurate seismic wavefields, accounting for fully 3D Earth models. However, code performance often governs whether seismic inversions become feasible or remain elusive. We report here on extending these high-order finite-element packages to further exploit graphic processing units (GPUs) and perform numerical simulations of seismic wave propagation on large GPU clusters. These enhanced packages can be readily run either on multi-core CPUs only or together with many-core GPU acceleration devices. One of the challenges in parallelizing finite element codes is the potential for race conditions during the assembly phase. We therefore investigated different methods such as mesh coloring or atomic updates on the GPU. In order to achieve strong scaling, we needed to ensure good overlap of data motion at all levels, including internode and host-accelerator transfers. These new MPI/CUDA solvers exhibit excellent scalability and achieve speedup on a node-to-node basis over the carefully tuned equivalent multi-core MPI solver. We present case studies run on a Cray XK6 GPU architecture up to 896 nodes to demonstrate the performance of both the forward and adjoint functionality of the code packages. Running simulations on such dedicated GPU clusters further reduces computation times and pushes seismic inversions into a new, higher frequency realm.
Analysis of Correlated Coupling of Monte Carlo Forward and Adjoint Histories
Ueki, Taro; Hoogenboom, J.E.; Kloosterman, J. L.
2001-02-15
In Monte Carlo correlated coupling, forward and adjoint particle histories are initiated in exactly opposite directions at an arbitrarily placed surface between a physical source and a physical detector. It is shown that this coupling calculation can become more efficient than standard forward calculations. In many cases, the basic form of correlated coupling is less efficient than standard forward calculations. This inherent inefficiency can be overcome by applying a black absorber perturbation to either the forward or the adjoint problem and by processing the product of batch averages as one statistical entity. The usage of the black absorber is based on the invariance of the response flow integral with a material perturbation in either the physical detector side volume in the forward problem or the physical source side volume in the adjoint problem. The batch-average product processing makes use of a quadratic increase of the nonzero coupled-score probability. All the developments have been done in such a way that improved efficiency schemes available in widely distributed Monte Carlo codes can be applied to both the forward and adjoint simulations. Also, the physical meaning of the black absorber perturbation is interpreted based on surface crossing and is numerically validated. In addition, the immediate reflection at the intermediate surface with a controlled direction change is investigated within the invariance framework. This approach can be advantageous for a void streaming problem.
Canonical quantization of lattice Higgs-Maxwell-Chern-Simons fields: Krein Self-adjointness
Bowman, Daniel A.; Challifour, John L.
2006-10-15
It is shown how techniques from constructive quantum field theory may be applied to indefinite metric gauge theories in Hilbert space for the case of a Higgs-Maxwell-Chern-Simons theory on a lattice. The Hamiltonian operator is shown to be Krein essentially self-adjoint by means of unbounded but Krein unitary transformations relating the Hamiltonian to an essentially maximal accretive operator.
NASA Astrophysics Data System (ADS)
Marotzke, Jochem; Giering, Ralf; Zhang, Kate Q.; Stammer, Detlef; Hill, Chris; Lee, Tong
1999-12-01
We first describe the principles and practical considerations behind the computer generation of the adjoint to the Massachusetts Institute of Technology ocean general circulation model (GCM) using R. Giering's software tool Tangent-Linear and Adjoint Model Compiler (TAMC). The TAMC's recipe for (FORTRAN-) line-by-line generation of adjoint code is explained by interpreting an adjoint model strictly as the operator that gives the sensitivity of the output of a model to its input. Then, the sensitivity of 1993 annual mean heat transport across 29°N in the Atlantic, to the hydrography on January 1, 1993, is calculated from a global solution of the GCM. The "kinematic sensitivity" to initial temperature variations is isolated, showing how the latter would influence heat transport if they did not affect the density and hence the flow. Over 1 year the heat transport at 29°N is influenced kinematically from regions up to 20° upstream in the western boundary current and up to 5° upstream in the interior. In contrast, the dynamical influences of initial temperature (and salinity) perturbations spread from as far as the rim of the Labrador Sea to the 29°N section along the western boundary. The sensitivities calculated with the adjoint compare excellently to those from a perturbation calculation with the dynamical model. Perturbations in initial interior salinity influence meridional overturning and heat transport when they have propagated to the western boundary and can thus influence the integrated east-west density difference. Our results support the notion that boundary monitoring of meridional mass and heat transports is feasible.
Method for joining metal by solid-state bonding
Burkhart, L. Elkin; Fultz, Chester R.; Maulden, Kerry A.
1979-01-01
The present development is directed to a method for joining metal at relatively low temperatures by solid-state bonding. Planar surfaces of the metal workpieces are placed in a parallel abutting relationship with one another. A load is applied to at least one of the workpieces for forcing the workpieces together while one of the workpieces is relatively slowly oscillated in a rotary motion over a distance of about 1.degree.. After a preselected number of oscillations, the rotary motion is terminated and the bond between the abutting surfaces is effected. An additional load may be applied to facilitate the bond after terminating the rotary motion.
Wavelet-based multiscale adjoint waveform-difference tomography using body and surface waves
NASA Astrophysics Data System (ADS)
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.
A rejection method for selection of scattered states
NASA Astrophysics Data System (ADS)
Lawson, William S.
1994-05-01
A rejection method is presented that sidesteps much of the labor necessary in the usual techniques for choosing a scattered state after an electron-phonon collision with full band structure. The phonon wave number is chosen randomly, then tested to see if the resultant collision will satisfy energy conservation to within some accuracy. If not, the collision is rejected, and if so, then the wave number is adjusted in order to enforce energy conservation more precisely. The price one pays is in a high rejection rate. If the cost of a rejection is small, however, this rejection rate can be tolerated. This method will not compete with analytical models (near valley minima), but may outperform the more usual techniques. Accuracies of a few percent are practical. Simulations were preformed with the first conduction band of gallium arsenide.
Reliable Transition State Searches Integrated with the Growing String Method.
Zimmerman, Paul
2013-07-01
The growing string method (GSM) is highly useful for locating reaction paths connecting two molecular intermediates. GSM has often been used in a two-step procedure to locate exact transition states (TS), where GSM creates a quality initial structure for a local TS search. This procedure and others like it, however, do not always converge to the desired transition state because the local search is sensitive to the quality of the initial guess. This article describes an integrated technique for simultaneous reaction path and exact transition state search. This is achieved by implementing an eigenvector following optimization algorithm in internal coordinates with Hessian update techniques. After partial convergence of the string, an exact saddle point search begins under the constraint that the maximized eigenmode of the TS node Hessian has significant overlap with the string tangent near the TS. Subsequent optimization maintains connectivity of the string to the TS as well as locks in the TS direction, all but eliminating the possibility that the local search leads to the wrong TS. To verify the robustness of this approach, reaction paths and TSs are found for a benchmark set of more than 100 elementary reactions. PMID:26583985
The use of aerospace methods for forest state assessment.
Isaev, A S
1988-01-01
Siberian forests occupy a significant part of the Asian continent. Their role as an essential component of the Earth's surface, biomass and oxygen producer is increasing annually. Expanded reproduction of taiga forests necessitated by the intensive development of Siberian productive forces, results in an evergrowing need of forest productivity constancy and increase. Proper forest exploitation is a crucial part of the solution of such important problems as the rational use of land and water resources, stable crop yields, and the creation of favourable conditions for human life.To solve these important economic problems, the Siberian branch of the USSR Academy of Sciences has devised a long-term programme of ecological monitoring of Siberian forest resources using aerospace techniques. The programme provides for the establishment and improvement of ecogeographical and physicotechnological principles of the remote sensing of forests and the development of fundamental forest-biological research based on new methodologies, the results of which are used to solve urgent forestry and nature protection problems. The research is carried out in the following major directions: studying spectral characteristics of forest vegetation for forest-state indication; thematic mapping of taiga territories; assessing biological productivity of natural complexes; environmental state monitoring; fire protection of forests; pest and disease control; developin instruments and methods for automatized aerospace data processing for real-time use.We consider forest-state monitoring to be one of the crucial tools in providing the optimum use of forest ecosystems for resource and ecological functions. PMID:24248966
NASA Astrophysics Data System (ADS)
Maziero, Jonas
2015-12-01
The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here, we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sampling of unbiased discrete probability distributions (DPD). Afterwards, the creation of random density matrices is addressed. In this context, we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random DPDs and random unitary matrices. In the sequence, the Bloch vector parametrization method is described. This approach, despite being useful in several instances, is not in general convenient for RQS generation. In the last part of the article, we regard the overparametrized method (OPM) and the related Ginibre and Bures techniques. The OPM can be used to create random positive semidefinite matrices with unit trace from randomly produced general complex matrices in a simple way that is friendly for numerical implementations. We consider a physically relevant issue related to the possible domains that may be used for the real and imaginary parts of the elements of such general complex matrices. Subsequently, a too fast concentration of measure in the quantum state space that appears in this parametrization is noticed.
State-of-the-art methods for multiphase flow pipelines
Crowley, C.J.; Barry, J.J.; Rothe, P.H.
1989-08-01
This report is the culmination of work on Design Methods for Multiphase Flow in Gas Pipelines'' sponsored by the Pipeline Research Committee of the American Gas Association on projects PR 172--609 and PR 172--904. Results from a series of projects to obtain pipeline data in the field, collect operating pipeline data, perform key laboratory experiments at prototypical conditions (large pipe size and high gas density), and to develop and recommend design methods over the past several years have been synthesized to create this report. Technical supervision of these projects has been provided by the Two-Phase Flow Supervisory Committee. This report concisely documents the state of the art in two-phase flow methods, in a manner suitable for use by analysts who want to develop computerized methods to perform the multiphase calculations. This document updates a previous report prepared approximately four years ago (Crowley and Rothe, 1986). Detailed background discussion of the development and selection of the multiphase models is presented in Volume 3 of that reference.
Hyperbolic method for magnetic reconnection process in steady state magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Baty, Hubert; Nishikawa, Hiroaki
2016-06-01
A recent numerical approach for solving the advection-diffusion and Navier-Stokes equations is extended for the first time to a magnetohydrodynamic (MHD) model, aiming in particular consistent improvements over classical methods for investigating the magnetic reconnection process. In this study, we mainly focus on a two-dimensional incompressible set of resistive MHD equations written in flux-vorticity scalar variables. The originality of the method is based on hyperbolic reformulation of the dissipative terms, leading to the construction of an equivalent hyperbolic first-order (spatial derivatives) system. This enables the use of approximate Riemann solvers for handling dissipative and advective flux in the same way. A simple second-order finite-volume discretization on rectangular grids using an upwind flux is employed. The advantages of this method are illustrated by a comparison to two particular analytical steady state solutions of the inviscid magnetic reconnection mechanism, namely the magnetic annihilation and the reconnective diffusion problems. In particular, the numerical solution is obtained with the same order of accuracy for the solution and gradient for a wide range of magnetic Reynolds numbers, without any deterioration characteristic of more conventional schemes. The amelioration of the hyperbolic method and its extension to time-dependent MHD problems related to solar flares mechanisms is also discussed.
Perturbation method to calculate the density of states
NASA Astrophysics Data System (ADS)
Persson, Rasmus A. X.
2012-12-01
Monte Carlo switching moves (“perturbations”) are defined between two or more classical Hamiltonians sharing a common ground-state energy. The ratio of the density of states (DOS) of one system to that of another is related to the ensemble averages of the microcanonical acceptance probabilities of switching between these Hamiltonians, analogously to the case of Bennett's acceptance ratio method for the canonical ensemble [C. H. Bennett, J. Comput. Phys.JCTPAH0021-999110.1016/0021-9991(76)90078-4 22, 245 (1976)]. Thus, if the DOS of one of the systems is known, one obtains those of the others and, hence, the partition functions. As a simple test case, the vapor pressure of an anharmonic Einstein crystal is computed, using the harmonic Einstein crystal as the reference system in one dimension; an auxiliary calculation is also performed in three dimensions. As a further example of the algorithm, the energy dependence of the ratio of the DOS of the square-well and hard-sphere tetradecamers is determined, from which the temperature dependence of the constant-volume heat capacity of the square-well system is calculated and compared with canonical Metropolis Monte Carlo estimates. For these cases and reference systems, the perturbation calculations exhibit a higher degree of convergence per Monte Carlo cycle than Wang-Landau (WL) sampling, although for the one-dimensional oscillator the WL sampling is ultimately more efficient for long runs. Last, we calculate the vapor pressure of liquid gold using an empirical Sutton-Chen many-body potential and the ideal gas as the reference state. Although this proves the general applicability of the method, by its inherent perturbation approach the algorithm is suitable for those particular cases where the properties of a related system are well known.
Nodal weighting factor method for ex-core fast neutron fluence evaluation
Chiang, R. T.
2012-07-01
The nodal weighting factor method is developed for evaluating ex-core fast neutron flux in a nuclear reactor by utilizing adjoint neutron flux, a fictitious unit detector cross section for neutron energy above 1 or 0.1 MeV, the unit fission source, and relative assembly nodal powers. The method determines each nodal weighting factor for ex-core neutron fast flux evaluation by solving the steady-state adjoint neutron transport equation with a fictitious unit detector cross section for neutron energy above 1 or 0.1 MeV as the adjoint source, by integrating the unit fission source with a typical fission spectrum to the solved adjoint flux over all energies, all angles and given nodal volume, and by dividing it with the sum of all nodal weighting factors, which is a normalization factor. Then, the fast neutron flux can be obtained by summing the various relative nodal powers times the corresponding nodal weighting factors of the adjacent significantly contributed peripheral assembly nodes and times a proper fast neutron attenuation coefficient over an operating period. A generic set of nodal weighting factors can be used to evaluate neutron fluence at the same location for similar core design and fuel cycles, but the set of nodal weighting factors needs to be re-calibrated for a transition-fuel-cycle. This newly developed nodal weighting factor method should be a useful and simplified tool for evaluating fast neutron fluence at selected locations of interest in ex-core components of contemporary nuclear power reactors. (authors)
Finn, John M.
2015-03-15
Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012
Finn, John M.
2015-03-01
Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a 'special divergence-free' property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. Wemore » also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Ref. [11], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Ref. [35], appears to work very well.« less
Systematic variational method for statistical nonlinear state and parameter estimation
NASA Astrophysics Data System (ADS)
Ye, Jingxin; Rey, Daniel; Kadakia, Nirag; Eldridge, Michael; Morone, Uriel I.; Rozdeba, Paul; Abarbanel, Henry D. I.; Quinn, John C.
2015-11-01
In statistical data assimilation one evaluates the conditional expected values, conditioned on measurements, of interesting quantities on the path of a model through observation and prediction windows. This often requires working with very high dimensional integrals in the discrete time descriptions of the observations and model dynamics, which become functional integrals in the continuous-time limit. Two familiar methods for performing these integrals include (1) Monte Carlo calculations and (2) variational approximations using the method of Laplace plus perturbative corrections to the dominant contributions. We attend here to aspects of the Laplace approximation and develop an annealing method for locating the variational path satisfying the Euler-Lagrange equations that comprises the major contribution to the integrals. This begins with the identification of the minimum action path starting with a situation where the model dynamics is totally unresolved in state space, and the consistent minimum of the variational problem is known. We then proceed to slowly increase the model resolution, seeking to remain in the basin of the minimum action path, until a path that gives the dominant contribution to the integral is identified. After a discussion of some general issues, we give examples of the assimilation process for some simple, instructive models from the geophysical literature. Then we explore a slightly richer model of the same type with two distinct time scales. This is followed by a model characterizing the biophysics of individual neurons.
Systematic variational method for statistical nonlinear state and parameter estimation.
Ye, Jingxin; Rey, Daniel; Kadakia, Nirag; Eldridge, Michael; Morone, Uriel I; Rozdeba, Paul; Abarbanel, Henry D I; Quinn, John C
2015-11-01
In statistical data assimilation one evaluates the conditional expected values, conditioned on measurements, of interesting quantities on the path of a model through observation and prediction windows. This often requires working with very high dimensional integrals in the discrete time descriptions of the observations and model dynamics, which become functional integrals in the continuous-time limit. Two familiar methods for performing these integrals include (1) Monte Carlo calculations and (2) variational approximations using the method of Laplace plus perturbative corrections to the dominant contributions. We attend here to aspects of the Laplace approximation and develop an annealing method for locating the variational path satisfying the Euler-Lagrange equations that comprises the major contribution to the integrals. This begins with the identification of the minimum action path starting with a situation where the model dynamics is totally unresolved in state space, and the consistent minimum of the variational problem is known. We then proceed to slowly increase the model resolution, seeking to remain in the basin of the minimum action path, until a path that gives the dominant contribution to the integral is identified. After a discussion of some general issues, we give examples of the assimilation process for some simple, instructive models from the geophysical literature. Then we explore a slightly richer model of the same type with two distinct time scales. This is followed by a model characterizing the biophysics of individual neurons. PMID:26651756
NASA Astrophysics Data System (ADS)
Pankratov, Oleg; Kuvshinov, Alexey
2015-03-01
3-D electromagnetic (EM) studies of the Earth have advanced significantly over the past decade. Despite a certain success of the 3-D EM inversions of real data sets, the quantitative assessment of the recovered models is still a challenging problem. It is known that one can gain valuable information about model uncertainties from the analysis of Hessian matrix. However, even with modern computational capabilities the calculation of the Hessian matrix based on numerical differentiation is extremely time consuming. Much more efficient way to compute the Hessian matrix is provided by an `adjoint sources' methodology. The computation of Hessian matrix (and Hessian-vector products) using adjoint formulation is now well-established approach, especially in seismic inverse modelling. As for EM inverse modelling we did not find in the literature a description of the approach, which would allow EM researchers to apply this methodology in a straightforward manner to their scenario of interest. In the paper, we present formalism for the efficient calculation of the Hessian matrix using adjoint sources approach. We also show how this technique can be implemented to calculate multiple Hessian-vector products very efficiently. The formalism is general in the sense that it allows to work with responses that arise in EM problem set-ups either with natural- or controlled-source excitations. The formalism allows for various types of parametrization of the 3-D conductivity distribution. Using this methodology one can readily obtain appropriate formulae for the specific sounding methods. To illustrate the concept we provide such formulae for two EM techniques: magnetotellurics and controlled-source sounding with vertical magnetic dipole as a source.
Dietze, K.; Fort, E.; Rahlfs, S.; Rimpault, G.; Salvatores, M.
1994-12-31
The Rossendorf RRRJSEG configurations characterized by, energy-independent or continuously rising adjoint spectra have been recalculated using the full European scheme JEF2/ECCO/ERANOS. C/E-values are given for structural materials and fission product nuclides using the results of sample reactivity measurements at the central position of these configurations. Due to the specially designed adjoint spectra, capture or scattering cross- sections can be checked separately. Recommendations for data corrections are given based on perturbation theory calculations.
Fast state-space methods for inferring dendritic synaptic connectivity.
Pakman, Ari; Huggins, Jonathan; Smith, Carl; Paninski, Liam
2014-06-01
We present fast methods for filtering voltage measurements and performing optimal inference of the location and strength of synaptic connections in large dendritic trees. Given noisy, subsampled voltage observations we develop fast l1-penalized regression methods for Kalman state-space models of the neuron voltage dynamics. The value of the l1-penalty parameter is chosen using cross-validation or, for low signal-to-noise ratio, a Mallows' Cp-like criterion. Using low-rank approximations, we reduce the inference runtime from cubic to linear in the number of dendritic compartments. We also present an alternative, fully Bayesian approach to the inference problem using a spike-and-slab prior. We illustrate our results with simulations on toy and real neuronal geometries. We consider observation schemes that either scan the dendritic geometry uniformly or measure linear combinations of voltages across several locations with random coefficients. For the latter, we show how to choose the coefficients to offset the correlation between successive measurements imposed by the neuron dynamics. This results in a "compressed sensing" observation scheme, with an important reduction in the number of measurements required to infer the synaptic weights. PMID:24077932
Methods to determine hydration states of minerals and cement hydrates
Baquerizo, Luis G.; Matschei, Thomas; Scrivener, Karen L.; Saeidpour, Mahsa; Thorell, Alva; Wadsö, Lars
2014-11-15
This paper describes a novel approach to the quantitative investigation of the impact of varying relative humidity (RH) and temperature on the structure and thermodynamic properties of salts and crystalline cement hydrates in different hydration states (i.e. varying molar water contents). The multi-method approach developed here is capable of deriving physico-chemical boundary conditions and the thermodynamic properties of hydrated phases, many of which are currently missing from or insufficiently reported in the literature. As an example the approach was applied to monosulfoaluminate, a phase typically found in hydrated cement pastes. New data on the dehydration and rehydration of monosulfoaluminate are presented. Some of the methods used were validated with the system Na{sub 2}SO{sub 4}–H{sub 2}O and new data related to the absorption of water by anhydrous sodium sulfate are presented. The methodology and data reported here should permit better modeling of the volume stability of cementitious systems exposed to various different climatic conditions.
Adjoint Airfoil Optimization of Darrieus-Type Vertical Axis Wind Turbine
NASA Astrophysics Data System (ADS)
Fuchs, Roman; Nordborg, Henrik
2012-11-01
We present the feasibility of using an adjoint solver to optimize the torque of a Darrieus-type vertical axis wind turbine (VAWT). We start with a 2D cross section of a symmetrical airfoil and restrict us to low solidity ratios to minimize blade vortex interactions. The adjoint solver of the ANSYS FLUENT software package computes the sensitivities of airfoil surface forces based on a steady flow field. Hence, we find the torque of a full revolution using a weighted average of the sensitivities at different wind speeds and angles of attack. The weights are computed analytically, and the range of angles of attack is given by the tip speed ratio. Then the airfoil geometry is evolved, and the proposed methodology is evaluated by transient simulations.
Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas
NASA Technical Reports Server (NTRS)
Rallabhandi, Sriram K.
2013-01-01
This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent area cost functionals are discussed and further refined using ground loudness based objectives.
Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
NASA Astrophysics Data System (ADS)
Mantile, Andrea; Posilicano, Andrea; Sini, Mourad
2016-07-01
The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the "free" operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.
Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
Catterall, Simon; Galvez, Richard; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2010-08-26
We report on the results of numerical simulations of SU(N) lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with {Lambda} sites in each direction in the large-N limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of {Lambda}, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume 2{sup 4}. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit N {yields} {infinity}, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.
Adjoint-based uncertainty quantification and sensitivity analysis for reactor depletion calculations
NASA Astrophysics Data System (ADS)
Stripling, Hayes Franklin
Depletion calculations for nuclear reactors model the dynamic coupling between the material composition and neutron flux and help predict reactor performance and safety characteristics. In order to be trusted as reliable predictive tools and inputs to licensing and operational decisions, the simulations must include an accurate and holistic quantification of errors and uncertainties in its outputs. Uncertainty quantification is a formidable challenge in large, realistic reactor models because of the large number of unknowns and myriad sources of uncertainty and error. We present a framework for performing efficient uncertainty quantification in depletion problems using an adjoint approach, with emphasis on high-fidelity calculations using advanced massively parallel computing architectures. This approach calls for a solution to two systems of equations: (a) the forward, engineering system that models the reactor, and (b) the adjoint system, which is mathematically related to but different from the forward system. We use the solutions of these systems to produce sensitivity and error estimates at a cost that does not grow rapidly with the number of uncertain inputs. We present the framework in a general fashion and apply it to both the source-driven and k-eigenvalue forms of the depletion equations. We describe the implementation and verification of solvers for the forward and ad- joint equations in the PDT code, and we test the algorithms on realistic reactor analysis problems. We demonstrate a new approach for reducing the memory and I/O demands on the host machine, which can be overwhelming for typical adjoint algorithms. Our conclusion is that adjoint depletion calculations using full transport solutions are not only computationally tractable, they are the most attractive option for performing uncertainty quantification on high-fidelity reactor analysis problems.
Towards Adjoint Finite Source Inversion: Application to the 2011 M9 Tohoku Earthquake
NASA Astrophysics Data System (ADS)
Somala, S.; Galvez, P.; Inbal, A.; Ampuero, J. P.; Lapusta, N.
2011-12-01
The recent 2011 M9 Tohoku, Japan, earthquake was recorded by thousands of sensors at near-fault distance, including broad band, strong motion and continuous GPS sensors. This event provides a unique opportunity to image the earthquake rupture process with high resolution. In order to enable the exploitation of the immense dataset available, orders of magnitude larger than in previous earthquakes, we are developing a scalable source inversion procedure based on time-reversal adjoint inversion. We adopt the linear least squares formulation of the source inversion problem, whose basic unknown is the spatio-temporal distribution of slip rate. We formulate an iterative conjugate gradient procedure to minimize the L2 norm of ground velocity residuals between data and synthetics. Each iteration involves one time-reversal (adjoint) and one forward simulation. Exploiting the time-reversal symmetry and the reciprocity principle of elastodynamics, the adjoint is computed by a wave propagation simulation in which time-reversed seismogram residuals are imposed as point forces at the stations simulated. The resulting fault tractions on a locked fault are the adjoint fields, related to the gradient of the misfit function with respect to the model. The simulations are performed with a recent extension of the SPECFEM3D spectral element code to dynamic and kinematic finite sources on unstructured meshes (Galvez et al, session S24 of this meeting). The non-planar geometry of the megathrust fault is accounted for in the spectral element mesh (generated with CUBIT). The subsurface structure is incorporated, on a coarse scale, using regional 3D velocity models, e.g. from the Japan Seismic Hazard Information Station (J-SHIS) website. We will report on the results of our initial efforts, focused on exploiting the continuous 1 Hz GPS signals recorded in Japan to understand the low frequency aspects of the rupture process of the 2011 Tohoku earthquake.
Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
Bagarello, F.
2015-05-15
We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered in the paper. An example taken from the literature is discussed in detail.
Inequivalence of unitarity and self-adjointness: An example in quantum cosmology
Lemos, N.A. )
1990-02-15
An example of a quantum cosmological model is presented whose dynamics is unitary although the time-dependent Hamiltonian operator fails to be self-adjoint (because it is not defined) for a particular value of {ital t}. The model is shown to be singular, and this disproves a conjecture put forward by Gotay and Demaret to the effect that unitary quantum dynamics in a slow-time'' gauge is always nonsingular.
NASA Astrophysics Data System (ADS)
Wells, K. C.; Millet, D. B.; Bousserez, N.; Henze, D. K.; Chaliyakunnel, S.; Griffis, T. J.; Dlugokencky, E. J.; Prinn, R. G.; O'Doherty, S.; Weiss, R. F.; Dutton, G. S.; Elkins, J. W.; Krummel, P. B.; Langenfelds, R. L.; Steele, P.
2015-12-01
Nitrous oxide (N2O) is a long-lived greenhouse gas with a global warming potential approximately 300 times that of CO2, and plays a key role in stratospheric ozone depletion. Human perturbation of the nitrogen cycle has led to a rise in atmospheric N2O, but large uncertainties exist in the spatial and temporal distribution of its emissions. Here we employ a 4D-Var inversion framework for N2O based on the GEOS-Chem chemical transport model and its adjoint to derive new constraints on the space-time distribution of global land and ocean N2O fluxes. Based on an ensemble of global surface measurements, we find that emissions are overestimated over Northern Hemisphere land areas and underestimated in the Southern Hemisphere. Assigning these biases to particular land or ocean regions is more difficult given the long lifetime of N2O. To quantitatively evaluate where the current N2O observing network provides local and regional emission constraints, we apply a new, efficient information content analysis technique involving radial basis functions. The technique yields optimal state vector dimensions for N2O source inversions, with model grid cells grouped in space and time according to the resolution that can actually be provided by the network of global observations. We then use these optimal state vectors in an analytical inversion to refine current top-down emission estimates.
Chou, Chia-Chun; Kouri, Donald J
2013-04-25
We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom. PMID:23531015
Self-adjointness of the Fourier expansion of quantized interaction field Lagrangians
Paneitz, S. M.; Segal, I. E.
1983-01-01
Regularity properties significantly stronger than were previously known are developed for four-dimensional non-linear conformally invariant quantized fields. The Fourier coefficients of the interaction Lagrangian in the interaction representation—i.e., evaluated after substitution of the associated quantized free field—is a densely defined operator on the associated free field Hilbert space K. These Fourier coefficients are with respect to a natural basis in the universal cosmos ˜M, to which such fields canonically and maximally extend from Minkowski space-time M0, which is covariantly a submanifold of ˜M. However, conformally invariant free fields over M0 and ˜M are canonically identifiable. The kth Fourier coefficient of the interaction Lagrangian has domain inclusive of all vectors in K to which arbitrary powers of the free hamiltonian in ˜M are applicable. Its adjoint in the rigorous Hilbert space sense is a-k in the case of a hermitian Lagrangian. In particular (k = 0) the leading term in the perturbative expansion of the S-matrix for a conformally invariant quantized field in M0 is a self-adjoint operator. Thus, e.g., if ϕ(x) denotes the free massless neutral scalar field in M0, then ∫M0:ϕ(x)4:d4x is a self-adjoint operator. No coupling constant renormalization is involved here. PMID:16593346
NASA Astrophysics Data System (ADS)
Boulin, P. F.; Bretonnier, P.; Gland, N.
2010-12-01
Very low permeability geomaterials (order of nanoDarcy (10-21 m2)), such as clays rocks, are studied for many industrial applications such as production from unconventional reserves of oil and gas, CO2 geological storage and deep geological disposal of high-level long-lived nuclear wastes. For these last two applications, clay efficiency as barrier relies mainly on their very low permeability. Laboratory measurement of low permeability to water (below 10-19 m2) remains a technical challenge. Some authors argue that steady state methods are irrelevant due to the time required to stabilize water fluxes in such low permeability media. Most of the authors measuring low permeabilities use a transient technique called pulse decay. This study aims to compare objectively these different types of permeability tests performed on a single clay sample. For the steady state method, a high precision pump was used to impose a pressure gradient and to measure the small resulting water flow rate at steady state. We show that with a suitable set-up, the steady state method enables to measure a very low permeability of 8 10-22 m2 in a period of three days. For a comparable duration, the pulse decay test, most commonly used for such low permeability measurements, provides only an average estimate of the permeability. Permeability measurements by pulse decay require to perform simulations to interpret the pressure relaxation signals. Many uncertainties remain such as the determination of the reservoirs storage factor, micro leakage effect, or the determination of the initial pulse pressure. All these uncertainties have a very significant impact on the determination of sample permeability and specific storage. Opposite to the wide-spread idea that transient techniques are required to measure very low permeability, we show that direct steady state measurement of water permeability with suitable equipments can be much faster and more accurate than measurement by pulse decay, especially in
The Methods and Effectiveness of State Licensing of Proprietary Institutions.
ERIC Educational Resources Information Center
State Higher Education Executive Officers Association.
A study was undertaken of proprietary school oversight and regulation in order to seek ways to improve state oversight of the proprietary sector. Twenty states participated in the study which used questionnaires sent to key state contact persons, telephone interviews conducted primarily with persons who had received the questionnaires and…
Laser viability method for red blood cell-state monitoring
NASA Astrophysics Data System (ADS)
Lapotko, Dmitry; Kuchinsky, Georgy; Antonishina, Elena; Scoromnik, Elena
1996-01-01
The method for RBC state control is based upon single cell viability control after illumination with laser pulse. Heat shock resulting from absorption of laser energy by a cell is considered as a cell load. This load acts from inside of the cell, is pulsed (10-5) and can be delivered directly to the chosen cells. The result of each illumination as cell survival or damage is controlled optically by monitoring the cells' response on a pulse through photothermal technique. Under fixed laser parameters the percentage of damaged cells is viability index (VI) for a certain cell population. The testing procedure includes consequential illumination of each cell in population and calculation of VI. Experimental set up is based upon optical microscope. Dual laser thermal lens technique is used for cell illumination and monitoring. For cell loading 5 ns pulses, 400 divided by 600 nm with energies up to 20 (mu) J are generated by tunable dye laser. Cell monitoring is realized with cw He-Ne (632.8 nm) laser and photodetector. All data acquisition routines are automated. Up to 3 cell suspensions can be studied in a multisample chamber designed to secure cells. An amount of cell suspension required is 1 (mu) l. One population test at a fixed wavelength takes 2 divided by 3 min. In experiments with rats, treated with LPS E. Coli injection to stimulate fever and a septic stress we found that variation of RBC viability becomes apparent in 20 - 30 min after injection, while the clinical changes (blood pressure, body temperature, skin temperature) become detectable after 1 hour. The results obtained show that the method can reveal additional properties of the cells most abundant for monitoring and diagnostic tasks.
Investigating Sensitivity to Saharan Dust in Tropical Cyclone Formation Using Nasa's Adjoint Model
NASA Technical Reports Server (NTRS)
Holdaway, Daniel
2015-01-01
As tropical cyclones develop from easterly waves coming of the coast of Africa they interact with dust from the Sahara desert. There is a long standing debate over whether this dust inhibits or advances the developing storm and how much influence it has. Dust can surround the storm and absorb incoming solar radiation, cooling the air below. As a result an energy source for the system is potentially diminished, inhibiting growth of the storm. Alternatively dust may interact with clouds through micro-physical processes, for example by causing more moisture to condense, potentially increasing the strength. As a result of climate change, concentrations and amount of dust in the atmosphere will likely change. It it is important to properly understand its effect on tropical storm formation. The adjoint of an atmospheric general circulation model provides a very powerful tool for investigating sensitivity to initial conditions. The National Aeronautics and Space Administration (NASA) has recently developed an adjoint version of the Goddard Earth Observing System version 5 (GEOS-5) dynamical core, convection scheme, cloud model and radiation schemes. This is extended so that the interaction between dust and radiation is also accounted for in the adjoint model. This provides a framework for examining the sensitivity to dust in the initial conditions. Specifically the set up allows for an investigation into the extent to which dust affects cyclone strength through absorption of radiation. In this work we investigate the validity of using an adjoint model for examining sensitivity to dust in hurricane formation. We present sensitivity results for a number of systems that developed during the Atlantic hurricane season of 2006. During this period there was a significant outbreak of Saharan dust and it is has been argued that this outbreak was responsible for the relatively calm season. This period was also covered by an extensive observation campaign. It is shown that the
NASA Astrophysics Data System (ADS)
Mazaheri, K.; Nejati, A.; Chaharlang Kiani, K.; Taheri, R.
2015-08-01
A shock control bump (SCB) is a flow control method which uses local small deformations in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, we have used a multi-point adjoint optimization scheme to optimize shape and location of the SCB. Practically, this introduces transonic airfoils equipped with the SCB which are simultaneously optimized for different off-design transonic flight conditions. Here, we use this optimization algorithm to enhance and optimize the performance of SCBs in two benchmark airfoils, i.e., RAE-2822 and NACA-64A010, over a wide range of off-design Mach numbers. All results are compared with the usual single-point optimization. We use numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm to find the optimum location and shape of the SCB. We show that the application of SCBs may increase the aerodynamic performance of an RAE-2822 airfoil by 21.9 and by 22.8 % for a NACA-64A010 airfoil compared to the no-bump design in a particular flight condition. We have also investigated the simultaneous usage of two bumps for the upper and the lower surfaces of the airfoil. This has resulted in a 26.1 % improvement for the RAE-2822 compared to the clean airfoil in one flight condition.
NASA Technical Reports Server (NTRS)
Wang, Jun; Xu, Xiaoguang; Henze, Daven K.; Zeng, Jing; Ji, Qiang; Tsay, Si-Chee; Huang, Jianping
2012-01-01
Predicting the influences of dust on atmospheric composition, climate, and human health requires accurate knowledge of dust emissions, but large uncertainties persist in quantifying mineral sources. This study presents a new method for combined use of satellite-measured radiances and inverse modeling to spatially constrain the amount and location of dust emissions. The technique is illustrated with a case study in May 2008; the dust emissions in Taklimakan and Gobi deserts are spatially optimized using the GEOSChem chemical transport model and its adjoint constrained by aerosol optical depth (AOD) that are derived over the downwind dark-surface region in China from MODIS (Moderate Resolution Imaging Spectroradiometer) reflectance with the aerosol single scattering properties consistent with GEOS-chem. The adjoint inverse modeling yields an overall 51% decrease in prior dust emissions estimated by GEOS-Chem over the Taklimakan-Gobi area, with more significant reductions south of the Gobi Desert. The model simulation with optimized dust emissions shows much better agreement with independent observations from MISR (Multi-angle Imaging SpectroRadiometer) AOD and MODIS Deep Blue AOD over the dust source region and surface PM10 concentrations. The technique of this study can be applied to global multi-sensor remote sensing data for constraining dust emissions at various temporal and spatial scales, and hence improving the quantification of dust effects on climate, air quality, and human health.
NASA Astrophysics Data System (ADS)
Wang, Jun; Xu, Xiaoguang; Henze, Daven K.; Zeng, Jing; Ji, Qiang; Tsay, Si-Chee; Huang, Jianping
2012-04-01
Predicting the influences of dust on atmospheric composition, climate, and human health requires accurate knowledge of dust emissions, but large uncertainties persist in quantifying mineral sources. This study presents a new method for combined use of satellite-measured radiances and inverse modeling to spatially constrain the amount and location of dust emissions. The technique is illustrated with a case study in May 2008; the dust emissions in Taklimakan and Gobi deserts are spatially optimized using the GEOS-Chem chemical transport model and its adjoint constrained by aerosol optical depth (AOD) that are derived over the downwind dark-surface region in China from MODIS (Moderate Resolution Imaging Spectroradiometer) reflectance with the aerosol single scattering properties consistent with GEOS-chem. The adjoint inverse modeling yields an overall 51% decrease in prior dust emissions estimated by GEOS-Chem over the Taklimakan-Gobi area, with more significant reductions south of the Gobi Desert. The model simulation with optimized dust emissions shows much better agreement with independent observations from MISR (Multi-angle Imaging SpectroRadiometer) AOD and MODIS Deep Blue AOD over the dust source region and surface PM10 concentrations. The technique of this study can be applied to global multi-sensor remote sensing data for constraining dust emissions at various temporal and spatial scales, and hence improving the quantification of dust effects on climate, air quality, and human health.
CMT Source Inversions for Massive Data Assimilation in Global Adjoint Tomography
NASA Astrophysics Data System (ADS)
Lei, W.; Ruan, Y.; Bozdag, E.; Lefebvre, M. P.; Smith, J. A.; Modrak, R. T.; Komatitsch, D.; Song, X.; Liu, Q.; Tromp, J.; Peter, D. B.
2015-12-01
Full Waveform Inversion (FWI) is a vital tool for probing the Earth's interior and enhancing our knowledge of the underlying dynamical processes [e.g., Liu et al., 2012]. Using the adjoint tomography method, we have successfully obtained a first-generation global FWI model named M15 [Bozdag et al., 2015]. To achieve higher resolution of the emerging new structural features and to accommodate azimuthal anisotropy and anelasticity in the next-generation model, we expanded our database from 256 to 4,224 earthquakes. Previous studies have shown that ray-theory-based Centroid Moment Tensor (CMT) inversion algorithms can produce systematic biases in earthquake source parameters due to tradeoffs with 3D crustal and mantle heterogeneity [e.g., Hjorleifsdottir et al., 2010]. To reduce these well-known tradeoffs, we performed CMT inversions in our current 3D global model before resuming the structural inversion with the expanded database. Initial source parameters are selected from the global CMT database [Ekstrom et al., 2012], with moment magnitudes ranging from 5.5 to 7.0 and occurring between 1994 and 2015. Data from global and regional networks were retrieved from the IRIS DMC. Synthetic seismograms were generated based on the spectral-element-based seismic wave propagation solver (SPECFEM3D GLOBE) in model M15. We used a source inversion algorithm based on a waveform misfit function while allowing time shifts between data and synthetics to accommodate additional unmodeled 3D heterogeneity [Liu et al., 2004]. To accommodate the large number of earthquakes and time series (more than 10,000,000 records), we implemented a source inversion workflow based on the newly developed Adaptive Seismic Data Format (ASDF) [Krischer, Smith, et al., 2015] and ObsPy [Krischer et al., 2015]. In ASDF, each earthquake is associated with a single file, thereby eliminating I/O bottlenecks in the workflow and facilitating fast parallel processing. Our preliminary results indicate that errors
Dynamic State Estimation Utilizing High Performance Computing Methods
Schneider, Kevin P.; Huang, Zhenyu; Yang, Bo; Hauer, Matthew L.; Nieplocha, Jaroslaw
2009-03-18
The state estimation tools which are currently deployed in power system control rooms are based on a quasi-steady-state assumption. As a result, the suite of operational tools that rely on state estimation results as inputs do not have dynamic information available and their accuracy is compromised. This paper presents an overview of the Kalman Filtering process and then focuses on the implementation of the predication component on multiple processors.
NASA Astrophysics Data System (ADS)
Lapina, K.; Henze, D. K.; Milford, J. B.
2014-12-01
Frequent exposure to elevated levels of ozone leads to negative impacts on ecosystems including the loss of ozone-sensitive tree species and agricultural crops in many regions of the United States. Information on emission sources contributing to these losses is crucial for developing a successful strategy to mitigate the negative effects of ozone on vegetation. A cumulative ozone exposure metric, W126, has been considered by the US EPA for use as secondary ozone standard. The rural West of the US has been demonstrated to have an especially great potential for disconnect between attaining primary versus W126-based ozone standards. In this work we separate the relative impact of emissions sources for the W126 in the Western US using forward and adjoint simulations with the global chemical transport model GEOS-Chem. The obtained source contributions are separated by different locations, species, and sectors and are combined with representative concentration pathway (RCP) anthropogenic emission scenarios to project future changes in W126 through 2050. Focusing on the foreign influences we find that the change in Chinese emissions alone is projected to lead to up to 20% increase in the W126 levels in the West and is strongly dependent on the RCP scenario. We further use concentration-response functions based on the W126 index to estimate the loss of four ozone-sensitive species in the West - ponderosa pine, Douglas Fir, red alder and quacking aspen.
Lower bounds for eigenvalues of self-adjoint problems
Gundersen, Gary G.
1979-01-01
The equation y″ + [λ - q(x)]y = 0 on (0, ∞) or (-∞, ∞), in which q(x) → ∞ as x → ∞ or x → ± ∞, has a complete set of eigenfunctions with discrete eigenvalues {λn}n=0∞. We derive an inequality that contains λn, by using a quick and elementary method that does not employ a comparison theorem or assume anything special. Explicit lower bounds for λn can often be easily obtained, and three examples are given. The method also gives respectable lower bounds for λn in the classical Sturm—Liouville case. PMID:16592718
NASA Astrophysics Data System (ADS)
Stück, Arthur
2015-11-01
Inconsistent discrete expressions in the boundary treatment of Navier-Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection-diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yields second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier-Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.
NASA Astrophysics Data System (ADS)
Guerrette, J. J.; Henze, D. K.
2015-02-01
Here we present the online meteorology and chemistry adjoint and tangent linear model, WRFPLUS-Chem, which incorporates modules to treat boundary layer mixing, emission, aging, dry deposition, and advection of black carbon aerosol. We also develop land surface and surface layer adjoints to account for coupling between radiation and vertical mixing. Model performance is verified against finite difference derivative approximations. A second order checkpointing scheme is created to reduce computational costs and enable simulations longer than six hours. The adjoint is coupled to WRFDA-Chem, in order to conduct a sensitivity study of anthropogenic and biomass burning sources throughout California during the 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) field campaign. A cost function weighting scheme was devised to increase adjoint sensitivity robustness in future inverse modeling studies. Results of the sensitivity study show that, for this domain and time period, anthropogenic emissions are over predicted, while wildfire emissions are under predicted. We consider the diurnal variation in emission sensitivities to determine at what time sources should be scaled up or down. Also, adjoint sensitivities for two choices of land surface model indicate that emission inversion results would be sensitive to forward model configuration. The tools described here are the first step in conducting four-dimensional variational data assimilation in a coupled meteorology-chemistry model, which will potentially provide new constraints on aerosol precursor emissions and their distributions. Such analyses will be invaluable to assessments of particulate matter health and climate impacts.
A user's manual for MASH 1. 0: A Monte Carlo Adjoint Shielding Code System
Johnson, J.O.
1992-03-01
The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the dose importance'' of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.
Approximations of Strongly Continuous Families of Unbounded Self-Adjoint Operators
NASA Astrophysics Data System (ADS)
Ben-Artzi, Jonathan; Holding, Thomas
2016-07-01
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approximations is constructed. An important feature of these approximations is that they are valid for the entire family uniformly. An application of this result to the study of plasma instabilities is illustrated.
Self-adjointness and the Casimir effect with confined quantized spinor matter
NASA Astrophysics Data System (ADS)
Sitenko, Yurii A.
2016-01-01
A generalization of the MIT bag boundary condition for spinor matter is proposed basing on the requirement that the Dirac hamiltonian operator be self-adjoint. An influence of a background magnetic field on the vacuum of charged spinor matter confined between two parallel material plates is studied. Employing the most general set of boundary conditions at the plates in the case of the uniform magnetic field directed orthogonally to the plates, we find the pressure from the vacuum onto the plates. In physically plausible situations, the Casimir effect is shown to be repulsive, independently of a choice of boundary conditions and of a distance between the plates.
Approximations of Strongly Continuous Families of Unbounded Self-Adjoint Operators
NASA Astrophysics Data System (ADS)
Ben-Artzi, Jonathan; Holding, Thomas
2016-05-01
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approximations is constructed. An important feature of these approximations is that they are valid for the entire family uniformly. An application of this result to the study of plasma instabilities is illustrated.
Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter
Aoki, Hajime
2010-10-15
We formulate a Ginsparg-Wilson relation on a fuzzy 2-sphere for matter in the adjoint representation of the gauge group. Because of the Ginsparg-Wilson relation, an index theorem is satisfied. Our formulation is applicable to topologically nontrivial configurations as monopoles. It gives a solid basis for obtaining chiral fermions, which are an important ingredient of the standard model, from matrix model formulations of the superstring theory, such as the IIB matrix model, by considering topological configurations in the extra dimensions. We finally discuss whether this mechanism really works.
Adjoint transport calculations for sensitivity analysis of the Hiroshima air-over-ground environment
Broadhead, B.L.; Cacuci, D.G.; Pace, J.V. III
1984-01-01
A major effort within the US Dose Reassessment Program is aimed at recalculating the transport of initial nuclear radiation in an air-over-ground environment. This paper is the first report of results from adjoint calculations in the Hiroshima air-over-ground environment. The calculations use a Hiroshima/Nagasaki multi-element ground, ENDF/B-V nuclear data, one-dimensional ANISN flux weighting for neutron and gamma cross sections, a source obtained by two-dimensional hydrodynamic and three-dimensional transport calculations, and best-estimate atmospheric conditions from Japanese sources. 7 references, 2 figures.
A forward operator and its adjoint for GPS slant total delays
NASA Astrophysics Data System (ADS)
Zus, Florian; Dick, Galina; Heise, Stefan; Wickert, Jens
2015-05-01
In a recent study we developed a fast and accurate algorithm to compute Global Positioning System (GPS) Slant Total Delay (STDs) utilizing numerical weather model data. Having developed a forward operator we construct in this study the tangent linear (adjoint) operator by application of the chain rule of differential calculus in forward (reverse) mode. Armed with these operators we show in a simulation study the potential benefit of GPS STDs in inverse modeling. We conclude that the developed operators are tailored for three (four)-dimensional variational data assimilation and/or travel time tomography.
Infrared fixed point in SU(2) gauge theory with adjoint fermions
DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
2011-04-01
We apply Schroedinger-functional techniques to the SU(2) lattice gauge theory with N{sub f}=2 flavors of fermions in the adjoint representation. Our use of hypercubic smearing enables us to work at stronger couplings than did previous studies, before encountering a critical point and a bulk phase boundary. Measurement of the running coupling constant gives evidence of an infrared fixed point g{sub *} where 1/g{sub *}{sup 2}=0.20(4)(3). At the fixed point, we find a mass anomalous dimension {gamma}{sub m}(g{sub *})=0.31(6).
Pressure updating methods for the steady-state fluid equations
NASA Technical Reports Server (NTRS)
Fiterman, A.; Turkel, E.; Vatsa, V.
1995-01-01
We consider the steady state equations for a compressible fluid. Since we wish to solve for a range of speeds we must consider the equations in conservation form. For transonic speeds these equations are of mixed type. Hence, the usual approach is to add time derivatives to the steady state equations and then march these equations in time. One then adds a time derivative of the density to the continuity equation, a derivative of the momentum to the momentum equation and a derivative of the total energy to the energy equation. This choice is dictated by the time consistent equations. However, since we are only interested in the steady state this is not necessary. Thus we shall consider the possibility of adding a time derivative of the pressure to the continuity equation and similar modifications for the energy equation. This can then be generalized to adding combinations of time derivatives to each equation since these vanish in the steady state. When using acceleration techniques such as residual smoothing, multigrid, etc. these are applied to the pressure rather than the density. Hence, the code duplicates the behavior of the incompressible equations for low speeds.
Bound States of Dipolr Molecules Studied with the Berggren Expnsiion Method
Fossez, K.; Michel, N.; Nazarewicz, Witold
2013-01-01
Bound states of dipole-bound anions are studied by using a nonadiabatic pseudopotential method and the Berggren expansion involving bound states, decaying resonant states, and nonresonant scattering continuum. The method is benchmarked by using the traditional technique of direct integration of coupled-channel equations. A good agreement between the two methods has been found for well-bound states. For weakly bound subthreshold states with binding energies comparable to rotational energies of the anion, the direct integration approach breaks down and the Berggren expansion method becomes the tool of choice.
20 CFR 1001.150 - Method of calculating State basic grant awards.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 20 Employees' Benefits 3 2010-04-01 2010-04-01 false Method of calculating State basic grant... Grant Funds to State Agencies § 1001.150 Method of calculating State basic grant awards. (a) In... the Current Population Survey (CPS) and the unemployment data will be obtained from the Local...
Filatov, Michael; Huix-Rotllant, Miquel; Burghardt, Irene
2015-05-14
State-averaged (SA) variants of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, SA-REKS and state-interaction (SI)-SA-REKS, implement ensemble density functional theory for variationally obtaining excitation energies of molecular systems. In this work, the currently existing version of the SA-REKS method, which included only one excited state into the ensemble averaging, is extended by adding more excited states to the averaged energy functional. A general strategy for extension of the REKS-type methods to larger ensembles of ground and excited states is outlined and implemented in extended versions of the SA-REKS and SI-SA-REKS methods. The newly developed methods are tested in the calculation of several excited states of ground-state multi-reference systems, such as dissociating hydrogen molecule, and excited states of donor–acceptor molecular systems. For hydrogen molecule, the new method correctly reproduces the distance dependence of the lowest excited state energies and describes an avoided crossing between the doubly excited and singly excited states. For bithiophene–perylenediimide stacked complex, the SI-SA-REKS method correctly describes crossing between the locally excited state and the charge transfer excited state and yields vertical excitation energies in good agreement with the ab initio wavefunction methods.
Position sensitive solid-state photomultipliers, systems and methods
Shah, Kanai S; Christian, James; Stapels, Christopher; Dokhale, Purushottam; McClish, Mickel
2014-11-11
An integrated silicon solid state photomultiplier (SSPM) device includes a pixel unit including an array of more than 2.times.2 p-n photodiodes on a common substrate, a signal division network electrically connected to each photodiode, where the signal division network includes four output connections, a signal output measurement unit, a processing unit configured to identify the photodiode generating a signal or a center of mass of photodiodes generating a signal, and a global receiving unit.
Dupree, S. A.
1980-06-01
The use of adjoint techniques to determine the interaction of externally incident collimated beams of particles with cylindrical targets is a convenient means of examining a class of problems important in radiation transport studies. The theory relevant to such applications is derived, and a simple example involving a fissioning target is discussed. Results from both discrete ordinates and Monte Carlo transport-code calculations are presented, and comparisons are made with results obtained from forward calculations. The accuracy of the discrete ordinates adjoint results depends on the order of angular quadrature used in the calculation. Reasonable accuracy by using EQN quadratures can be expected from order S/sub 16/ or higher.
Hilbert-Schmidt Inner Product for an Adjoint Representation of the Quantum Algebra U⌣Q(SU2)
NASA Astrophysics Data System (ADS)
Fakhri, Hossein; Nouraddini, Mojtaba
2015-10-01
The Jordan-Schwinger realization of quantum algebra U⌣q(su2) is used to construct the irreducible submodule Tl of the adjoint representation in two different bases. The two bases are known as types of irreducible tensor operators of rank l which are related to each other by the involution map. The bases of the submodules are equipped with q-analogues of the Hilbert-Schmidt inner product and it is also shown that the adjoint representation corresponding to one of those submodules is a *-representation.
Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport
Liscum-Powell, J.L.; Lorence, L.J. Jr.; Morel, J.E.; Prinja, A.K.
1999-07-08
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{sub 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{sub n} discretization.
Improving the Fit of a Land-Surface Model to Data Using its Adjoint
NASA Astrophysics Data System (ADS)
Raoult, Nina; Jupp, Tim; Cox, Peter; Luke, Catherine
2016-04-01
Land-surface models (LSMs) are crucial components of the Earth System Models (ESMs) which are used to make coupled climate-carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. In this study, JULES is automatically differentiated using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimation system has been developed, to search for locally optimum parameter sets by calibrating against observations. We present an introduction to the adJULES system and demonstrate its ability to improve the model-data fit using eddy covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the 5 Plant Functional Types (PFTS) in JULES. The optimised PFT-specific parameters improve the performance of JULES over 90% of the FLUXNET sites used in the study. These reductions in error are shown and compared to reductions found due to site-specific optimisations. Finally, we show that calculation of the 2nd derivative of JULES allows us to produce posterior probability density functions of the parameters and how knowledge of parameter values is constrained by observations.
Improving the Fit of a Land-Surface Model to Data Using its Adjoint
NASA Astrophysics Data System (ADS)
Raoult, N.; Jupp, T. E.; Cox, P. M.; Luke, C.
2015-12-01
Land-surface models (LSMs) are of growing importance in the world of climate prediction. They are crucial components of larger Earth system models that are aimed at understanding the effects of land surface processes on the global carbon cycle. The Joint UK Land Environment Simulator (JULES) is the land-surface model used by the UK Met Office. It has been automatically differentiated using commercial software from FastOpt, resulting in an analytical gradient, or 'adjoint', of the model. Using this adjoint, the adJULES parameter estimation system has been developed, to search for locally optimum parameter sets by calibrating against observations. adJULES presents an opportunity to confront JULES with many different observations, and make improvements to the model parameterisation. In the newest version of adJULES, multiple sites can be used in the calibration, to giving a generic set of parameters that can be generalised over plant functional types. We present an introduction to the adJULES system and its applications to data from a variety of flux tower sites. We show that calculation of the 2nd derivative of JULES allows us to produce posterior probability density functions of the parameters and how knowledge of parameter values is constrained by observations.
Paulot, Fabien; Jacob, Daniel J; Henze, Daven K
2013-04-01
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. PMID:23458244
Adjoint S U (5 ) GUT model with T7 flavor symmetry
NASA Astrophysics Data System (ADS)
Arbeláez, Carolina; Cárcamo Hernández, A. E.; Kovalenko, Sergey; Schmidt, Iván
2015-12-01
We propose an adjoint S U (5 ) GUT model with a T7 family symmetry and an extra Z2⊗Z3⊗Z4⊗Z4'⊗Z12 discrete group that successfully describes the prevailing Standard Model fermion mass and mixing pattern. The observed hierarchy of the charged fermion masses and the quark mixing angles arises from the Z3⊗Z4⊗Z12 symmetry breaking, which occurs near the GUT scale. The light active neutrino masses are generated by type-I and type-III seesaw mechanisms mediated by the fermionic S U (5 ) singlet and the adjoint 24 -plet. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be mβ β=4 and 50 meV for the normal and the inverted neutrino spectra, respectively. We construct several benchmark scenarios, which lead to S U (5 ) gauge coupling unification and are compatible with the known phenomenological constraints originating from the lightness of neutrinos, proton decay, dark matter, etc. These scenarios contain TeV-scale colored fields, which could give rise to a visible signal or be stringently constrained at the LHC.
NASA Astrophysics Data System (ADS)
Capps, S. L.; Pinder, R. W.; Loughlin, D. H.; Bash, J. O.; Turner, M. D.; Henze, D. K.; Percell, P.; Zhao, S.; Russell, M. G.; Hakami, A.
2014-12-01
Tropospheric ozone (O3) affects the productivity of ecosystems in addition to degrading human health. Concentrations of this pollutant are significantly influenced by precursor gas emissions, many of which emanate from energy production and use processes. Energy system optimization models could inform policy decisions that are intended to reduce these harmful effects if the contribution of precursor gas emissions to human health and ecosystem degradation could be elucidated. Nevertheless, determining the degree to which precursor gas emissions harm ecosystems and human health is challenging because of the photochemical production of ozone and the distinct mechanisms by which ozone causes harm to different crops, tree species, and humans. Here, the adjoint of a regional chemical transport model is employed to efficiently calculate the relative influences of ozone precursor gas emissions on ecosystem and human health degradation, which informs an energy system optimization. Specifically, for the summer of 2007 the Community Multiscale Air Quality (CMAQ) model adjoint is used to calculate the location- and sector-specific influences of precursor gas emissions on potential productivity losses for the major crops and sensitive tree species as well as human mortality attributable to chronic ozone exposure in the continental U.S. The atmospheric concentrations are evaluated with 12-km horizontal resolution with crop production and timber biomass data gridded similarly. These location-specific factors inform the energy production and use technologies selected in the MARKet ALlocation (MARKAL) model.
Eguchi-Kawai reduction with one flavor of adjoint Möbius fermion
NASA Astrophysics Data System (ADS)
Cunningham, William; Giedt, Joel
2016-02-01
We study the single site lattice gauge theory of S U (N ) coupled to one Dirac flavor of fermion in the adjoint representation. We utilize Möbius fermions for this study, and accelerate the calculation with graphics processing units. Our Monte Carlo simulations indicate that for sufficiently large inverse 't Hooft coupling b =1 /g2N , and for N ≤10 the distribution of traced Polyakov loops has "fingers" that extend from the origin. However, in the massless case the distribution of eigenvalues of the untraced Polyakov loop becomes uniform at large N , indicating preservation of center symmetry in the thermodynamic limit. By contrast, for a large mass and large b , the distribution is highly nonuniform in the same limit, indicating spontaneous center symmetry breaking. These conclusions are confirmed by comparing to the quenched case, as well as by examining another observable based on the average value of the modulus of the traced Polyakov loop. The result of this investigation is that with massless adjoint fermions center symmetry is stabilized and the Eguchi-Kawai reduction should be successful; this is in agreement with most other studies.
Green's function method for single-particle resonant states in relativistic mean field theory
NASA Astrophysics Data System (ADS)
Sun, T. T.; Zhang, S. Q.; Zhang, Y.; Hu, J. N.; Meng, J.
2014-11-01
Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particles as a reference, the energies and widths of single-particle resonant states are extracted from the density of states without any ambiguity. As an example, the energies and widths for single-neutron resonant states in 120Sn are compared with those obtained by the scattering phase-shift method, the analytic continuation in the coupling constant approach, the real stabilization method, and the complex scaling method. Excellent agreements with these methods are found for the energies and widths of single-neutron resonant states.
NASA Astrophysics Data System (ADS)
Wang, Y.; Forsyth, D. W.; Savage, B.
2010-12-01
In our previous surface wave study in Gulf of California area, we developed a moderate-resolution 3D shear velocity model by employing two-plane wave field representation array technique and 2D finite frequency kernels based on Born’s approximation. Using both amplitude and phase information of 22-111s teleseismic Rayleigh wave, we were able to constrain a lateral resolution on the order of 100 km in the upper 160 km depth. In order to enhance resolution beneath the highly heterogeneous Gulf region, we carry on further study using Spectral element method (SEM) for forward wave propagation simulation and adjoint method for tomographic inversion. The code we are using is SPECFEM3D_GLOBE by Komatitsch and Tromp et al. To enhance the resolution in the Gulf, we will minimize the waveform difference between the regional earthquake seismograms, recorded by NARS-Baja seismic array and stations in southern California, and synthetic seismograms simulated by SEM, to iteratively update the current model based on an adjoint inversion. Taking our current 3D moderate-resolution model as starting point and a recently developed crustal structure of Gulf region should help to reduce the number of iterations. There are two reasons that resolution should be enhanced compared to surface wave tomography: first, regional events contain more high frequency signals than teleseismic events; second, SEM is a full waveform synthesis method avoiding many of the usual approximations in tomographic studies. Improved tomographic images of 3D velocity heterogeneities in the upper mantle of Gulf of California will help to identify compositional and temperature variations, leading to a better understanding of mantle dynamics in the region.
49 CFR 1135.2 - Revenue Shortfall Allocation Method: Annual State tax information.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 8 2010-10-01 2010-10-01 false Revenue Shortfall Allocation Method: Annual State... RECOVERY PROCEDURES § 1135.2 Revenue Shortfall Allocation Method: Annual State tax information. (a) To enable the Board to calculate the revenue shortfall allocation method (RSAM), which is one of the...
The present state and future directions of PDF methods
NASA Technical Reports Server (NTRS)
Pope, S. B.
1992-01-01
The objectives of the workshop are presented in viewgraph format, as is this entire article. The objectives are to discuss the present status and the future direction of various levels of engineering turbulence modeling related to Computational Fluid Dynamics (CFD) computations for propulsion; to assure that combustion is an essential part of propulsion; and to discuss Probability Density Function (PDF) methods for turbulent combustion. Essential to the integration of turbulent combustion models is the development of turbulent model, chemical kinetics, and numerical method. Some turbulent combustion models typically used in industry are the k-epsilon turbulent model, the equilibrium/mixing limited combustion, and the finite volume codes.
Concrete Mixing Methods and Concrete Mixers: State of the Art.
Ferraris, C F
2001-01-01
As for all materials, the performance of concrete is determined by its microstructure. Its microstructure is determined by its composition, its curing conditions, and also by the mixing method and mixer conditions used to process the concrete. This paper gives an overview of the various types of mixing methods and concrete mixers commercially available used by the concrete industry. There are two main types of mixers used: batch mixers and continuous mixers. Batch mixers are the most common. To determine the mixing method best suited for a specific application, factors to be considered include: location of the construction site (distance from the batching plant), the amount of concrete needed, the construction schedule (volume of concrete needed per hour), and the cost. Ultimately, the quality of the concrete produced determines its performance after placement. An important measure of the quality is the homogeneity of the material after mixing. This paper will review mixing methods in regards to the quality of the concrete produced. Some procedures used to determine the effectiveness of the mixing will be examined. PMID:27500029
Concrete Mixing Methods and Concrete Mixers: State of the Art
Ferraris, Chiara F.
2001-01-01
As for all materials, the performance of concrete is determined by its microstructure. Its microstructure is determined by its composition, its curing conditions, and also by the mixing method and mixer conditions used to process the concrete. This paper gives an overview of the various types of mixing methods and concrete mixers commercially available used by the concrete industry. There are two main types of mixers used: batch mixers and continuous mixers. Batch mixers are the most common. To determine the mixing method best suited for a specific application, factors to be considered include: location of the construction site (distance from the batching plant), the amount of concrete needed, the construction schedule (volume of concrete needed per hour), and the cost. Ultimately, the quality of the concrete produced determines its performance after placement. An important measure of the quality is the homogeneity of the material after mixing. This paper will review mixing methods in regards to the quality of the concrete produced. Some procedures used to determine the effectiveness of the mixing will be examined.
HT2DINV: A 2D forward and inverse code for steady-state and transient hydraulic tomography problems
NASA Astrophysics Data System (ADS)
Soueid Ahmed, A.; Jardani, A.; Revil, A.; Dupont, J. P.
2015-12-01
Hydraulic tomography is a technique used to characterize the spatial heterogeneities of storativity and transmissivity fields. The responses of an aquifer to a source of hydraulic stimulations are used to recover the features of the estimated fields using inverse techniques. We developed a 2D free source Matlab package for performing hydraulic tomography analysis in steady state and transient regimes. The package uses the finite elements method to solve the ground water flow equation for simple or complex geometries accounting for the anisotropy of the material properties. The inverse problem is based on implementing the geostatistical quasi-linear approach of Kitanidis combined with the adjoint-state method to compute the required sensitivity matrices. For undetermined inverse problems, the adjoint-state method provides a faster and more accurate approach for the evaluation of sensitivity matrices compared with the finite differences method. Our methodology is organized in a way that permits the end-user to activate parallel computing in order to reduce the computational burden. Three case studies are investigated demonstrating the robustness and efficiency of our approach for inverting hydraulic parameters.
Development of Methods of Characterizing Coal in Its Plastic State
NASA Technical Reports Server (NTRS)
Lloyd, W. G.
1978-01-01
Coal in its plastic state (typically 400-460 C) was examined by the isothermal Gieseler plastometry of seven selected coals of widely varying plastic properties. Kinetic models were proposed for the isothermal plastometric curves. Plastic behavior was compared with a variety of laboratory analyses and characterizations of these coals, including classical coal analysis; mineral analysis; microstructural analysis (extractable fractions, surface area measurement, and petrographic analysis); and thermal analysis (thermogravimetric analysis, thermomechanical analysis, and differential scanning calorimetry). The phenomenon of a sharp, large, poorly reproducible exotherm in the differential scanning calorimetric analysis of coking coals was examined. Several coal extrudates show mineral distribution, organic maceral composition and overall calorific value to be little affected by 800 F extrusion. Volatile matter and plastic properties are moderately reduced, and the network structure (as gauged by extractables) appears to be slightly degraded in the extrusion process.
An Expansion of the Trait-State-Occasion Model: Accounting for Shared Method Variance
ERIC Educational Resources Information Center
LaGrange, Beth; Cole, David A.
2008-01-01
This article examines 4 approaches for explaining shared method variance, each applied to a longitudinal trait-state-occasion (TSO) model. Many approaches have been developed to account for shared method variance in multitrait-multimethod (MTMM) data. Some of these MTMM approaches (correlated method, orthogonal method, correlated method minus one,…
NASA Astrophysics Data System (ADS)
Galanti, Eli; Kaspi, Yohai
2014-05-01
In approximately three years Juno and Cassini will both perform close flybys of Jupiter and Saturn respectively, obtaining a high precision gravity spectrum for these planets. This data can be used to estimate the depth of the observed flows on these planets. Here we use a hierarchy of dynamical models in order to relate the three-dimensional flow to perturbations of the density field, and therefore to the gravity field. The models are set up to allow either zonal flow only, or a full horizontal flow in both zonal and meridional directions based on the observed cloud-level winds. In addition, dynamical perturbations resulting from the the non-spherical shape of the planets are accounted for.In order to invert the gravity field to be measured by Juno and Cassini into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration of the dynamical model. This tool can be used for examination of various scenarios, including cases in which the depth of the winds depend on latitudinal position. We show that given the expected sensitivities of Juno and Cassini, it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn. This hold for a large range of zonal wind possible penetration depths, from ~100km to ~10000km, and for winds depth that vary with latitude. This method proves to be useful also when Incorporating the full horizontal flow, and thus taking into account gravity perturbations that vary with longitude. We show that our adjoint based inversion method allows not only to estimate the depth of the circulation, but allows via iterations with the spacecraft trajectory estimation model to improve the inferred gravity field.
NASA Astrophysics Data System (ADS)
Galanti, Eli; Kaspi, Yohai
2014-11-01
In approximately two years Juno and Cassini will both perform close flybys of Jupiter and Saturn respectively, obtaining a high precision gravity spectrum for these planets. This data can be used to estimate the depth of the observed flows on these planets. Here we use a hierarchy of dynamical models in order to relate the three dimensional flow to perturbations of the density field, and therefore to the gravity field. The models are set up to allow either zonal flow only, or a full horizontal flow in both zonal and meridional directions based on the observed cloud-level winds. In addition, dynamical perturbations resulting from the non-spherical shape of the planets are accounted for. In order to invert the gravity field to be measured by Juno and Cassini into the 3D circulation, an adjoint inverse model is constructed for the dynamical model, thus allowing backward integration of the dynamical model. This tool can be used for examination of various scenarios, including cases in which the depth of the winds depends on latitudinal position.We show that given the expected sensitivities of Juno and Cassini, it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn. This holds for a large range of zonal wind possible penetration depths, from ~100km to ~10000km, and for winds depth that vary with latitude. This method proves to be useful also when incorporating the full horizontal flow, and thus taking into account gravity perturbations that vary with longitude. We show that our adjoint based inversion method allows not only to estimate the depth of the circulation, but allows via iterations with the spacecraft trajectory estimation model to improve the inferred gravity field.
Solid state neutron detector and method for use
Doty, F. Patrick; Zwieback, Ilya; Ruderman, Warren
2002-01-01
Crystals of lithium tetraborate or alpha-barium borate had been found to be neutron detecting materials. The crystals are prepared using known crystal growing techniques, wherein the process does not include the common practice of using a fluxing agent, such as sodium oxide or sodium fluoride, to reduce the melting temperature of the crystalline compound. Crystals prepared by this method can be sliced into thin single or polycrystalline wafers, or ground to a powder and prepared as a sintered compact or a print paste, and then configured with appropriate electronic hardware, in order to function as neutron detectors.
Electromagnetic methods for development and production: State of the art
Wilt, M.; Alumbaugh, D.
1997-10-01
Electromagnetic (EM) methods, long used for borehole logging as a formation evaluation tool in developed oil fields, are rarely applied in surface or crosshole configurations or applied in cased wells. This is largely due to the high levels of cultural noise and the preponderance of steel well casing. However, recent experimental success with crosshole EM systems for water and steam flood monitoring using fiberglass cased wells has shown promise in applying these techniques to development and production (D & P) problems. This paper describes technological solutions that will allow for successful application of EM techniques in oil fields, despite surface noise and steel casing. First an example sites the application of long offset logging to map resistivity structure away from the borehole. Next, a successful application of crosshole EM where one of the wells is steel cased is described. The potential application of earth`s field nuclear magnetic resonance (NMR) to map fluid saturation at large distances from the boreholes is also discussed.
20 CFR 1001.150 - Method of calculating State basic grant awards.
Code of Federal Regulations, 2011 CFR
2011-04-01
... Grant Funds to State Agencies § 1001.150 Method of calculating State basic grant awards. (a) In... awards. 1001.150 Section 1001.150 Employees' Benefits OFFICE OF THE ASSISTANT SECRETARY FOR VETERANS... established by § 1001.151(a). The intent will be to award these undistributed basic grant funds to States...
20 CFR 1001.150 - Method of calculating State basic grant awards.
Code of Federal Regulations, 2014 CFR
2014-04-01
... Grant Funds to State Agencies § 1001.150 Method of calculating State basic grant awards. (a) In... awards. 1001.150 Section 1001.150 Employees' Benefits OFFICE OF THE ASSISTANT SECRETARY FOR VETERANS... established by § 1001.151(a). The intent will be to award these undistributed basic grant funds to States...
20 CFR 1001.150 - Method of calculating State basic grant awards.
Code of Federal Regulations, 2012 CFR
2012-04-01
... Grant Funds to State Agencies § 1001.150 Method of calculating State basic grant awards. (a) In... awards. 1001.150 Section 1001.150 Employees' Benefits OFFICE OF THE ASSISTANT SECRETARY FOR VETERANS... established by § 1001.151(a). The intent will be to award these undistributed basic grant funds to States...
20 CFR 1001.150 - Method of calculating State basic grant awards.
Code of Federal Regulations, 2013 CFR
2013-04-01
... Grant Funds to State Agencies § 1001.150 Method of calculating State basic grant awards. (a) In... awards. 1001.150 Section 1001.150 Employees' Benefits OFFICE OF THE ASSISTANT SECRETARY FOR VETERANS... established by § 1001.151(a). The intent will be to award these undistributed basic grant funds to States...
Topology optimization in thermal-fluid flow using the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Yaji, Kentaro; Yamada, Takayuki; Yoshino, Masato; Matsumoto, Toshiro; Izui, Kazuhiro; Nishiwaki, Shinji
2016-02-01
This paper proposes a topology optimization method for thermal-fluid flow problems using the lattice Boltzmann method (LBM). The design sensitivities are derived based on the adjoint lattice Boltzmann method (ALBM), whose basic idea is that the adjoint problem is first formulated using a continuous adjoint approach, and the adjoint problem is then solved using the LBM. In this paper, the discrete velocity Boltzmann equation, in which only the particle velocities are discretized, is introduced to the ALBM to deal with the various boundary conditions in the LBM. The novel sensitivity analysis is applied in two flow channel topology optimization problems: 1) a pressure drop minimization problem, and 2) a heat exchange maximization problem. Several numerical examples are provided to confirm the utility of the proposed method.
Discrete Adjoint-Based Design for Unsteady Turbulent Flows On Dynamic Overset Unstructured Grids
NASA Technical Reports Server (NTRS)
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.
Nuclide Importance and the Steady-State Burnup Equation
Sekimoto, Hiroshi; Nemoto, Atsushi
2000-05-15
Conventional methods for evaluating some characteristic values of nuclides relating to burnup in a given neutron spectrum are reviewed in a mathematically systematic way, and a new method based on the importance theory is proposed. In this method, these characteristic values of a nuclide are equivalent to the importances of the nuclide. By solving the equation adjoint to the steady-state burnup equation with a properly chosen source term, the importances for all nuclides are obtained simultaneously.The fission number importance, net neutron importance, fission neutron importance, and absorbed neutron importance are evaluated and discussed. The net neutron importance is a measure directly estimating neutron economy, and it can be evaluated simply by calculating the fission neutron importance minus the absorbed neutron importance, where only the absorbed neutron importance depends on the fission product. The fission neutron importance and absorbed neutron importance are analyzed separately, and detailed discussions of the fission product effects are given for the absorbed neutron importance.
NASA Astrophysics Data System (ADS)
Chen, Min; Niu, Fenglin; Liu, Qinya; Tromp, Jeroen; Zheng, Xiufen
2015-03-01
We present a 3-D radially anisotropic model of the crust and mantle beneath East Asia down to 900 km depth. Adjoint tomography based on a spectral element method is applied to a phenomenal data set comprising 1.7 million frequency-dependent traveltime measurements from waveforms of 227 earthquakes recorded by 1869 stations. Compressional wave speeds are independently constrained and simultaneously inverted along with shear wave speeds (VSH and VSV) using the same waveform data set with comparable resolution. After 20 iterations, the new model (named EARA2014) exhibits sharp and detailed wave speed anomalies with improved correlations with surface tectonic units compared to previous models. In the upper 100 km, high wave speed (high-V) anomalies correlate very well with the Junggar and Tarim Basins, the Ordos Block, and the Yangtze Platform, while strong low wave speed (low-V) anomalies coincide with the Qiangtang Block, the Songpan Ganzi Fold Belt, the Chuandian Block, the Altay-Sayan Mountain Range, and the back-arc basins along the Pacific and Philippine Sea Plate margins. At greater depths, narrow high-V anomalies correspond to major subduction zones and broad high-V anomalies to cratonic roots in the upper mantle and fragmented slabs in the mantle transition zone. In particular, EARA2014 reveals a strong high-V structure beneath Tibet, appearing below 100 km depth and extending to the bottom of the mantle transition zone, and laterally spanning across the Lhasa and Qiangtang Blocks. In this paper we emphasize technical aspects of the model construction and provide a general discussion through comparisons.
A User's Manual for MASH V1.5 - A Monte Carlo Adjoint Shielding Code System
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.
NASA Astrophysics Data System (ADS)
Kubina, Filip; Moczo, Peter; Kristek, Jozef; Michlik, Filip
2016-04-01
Adjoint tomography has proven an irreplaceable useful tool in exploring Earth's structure in the regional and global scales. It has not been widely applied for improving models of local surface sedimentary structures (LSSS) in numerical predictions of earthquake ground motion (EGM). Anomalous earthquake motions and corresponding damage in earthquakes are often due to site effects in local surface sedimentary basins. Because majority of world population is located atop surface sedimentary basins, it is important to predict EGM at these sites during future earthquakes. A major lesson learned from dedicated international tests focused on numerical prediction of EGM in LSSS is that it is hard to reach better agreement between data and synthetics without an improved structural model. If earthquake records are available for sites atop a LSSS it is natural to consider them for improving the structural model. Computationally efficient adjoint tomography might be a proper tool. A seismic wavefield in LSSS is relatively very complex due to diffractions, conversions, interference and often also resonant phenomena. In shallow basins, the first arrivals are not suitable for inversion due to almost vertical incidence and thus insufficient vertical resolution. Later wavefield consists mostly of local surface waves often without separated wave groups. Consequently, computed kernels are complicated and not suitable for inversion without pre-processing. The spatial complexity of a kernel can be dramatic in a typical situation with relatively low number of sources (local earthquakes) and surface receivers. This complexity can be simplified by directionally-dependent smoothing and spatially-dependent normalization that condition reasonable convergence. A multiscale approach seems necessary given the usual difference between the available and true models. Interestingly, only a successive inversion of μ and λ elastic moduli, and different scale sequences lead to good results.
The efficiency of geophysical adjoint codes generated by automatic differentiation tools
NASA Astrophysics Data System (ADS)
Vlasenko, A. V.; Köhl, A.; Stammer, D.
2016-02-01
The accuracy of numerical models that describe complex physical or chemical processes depends on the choice of model parameters. Estimating an optimal set of parameters by optimization algorithms requires knowledge of the sensitivity of the process of interest to model parameters. Typically the sensitivity computation involves differentiation of the model, which can be performed by applying algorithmic differentiation (AD) tools to the underlying numerical code. However, existing AD tools differ substantially in design, legibility and computational efficiency. In this study we show that, for geophysical data assimilation problems of varying complexity, the performance of adjoint codes generated by the existing AD tools (i) Open_AD, (ii) Tapenade, (iii) NAGWare and (iv) Transformation of Algorithms in Fortran (TAF) can be vastly different. Based on simple test problems, we evaluate the efficiency of each AD tool with respect to computational speed, accuracy of the adjoint, the efficiency of memory usage, and the capability of each AD tool to handle modern FORTRAN 90-95 elements such as structures and pointers, which are new elements that either combine groups of variables or provide aliases to memory addresses, respectively. We show that, while operator overloading tools are the only ones suitable for modern codes written in object-oriented programming languages, their computational efficiency lags behind source transformation by orders of magnitude, rendering the application of these modern tools to practical assimilation problems prohibitive. In contrast, the application of source transformation tools appears to be the most efficient choice, allowing handling even large geophysical data assimilation problems. However, they can only be applied to numerical models written in earlier generations of programming languages. Our study indicates that applying existing AD tools to realistic geophysical problems faces limitations that urgently need to be solved to allow the
A Novel Clustering Method Curbing the Number of States in Reinforcement Learning
NASA Astrophysics Data System (ADS)
Kotani, Naoki; Nunobiki, Masayuki; Taniguchi, Kenji
We propose an efficient state-space construction method for a reinforcement learning. Our method controls the number of categories with improving the clustering method of Fuzzy ART which is an autonomous state-space construction method. The proposed method represents weight vector as the mean value of input vectors in order to curb the number of new categories and eliminates categories whose state values are low to curb the total number of categories. As the state value is updated, the size of category becomes small to learn policy strictly. We verified the effectiveness of the proposed method with simulations of a reaching problem for a two-link robot arm. We confirmed that the number of categories was reduced and the agent achieved the complex task quickly.
Comparative Study of Three Data Assimilation Methods for Ice Sheet Model Initialisation
NASA Astrophysics Data System (ADS)
Mosbeux, Cyrille; Gillet-Chaulet, Fabien; Gagliardini, Olivier
2015-04-01
The current global warming has direct consequences on ice-sheet mass loss contributing to sea level rise. This loss is generally driven by an acceleration of some coastal outlet glaciers and reproducing these mechanisms is one of the major issues in ice-sheet and ice flow modelling. The construction of an initial state, as close as possible to current observations, is required as a prerequisite before producing any reliable projection of the evolution of ice-sheets. For this step, inverse methods are often used to infer badly known or unknown parameters. For instance, the adjoint inverse method has been implemented and applied with success by different authors in different ice flow models in order to infer the basal drag [ Schafer et al., 2012; Gillet-chauletet al., 2012; Morlighem et al., 2010]. Others data fields, such as ice surface and bedrock topography, are easily measurable with more or less uncertainty but only locally along tracks and interpolated on finer model grid. All these approximations lead to errors on the data elevation model and give rise to an ill-posed problem inducing non-physical anomalies in flux divergence [Seroussi et al, 2011]. A solution to dissipate these divergences of flux is to conduct a surface relaxation step at the expense of the accuracy of the modelled surface [Gillet-Chaulet et al., 2012]. Other solutions, based on the inversion of ice thickness and basal drag were proposed [Perego et al., 2014; Pralong & Gudmundsson, 2011]. In this study, we create a twin experiment to compare three different assimilation algorithms based on inverse methods and nudging to constrain the bedrock friction and the bedrock elevation: (i) cyclic inversion of friction parameter and bedrock topography using adjoint method, (ii) cycles coupling inversion of friction parameter using adjoint method and nudging of bedrock topography, (iii) one step inversion of both parameters with adjoint method. The three methods show a clear improvement in parameters
Wasielewski, Michael R.; Gaines, George L.; Niemczyk, Mark P.; Johnson, Douglas G.; Gosztola, David J.; O'Neil, Michael P.
1996-01-01
A light-intensity dependent molecular switch comprised of a compound which shuttles an electron or a plurality of electrons from a plurality of electron donors to an electron acceptor upon being stimulated with light of predetermined wavelengths, said donors selected from porphyrins and other compounds, and a method for making said compound.
Organic solid state optical switches and method for producing organic solid state optical switches
Wasielewski, M.R.; Gaines, G.L.; Niemczyk, M.P.; Johnson, D.G.; Gosztola, D.J.; O`Neil, M.P.
1993-01-01
This invention consists of a light-intensity dependent molecular switch comprised of a compound which shuttles an electron or a plurality of electrons from a plurality of electron donors to an electron acceptor upon being stimulated with light of predetermined wavelengths, and a method for making said compound.
Tuna, Deniz; Lu, You; Koslowski, Axel; Thiel, Walter
2016-09-13
The semiempirical orthogonalization-corrected OMx methods have recently been shown to perform well in extensive ground-state benchmarks. They can also be applied to the computation of electronically excited states when combined with a suitable multireference configuration interaction (MRCI) treatment. We report on a comprehensive evaluation of the performance of the OMx/MRCI methods for electronically excited states. The present benchmarks cover vertical excitation energies, excited-state equilibrium geometries (including an analysis of significant changes between ground- and excited-state geometries), minimum-energy conical intersections, ground- and excited-state zero-point vibrational energies, and 0-0 transition energies for a total of 520 molecular structures and 412 excited states. For comparison, we evaluate the TDDFT/B3LYP method for all benchmark sets, and the CC2, MRCISD, and CASPT2 methods for some of them. We find that the current OMx/MRCI methods perform reasonably well for many of the excited-state properties. However, in comparison to the first-principles methods, there are also a number of shortcomings that should be addressed in future developments. PMID:27380455
Methods and systems for thermodynamic evaluation of battery state of health
Yazami, Rachid; McMenamin, Joseph; Reynier, Yvan; Fultz, Brent T
2014-12-02
Described are systems and methods for accurately characterizing thermodynamic and materials properties of electrodes and battery systems and for characterizing the state of health of electrodes and battery systems. Measurement of physical attributes of electrodes and batteries corresponding to thermodynamically stabilized electrode conditions permit determination of thermodynamic parameters, including state functions such as the Gibbs free energy, enthalpy and entropy of electrode/electrochemical cell reactions, that enable prediction of important performance attributes of electrode materials and battery systems, such as energy, power density, current rate, cycle life and state of health. Also provided are systems and methods for charging a battery according to its state of health.
NASA Astrophysics Data System (ADS)
Castaings, W.; Dartus, D.; Le Dimet, F.-X.; Saulnier, G.-M.
2009-04-01
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.
NASA Astrophysics Data System (ADS)
Lemieux, M.-A.; Tremblay, A.-M. S.
1987-07-01
It is shown that various numerical methods to compute densities of states, projected densities of states (relevant for light scattering spectra), electrical or elastic properties of disordered media can all be considered as special cases of a general approach to these problems. This approach is based on a recursive evaluation of a generating function which in appropriate limits reduces, for example, to the approach based on the negative-eigenvalue theorem or to Gaussian elimination optimized for symmetric sparse matrices. The approach is simple and systematic. It also leads to an alternate proof of the negative-eigenvalue theorem. The general formalism and various special cases are discussed in detail. Comparisons with other methods such as the transfer-matrix, conjugate-gradient, and Haydock-Lanczos methods are provided.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems. PMID:25833428
NASA Astrophysics Data System (ADS)
Bakkiyaraj, Ashok; Kumarappan, N.
2015-09-01
This paper presents a new approach for evaluating the reliability indices of a composite power system that adopts binary differential evolution (BDE) algorithm in the search mechanism to select the system states. These states also called dominant states, have large state probability and higher loss of load curtailment necessary to maintain real power balance. A chromosome of a BDE algorithm represents the system state. BDE is not applied for its traditional application of optimizing a non-linear objective function, but used as tool for exploring more number of dominant states by producing new chromosomes, mutant vectors and trail vectors based on the fitness function. The searched system states are used to evaluate annualized system and load point reliability indices. The proposed search methodology is applied to RBTS and IEEE-RTS test systems and results are compared with other approaches. This approach evaluates the indices similar to existing methods while analyzing less number of system states.
NASA Astrophysics Data System (ADS)
Sokolov, Yurii L.
1999-05-01
A new approach to the observation of the stationary interference pattern of atomic states is suggested. A number of experiments performed from 1970 to 1998 using various interferometer designs are described. Among these are the precision measurements of Lamb shift in the hydrogen atom and the discovery, in the course of this work, of a long-range interaction between the moving excited hydrogen atom and the metal surface.
NASA Astrophysics Data System (ADS)
Aslan, Serdar; Taylan Cemgil, Ali; Akın, Ata
2016-08-01
Objective. In this paper, we aimed for the robust estimation of the parameters and states of the hemodynamic model by using blood oxygen level dependent signal. Approach. In the fMRI literature, there are only a few successful methods that are able to make a joint estimation of the states and parameters of the hemodynamic model. In this paper, we implemented a maximum likelihood based method called the particle smoother expectation maximization (PSEM) algorithm for the joint state and parameter estimation. Main results. Former sequential Monte Carlo methods were only reliable in the hemodynamic state estimates. They were claimed to outperform the local linearization (LL) filter and the extended Kalman filter (EKF). The PSEM algorithm is compared with the most successful method called square-root cubature Kalman smoother (SCKS) for both state and parameter estimation. SCKS was found to be better than the dynamic expectation maximization (DEM) algorithm, which was shown to be a better estimator than EKF, LL and particle filters. Significance. PSEM was more accurate than SCKS for both the state and the parameter estimation. Hence, PSEM seems to be the most accurate method for the system identification and state estimation for the hemodynamic model inversion literature. This paper do not compare its results with Tikhonov-regularized Newton—CKF (TNF-CKF), a recent robust method which works in filtering sense.
Racine, Julien; Hagebaum-Reignier, Denis; Carissan, Yannick; Humbel, Stéphane
2016-03-30
A method is proposed to obtain coefficients and weights of valence bond (VB) determinants from multi configurational wave functions. This reading of the wave functions can apply to ground states as well as excited states. The method is based on projection operators. Both energetic and overlap-based criteria are used to assess the quality of the resulting VB wave function. The approach gives a simple access to a VB rewriting for low-lying states, and it is applied to the allyl cation, to the allyl radical and to the ethene (notably to the V-state). For these states, large overlap between VB and multi reference wave functions are easily obtained. The approach proves to be useful to propose an interpretation of the nature of the V-state of ethene. PMID:26786547
NASA Technical Reports Server (NTRS)
Ustinov, E.
1999-01-01
Sensitivity analysis based on using of the adjoint equation of radiative transfer is applied to the case of atmospheric remote sensing in the thermal spectral region with non-negligeable atmospheric scattering.
Duan, Qian-Qian; Yang, Gen-Ke; Pan, Chang-Chun
2014-01-01
A hybrid optimization algorithm combining finite state method (FSM) and genetic algorithm (GA) is proposed to solve the crude oil scheduling problem. The FSM and GA are combined to take the advantage of each method and compensate deficiencies of individual methods. In the proposed algorithm, the finite state method makes up for the weakness of GA which is poor at local searching ability. The heuristic returned by the FSM can guide the GA algorithm towards good solutions. The idea behind this is that we can generate promising substructure or partial solution by using FSM. Furthermore, the FSM can guarantee that the entire solution space is uniformly covered. Therefore, the combination of the two algorithms has better global performance than the existing GA or FSM which is operated individually. Finally, a real-life crude oil scheduling problem from the literature is used for conducting simulation. The experimental results validate that the proposed method outperforms the state-of-art GA method. PMID:24772031
Load Modeling and State Estimation Methods for Power Distribution Systems: Final Report
Tom McDermott
2010-05-07
The project objective was to provide robust state estimation for distribution systems, comparable to what has been available on transmission systems for decades. This project used an algorithm called Branch Current State Estimation (BCSE), which is more effective than classical methods because it decouples the three phases of a distribution system, and uses branch current instead of node voltage as a state variable, which is a better match to current measurement.
Studying Dutch emigration to the United States: new methods and concepts.
Swierenga, R P
1984-01-01
The author considers how modern computerized methods could be applied to the study of migration from the Netherlands to the United States. An example is presented using data on Dutch migration from 1835 to 1880. The sources of available data in the Netherlands and the United States are reviewed. PMID:12267139
Application of the Feynman-Kac Method to Find the Excited States of Quantum Systems
NASA Astrophysics Data System (ADS)
Rejcek, James Michael
1995-01-01
Exact and numerical calculations using the Feynman -Kac integral method to find the ground state of several atomic systems including hydrogen, the harmonic and infinite square wells are presented. In addition, the first few excited states are calculated applying group theory to known symmetries in order to find wave nodes of the Hamiltonian. Statistical uncertainty and the use of failure trees are also introduced.
Tame, M. S.; Kim, M. S.
2010-09-15
We show that fundamental versions of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms can be performed using a small entangled cluster state resource of only six qubits. We then investigate the minimal resource states needed to demonstrate general n-qubit versions and a scalable method to produce them. For this purpose, we propose a versatile photonic on-chip setup.
Yazdani, Ali; Ong, N. Phuan; Cava, Robert J.
2016-05-03
An interconnect is disclosed with enhanced immunity of electrical conductivity to defects. The interconnect includes a material with charge carriers having topological surface states. Also disclosed is a method for fabricating such interconnects. Also disclosed is an integrated circuit including such interconnects. Also disclosed is a gated electronic device including a material with charge carriers having topological surface states.
Optimization methods, flux conserving methods for steady state Navier-Stokes equation
NASA Technical Reports Server (NTRS)
Adeyeye, John; Attia, Nauib
1995-01-01
Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.
NASA Astrophysics Data System (ADS)
Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander
2016-02-01
We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated
NASA Astrophysics Data System (ADS)
An, Xing Qin; Xian Zhai, Shi; Jin, Min; Gong, Sunling; Wang, Yu
2016-06-01
The aerosol adjoint module of the atmospheric chemical modeling system GRAPES-CUACE (Global-Regional Assimilation and Prediction System coupled with the CMA Unified Atmospheric Chemistry Environment) is constructed based on the adjoint theory. This includes the development and validation of the tangent linear and the adjoint models of the three parts involved in the GRAPES-CUACE aerosol module: CAM (Canadian Aerosol Module), interface programs that connect GRAPES and CUACE, and the aerosol transport processes that are embedded in GRAPES. Meanwhile, strict mathematical validation schemes for the tangent linear and the adjoint models are implemented for all input variables. After each part of the module and the assembled tangent linear and adjoint models is verified, the adjoint model of the GRAPES-CUACE aerosol is developed and used in a black carbon (BC) receptor-source sensitivity analysis to track influential haze source areas in north China. The sensitivity of the average BC concentration over Beijing at the highest concentration time point (referred to as the Objective Function) is calculated with respect to the BC amount emitted over the Beijing-Tianjin-Hebei region. Four types of regions are selected based on the administrative division or the sensitivity coefficient distribution. The adjoint sensitivity results are then used to quantify the effect of reducing the emission sources at different time intervals over different regions. It is indicated that the more influential regions (with relatively larger sensitivity coefficients) do not necessarily correspond to the administrative regions. Instead, the influence per unit area of the sensitivity selected regions is greater. Therefore, controlling the most influential regions during critical time intervals based on the results of the adjoint sensitivity analysis is much more efficient than controlling administrative regions during an experimental time period.
A shape optimisation method of a body located in adiabatic flows
NASA Astrophysics Data System (ADS)
Okumura, Hiroshi; Hikino, Yoichi; Kawahara, Mutsuto
2013-07-01
The purpose of this study is to derive an optimal shape of a body located in adiabatic flow. In this study, we use the equation of motion, the equation of continuity and the pressure-density relation derived from the Poisson's law as the governing equation. The formulation is based on an optimal control theory in which a performance function of fluid force is taken into consideration. The performance function should be minimised satisfying the governing equations. This problem can be solved without constraints by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimisation technique, the Galerkin finite element method is used as a spatial discretisation and the implicit scheme is used as a temporal discretisation to solve the state equations. The mixed interpolation, the bubble function for velocity and the linear function for density, is employed as the interpolation. The optimal shape is obtained for a body in adiabatic flows.
NASA Technical Reports Server (NTRS)
Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.
1993-01-01
An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.
Umezawa, Naoto; Tsuneyuki, Shinji
2004-10-15
We have implemented the excited electronic state calculations for a helium atom by the transcorrelated variational Monte Carlo (TC-VMC) method. In this method, Jastrow-Slater-type wave function is efficiently optimized not only for the Jastrow factor but also for the Slater determinant. Since the formalism for the TC-VMC method is based on the variance minimization, excited states as well as the ground state calculations are feasible. It is found that both the first and the second excitation energies given by TC-VMC are much closer to the experimental data than those given by the variational Monte Carlo method with using the Hartree-Fock orbitals. The successful results in the TC-VMC method are considered to be due to the nodal optimization of the wave functions. PMID:15473772
NASA Astrophysics Data System (ADS)
Guerrette, J. J.; Henze, D. K.
2015-06-01
Here we present the online meteorology and chemistry adjoint and tangent linear model, WRFPLUS-Chem (Weather Research and Forecasting plus chemistry), which incorporates modules to treat boundary layer mixing, emission, aging, dry deposition, and advection of black carbon aerosol. We also develop land surface and surface layer adjoints to account for coupling between radiation and vertical mixing. Model performance is verified against finite difference derivative approximations. A second-order checkpointing scheme is created to reduce computational costs and enable simulations longer than 6 h. The adjoint is coupled to WRFDA-Chem, in order to conduct a sensitivity study of anthropogenic and biomass burning sources throughout California during the 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) field campaign. A cost-function weighting scheme was devised to reduce the impact of statistically insignificant residual errors in future inverse modeling studies. Results of the sensitivity study show that, for this domain and time period, anthropogenic emissions are overpredicted, while wildfire emission error signs vary spatially. We consider the diurnal variation in emission sensitivities to determine at what time sources should be scaled up or down. Also, adjoint sensitivities for two choices of land surface model (LSM) indicate that emission inversion results would be sensitive to forward model configuration. The tools described here are the first step in conducting four-dimensional variational data assimilation in a coupled meteorology-chemistry model, which will potentially provide new constraints on aerosol precursor emissions and their distributions. Such analyses will be invaluable to assessments of particulate matter health and climate impacts.
A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates
Wang, Hanquan
2014-10-01
In this paper, a projection gradient method is presented for computing ground state of spin-2 Bose–Einstein condensates (BEC). We first propose the general projection gradient method for solving energy functional minimization problem under multiple constraints, in which the energy functional takes real functions as independent variables. We next extend the method to solve a similar problem, where the energy functional now takes complex functions as independent variables. We finally employ the method into finding the ground state of spin-2 BEC. The key of our method is: by constructing continuous gradient flows (CGFs), the ground state of spin-2 BEC can be computed as the steady state solution of such CGFs. We discretized the CGFs by a conservative finite difference method along with a proper way to deal with the nonlinear terms. We show that the numerical discretization is normalization and magnetization conservative and energy diminishing. Numerical results of the ground state and their energy of spin-2 BEC are reported to demonstrate the effectiveness of the numerical method.
Adjoint-based computation of U.S. nationwide ozone exposure isopleths
NASA Astrophysics Data System (ADS)
Ashok, Akshay; Barrett, Steven R. H.
2016-05-01
Population exposure to daily maximum ozone is associated with an increased risk of premature mortality, and efforts to mitigate these impacts involve reducing emissions of nitrogen oxides (NOx) and volatile organic compounds (VOCs). We quantify the dependence of U.S. national exposure to annually averaged daily maximum ozone on ambient VOC and NOx concentrations through ozone exposure isopleths, developed using emissions sensitivities from the adjoint of the GEOS-Chem air quality model for 2006. We develop exposure isopleths for all locations within the contiguous US and derive metrics based on the isopleths that quantify the impact of emissions on national ozone exposure. This work is the first to create ozone exposure isopleths using adjoint sensitivities and at a large scale. We find that across the US, 29% of locations experience VOC-limited conditions (where increased NOx emissions lower ozone) during 51% of the year on average. VOC-limited conditions are approximately evenly distributed diurnally and occur more frequently during the fall and winter months (67% of the time) than in the spring and summer (37% of the time). The VOC/NOx ratio of the ridge line on the isopleth diagram (denoting a local maximum in ozone exposure with respect to NOx concentrations) is 9.2 ppbC/ppb on average across grid cells that experience VOC-limited conditions and 7.9, 10.1 and 6.7 ppbC/ppb at the three most populous US cities of New York, Los Angeles and Chicago, respectively. Emissions that are ozone exposure-neutral during VOC-limited exposure conditions result in VOC/NOx concentration ratios of 0.63, 1.61 and 0.72 ppbC/ppb at each of the three US cities respectively, and between 0.01 and 1.91 ppbC/ppb at other locations. The sensitivity of national ozone exposure to NOx and VOC emissions is found to be highest near major cities in the US. Together, this information can be used to assess the effectiveness of NOx and VOC emission reductions on mitigating ozone exposure in the
State of charge monitoring methods for vanadium redox flow battery control
NASA Astrophysics Data System (ADS)
Skyllas-Kazacos, Maria; Kazacos, Michael
2011-10-01
During operation of redox flow batteries, differential transfer of ions and electrolyte across the membrane and gassing side reactions during charging, can lead to an imbalance between the two half-cells that results in loss of capacity. This capacity loss can be corrected by either simple remixing of the two solutions, or by chemical or electrochemical rebalancing. In order to develop automated electrolyte management systems therefore, the state-of-charge of each half-cell electrolyte needs to be known. In this study, two state-of-charge monitoring methods are investigated for use in the vanadium redox flow battery. The first method utilizes conductivity measurements to independently measure the state-of-charge of each half-cell electrolyte. The second method is based on spectrophotometric principles and uses the different colours of the charged and discharged anolyte and catholyte to monitor system balance and state-of charge of each half-cell of the VRB during operation.
A novel method for the injection and manipulation of magnetic charge states in nanostructures.
Gartside, J C; Burn, D M; Cohen, L F; Branford, W R
2016-01-01
Realising the promise of next-generation magnetic nanotechnologies is contingent on the development of novel methods for controlling magnetic states at the nanoscale. There is currently demand for simple and flexible techniques to access exotic magnetisation states without convoluted fabrication and application processes. 360° domain walls (metastable twists in magnetisation separating two domains with parallel magnetisation) are one such state, which is currently of great interest in data storage and magnonics. Here, we demonstrate a straightforward and powerful process whereby a moving magnetic charge, provided experimentally by a magnetic force microscope tip, can write and manipulate magnetic charge states in ferromagnetic nanowires. The method is applicable to a wide range of nanowire architectures with considerable benefits over existing techniques. We confirm the method's efficacy via the injection and spatial manipulation of 360° domain walls in Py and Co nanowires. Experimental results are supported by micromagnetic simulations of the tip-nanowire interaction. PMID:27615372
Systems and Methods for Automated Vessel Navigation Using Sea State Prediction
NASA Technical Reports Server (NTRS)
Huntsberger, Terrance L. (Inventor); Rankin, Arturo (Inventor); Aghazarian, Hrand (Inventor); Howard, Andrew B. (Inventor); Reinhart, Rene Felix (Inventor)
2015-01-01
Systems and methods for sea state prediction and autonomous navigation in accordance with embodiments of the invention are disclosed. One embodiment of the invention includes a method of predicting a future sea state including generating a sequence of at least two 3D images of a sea surface using at least two image sensors, detecting peaks and troughs in the 3D images using a processor, identifying at least one wavefront in each 3D image based upon the detected peaks and troughs using the processor, characterizing at least one propagating wave based upon the propagation of wavefronts detected in the sequence of 3D images using the processor, and predicting a future sea state using at least one propagating wave characterizing the propagation of wavefronts in the sequence of 3D images using the processor. Another embodiment includes a method of autonomous vessel navigation based upon a predicted sea state and target location.
Two-state model based on the block-localized wave function method.
Mo, Yirong
2007-06-14
The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV). PMID:17581041
Adjoint-based estimation of plate coupling in a non-linear mantle flow model: theory and examples
NASA Astrophysics Data System (ADS)
Ratnaswamy, Vishagan; Stadler, Georg; Gurnis, Michael
2015-08-01
We develop and validate a systematic approach to infer plate boundary strength and rheological parameters in models of mantle flow from surface velocity observations. Based on a realistic rheological model that includes yielding and strain rate weakening from dislocation creep, we formulate the inverse problem in a Bayesian inference framework. To study the distribution of parameters that are consistent with the observations, we compute the maximum a posteriori (MAP) point, Gaussian approximations of the parameter distribution around that MAP point, and employ Markov Chain Monte Carlo (MCMC) sampling methods. The computation of the MAP point and the Gaussian approximation require first and second derivatives of an objective function subject to non-linear Stokes equations; these derivatives are computed efficiently using adjoint Stokes equations. We set up 2-D numerical experiments with many of the elements expected in a global geophysical inversion. This setup incorporates three subduction zones with slab and weak zone (interplate fault) geometry consistent with average seismic characteristics. With these experiments, we demonstrate that when the temperature field is known, we can recover the strength of plate boundaries, the yield stress and strain rate exponent in the upper mantle. When the number of uncertain parameters increases, there are trade-offs between the inferred parameters. These trade-offs depend on how well the observational data represents the surface velocities, and on the weakness of plate boundaries. As the plate boundary coupling drops below a threshold, the uncertainty of the inferred parameters increases due to insensitivity of plate motion to plate coupling. Comparing the trade-offs between inferred rheological parameters found from the Gaussian approximation of the parameter distribution and from MCMC sampling, we conclude that the Gaussian approximation-which is significantly cheaper to compute-is often a good approximation, in particular
Method for Synthesizing Metal Nanowires in Anodic Alumina Membranes Using Solid State Reduction
NASA Technical Reports Server (NTRS)
Martinez-Inesta, Maria M (Inventor); Feliciano, Jennie (Inventor); Quinones-Fontalvo, Leonel (Inventor)
2016-01-01
The invention proposes a novel method for the fabrication of regular arrays of MNWs using solid-state reduction (SSR). Using this method copper (Cu), silver (Ag), and palladium (Pd) nanowire (NWs) arrays were synthesized using anodic alumina membranes (AAMs) as templates. Depending on the metal loading used the NWs reached different diameters.
Method and System for Controlling a Dexterous Robot Execution Sequence Using State Classification
NASA Technical Reports Server (NTRS)
Sanders, Adam M. (Inventor); Platt, Robert J., Jr. (Inventor); Quillin, Nathaniel (Inventor); Permenter, Frank Noble (Inventor); Pfeiffer, Joseph (Inventor)
2014-01-01
A robotic system includes a dexterous robot and a controller. The robot includes a plurality of robotic joints, actuators for moving the joints, and sensors for measuring a characteristic of the joints, and for transmitting the characteristics as sensor signals. The controller receives the sensor signals, and is configured for executing instructions from memory, classifying the sensor signals into distinct classes via the state classification module, monitoring a system state of the robot using the classes, and controlling the robot in the execution of alternative work tasks based on the system state. A method for controlling the robot in the above system includes receiving the signals via the controller, classifying the signals using the state classification module, monitoring the present system state of the robot using the classes, and controlling the robot in the execution of alternative work tasks based on the present system state.
Solid-state dimer method for calculating solid-solid phase transitions
Xiao, Penghao; Henkelman, Graeme; Sheppard, Daniel; Rogal, Jutta
2014-05-07
The dimer method is a minimum mode following algorithm for finding saddle points on a potential energy surface of atomic systems. Here, the dimer method is extended to include the cell degrees of freedom for periodic solid-state systems. Using this method, reaction pathways of solid-solid phase transitions can be determined without having to specify the final state structure or reaction mechanism. Example calculations include concerted phase transitions between CdSe polymorphs and a nucleation and growth mechanism for the A15 to BCC transition in Mo.
Application to MISR Land Products of an RPV Model Inversion Package Using Adjoint and Hessian Codes
NASA Astrophysics Data System (ADS)
Lavergne, T.; Kaminski, T.; Pinty, B.; Taberner, M.; Gobron, N.; Verstraete, M. M.; Vossbeck, M.; Widlowski, J.-L.; Giering, R.
The capability of the non-linear Rahman-Pinty-Verstraete RPV model to 1 accurately fit a large variety of Bidirectional Reflectance Factor BRF fields and 2 return parameter values of interest for land surface applications motivate the development of a computer efficient inversion package The present paper describes such a package based on the 3 and 4 parameter versions of the RPV model This software environment implements the adjoint code generated using automatic differentiation techniques of the cost function This cost function itself balances two main contributions reflecting 1 the a priori knowledge on the model parameter values and 2 BRF uncertainties together with the requirement to minimize the mismatch between the measurements and the RPV simulations The individual weights of these contributions are specified notably via covariance matrices of the uncertainties in the a priori knowledge on the model parameters and the observations This package also reports on the probability density functions of the retrieved model parameter values that thus permit the user to evaluate the a posteriori uncertainties on these retrievals This is achieved by evaluating the Hessian of the cost function at its minimum Results from a variety of tests are shown in order to document and analyze software performance against complex synthetic BRF fields simulated by radiation transfer models as well as against actual MISR-derived surface BRF products
Large-N reduction in QCD-like theories with massive adjoint fermions
Azeyanagi, Tatsuo; Hanada, Masanori; Unsal, Mithat; Yacoby, Ran; /Weizmann Inst.
2010-08-26
Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R3 x S1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1{sup 3} x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.
NASA Astrophysics Data System (ADS)
Yumimoto, Keiya; Uno, Itsushi
We developed a four-dimensional variational (4DVAR) data assimilation system for a regional chemical transport model (CTM). In this study, we applied it to inverse modeling of CO emissions in the eastern Asia during April 2001 and demonstrated the feasibility of our assimilation system. Three ground-based observations were used for data assimilation. Assimilated results showed better agreement with observations; they reduced the RMS difference by 16-27%. Observations obtained on board the R/V Ronald H. Brown were used for independent validation of the assimilated results. The CO emissions over industrialized east central China between Shanghai and Beijing were increased markedly by the assimilation. The results show that the annual anthropogenic (fossil and biofuel combustion) CO emissions over China are 147 Tg. Sensitivity analyses using the adjoint model indicate that the high CO concentration measured on 17 April at Rishiri, Japan (which the assimilation was unable to reproduce) originated in Russia or had traveled from outside the Asian region (e.g. Europe).
Focus point gauge mediation with incomplete adjoint messengers and gauge coupling unification
NASA Astrophysics Data System (ADS)
Bhattacharyya, Gautam; Yanagida, Tsutomu T.; Yokozaki, Norimi
2015-10-01
As the mass limits on supersymmetric particles are gradually pushed to higher values due to their continuing non-observation at the CERN LHC, looking for focus point regions in the supersymmetric parameter space, which shows considerably reduced fine-tuning, is increasingly more important than ever. We explore this in the context of gauge mediated supersymmetry breaking with messengers transforming in the adjoint representation of the gauge group, namely, octet of color SU(3) and triplet of weak SU(2). A distinctive feature of this scenario is that the focus point is achieved by fixing a single combination of parameters in the messenger sector, which is invariant under the renormalization group evolution. Because of this invariance, the focus point behavior is well under control once the relevant parameters are fixed by a more fundamental theory. The observed Higgs boson mass is explained with a relatively mild fine-tuning Δ = 60- 150. Interestingly, even in the presence of incomplete messenger multiplets of the SU(5) GUT group, the gauge couplings still unify perfectly, but at a scale which is one or two orders of magnitude above the conventional GUT scale. Because of this larger unification scale, the colored Higgs multiplets become too heavy to trigger proton decay at a rate larger than the experimentally allowed limit.
Adjoint-based optimization for the understanding of the aerodynamics of a flapping plate
NASA Astrophysics Data System (ADS)
Wei, Mingjun; Xu, Min
2015-11-01
An adjoint-based optimization is applied on a rigid flapping plate and a flexible flapping plate for drag reduction and for propulsive efficiency. Non-cylindrical calculus is introduced to handle the moving boundary. The rigid plate has a combined plunging and pitching motion with incoming flow, the control parameter is the phase delay which is considered first as a constant then as an arbitrary time-varying function. The optimal controls with different cost functions provide different strategies to reach maximum drag reduction or propulsive efficiency. The flexible plate has plunging, pitching, and deformation which is defined by the first two natural modes. With the same optimization goals, the control is instead the amplitude and phase delay of the pitching, the first eigen mode, and the second eigen mode. Similar analyses are taken to understand the conditions for drag reduction and propulsive efficiency when flexibility is involved. It is also shown that the flexibility plays a more important role at lower Reynolds number. Supported by AFOSR.
Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation
NASA Technical Reports Server (NTRS)
Park, Michael A.
2002-01-01
Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.
Improving NO(x) cap-and-trade system with adjoint-based emission exchange rates.
Mesbah, S Morteza; Hakami, Amir; Schott, Stephan
2012-11-01
Cap-and-trade programs have proven to be effective instruments for achieving environmental goals while incurring minimum cost. The nature of the pollutant, however, affects the design of these programs. NO(x), an ozone precursor, is a nonuniformly mixed pollutant with a short atmospheric lifetime. NO(x) cap-and-trade programs in the U.S. are successful in reducing total NO(x) emissions but may result in suboptimal environmental performance because location-specific ozone formation potentials are neglected. In this paper, the current NO(x) cap-and-trade system is contrasted to a hypothetical NO(x) trading policy with sensitivity-based exchange rates. Location-specific exchange rates, calculated through adjoint sensitivity analysis, are combined with constrained optimization for prediction of NO(x) emissions trading behavior and post-trade ozone concentrations. The current and proposed policies are examined in a case study for 218 coal-fired power plants that participated in the NO(x) Budget Trading Program in 2007. We find that better environmental performance at negligibly higher system-wide abatement cost can be achieved through inclusion of emission exchange rates. Exposure-based exchange rates result in better environmental performance than those based on concentrations. PMID:23050674
NASA Astrophysics Data System (ADS)
Äkäslompolo, S.; Bonheure, G.; Tardini, G.; Kurki-Suonio, T.; The ASDEX Upgrade Team
2015-10-01
The activation probe is a robust tool to measure flux of fusion products from a magnetically confined plasma. A carefully chosen solid sample is exposed to the flux, and the impinging ions transmute the material making it radioactive. Ultra-low level gamma-ray spectroscopy is used post mortem to measure the activity and, thus, the number of fusion products. This contribution presents the numerical analysis of the first measurement in the ASDEX Upgrade tokamak, which was also the first experiment to measure a single discharge. The ASCOT suite of codes was used to perform adjoint/reverse Monte Carlo calculations of the fusion products. The analysis facilitates, for the first time, a comparison of numerical and experimental values for absolutely calibrated flux. The results agree to within a factor of about two, which can be considered a quite good result considering the fact that all features of the plasma cannot be accounted in the simulations.Also an alternative to the present probe orientation was studied. The results suggest that a better optimized orientation could measure the flux from a significantly larger part of the plasma. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
Higher representations on the lattice: Numerical simulations, SU(2) with adjoint fermions
Del Debbio, Luigi; Patella, Agostino; Pica, Claudio
2010-05-01
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group and present in detail the implementation of the hybrid Monte Carlo (HMC)/rational HMC algorithm for simulating dynamical fermions. We discuss the validation of the implementation through an extensive set of tests and the stability of simulations by monitoring the distribution of the lowest eigenvalue of the Wilson-Dirac operator. Working with two flavors of Wilson fermions in the adjoint representation, benchmark results for realistic lattice simulations are presented. Runs are performed on different lattice sizes ranging from 4{sup 3}x8 to 24{sup 3}x64 sites. For the two smallest lattices we also report the measured values of benchmark mesonic observables. These results can be used as a baseline for rapid cross-checks of simulations in higher representations. The results presented here are the first steps toward more extensive investigations with controlled systematic errors, aiming at a detailed understanding of the phase structure of these theories, and of their viability as candidates for strong dynamics beyond the standard model.
A fully implicit method for 3D quasi-steady state magnetic advection-diffusion.
Siefert, Christopher; Robinson, Allen Conrad
2009-09-01
We describe the implementation of a prototype fully implicit method for solving three-dimensional quasi-steady state magnetic advection-diffusion problems. This method allows us to solve the magnetic advection diffusion equations in an Eulerian frame with a fixed, user-prescribed velocity field. We have verified the correctness of method and implementation on two standard verification problems, the Solberg-White magnetic shear problem and the Perry-Jones-White rotating cylinder problem.
Hong, Changki; Hwang, Jeewon; Cho, Kwang-Hyun; Shin, Insik
2015-01-01
Boolean networks have been widely used to model biological processes lacking detailed kinetic information. Despite their simplicity, Boolean network dynamics can still capture some important features of biological systems such as stable cell phenotypes represented by steady states. For small models, steady states can be determined through exhaustive enumeration of all state transitions. As the number of nodes increases, however, the state space grows exponentially thus making it difficult to find steady states. Over the last several decades, many studies have addressed how to handle such a state space explosion. Recently, increasing attention has been paid to a satisfiability solving algorithm due to its potential scalability to handle large networks. Meanwhile, there still lies a problem in the case of large models with high maximum node connectivity where the satisfiability solving algorithm is known to be computationally intractable. To address the problem, this paper presents a new partitioning-based method that breaks down a given network into smaller subnetworks. Steady states of each subnetworks are identified by independently applying the satisfiability solving algorithm. Then, they are combined to construct the steady states of the overall network. To efficiently apply the satisfiability solving algorithm to each subnetwork, it is crucial to find the best partition of the network. In this paper, we propose a method that divides each subnetwork to be smallest in size and lowest in maximum node connectivity. This minimizes the total cost of finding all steady states in entire subnetworks. The proposed algorithm is compared with others for steady states identification through a number of simulations on both published small models and randomly generated large models with differing maximum node connectivities. The simulation results show that our method can scale up to several hundreds of nodes even for Boolean networks with high maximum node connectivity. The
Inconsistent responses in three preference-elicitation methods for health states.
Badia, X; Roset, M; Herdman, M
1999-10-01
Values for health states obtained from the general population can be used in the development of cost-utility algorithms such as Quality Adjusted Life Years (QALYs) to aid in resource allocation decisions. These values are obtained using methods such as the visual analogue scale, the time trade-off or the standard gamble. However, all of these methods suffer, to some extent, from the problem of inconsistent responses. In this paper, we examine the degree to which three preference-elicitation methods-ranking, VAS and TTO--produce inconsistent responses, the effect of sociodemographic and health variables on the numbers of inconsistencies produced, and the effect of including inconsistent responses on the ordering of health states in EQ-5D VAS and TTO tariffs. Health states valued were a sub-set of 43 health states generated by the EuroQol-5D instrument, which were valued as part of a larger study to obtain a tariff of VAS and TTO values for use with the Spanish version of the EQ-5D. Two types of inconsistency--internal and criterion inconsistency were tested, and both the numbers of inconsistencies produced by each method, and the 'size' of those inconsistencies, i.e. the distance in terms of severity between health states rated inconsistently, were tested. The study showed that although the TTO produces higher numbers of inconsistent responses, the numbers of inconsistent responses in all methods were low, and did not affect rankings in the final tariff of values. Older respondents and those with lower levels of education produced significantly higher numbers of inconsistencies, though health characteristics were not significant. On the ranking and VAS methods, the number of inconsistencies doubled between the two interviewers. Efforts should be made to reduce inconsistencies, particularly among older and lesser educated respondents. Future research should concentrate on determining how inconsistencies might affect the values assigned to health states in the final
NASA Astrophysics Data System (ADS)
Becker, A.; Wotawa, G.; de Geer, L.
2006-05-01
The Provisional Technical Secretariat (PTS) of the CTBTO Preparatory Commission maintains and permanently updates a source-receptor matrix (SRM) describing the global monitoring capability of a highly sensitive 80 stations radionuclide (RN) network in order to verify states signatories' compliance of the comprehensive nuclear-test-ban treaty (CTBT). This is done by means of receptor-oriented Lagrangian particle dispersion modeling (LPDM) to help determine the region from which suspicious radionuclides may originate. In doing so the LPDM FLEXPART5.1 is integrated backward in time based on global analysis wind fields yielding global source-receptor sensitivity (SRS) fields stored in three-hour frequency and at 1º horizontal resolution. A database of these SRS fields substantially helps in improving the interpretation of the RN samples measurements and categorizations because it enables the testing of source-hypothesis's later on in a pure post-processing (SRM inversion) step being feasible on hardware with specifications comparable to currently sold PC's or Notebooks and at any place (decentralized), provided access to the SRS fields is warranted. Within the CTBT environment it is important to quickly achieve decision-makers confidence in the SRM based backtracking products issued by the PTS in the case of the occurrence of treaty relevant radionuclides. Therefore the PTS has set up a highly automated response system together with the Regional Specialized Meteorological Centers of the World Meteorological Organization in the field of dispersion modeling who committed themselves to provide the PTS with the same standard SRS fields as calculated by their systems for CTBT relevant cases. This system was twice utilized in 2005 in order to perform adjoint ensemble dispersion modeling (EDM) and demonstrated the potential of EDM based backtracking to improve the accuracy of the source location related to singular nuclear events thus serving the backward analogue to the
Echo state network prediction method and its application in flue gas turbine condition prediction
NASA Astrophysics Data System (ADS)
Wang, Shaohong; Chen, Tao; Xu, Xiaoli
2010-12-01
On the background of the complex production process of fluid catalytic cracking energy recovery system in large-scale petrochemical refineries, this paper introduced an improved echo state network (ESN) model prediction method which is used to address the condition trend prediction problem of the key power equipment--flue gas turbine. Singular value decomposition method was used to obtain the ESN output weight. Through selecting the appropriate parameters and discarding small singular value, this method overcame the defective solution problem in the prediction by using the linear regression algorithm, improved the prediction performance of echo state network, and gave the network prediction process. In order to solve the problem of noise contained in production data, the translation-invariant wavelet transform analysis method is combined to denoise the noisy time series before prediction. Condition trend prediction results show the effectiveness of the proposed method.
Piezoelectrically forced vibrations of electroded doubly rotated quartz plates by state space method
NASA Technical Reports Server (NTRS)
Chander, R.
1990-01-01
The purpose of this investigation is to develop an analytical method to study the vibration characteristics of piezoelectrically forced quartz plates. The procedure can be summarized as follows. The three dimensional governing equations of piezoelectricity, the constitutive equations and the strain-displacement relationships are used in deriving the final equations. For this purpose, a state vector consisting of stresses and displacements are chosen and the above equations are manipulated to obtain the projection of the derivative of the state vector with respect to the thickness coordinate on to the state vector itself. The solution to the state vector at any plane is then easily obtained in a closed form in terms of the state vector quantities at a reference plane. To simplify the analysis, simple thickness mode and plane strain approximations are used.
Brabec, Jiri; Bhaskaran-Nair, Kiran; Govind, Niranjan; Pittner, Jiri; Kowalski, Karol
2012-11-07
The concept of the model space underlying multireference coupled-cluster (MRCC) formulations is a powerful tool to deal with complex correlation effects for various electronic states. Here, we demonstrate that iterative state-specific MRCC methods (SS-MRCC) based on properly defined model spaces can be used to describe core-level excited states even when canonical Hartree-Fock orbitals are utilized. We show that the SS-MRCC models with single and double excitations (SSMRCCSD) are comparable in accuracy to high-level single reference equation-of-motion coupled cluster (EOMCC) formalism. We also demonstrate that the SS-MRCC methods are capable of providing high accuracy results without experiencing numerical problems of the EOMCC methods.
A multi-state trajectory method for non-adiabatic dynamics simulations.
Tao, Guohua
2016-03-01
A multi-state trajectory approach is proposed to describe nuclear-electron coupled dynamics in nonadiabatic simulations. In this approach, each electronic state is associated with an individual trajectory, among which electronic transition occurs. The set of these individual trajectories constitutes a multi-state trajectory, and nuclear dynamics is described by one of these individual trajectories as the system is on the corresponding state. The total nuclear-electron coupled dynamics is obtained from the ensemble average of the multi-state trajectories. A variety of benchmark systems such as the spin-boson system have been tested and the results generated using the quasi-classical version of the method show reasonably good agreement with the exact quantum calculations. Featured in a clear multi-state picture, high efficiency, and excellent numerical stability, the proposed method may have advantages in being implemented to realistic complex molecular systems, and it could be straightforwardly applied to general nonadiabatic dynamics involving multiple states. PMID:26957158
Iterative methods for the WLS state estimation on RISC, vector, and parallel computers
Nieplocha, J.; Carroll, C.C.
1993-10-01
We investigate the suitability and effectiveness of iterative methods for solving the weighted-least-square (WLS) state estimation problem on RISC, vector, and parallel processors. Several of the most popular iterative methods are tested and evaluated. The best performing preconditioned conjugate gradient (PCG) is very well suited for vector and parallel processing as is demonstrated for the WLS state estimation of the IEEE standard test systems. A new sparse matrix format for the gain matrix improves vector performance of the PCG algorithm and makes it competitive to the direct solver. Internal parallelism in RISC processors, used in current multiprocessor systems, can be taken advantage of in an implementation of this algorithm.
Cvitas, Marko T; Althorpe, Stuart C
2009-04-23
We describe a quantum wave packet method for computing the state-to-state quantum dynamics of 4-atom AB + CD --> ABC + D reactions. The approach is an extension to 4-atom reactions of a version of the reactant-product decoupling (RPD) approach, applied previously to 3-atom reactions ( J. Chem. Phys. 2001, 114 , 1601 ). The approach partitions the coordinate space of the reaction into separate reagent, strong-interaction, and product regions, using a system of artificial absorbing and reflecting potentials. It employs a partitioned version of the split-operator propagator, which is more efficient than partitioning the (exact) time-dependent Schrodinger equation. The wave packet bounces off a reflecting potential in the entrance channel, which generates a source term; this is transformed efficiently from reagent to product Jacobi coordinates by exploiting some simple angular momentum properties. The efficiency and accuracy of the method is demonstrated by numerical tests on the benchmark OH + H(2) --> H(2)O + H reaction. PMID:19298045
A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems
Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing
2012-01-01
An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849
A chain-of-states acceleration method for the efficient location of minimum energy paths
Hernández, E. R. Herrero, C. P.; Soler, J. M.
2015-11-14
We describe a robust and efficient chain-of-states method for computing Minimum Energy Paths (MEPs) associated to barrier-crossing events in poly-atomic systems, which we call the acceleration method. The path is parametrized in terms of a continuous variable t ∈ [0, 1] that plays the role of time. In contrast to previous chain-of-states algorithms such as the nudged elastic band or string methods, where the positions of the states in the chain are taken as variational parameters in the search for the MEP, our strategy is to formulate the problem in terms of the second derivatives of the coordinates with respect to t, i.e., the state accelerations. We show this to result in a very simple and efficient method for determining the MEP. We describe the application of the method to a series of test cases, including two low-dimensional problems and the Stone-Wales transformation in C{sub 60}.
A combined method for determining reaction paths, minima, and transition state geometries
NASA Astrophysics Data System (ADS)
Ayala, Philippe Y.; Schlegel, H. Bernhard
1997-07-01
Mapping out a reaction mechanism involves optimizing the reactants and products, finding the transition state and following the reaction path connecting them. Transition states can be difficult to locate and reaction paths can be expensive to follow. We describe an efficient algorithm for determining the transition state, minima and reaction path in a single procedure. Starting with an approximate path represented by N points, the path is iteratively relaxed until one of the N points reached the transition state, the end points optimize to minima and the remaining points converged to a second order approximation of the steepest descent path. The method appears to be more reliable than conventional transition state optimization algorithms, and requires only energies and gradients, but not second derivative calculations. The procedure is illustrated by application to a number of model reactions. In most cases, the reaction mechanism can be described well using 5 to 7 points to represent the transition state, the minima and the path. The computational cost of relaxing the path is less than or comparable to the cost of standard techniques for finding the transition state and the minima, determining the transition vector and following the reaction path on both sides of the transition state.
Aerosol Health Impact Source Attribution Studies with the CMAQ Adjoint Air Quality Model
NASA Astrophysics Data System (ADS)
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
New Methods for Applying Statistical State Dynamics to Problems in Atmospheric Turbulence
NASA Astrophysics Data System (ADS)
Farrell, B.; Ioannou, P. J.
2015-12-01
Adopting the perspective of statistical state dynamics (SSD) has led to a number of recent advances inunderstanding and simulating atmospheric turbulence at both boundary layer and planetary scale. Traditionally, realizations have been used to study turbulence and if a statistical quantity was needed it was obtained by averaging. However, it is now becomimg more widely appreciated that there are important advantages to studying the statistical state dynamics (SSD) directly. In turbulent systems statistical quantities are often the most useful and the advantage of obtaining these quantities directly as state variables is obvious. Moreover, quantities such as the probability density function (pdf) are often difficult to obtain accurately by sampling state trajectories. In the event that the pdf is itself time dependent or even chaotic, as is the case in the turbulence of the planetary boundary layer, the pdf can only be obtained as a state variable. However, perhaps the greatest advantage of the SSD approach is that it reveals directly the essential cooperative mechanisms of interaction among spatial and temporal scales that underly the turbulent state. In order to exploit these advantages of the SSD approach to geophysical turbulence, new analytical and computational methods are being developed. Example problems in atmospheric turbulence will be presented in which these new SSD analysis and computational methods are used.
Modified Inverse First Order Reliability Method (I-FORM) for Predicting Extreme Sea States.
Eckert-Gallup, Aubrey Celia; Sallaberry, Cedric Jean-Marie; Dallman, Ann Renee; Neary, Vincent Sinclair
2014-09-01
Environmental contours describing extreme sea states are generated as the input for numerical or physical model simulation s as a part of the stand ard current practice for designing marine structure s to survive extreme sea states. Such environmental contours are characterized by combinations of significant wave height ( ) and energy period ( ) values calculated for a given recurrence interval using a set of data based on hindcast simulations or buoy observations over a sufficient period of record. The use of the inverse first - order reliability method (IFORM) i s standard design practice for generating environmental contours. In this paper, the traditional appli cation of the IFORM to generating environmental contours representing extreme sea states is described in detail and its merits and drawbacks are assessed. The application of additional methods for analyzing sea state data including the use of principal component analysis (PCA) to create an uncorrelated representation of the data under consideration is proposed. A reexamination of the components of the IFORM application to the problem at hand including the use of new distribution fitting techniques are shown to contribute to the development of more accurate a nd reasonable representations of extreme sea states for use in survivability analysis for marine struc tures. Keywords: In verse FORM, Principal Component Analysis , Environmental Contours, Extreme Sea State Characteri zation, Wave Energy Converters
State-To Spectroscopy and Dynamics of Ions and Neutrals by Photoionization and Photoelectron Methods
NASA Astrophysics Data System (ADS)
Ng, Cheuk-Yiu
2014-06-01
Recent advances in high-resolution photoionization, photoelectron, and photodissociation studies based on single-photon vacuum ultraviolet (VUV) and two-color infrared (IR)-VUV, visible (VIS)-ultraviolet (UV), and VUV-VUV laser excitations are illustrated with selected examples. We show that VUV laser photoionization coupled with velocity-map-imaging (VMI)-threshold photoelectron (VMI-TPE) detection can achieve comparable energy resolutions, but higher detection sensitivities than those observed in VUV laser pulsed field ionization-photoelectron (PFI-PE) measurements. For molecules with known intermediate states, IR-VUV and VIS-UV excitation schemes are highly sensitive for rovibronically selected and resolved PFI-PE studies. The successful applications of the VUV-PFI-PE, VUV-VMI-TPE and VIS-UV-PFI-PE methods to state-resolved and state-to-state photoelectron studies of transient radicals and transitional metal-containing molecules are highlighted. The most recently established VUV-VUV pump-probe time-slice VMI-photoion method is shown to be promising for state-to-state photodissociation studies of small molecules relevant to planetary atmospheres and for the fundamental understanding of photodissociation dynamics.
On orthogonality constrained multiple core-hole states and optimized effective potential method.
Glushkov, V N; Assfeld, X
2012-10-01
An attempt to construct a multiple core-hole state within the optimized effective potential (OEP) methodology is presented. In contrast to the conventional Δ-self-consistent field method for hole states, the effects of removing an electron is achieved using some orthogonality constraints imposed on the orbitals so that a Slater determinant describing a hole state is constrained to be orthogonal to that of a neutral system. It is shown that single, double, and multiple core-hole states can be treated within a unified framework and can be easily implemented for atoms and molecules. For this purpose, a constrained OEP method proposed earlier for excited states (Glushkov and Levy, J. Chem. Phys. 2007, 126, 174106) is further developed to calculate single and double core ionization energies using a local effective potential expressed as a direct mapping of the external potential. The corresponding equations, determining core-hole orbitals from a one-particle Schrödinger equation with a local potential as well as correlation corrections derived from the second-order many-body perturbation theory are given. One of the advantages of the present direct mapping formulation is that the effective potential, which plays the role of the Kohn-Sham potential, has the symmetry of the external potential. Single and double core ionization potentials computed with the presented scheme were found to be in agreement with data available from experiment and other calculations. We also discuss core-hole state local potentials for the systems studied. PMID:22696265
NASA Astrophysics Data System (ADS)
Guven, B.; Olaguer, E. P.; Herndon, S. C.; Kolb, C. E.; Cuclis, A.
2012-12-01
During the "Formaldehyde and Olefins from Large Industrial Sources" (FLAIR) study in 2009, the Aerodyne Research Inc. (ARI) mobile laboratory performed real-time in situ measurements of VOCs, NOx and HCHO in Texas City, TX on May 7, 2009 from 11 am to 3 pm. This high resolution dataset collected in a predominantly industrial area provides an ideal test bed for advanced source attribution. Our goal was to identify and quantify emission sources within the largest facility in Texas City most likely responsible for measured benzene concentrations. For this purpose, fine horizontal resolution (200 m x 200 m) 4D variational (4Dvar) inverse modeling was performed by running the HARC air quality transport model in adjoint mode based on ambient concentrations measured by the mobile laboratory. The simulations were conducted with a horizontal domain size of 4 km x 4 km for a four-hour period (11 am to 3 pm). Potential emission unit locations within the facility were specified using a high spatial resolution digital model of the largest industrial complex in the area. The HARC model was used to infer benzene emission rates from all potential source locations that would account for the benzene concentrations measured by the Aerodyne mobile laboratory in the vicinity of the facility. A Positive Matrix Factorization receptor model was also applied to the concentrations of other compounds measured by the mobile lab to support the source attribution by the inverse model. Although previous studies attributed measured benzene concentrations during the same time period to a cooling tower unit at the industrial complex, this study found that some of the flare units in the facility were also associated with the elevated benzene concentrations. The emissions of some of these flare units were found to be greater than reported in emission inventories, by up to two orders of magnitude.
Resting state fMRI: A review of methods and clinical applications
Lee, Megan H.; Smyser, Christopher D.; Shimony, Joshua S.
2014-01-01
Resting state fMRI measures spontaneous, low frequency fluctuations in the BOLD signal to investigate the functional architecture of the brain. Application of this technique has allowed for the identification of various RSNs, or spatially distinct areas of the brain that demonstrate synchronous BOLD fluctuations at rest. Various methods exist for analyzing resting state data, including seed based approaches, independent component analysis, graph methods, clustering algorithms, neural networks, and pattern classifiers. Clinical applications of resting state fMRI are at an early stage of development. However, its use in presurgical planning for brain tumor and epilepsy patients demonstrates early promise, and the technique may also have a future role in providing diagnostic and prognostic information for neurological and psychiatric diseases. PMID:22936095
Teaching the Properties of Chromium's Oxidation States with a Case Study Method
ERIC Educational Resources Information Center
Ozdilek, Zehra
2015-01-01
The purpose of this study was to investigate how a mixed-method case study affects pre-service science teachers' awareness of hexavalent chromium pollution and content knowledge about the properties of chromium's different oxidation states. The study was conducted in Turkey with 55 sophomores during the fall semester of 2013-2014. The…
Generalization of the cavity method for adiabatic evolution of Gibbs states
NASA Astrophysics Data System (ADS)
Zdeborová, Lenka; Krzakala, Florent
2010-06-01
Mean-field glassy systems have a complicated energy landscape and an enormous number of different Gibbs states. In this paper, we introduce a generalization of the cavity method in order to describe the adiabatic evolution of these glassy Gibbs states as an external parameter, such as the temperature, is tuned. We give a general derivation of the method and describe in details the solution of the resulting equations for the fully connected p -spin model, the XOR-satisfiability (SAT) problem and the antiferromagnetic Potts glass (coloring problem). As direct results of the states following method we present a study of very slow Monte Carlo annealings, the demonstration of the presence of temperature chaos in these systems and the identification of an easy/hard transition for simulated annealing in constraint optimization problems. We also discuss the relation between our approach and the Franz-Parisi potential, as well as with the reconstruction problem on trees in computer science. A mapping between the states following method and the physics on the Nishimori line is also presented.
45 CFR 235.50 - State plan requirements for methods of personnel administration.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 45 Public Welfare 2 2010-10-01 2010-10-01 false State plan requirements for methods of personnel administration. 235.50 Section 235.50 Public Welfare Regulations Relating to Public Welfare OFFICE OF FAMILY ASSISTANCE (ASSISTANCE PROGRAMS), ADMINISTRATION FOR CHILDREN AND FAMILIES, DEPARTMENT OF HEALTH AND HUMAN SERVICES ADMINISTRATION...
Technology Transfer Automated Retrieval System (TEKTRAN)
Several flux-calculation (FC) schemes are available for determining soil-to-atmosphere emissions of nitrous oxide (N2O) and other trace gases using data from non-steady-state flux chambers. Recently developed methods claim to provide more accuracy in estimating the true pre-deployment flux (f0) comp...
46 CFR 356.7 - Methods of establishing ownership by United States Citizens.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 8 2014-10-01 2014-10-01 false Methods of establishing ownership by United States Citizens. 356.7 Section 356.7 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION MISCELLANEOUS REQUIREMENTS FOR VESSELS OF 100 FEET OR GREATER IN REGISTERED LENGTH TO OBTAIN A FISHERY ENDORSEMENT TO...
46 CFR 356.7 - Methods of establishing ownership by United States Citizens.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 8 2011-10-01 2011-10-01 false Methods of establishing ownership by United States Citizens. 356.7 Section 356.7 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION MISCELLANEOUS REQUIREMENTS FOR VESSELS OF 100 FEET OR GREATER IN REGISTERED LENGTH TO OBTAIN A FISHERY ENDORSEMENT TO...
46 CFR 356.7 - Methods of establishing ownership by United States Citizens.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 8 2012-10-01 2012-10-01 false Methods of establishing ownership by United States Citizens. 356.7 Section 356.7 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION MISCELLANEOUS REQUIREMENTS FOR VESSELS OF 100 FEET OR GREATER IN REGISTERED LENGTH TO OBTAIN A FISHERY ENDORSEMENT TO...
46 CFR 356.7 - Methods of establishing ownership by United States Citizens.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Methods of establishing ownership by United States Citizens. 356.7 Section 356.7 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION MISCELLANEOUS REQUIREMENTS FOR VESSELS OF 100 FEET OR GREATER IN REGISTERED LENGTH TO OBTAIN A FISHERY ENDORSEMENT TO...
46 CFR 356.7 - Methods of establishing ownership by United States Citizens.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 8 2013-10-01 2013-10-01 false Methods of establishing ownership by United States Citizens. 356.7 Section 356.7 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION MISCELLANEOUS REQUIREMENTS FOR VESSELS OF 100 FEET OR GREATER IN REGISTERED LENGTH TO OBTAIN A FISHERY ENDORSEMENT TO...
45 CFR 235.50 - State plan requirements for methods of personnel administration.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 45 Public Welfare 2 2011-10-01 2011-10-01 false State plan requirements for methods of personnel administration. 235.50 Section 235.50 Public Welfare Regulations Relating to Public Welfare OFFICE OF FAMILY ASSISTANCE (ASSISTANCE PROGRAMS), ADMINISTRATION FOR CHILDREN AND FAMILIES, DEPARTMENT OF HEALTH AND HUMAN SERVICES ADMINISTRATION...
NASA Technical Reports Server (NTRS)
Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.
1997-01-01
Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.
A two-layer approach to the coupled coherent states method
NASA Astrophysics Data System (ADS)
Green, James A.; Grigolo, Adriano; Ronto, Miklos; Shalashilin, Dmitrii V.
2016-01-01
In this paper, a two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system. This leads to a flexible representation of the wavefunction, making the method particularly suited to the study of composite systems. It was tested on a 20-dimensional asymmetric system-bath tunnelling problem, with results compared to a benchmark calculation, as well as existing CCS, matching-pursuit/split-operator Fourier transform, and configuration interaction expansion methods. The two-layer method was found to lead to improved short and long term propagation over standard CCS, alongside improved numerical efficiency and parallel scalability. These promising results provide impetus for future development of the method for on-the-fly direct dynamics calculations.
Equation of state for neutron stars with hyperons using a variational method
NASA Astrophysics Data System (ADS)
Togashi, H.; Hiyama, E.; Yamamoto, Y.; Takano, M.
2016-03-01
We investigate the effects of the odd-state part of bare Λ Λ interactions on the structure of neutron stars (NSs) by constructing equations of state (EOSs) for uniform nuclear matter containing Λ and Σ- hyperons with use of the cluster variational method. The isoscalar part of the Argonne v18 two-nucleon potential and the Urbana IX three-nucleon potential are employed as the interactions between nucleons, whereas, as the bare Λ N and even-state Λ Λ interactions, two-body central potentials that are determined so as to reproduce the experimental data on single- and double-Λ hypernuclei are adopted. In addition, the Σ-N interaction is constructed so as to reproduce the empirical single-particle potential of Σ- in symmetric nuclear matter. Since the odd-state part of the Λ Λ interaction is not known owing to lack of experimental data, we construct four EOSs of hyperonic nuclear matter, each with a different odd-state part of the Λ Λ interaction. The EOS obtained for NS matter becomes stiffer as the odd-state Λ Λ interaction becomes more repulsive, and correspondingly the maximum mass of NSs increases. It is interesting that the onset density of Σ- depends strongly on the repulsion of the odd-state Λ Λ interaction. Furthermore, we take into account the three-baryon repulsive force to obtain results that are consistent with observational data on heavy NSs.