Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation
Canet, Elisabeth; Jault, Dominique
2010-01-01
We introduce a quasi-geostrophic model of core dynamics, which aims at describ- ing core processes on geomagnetic secular variation timescales. It extends the for- malism of Alfv ?en torsional oscillations by incorporating non-zonal motions. Within this framework, the magnetohydrodynamics takes place in the equatorial plane; it involves quadratic magnetic quantities, which are averaged along the direction of ro- tation of the Earth. In addition, the equatorial flow is projected on the core-mantle boundary. It interacts with the magnetic field at the core surface, through the radial component of the magnetic induction equation. That part of the model connects the dynamics and the observed secular variation, with the radial component of the magnetic field acting as a passive tracer. We resort to variational data assimilation to construct formally the relationship between model predictions and observations. Variational data assimilation seeks to minimize an objective function, by computing its sensitivity to its...
On the quasi-hydrostatic quasi-geostrophic model
Lucas, Carine; Mcwilliams, James C.; Rousseau, Antoine
2015-01-01
This paper introduces a rigorous derivation of the quasi-hydrostatic quasi-geostrophic (QHQG) equations of large scale ocean as the Rossby number goes to zero. We follow classical techniques for the derivation of the quasi-geostrophic (QG) equations (as in [BB94]), but the primitive equations that we consider account for the nontraditional rotating terms, as in [LPR10]. We end up with a slightly different QG model with a tilted vertical direction, which has been illustrated in previous works ...
A Multiscale Dynamo Model Driven by Quasi-geostrophic Convection
Calkins, MA; Julien, K; Tobias, SM; Aurnou, JM
2015-01-01
© 2015 Cambridge University Press. A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three time scales that respectively characterize the convective time scal...
Downscaling ocean conditions: Experiments with a quasi-geostrophic model
Katavouta, A.; Thompson, K. R.
2013-12-01
The predictability of small-scale ocean variability, given the time history of the associated large-scales, is investigated using a quasi-geostrophic model of two wind-driven gyres separated by an unstable, mid-ocean jet. Motivated by the recent theoretical study of Henshaw et al. (2003), we propose a straightforward method for assimilating information on the large-scale in order to recover the small-scale details of the quasi-geostrophic circulation. The similarity of this method to the spectral nudging of limited area atmospheric models is discussed. Results from the spectral nudging of the quasi-geostrophic model, and an independent multivariate regression-based approach, show that important features of the ocean circulation, including the position of the meandering mid-ocean jet and the associated pinch-off eddies, can be recovered from the time history of a small number of large-scale modes. We next propose a hybrid approach for assimilating both the large-scales and additional observed time series from a limited number of locations that alone are too sparse to recover the small scales using traditional assimilation techniques. The hybrid approach improved significantly the recovery of the small-scales. The results highlight the importance of the coupling between length scales in downscaling applications, and the value of assimilating limited point observations after the large-scales have been set correctly. The application of the hybrid and spectral nudging to practical ocean forecasting, and projecting changes in ocean conditions on climate time scales, is discussed briefly.
A BAROTROPIC QUASI-GEOSTROPHIC MODEL WITH LARGE-SCALE TOPOGRAPHY, FRICTION AND HEATING
无
2000-01-01
Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analysis and small parameter method. It is shown that this equation is a basic one, which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the friction and heating effect of large-scale topography are neglected, this model will degenerate to the general barotropic quasi-geostrophic one.
Omrani, H.; Drobinski, P.; Dubos, T.
2009-09-01
In this work, we consider the effect of indiscriminate nudging time on the large and small scales of an idealized limited area model simulation. The limited area model is a two layer quasi-geostrophic model on the beta-plane driven at its boundaries by its « global » version with periodic boundary condition. This setup mimics the configuration used for regional climate modelling. Compared to a previous study by Salameh et al. (2009) who investigated the existence of an optimal nudging time minimizing the error on both large and small scale in a linear model, we here use a fully non-linear model which allows us to represent the chaotic nature of the atmosphere: given the perfect quasi-geostrophic model, errors in the initial conditions, concentrated mainly in the smaller scales of motion, amplify and cascade into the larger scales, eventually resulting in a prediction with low skill. To quantify the predictability of our quasi-geostrophic model, we measure the rate of divergence of the system trajectories in phase space (Lyapunov exponent) from a set of simulations initiated with a perturbation of a reference initial state. Predictability of the "global", periodic model is mostly controlled by the beta effect. In the LAM, predictability decreases as the domain size increases. Then, the effect of large-scale nudging is studied by using the "perfect model” approach. Two sets of experiments were performed: (1) the effect of nudging is investigated with a « global » high resolution two layer quasi-geostrophic model driven by a low resolution two layer quasi-geostrophic model. (2) similar simulations are conducted with the two layer quasi-geostrophic LAM where the size of the LAM domain comes into play in addition to the first set of simulations. In the two sets of experiments, the best spatial correlation between the nudge simulation and the reference is observed with a nudging time close to the predictability time.
QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments
Y. H. Yamazaki
2008-09-01
Full Text Available QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.
QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments
Y. H. Yamazaki
2009-02-01
Full Text Available QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.
Theoretical comparison of subgrid turbulence in atmospheric and oceanic quasi-geostrophic models
Kitsios, Vassili; Frederiksen, Jorgen S.; Zidikheri, Meelis J.
2016-04-01
Due to the massive disparity between the largest and smallest eddies in the atmosphere and ocean, it is not possible to simulate these flows by explicitly resolving all scales on a computational grid. Instead the large scales are explicitly resolved, and the interactions between the unresolved subgrid turbulence and large resolved scales are parameterised. If these interactions are not properly represented then an increase in resolution will not necessarily improve the accuracy of the large scales. This has been a significant and long-standing problem since the earliest climate simulations. Historically subgrid models for the atmosphere and ocean have been developed in isolation, with the structure of each motivated by different physical phenomena. Here we solve the turbulence closure problem by determining the parameterisation coefficients (eddy viscosities) from the subgrid statistics of high-resolution quasi-geostrophic atmospheric and oceanic simulations. These subgrid coefficients are characterised into a set of simple unifying scaling laws, for truncations made within the enstrophy-cascading inertial range. The ocean additionally has an inverse energy cascading range, within which the subgrid model coefficients have different scaling properties. Simulations adopting these scaling laws are shown to reproduce the statistics of the reference benchmark simulations across resolved scales, with orders of magnitude improvement in computational efficiency. This reduction in both resolution dependence and computational effort will improve the efficiency and accuracy of geophysical research and operational activities that require data generated by general circulation models, including weather, seasonal, and climate prediction; transport studies; and understanding natural variability and extreme events.
Schubert, Sebastian
2014-01-01
The classical approach for studying atmospheric variability is based on defining a background state and studying the linear stability of the small fluctuations around such a state. Weakly non-linear theories can be constructed using higher order expansions terms. While these methods have undoubtedly great value for elucidating the relevant physical processes, they are unable to follow the dynamics of a turbulent atmosphere. We provide a first example of extension of the classical stability analysis to a non-linearly evolving atmosphere. The so-called covariant Lyapunov vectors (CLVs) provide a covariant basis describing the directions of exponential expansion and decay of perturbations to the non-linear trajectory of the flow. We use such a formalism to re-examine the basic barotropic and baroclinic processes of the atmosphere with a quasi-geostrophic beta-plane two-layer model in a periodic channel driven by a forced meridional temperature gradient $\\Delta T$. We explore three settings of $\\Delta T$, represe...
Vortex stability in a multi-layer quasi-geostrophic model: application to Mediterranean Water eddies
Carton, Xavier; Ménesguen, Claire; Meunier, Thomas [Laboratoire de Physique des Oceans, UBO/IFREMER/CNRS/IRD, Brest (France); Sokolovskiy, Mikhail [Institute of Water Problems of the RAS, Moscow (Russian Federation); Aguiar, Ana, E-mail: xcarton@univ-brest.fr [Instituto Dom Luiz, Universidade de Lisboa, Lisbon (Portugal)
2014-12-01
The stability of circular vortices to normal mode perturbations is studied in a multi-layer quasi-geostrophic model. The stratification is fitted on the Gulf of Cadiz where many Mediterranean Water (MW) eddies are generated. Observations of MW eddies are used to determine the parameters of the reference experiment; sensitivity tests are conducted around this basic case. The objective of the study is two-fold: (a) determine the growth rates and nonlinear evolutions of unstable perturbations for different three-dimensional (3D) velocity structures of the vortices, (b) check if the different structure of our idealized vortices, mimicking MW cyclones and anticyclones, can induce different stability properties in a model that conserves parity symmetry, and apply these results to observed MW eddies. The linear stability analysis reveals that, among many 3D distributions of velocity, the observed eddies are close to maximal stability, with instability time scales longer than 100 days (these time scales would be less than 10 days for vertically more sheared eddies). The elliptical deformation is most unstable for realistic eddies (the antisymmetric one dominates for small eddies and the triangular one for large eddies); the antisymmetric mode is stronger for cyclones than for anticyclones. Nonlinear evolutions of eddies with radii of about 30 km, and elliptically perturbed, lead to their re-organization into 3D tripoles; smaller eddies are stable and larger eddies break into 3D dipoles. Horizontally more sheared eddies are more unstable and sustain more asymmetric instabilities. In summary, few differences were found between cyclone and anticyclone stability, except for strong horizontal velocity shears. (paper)
Non-linear forcing singular vector of a two-dimensional quasi-geostrophic model
Wansuo Duan
2013-02-01
Full Text Available We propose a non-linear forcing singular vector (NFSV approach to infer the effect of non-linearity on the predictability associated with model errors. The NFSV is a generalisation of the forcing singular vector (FSV to non-linear fields and acts as a tendency perturbation that results in a significantly large perturbation growth. In predictability studies, the NFSV, as a tendency error, may provide useful information about model errors that cause severe prediction uncertainties. In this article, a two-dimensional quasi-geostrophic (QG model is used to study NFSVs and make a comparison between NFSVs and FSVs. We choose two basic flows: the first is a zonal steady flow (Ref-1, and the second is a meridional steady flow (Ref-2. The results demonstrate that the corresponding NFSVs contain a phase where the stream function tends to be contracted around regions of strong velocity shear. Furthermore, the NFSVs for the Ref-1 tend to have a meridional asymmetric spatial structure. Due to the absence of non-linearity, FSVs tend to have a larger spatial extension than NFSVs; in particular, the FSVs for the Ref-1 are almost symmetric in the stream function component. The prediction errors caused by FSVs in the non-linear QG model are generally smaller than those caused by FSVs in the linearised QG model; therefore, the non-linearity in the QG model would significantly saturate the perturbation growth. Nevertheless, the prediction errors caused by NFSVs (especially for the Ref-1 in the non-linear QG model are larger than those caused by FSVs, which further implies that the tendency errors of NFSV structures tend to reduce the damping effect of the non-linearity on the perturbation growth and are more applicable than those of FSV structures to describing the optimal mode of the model errors. The differences between NFSVs and FSVs demonstrate the usefulness of NFSVs in revealing the effects of non-linearity on predictability. The NFSV may be a useful non
Lucarini, V; VItolo, R; Itolo, Renato V; Lucarini, Valerio; Speranza, Antonio
2005-01-01
A quasi-geostrophic intermediate complexity model is considered, providing a schematic representation of the baroclinic conversion processes which characterize the physics of the mid-latitudes atmospheric circulation. The model is relaxed towards a given latitudinal temperature profile, which acts as baroclinic forcing, controlled by a parameter TE determining the forced equator-to-pole temperature gradient. As TE increases, a transition takes place from a stationary regime to a periodic regime, and eventually to an earth-like chaotic regime where evolution takes place on a strange attractor. The dependence of the attractor dimension, metric entropy, and bounding box volume in phase space is studied by varying both TE and model resolution. The statistical properties of observables having physical relevance, namely the total energy of the system and the latitudinally averaged zonal wind, are also examined. It is emphasized that while the attractor's properties are quite sensitive to model resolution, the globa...
San, Omer
2016-01-01
A single-layer, quasi-geostrophic (QG), large-scale ocean circulation model is developed in this paper to study available ocean current energy potentials harnessed by using the ocean current turbines. Power extraction is modeled by adding a parameterized Rayleigh friction term in the barotropic vorticity equation. Numerical assessments are performed by simulating a set of mid-latitude ocean basins in the beta plane, which are standard prototypes of more realistic ocean dynamics considering inter-decadal variability in turbulent equilibrium. A sensitivity analysis with respect to the turbine parameters is performed for various physical conditions. Results show that the proposed model captures the quasi-stationary ocean dynamics and provides the four-gyre circulation patterns in time mean. After an initial spin-up process, the proposed model reaches a statistically steady state at an average maximum speed between 1.5 m/s and 2.5 m/s, which is close to the observed maximum zonal velocities in the western boundar...
On nontraditional quasi-geostrophic equations
Lucas, Carine; Mcwilliams, James C.; Rousseau, Antoine
2015-01-01
International audience In this article, we work on nontraditional models where the so-called traditional approximation on the Coriolis force is removed. In the derivation of the quasi-geostrophic equations, we obtain new terms in δ/ε, where δ (aspect ratio) and ε (Rossby number) are both small numbers. We provide here some rigorous crossed-asymptotics with regards to these parameters , prove some mathematical and physical results on the nontraditional models, and situate them among traditi...
Rocha, C. B.; Tandon, A.; Da Silveira, I. C.
2012-12-01
Recent literature has focused theoretically on whether the Quasi-geostrophic (QG) modes and Surface Quasi-geostrophic (SQG) solutions can account for the vertical structure of oceanic flows. In an attempt to resolve this from data, we analyzed the vertical structure of the mesoscale variability in three moorings off Brazil -- two in the Brazil Current domain (MARLIM mooring at 22.45oS, 40.2oW; and WOCE 333 mooring, hereafter W333, at 27.5oS, 46.7oW) and one off-shore (WOCE 335 mooring, hereafter W335, at 28.5oS, 45.3oW). The MARLIM mooring has 9 conventional current meters and spans 300 days. The W333 (W335) has 4 (5) conventional current meters and an upward-looking ADCP and spans 650 days. We evaluated the ability of the QG modes and SQG solutions to account for the vertical structure of the EOFs at these moorings. Only the 1st EOF is statistically significant for three moorings, containing up to 90% of the variance. Although the traditional barotropic (BT) and 1st baroclinic (BC1) modes together contain up to 70% of the variance in the MARLIM and W335 moorings, their combination fails to represent the sharp near surface vertical decay. Higher order modes (2nd and 3rd baroclinic) are needed to account for this near surface variance. A mesoscale broad-banded linear combination of SQG solutions accounts for up to 90% of the variance at these moorings and it represents the near surface decay particularly well. Therefore either the inclusion of higher order QG modes, or, the SQG solutions, is consistent with the data. Indeed, the projection of the SQG solutions onto the traditional QG modes reveals that these two models do not exclude each other. For the W333 moorings the BT/BC1 linear combination accounts for 91% of the variance and does reproduce the near surface decay accurately. In this case, the SQG solutions contains 79% of the 1st EOF variance, although its exponential decay is not present in the data. In order to evaluate how these results can be changed by
Masuda, Akira
2011-01-01
Quasi-geostrophic current is expanded in terms of vertical modes such as barotropic and baroclinic ones. Then the evolution of quasi-geostrophic motion is understood from the behavior of each vertical mode. There are some subtle issues, however, as regards vertical modes: boundary conditions, difference between a level model and a layer model, and so on. A comprehensive formulation is given of the expansion of the quasi-geostrophic flows in terms of vertical modes both for a level model and f...
Global weak solutions to the inviscid 3D Quasi-Geostrophic equation
Puel, Marjolaine; Vasseur, Alexis F.
2014-01-01
In this article, the authors prove the existence of global weak solutions to the inviscid three-dimensional quasi-geostrophic equation. This equation models the evolution of the temperature on the surface of the earth. It is widely used in geophysics and meteorology.
Large Scale Quasi-geostrophic Magnetohydrodynamics
Balk, Alexander M
2014-01-01
We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the "shallow water" beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the inverse cascade; but contrary to the usual Q-G situation, the energy cascades to smaller length scales, while the enstrophy cascades to the larger scales. We find the Kolmogorov-type spectrum for the inverse cascade. The spectrum indicates the energy accumulation in larger scales. In addition to the energy and enstrophy, the obtained equation possesses an extra invariant. Its presence is shown to imply energy accumulation ...
Large-scale quasi-geostrophic magnetohydrodynamics
We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the 'shallow water' beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the inverse cascade; but contrary to the usual Q-G situation, the energy cascades to smaller length scales, while the enstrophy cascades to the larger scales. We find the Kolmogorov-type spectrum for the inverse cascade. The spectrum indicates the energy accumulation in larger scales. In addition to the energy and enstrophy, the obtained equation possesses an extra (adiabatic-type) invariant. Its presence implies energy accumulation in the 30° sector around zonal direction. With some special energy input, the extra invariant can lead to the accumulation of energy in zonal magnetic field; this happens if the input of the extra invariant is small, while the energy input is considerable.
Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores
Canet, Elisabeth; Fournier, Alexandre
2014-01-01
The core of a terrestrial-type planet consists of a spherical shell of rapidly rotating, electrically conducting, fluid. Such a body supports two distinct classes of quasi-geostrophic eigenmodes: fast, primarily hydrodynamic, inertial modes with period related to the rotation time scale and slow, primarily magnetic, magnetostrophic modes with much longer periods. Here, we investigate the properties of these hydromagnetic quasi-geostrophic modes as a function of non-dimensional parameters controlling the strength of the background magnetic field, the planetary rotation rate, and the amount of magnetic dissipation. ... read full length abstract in the paper.
An Ocean Drum: quasi-geostrophic energetics from a Riemann geometry perspective
Jaramillo, José Luis
2016-01-01
We revisit the discussion of the energetics of quasi-geostrophic flows from a geometric perspective based on the introduction of an effective metric, built in terms of the flow stratification and the Coriolis parameter. In particular, an appropriate notion of normal modes is defined through a spectral geometry problem in the ocean basin (a compact manifold with boundary) for the associated Laplace-Beltrami scalar operator. This spectral problem can be used to systematically encode non-local aspects of stratification and topography. As examples of applications we revisit the isotropy assumption in geostrophic turbulence, identify (a patch of) the hyperbolic space $\\mathbb{H}^3$ as the leading-order term in the effective geometry for the deep mesoscale ocean and, finally, discuss some diagnostic tools based on a simple statistical mechanics toy-model to be used in numerical simulations and/or observations of quasi-geostrophic flows.
An ocean drum: quasi-geostrophic energetics from a Riemann geometry perspective
Jaramillo, José Luis
2016-05-01
We revisit the discussion of the energetics of quasi-geostrophic flows from a geometric perspective based on the introduction of an effective metric, built in terms of the flow stratification and the Coriolis parameter. In particular, an appropriate notion of normal modes is defined through a spectral geometry problem in the ocean basin (a compact manifold with boundary) for the associated Laplace–Beltrami scalar operator. This spectral problem can be used to systematically encode non-local aspects of stratification and topography. As examples of applications we revisit the isotropy assumption in geostrophic turbulence, identify (a patch of) the hyperbolic space {{{H}}}3 as the leading-order term in the effective geometry for the deep mesoscale ocean and, finally, discuss some diagnostic tools based on a simple statistical mechanics toy-model to be used in numerical simulations and/or observations of quasi-geostrophic flows.
On Nonlinear Stability Theorems of 3D Quasi-geostrophic Flow
无
2006-01-01
Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an invariant of zonal momentum. When applied to the Eady model in a periodic channel with finite zonal length, the improved nonlinear stability criterion is identical to the linear normal-mode stability criterion provided the channel meridional width is no greater than 0.8605... times its channel length (which is the geophysically relevant case).
Generalized surface quasi-geostrophic equations with singular velocities
Chae, Dongho; Córdoba, Diego; Gancedo, Francisco; Wu, Jiahong
2011-01-01
This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The first family is a generalized surface quasi-geostrophic (SQG) equation with the velocity field $u$ related to the scalar $\\theta$ by $u=\
Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores
Canet, E.; Finlay, Chris; Fournier, A.
2014-01-01
The core of a terrestrial-type planet consists of a spherical shell of rapidly rotating, electrically conducting, fluid. Such a body supports two distinct classes of quasi-geostrophic (QG) eigenmodes: fast, primarily hydrodynamic, inertial modes with period related to the rotation time scale and...... is comparable to, or shorter than, their oscillation time scale.Based on our analysis, we expect Mercury to be in a regime where the slow magnetic modes are of quasi-free decay type. Earth and possibly Ganymede, with their larger Elsasser numbers, may possess slow modes that are in the transition...
Quasi-geostrophic modes in the Earth's fluid core with an outer stably stratified layer
Vidal, Jérémie
2015-01-01
Seismic waves sensitive to the outermost part of the Earth's liquid core seem to be affected by a stably stratified layer at the core-mantle boundary. Such a layer could have an observable signature in both long-term and short-term variations of the magnetic field of the Earth, which are used to probe the flow at the top of the core. Indeed, with the recent SWARM mission, it seems reasonable to be able to identify waves propagating in the core with period of several months, which may play an important role in the large-scale dynamics. In this paper, we characterize the influence of a stratified layer at the top of the core on deep quasi-geostrophic (Rossby) waves. We compute numerically the quasi-geostrophic eigenmodes of a rapidly rotating spherical shell, with a stably stratified layer near the outer boundary. Two simple models of stratification are taken into account, which are scaled with commonly accepted values of the Brunt-V{\\"a}is{\\"a}l{\\"a} frequency in the Earth's core. In the absence of magnetic fi...
Quasi-geostrophic dynamics in the presence of moisture gradients
Monteiro, Joy M
2016-01-01
The derivation of a quasi-geostrophic (QG) system from the rotating shallow water equations on a midlatitude beta-plane coupled with moisture is presented. Condensation is prescribed to occur whenever the moisture at a point exceeds a prescribed saturation value. It is seen that a slow condensation time scale is required to obtain a consistent set of equations at leading order. Further, since the advecting wind fields are geostrophic, changes in moisture (and hence, precipitation) occur only via non-divergent mechanisms. Following observations, a saturation profile with gradients in the zonal and meridional directions is prescribed. A purely meridional gradient has the effect of slowing down the dry Rossby waves, through a reduction in the "equivalent gradient" of the background potential vorticity. A large scale unstable moist mode results on the inclusion of a zonal gradient by itself, or in conjunction with a meridional moisture gradient. For gradients that are are representative of the atmosphere, the mos...
The effects of Ekman pumping on quasi-geostrophic Rayleigh-Benard convection
Plumley, Meredith; Marti, Philippe; Stellmach, Stephan
2016-01-01
Numerical simulations of 3D, rapidly rotating Rayleigh-Benard convection are performed using an asymptotic quasi-geostrophic model that incorporates the effects of no-slip boundaries through (i) parameterized Ekman pumping boundary conditions, and (ii) a thermal wind boundary layer that regularizes the enhanced thermal fluctuations induced by pumping. The fidelity of the model, obtained by an asymptotic reduction of the Navier-Stokes equations that implicitly enforces a pointwise geostrophic balance, is explored for the first time by comparisons of simulations against the findings of direct numerical simulations and laboratory experiments. Results from these methods have established Ekman pumping as the mechanism responsible for significantly enhancing the vertical heat transport. This asymptotic model demonstrates excellent agreement over a range of thermal forcing for Pr ~1 when compared with results from experiments and DNS at maximal values of their attainable rotation rates, as measured by the Ekman numb...
Canonical transfer and multiscale energetics for primitive and quasi-geostrophic atmospheres
Liang, X San
2016-01-01
The past years have seen the success of a novel multiscale energetic formalism in a variety of ocean and engineering fluid applications. In a self-contained way, this study introduces it to the atmospheric dynamical diagnostics, with important theoretical updates. Multiscale energy equations are derived using a new analysis apparatus, namely, multiscale window transform, with respect to both the primitive equation and quasi-geostrophic models. A reconstruction of the "atomic" energy fluxes on the multiple scale windows allows for a natural and unique separation of the in-scale transports and cross-scale transfers from the intertwined nonlinear processes. The resulting energy transfers bear a Lie bracket form, reminiscent of the Poisson bracket in Hamiltonian mechanics, we hence would call them "canonical". A canonical transfer process is a mere redistribution of energy among scale windows, without generating or destroying energy as a whole. By classification, a multiscale energetic cycle comprises of availabl...
Computation of rare transitions in the barotropic quasi-geostrophic equations
We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems. (paper)
Kinetic energy cascades in quasi-geostrophic convection in a spherical shell
We consider triadic nonlinear interaction in the Navier-Stokes equation for quasi-geostrophic convection in a spherical shell. This approach helps us understand the origin of kinetic energy transport in the system and the particular scheme of mode interaction, as well as the locality of energy transfer. The peculiarity of convection in the sphere, concerned with the excitation of Rossby waves, is considered. The obtained results are compared with the results of our previous study on Cartesian geometry. (paper)
Makeenko, Yu.; Zarembo, K.
1993-01-01
We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an arbitrary interaction potential and turns out to be equivalent to the one for the Hermitean one-matrix model with a logarithmic potential and, therefore, belongs to the same universality class. The explicit solutions for the fermionic two-matrix and $D$-di...
Similarity Reductions of Barotropic and Quasi-geostrophic Potential Vorticity Equation
HUANG Fei
2004-01-01
The (2+1)-dimensional nonlinear barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a beta-plane channel is investigated by using the classical Lie symmetry approach. Some types of group-invariant wave solutions are expressed by means of the lower-dimensional similarity reduction equations. In addition to the known periodic Rossby wave solutions, some new types of exact solutions such as the ring solitary waves and the breaking soliton type of vorticity solutions with nonlinear and nonconstant shears are also obtained.
Statistical mechanics of quasi-geostrophic flows on a rotating sphere
Statistical mechanics provides an elegant explanation for the appearance of coherent structures in two-dimensional inviscid turbulence: while the fine-grained vorticity field, described by the Euler equation, becomes more and more filamentary through time, its dynamical evolution is constrained by some global conservation laws (energy, Casimir invariants). As a consequence, the coarse-grained vorticity field can be predicted through standard statistical mechanics arguments (relying on the Hamiltonian structure of the two-dimensional Euler flow), for any given set of the integral constraints. It has been suggested that the theory applies equally well to geophysical turbulence; specifically in the case of the quasi-geostrophic equations, with potential vorticity playing the role of the advected quantity. In this study, we demonstrate analytically that the Miller–Robert–Sommeria theory leads to non-trivial statistical equilibria for quasi-geostrophic flows on a rotating sphere, with or without bottom topography. We first consider flows without bottom topography and with an infinite Rossby deformation radius, with and without conservation of angular momentum. When the conservation of angular momentum is taken into account, we report a second-order phase transition associated with spontaneous symmetry breaking. In a second step, we treat the general case of a flow with an arbitrary bottom topography and a finite Rossby deformation radius. Previous studies were restricted to flows in a planar domain with fixed or periodic boundary conditions with a beta-effect. In these different cases, we are able to classify the statistical equilibria for the large-scale flow through their macroscopic features. We build the phase diagrams of the system and discuss the relations of the various statistical ensembles
Global well-posedness for the 2D quasi-geostrophic equation in a critical Besov space
Atanas Stefanov
2007-01-01
We show that the 2D quasi-geostrophic equation has global and unique strong solution when the (large) data belongs in the critical scale invariant space $dot{B}^{2-2alpha}_{2, infty}cap L^{2/(2alpha-1)}$.
Global well-posedness for the 2D quasi-geostrophic equation in a critical Besov space
Atanas Stefanov
2007-11-01
Full Text Available We show that the 2D quasi-geostrophic equation has global and unique strong solution when the (large data belongs in the critical scale invariant space $dot{B}^{2-2alpha}_{2, infty}cap L^{2/(2alpha-1}$.
Global well-posedness for the 2 D quasi-geostrophic equation in a critical Besov space
Stefanov, Atanas
2006-01-01
We show that the the 2 D quasi-geostrophic equation has global and unique strong solution, when the (large) data belongs in the critical, scale invariant space $\\dot{B}^{2-2\\al}_{2, \\infty}\\cap L^{2/(2\\al-1)}$.
ADGEN: ADjoint GENerator for computer models
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
Badin, Gualtiero
2015-01-01
The role of short-wave instabilities on geostrophic turbulence is studied in a simplified model consisting of three layers in the quasi-geostrophic approximation. The linear stability analysis shows that short-wave instabilities are created by the interplay between the shear in the upper and the lower layers. If the stratification is non-uniform, in particular surface intensified, the linear growth rate is larger for short-wave instabilities than for long-wave instabilities and the layers are essentially decoupled, with the small scales growing independently. The fully developed homogeneous turbulence is studied in a number of numerical experiments. Results show that in both the case of equal layer depths and surface intensified stratification an inverse cascade in kinetic energy is observed. The modal kinetic energy spectra for the case with surface intensified stratification show higher energy for higher baroclinic numbers at small scales, due to the decoupling of the layers. As a result, while the case wit...
Quasi-geostrophic equations with initial data in Banach spaces of local measures
Sadek Gala
2005-06-01
Full Text Available This paper studies the well posedness of the initial value problem for the quasi-geostrophic type equations $$displaylines{ partial_{t}heta+u ablaheta+( -Delta ^{gamma}heta =0 quad hbox{on }mathbb{R}^{d}imes] 0,+infty[cr heta( x,0 =heta_{0}(x, quad xinmathbb{R}^{d} }$$ where 0 less than $gammaleq 1$ is a fixed parameter and the velocity field $u=(u_{1},u_{2},dots,u_{d} $ is divergence free; i.e., $ abla u=0$. The initial data $heta_{0}$ is taken in Banach spaces of local measures (see text for the definition, such as Multipliers, Lorentz and Morrey-Campanato spaces. We will focus on the subcritical case 1/2 less than $gammaleq1$ and we analyse the well-posedness of the system in three basic spaces: $L^{d/r,infty}$, $dot {X}_{r}$ and $dot {M}^{p,d/r}$, when the solution is global for sufficiently small initial data. Furtheremore, we prove that the solution is actually smooth. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.
Fully automatic adjoints: a robust and efficient mechanism for generating adjoint ocean models
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
Gauge Mediation Models with Adjoint Messengers
Gogoladze, Ilia; Shafi, Qaisar; Un, Cem Salih
2016-01-01
We present a class of models in the framework of gauge mediation supersymmetry breaking where the messenger fields transform in the adjoint representation of the Standard Model gauge symmetry. To avoid unacceptably light right-handed sleptons in the spectrum we introduce a non-zero U(1)_B-L D-term. This leads to an additional contribution to the soft supersymmetry breaking mass terms which makes the right-handed slepton masses compatible with the current experimental bounds. We show that in this framework the observed 125 GeV Higgs boson mass can be accommodated with the sleptons accessible at the LHC, while the squarks and gluinos lie in the multi-TeV range. We also discuss the issue of the fine-tuning and show that the desired relic dark matter abundance can also be accommodated.
黄代文
2007-01-01
@@ We consider the two-dimensional stochastic quasi-geostrophic equation[12p.234,13]((Э)/(Э)t+(Э)ψ/(Э)x(Э)/(Э)y-(Э)ψ/(Э)y(Э)/(Э)x)(△ψ-Fψ+β0y)=1/Re△2ψ-r/2△ψ+f(x,y,t) (1.1)on a regular bounded open domain D (С) R2,where ψis the stream function,F Froude Number (F≈O(1)),Re Reynolds number(Re≥102),β0a Positive constant(β0≈O(10-1)),r the Ekman dissipation constant(r≈O(1)),the external forcing term f(x,y,t)=-dW/dt(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the restrictions imposed below.
Fine resolution modeling with CMAQ-adjoint
Resler, Jaroslav; Eben, Kryštof; Juruš, Pavel
Chapel Hill : CMAS, 2010. [Annual CMAS Conference /9./. 11.10.2010-13.10.2010, Chapel Hill] R&D Projects: GA MŽP SP/1A4/107/07 Institutional research plan: CEZ:AV0Z10300504 Keywords : CMAQ * adjoint * MPI * parallel efficiency Subject RIV: DG - Athmosphere Sciences, Meteorology http://www.cmascenter.org/conference/2010/agenda.cfm
Funakoshi, Satoshi; Sato, Tomoyoshi; Miyazaki, Takeshi
2012-06-01
We investigate the statistical mechanics of quasi-geostrophic point vortices of mixed sign (bi-disperse system) numerically and theoretically. Direct numerical simulations under periodic boundary conditions are performed using a fast special-purpose computer for molecular dynamics (GRAPE-DR). Clustering of point vortices of like sign is observed and two-dimensional (2D) equilibrium states are formed. It is shown that they are the solutions of the 2D mean-field equation, i.e. the sinh-Poisson equation. The sinh-Poisson equation is generalized to study the 3D nature of the equilibrium states, and a new mean-field equation with the 3D Laplace operator is derived based on the maximum entropy theory. 3D solutions are obtained at very low energy level. These solution branches, however, cannot be traced up to the higher energy level at which the direct numerical simulations are performed, and transitions to 2D solution branches take place when the energy is increased.
Funakoshi, Satoshi; Sato, Tomoyoshi; Miyazaki, Takeshi, E-mail: funakosi@miyazaki.mce.uec.ac.jp, E-mail: miyazaki@mce.uec.ac.jp [Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, 1-5-1, Chofugaoka, Chofu, Tokyo 182-8585 (Japan)
2012-06-01
We investigate the statistical mechanics of quasi-geostrophic point vortices of mixed sign (bi-disperse system) numerically and theoretically. Direct numerical simulations under periodic boundary conditions are performed using a fast special-purpose computer for molecular dynamics (GRAPE-DR). Clustering of point vortices of like sign is observed and two-dimensional (2D) equilibrium states are formed. It is shown that they are the solutions of the 2D mean-field equation, i.e. the sinh-Poisson equation. The sinh-Poisson equation is generalized to study the 3D nature of the equilibrium states, and a new mean-field equation with the 3D Laplace operator is derived based on the maximum entropy theory. 3D solutions are obtained at very low energy level. These solution branches, however, cannot be traced up to the higher energy level at which the direct numerical simulations are performed, and transitions to 2D solution branches take place when the energy is increased. (paper)
Automatic differentiation, tangent linear models, and (pseudo) adjoints
Bischof, C.H.
1993-12-31
This paper provides a brief introduction to automatic differentiation and relates it to the tangent linear model and adjoint approaches commonly used in meteorology. After a brief review of the forward and reverse mode of automatic differentiation, the ADIFOR automatic differentiation tool is introduced, and initial results of a sensitivity-enhanced version of the MM5 PSU/NCAR mesoscale weather model are presented. We also present a novel approach to the computation of gradients that uses a reverse mode approach at the time loop level and a forward mode approach at every time step. The resulting ``pseudoadjoint`` shares the characteristic of an adjoint code that the ratio of gradient to function evaluation does not depend on the number of independent variables. In contrast to a true adjoint approach, however, the nonlinearity of the model plays no role in the complexity of the derivative code.
Searching for Standard Model Adjoint Scalars with Diboson Resonance Signatures
Carpenter, Linda M
2015-01-01
We explore the phenomenology of scalar fields in the adjoint representation of SM gauge groups. We write a general set of dimension 5 effective operators in which SM adjoint scalars couple to pairs of standard model bosons. Using these effective operators, we explore new possible decay channels of a scalar color octet into a gluon and a Z boson/ gluon and a photon. We recast several analyses from Run I of the LHC to find constraints on an a scalar octet decaying into these channels, and we project the discovery potential of color octets in our gluon+photon channel for the 14 TeV run of LHC.
Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems
Garg, Vikram V
2014-09-27
Background Models based on the Helmholtz `slip\\' approximation are often used for the simulation of electroosmotic flows. The objectives of this paper are to construct adjoint-consistent formulations of such models, and to develop adjoint-based numerical tools for adaptive mesh refinement and parameter sensitivity analysis. Methods We show that the direct formulation of the `slip\\' model is adjoint inconsistent, and leads to an ill-posed adjoint problem. We propose a modified formulation of the coupled `slip\\' model, which is shown to be well-posed, and therefore automatically adjoint-consistent. Results Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional microfluidics problems. Conclusions An adjoint-consistent formulation for Helmholtz `slip\\' models of electroosmotic flows has been proposed. This formulation provides adjoint solutions that can be reliably used for mesh refinement and sensitivity analysis.
Inverse Modeling of Emissions using the CMAQ Adjoint Model
Resler, Jaroslav; Eben, Kryštof; Juruš, Pavel; Krč, Pavel
Chapel Hill : CMAS, 2008, s. 1-5. [Annual CMAS Conference /7./. Chapel Hill (US), 06.10.2008-08.10.2008] R&D Projects: GA AV ČR 1ET400300414; GA MŽP SP/1A4/107/07 Institutional research plan: CEZ:AV0Z10300504 Keywords : 4DVar * data assimilation * inverse modelling * emission * CMAQ adjoint * tropospheric column of NO2 * satellite instruments * GOME2 * OMI Subject RIV: IN - Informatics, Computer Science http://www.cmascenter.org/conference/2008/agenda.cfm
Examination of Observation Impacts derived from OSEs and Adjoint Models
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.
Adjoint $SU(5)$ GUT model with $T_{7}$ flavor symmetry
Arbeláez, Carolina; Kovalenko, Sergey; Schmidt, Iván
2015-01-01
We propose an adjoint $SU(5)$ GUT model with a $T_{7}$ family symmetry and an extra $Z_{2}\\otimes Z_{2}^{\\prime }\\otimes Z_{3}\\otimes Z_{4}\\otimes Z_{12}$ discrete group, that successfully describes the prevailing Standard Model (SM) fermion mass and mixing pattern. The observed hierarchy of the charged fermion masses and the quark mixing angles arises from the $Z_{3}\\otimes Z_{4}\\otimes Z_{12}$ symmetry breaking, which occurs near the GUT scale. The light active neutrino masses are generated by type I and type III seesaw mechanisms mediated by the fermionic $SU(5)$ singlet and the adjoint $\\mathbf{24}$-plet. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be $m_{\\beta \\beta }=$ 4 and 50 meV for the normal and the inverted neutrino spectrum, respectively. We construct several benchmark scenarios, which lead to $SU(5)$ gauge coupling unification and are compatible with the known phenomenological constraints originating from the lightness of neutrinos, prot...
Adjoint Assimilation in Marine Ecosystem Models and an Example of Application
XU Qing; LIU Yuguang; L(U) Xianqing
2005-01-01
This paper aims at a review of the work carried out to date on the adjoint assimilation of data in marine ecosystem models since 1995. The structure and feature of the adjoint assimilation in marine ecosystem models are also introduced.To illustrate the application of the adjoint technique and its merits, a 4-variable ecosystem model coupled with a 3-D physical model is established for the Bohai Sea and the Yellow Sea. The chlorophyll concentration data derived from the SeaWiFS ocean colour data are assimilated in the model with the technique. Some results are briefly presented.
A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
Nishimura, Hiromichi; Ogilvie, Michael C.
2009-01-01
Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on $R^{3}\\times S^{1}$ can lead to a restoration of center symmetry and confinement for sufficiently small circumference $L$ of $S^{1}$. At small $L$, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop $P$ in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselv...
Efficient parameter estimation in 2D transport models based on an adjoint formalism
An adjoint based optimization procedure is elaborated to estimate transport coefficients for plasma edge models based on a limited set of known profiles at different locations. It is shown that a set of adjoint equations can accurately determine all sensitivities towards transport coefficients at once. A proof of principle is provided on a simple geometry. The methodology is subsequently applied to assess whether a simple edge model can be tuned toward full B2-EIRENE profiles for a JET-configuration. (paper)
A self-adjoint arrival time operator inspired by measurement models
Highlights: • Construction of a self-adjoint arrival time operator inspired by measurements. • Agreement with the strong measurement formula in the low momentum regime. • Review of self-adjoint and non-self-adjoint arrival time operators. • Discussion of the momentum operator on the half-line. • Discussion of the intuitive reasons obstructing self-adjointness. - Abstract: We introduce an arrival time operator which is self-adjoint and, unlike previously proposed arrival time operators, has a close link to simple measurement models. Its spectrum leads to an arrival time distribution which is a variant of the Kijowski distribution (a re-ordering of the current) in the large momentum regime but is proportional to the kinetic energy density in the small momentum regime, in agreement with measurement models. A brief derivation of the latter distribution is given. We make some simple observations about the physical reasons for self-adjointness, or its absence, in both arrival time operators and the momentum operator on the half-line and we also compare our operator with the dwell time operator
Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
Liu, Yizhuang; Zahed, Ismail
2016-01-01
We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $SU_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective theory with adjoint quarks with manifest $SU(N_f)\\times Z_{4N_f}$ symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for $N_f=1$. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through $SU(N_f)\\times Z_{4N...
Tracking influential haze source areas in North China using an adjoint model, GRAPES-CUACE
An, X. Q.; Zhai, S. X.; Jin, M.; Gong, S. L.; Wang, Y.
2015-08-01
Based upon the adjoint theory, the adjoint of the aerosol module in the atmospheric chemical modeling system GRAPES-CUACE (Global/Regional Assimilation and PrEdiction System coupled with the CMA Unified Atmospheric Chemistry Environment) was developed and tested for its correctness. Through statistic comparison, BC (black carbon aerosol) concentrations simulated by GRAPES-CUACE were generally consistent with observations from Nanjiao (one urban observation station) and Shangdianzi (one rural observation station) stations. To track the most influential emission-sources regions and the most influential time intervals for the high BC concentration during the simulation period, the adjoint model was adopted to simulate the sensitivity of average BC concentration over Beijing at the highest concentration time point (referred to as the Objective Function) with respect to BC emission amount over Beijing-Tianjin-Hebei region. Four types of regions were selected based on administrative division and sensitivity coefficient distribution. The adjoint model was used to quantify the effects of emission-sources reduction in different time intervals over different regions by one independent simulation. Effects of different emission reduction strategies based on adjoint sensitivity information show that the more influential regions (regions with relatively larger sensitivity coefficients) do not necessarily correspond to the administrative regions, and the influence effectiveness of sensitivity-oriented regions was greater than the administrative divisions. The influence of emissions on the objective function decreases sharply approximately for the pollutants emitted 17-18 h ago in this episode. Therefore, controlling critical emission regions during critical time intervals on the basis of adjoint sensitivity analysis is much more efficient than controlling administrative specified regions during an experiential time period.
The Hamiltonian of a system of quantum particles minimally coupled to a quantum field is considered for arbitrary coupling constants. The Hamiltonian has a translation invariant part. By means of functional integral representations the existence of an invariant domain under the action of the heat semigroup generated by a self-adjoint extension of the translation invariant part is shown. With a non-perturbative approach it is proved that the Hamiltonian is essentially self-adjoint on a domain. A typical example is the Pauli-Fierz model with spin 1/2 in nonrelativistic quantum electrodynamics for arbitrary coupling constants. (orig.)
Development of CO2 inversion system based on the adjoint of the global coupled transport model
Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon
2014-05-01
We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) Eulerian transport model (TM) and the Lagrangian plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the Lagrangian model FLEXPART. The Lagrangian component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the Lagrangian part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to Eulerian part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of Lagrangian model is required, making it applicable to combination of global NIES TM and any Lagrangian model; 2. Once run, the Lagrangian output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over
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.
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
Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance
Hochuli, Roman; Arridge, Simon; Cox, Ben
2016-01-01
Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A 2D radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance in heterogeneous media. A gradient-based optimisation scheme is then used to recover 2D absorption and scattering coefficients distributions from simulated photoacoustic measurements. It is shown that the functional gradients, which are a challenge to compute efficiently using MC models, can be calculated directly from the coefficients of the harmonic angular basis used in the forward and adjoint models. This work establishes a framework for transport-based quantitative photoacoustic tomography that can fully exploit emerging highly parallel computing architectures.
Coupling Unification and Dark Matter in a Standard Model Extension with Adjoint Majorana Fermions
Aizawa, Tasuku; Ibe, Masahiro; Kaneta, Kunio
2014-01-01
We revisit an extension of the Standard Model with Majorana fermions in the adjoint representations. There, a precise coupling unification and the good candidate for dark matter (the $SU(2)_L$ triplet fermion) are achieved simultaneously. In particular, we show that the $SU(3)_c$ octet fermion which is required for successful unification can be a good non-thermal source of the triplet fermion dark matter. We also show that the scenario predicts a rather short lifetime of the proton compared w...
Adjoint-based linear analysis in reduced-order thermo-acoustic models
Magri, Luca
2014-01-01
This paper presents the linear theory of adjoint equations as applied to thermo-acoustics. The purpose is to describe the mathematical foundations of adjoint equations for linear sensitivity analysis of thermo-acoustic systems, recently developed by Magri and Juniper (J. Fluid Mech. (2013), vol. 719, pp. 183--202). This method is applied pedagogically to a damped oscillator, for which analytical solutions are available, and then for an electrically heated Rijke tube with a mean-flow temperature discontinuity induced by the compact heat source. Passive devices that most affect the growth rate / frequency of the electrical Rijke-tube system are presented, including a discussion about the effect of modelling the mean-flow temperature discontinuity.
Tber, Moulay Hicham; Vidard, Arthur; Dauvergne, Benjamin
2007-01-01
The ocean general circulation model OPA is developed by the LODYC team at Paris VI university. OPA has recently undergone a major rewriting, migrating to FORTRAN95, and its adjoint code needs to be rebuilt. For earlier versions, the adjoint of OPA was written by hand at a high development cost. We use the Automatic Differentiation tool TAPENADE to build mechanicaly the tangent and adjoint codes of OPA. We validate the differentiated codes by comparison with divided differences, and also with an identical twin experiment. We apply state-of-the-art methods to improve the performance of the adjoint code. In particular we implement the Griewank and Walther's binomial checkpointing algorithm which gives us an optimal trade-off between time and memory consumption. We apply a specific strategy to differentiate the iterative linear solver that comes from the implicit time stepping scheme
The Adjoint Method Formulation for an Inverse Problem in the Generalized Black-Scholes Model
PIERRE NGNEPIEBA
2006-08-01
Full Text Available A general framework is developed to treat optimal control problems for a generalized Black-Scholes model, which is used for option pricing. The volatility function is retrieved from a set of market observations. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy between the model solution (pricing and the observed market price, via the unconstrained minimization algorithm of the quasi-Newton limited memory type. The gradient is computed via the adjoint method. The effectiveness of the method is demonstrated on an European call option.
Improving the Fit of a Land-Surface Model to Data Using its Adjoint
Raoult, Nina; Jupp, Tim; Cox, Peter; Luke, Catherine
2016-04-01
Land-surface models (LSMs) are crucial components of the Earth System Models (ESMs) which are used to make coupled climate-carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. In this study, JULES is automatically differentiated using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimation system has been developed, to search for locally optimum parameter sets by calibrating against observations. We present an introduction to the adJULES system and demonstrate its ability to improve the model-data fit using eddy covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the 5 Plant Functional Types (PFTS) in JULES. The optimised PFT-specific parameters improve the performance of JULES over 90% of the FLUXNET sites used in the study. These reductions in error are shown and compared to reductions found due to site-specific optimisations. Finally, we show that calculation of the 2nd derivative of JULES allows us to produce posterior probability density functions of the parameters and how knowledge of parameter values is constrained by observations.
The minimal adjoint-SU(5)xZ_4 GUT model
Emmanuel-Costa, D; Tortola, M
2013-01-01
An extension of the adjoint SU(5) model with a flavour symmetry based on the Z_4 group is investigated. The Z_4 symmetry is introduced with the aim of leading the up- and down-quark mass matrices to the Nearest-Neighbour-Interaction form. As a consequence of the discrete symmetry embedded in the SU(5) gauge group, the charged lepton mass matrix also gets the same form. Within this model, light neutrinos get their masses through type-I, type-III and one-loop radiative seesaw mechanisms, implemented, respectively, via a singlet, a triplet and an octet from the adjoint fermionic 24 fields. It is demonstrated that the neutrino phenomenology forces the introduction of at least three 24 fermionic multiplets. The symmetry SU(5)xZ_4 allows only two viable zero textures for the effective neutrino mass matrix. It is showed that one texture is only compatible with normal hierarchy and the other with inverted hierarchy in the light neutrino mass spectrum. Finally, it is also demonstrated that Z_4 freezes out the possibil...
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 sensitivity analysis of dynamic reliability models based on Markov chains - I: Theory
The development of the adjoint sensitivity analysis procedure (ASAP) for generic dynamic reliability models based on Markov chains is presented, together with applications of this procedure to the analysis of several systems of increasing complexity. The general theory is presented in Part I of this work and is accompanied by a paradigm application to the dynamic reliability analysis of a simple binary component, namely a pump functioning on an 'up/down' cycle until it fails irreparably. This paradigm example admits a closed form analytical solution, which permits a clear illustration of the main characteristics of the ASAP for Markov chains. In particular, it is shown that the ASAP for Markov chains presents outstanding computational advantages over other procedures currently in use for sensitivity and uncertainty analysis of the dynamic reliability of large-scale systems. This conclusion is further underscored by the large-scale applications presented in Part II. (authors)
Sensitivity analyses for mass transport model in porous media were performed by using adjoint method. The mass transport model employed is to evaluate the performance of engineered barrier of shallow land disposal, assuming that water flows through a cylinder packed with sand. In this model instantaneous sorption equilibrium between liquid and solid phases is assumed and two types of boundary conditions which represent the nuclide release from waste package, i.e. solubility-limited case and constant leaching case, are considered. From the sensitivity analysis, it was shown that the effect of longitudinal dispersion on performance measure is very small and calculated normalized sensitivity is in the order 10-4∼10-3 around the most probable value of longitudinal dispersion coefficient. This suggests that the term of longitudinal dispersion can be removed from the original model. In this case analytical solution is easily introduced for two boundary conditions respectively to evaluate the performance measure of the barrier system. These simplified models, in fact, gives larger estimate of the nuclide release from the engineered barrier system than that calculated from the model considering the longitudinal dispersion. They are acceptable from the standpoint of conservatism of safety assessment. (author)
Application to MISR Land Products of an RPV Model Inversion Package Using Adjoint and Hessian Codes
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
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
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.
D. A. Belikov
2015-07-01
Full Text Available We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA model that consists of the National Institute for Environmental Studies (NIES model as an Eulerian three-dimensional transport model (TM, and FLEXPART (FLEXible PARTicle dispersion model as the Lagrangian plume diffusion model (LPDM. The tangent and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving the performance of the computing, including MPI (Message Passing Interface. As results, the adjoint of Eulerian model is discrete. Construction of the adjoint of the Lagrangian component did not require any code modification, as LPDMs are able to track a significant number of particles back in time and thereby calculate the sensitivity of observations to the neighboring emissions areas. Eulerian and Lagrangian adjoint components were coupled at the time boundary in the global domain.The results are verified using a series of test experiments. The forward simulation shown the coupled model is effective in reproducing the seasonal cycle and short-term variability of CO2 even in the case of multiple limiting factors, such as high uncertainty of fluxes and the low resolution of the Eulerian model. The adjoint model demonstrates the high accuracy compared to direct forward sensitivity calculations and fast performance. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation.
Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander
2016-02-01
We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated
One-loop Test of Free SU(N) Adjoint Model Holography
Bae, Jin-Beom; Lal, Shailesh
2016-01-01
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 AdS$_4$ and AdS$_5$. 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 AdS$_5$ theory, whereas the AdS$_4$ calculation still remains t...
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.
Aerosol Health Impact Source Attribution Studies with the CMAQ Adjoint Air Quality Model
Turner, M. D.
Fine particulate matter (PM2.5) is an air pollutant consisting of a mixture of solid and liquid particles suspended in the atmosphere. Knowledge of the sources and distributions of PM2.5 is important for many reasons, two of which are that PM2.5 has an adverse effect on human health and also an effect on climate change. Recent studies have suggested that health benefits resulting from a unit decrease in black carbon (BC) are four to nine times larger than benefits resulting from an equivalent change in PM2.5 mass. The goal of this thesis is to quantify the role of emissions from different sectors and different locations in governing the total health impacts, risk, and maximum individual risk of exposure to BC both nationally and regionally in the US. We develop and use the CMAQ adjoint model to quantify the role of emissions from all modeled sectors, times, and locations on premature deaths attributed to exposure to BC. From a national analysis, we find that damages resulting from anthropogenic emissions of BC are strongly correlated with population and premature death. However, we find little correlation between damages and emission magnitude, suggesting that controls on the largest emissions may not be the most efficient means of reducing damages resulting from BC emissions. Rather, the best proxy for locations with damaging BC emissions is locations where premature deaths occur. Onroad diesel and nonroad vehicle emissions are the largest contributors to premature deaths attributed to exposure to BC, while onroad gasoline emissions cause the highest deaths per amount emitted. Additionally, emissions in fall and winter contribute to more premature deaths (and more per amount emitted) than emissions in spring and summer. From a regional analysis, we find that emissions from outside each of six urban areas account for 7% to 27% of the premature deaths attributed to exposure to BC within the region. Within the region encompassing New York City and Philadelphia
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
Suarez, Max J. (Editor); Yang, Wei-Yu; Todling, Ricardo; Navon, I. Michael
1997-01-01
A detailed description of the development of the tangent linear model (TLM) and its adjoint model of the Relaxed Arakawa-Schubert moisture parameterization package used in the NASA GEOS-1 C-Grid GCM (Version 5.2) is presented. The notational conventions used in the TLM and its adjoint codes are described in detail.
S. Blessing; Greatbatch, Richard; K. Fraedrich; Lunkeit, F.
2008-01-01
A tangent linear adjoint for a low-resolution dynamical model of the atmosphere is used to derive the optimal forcing perturbations for all state variables such that after a specified lead time the model response has a given projection, in terms of an energy norm, on the pattern associated with the 51-yr trend in the Northern Hemisphere winter tropospheric circulation, 1948/49–1998/99. A feature of the derived forcing sensitivity is a Rossby wave–like feature that emanates from the western tr...
Adjoint distributed catchment modelling for flood impact of rural land use and management change
O'Donnell, G. M.; Ewen, J.; O'Connell, P. E.
2010-12-01
Understanding the impact that changes in land use and management (LUM) can have on downstream flooding is a significant research challenge that requires a distributed physically-based modelling approach. A key issue in this regard is how to understand the role of the river channel network in propagating the effects of changes in runoff generation downstream to flood sites. The effects of LUM changes can be analysed as if they are perturbations in properties or rates that cause perturbations in flow to propagate through the network. A novel approach has been developed that computes the sensitivity of an impact (for example the impact on a flood level) to upstream perturbations. This is achieved using an adjoint hydraulic model of the channel network that computes sensitivities using algorithmic differentiation. The hydraulic model provides a detailed representation of the drainage network, based on field surveys of channel cross sections and channel roughness, and is linked to runoff generation elements (grid squares). Various sensitivities can be calculated, including sensitivities to perturbations in runoff generation parameters, thus providing some insight into the link between impact and the parameterisation used for runoff generation, and perturbation in the rate of lateral inflow to the network, as can be calculated using expert knowledge on the local effects of LUM on runoff from agricultural fields and hillslopes. The resulting sensitivities may be decomposed and presented as maps that show the relationship between perturbations and impacts, giving valuable insight into the link between cause and effects. Results are provided for the Hodder catchment, NW England (260 sq. km), which is undergoing large-scale changes in LUM. The application focuses on the role of hydrodynamic and geomorphologic dispersion in attenuating perturbations in network flow that result from perturbations to lateral inflows of the types expected if changes in LUM alter the timing or
Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model
Thies, J.; Wubs, F.W.; Dijkstra, H.A.
2009-01-01
To understand the physics and dynamics of the ocean circulation, techniques of numerical bifurcation theory such as continuation methods have proved to be useful. Up to now these techniques have been applied to models with relatively few degrees of freedom such as multi-layer quasi-geostrophic and s
Interactions of point vortices in the Zabusky-McWilliams model with a background flow
Connaughton, Colm
2011-01-01
We combine a simple quasi-geostrophic flow model with the Zabusky-McWilliams theory of atmospheric vortex dynamics to address a hurricane-tracking problem of interest to the insurance industry. This enables us to make predictions about the "follow-my-leader" phenomenon.
Inversion of CO and NOx emissions using the adjoint of the IMAGES model
J.-F. Müller
2005-01-01
Full Text Available We use ground-based observations of CO mixing ratios and vertical column abundances together with tropospheric NO2 columns from the GOME satellite instrument as constraints for improving the global annual emission estimates of CO and NOx for the year 1997. The agreement between concentrations calculated by the global 3-dimensional CTM IMAGES and the observations is optimized using the adjoint modelling technique, which allows to invert for CO and NOx fluxes simultaneously, taking their chemical interactions into account. Our analysis quantifies a total of 39 flux parameters, comprising anthropogenic and biomass burning sources over large continental regions, soil and lightning emissions of NOx, biogenic emissions of CO and non-methane hydrocarbons, as well as the deposition velocities of both CO and NOx. Comparison between observed, prior and optimized CO mixing ratios at NOAA/CMDL sites shows that the inversion performs well at the northern mid- and high latitudes, and that it is less efficient in the Southern Hemisphere, as expected due to the scarsity of measurements over this part of the globe. The inversion, moreover, brings the model much closer to the measured NO2 columns over all regions. Sensitivity tests show that anthropogenic sources exhibit weak sensitivity to changes of the a priori errors associated to the bottom-up inventory, whereas biomass burning sources are subject to a strong variability. Our best estimate for the 1997 global top-down CO source amounts to 2760 Tg CO. Anthropogenic emissions increase by 28%, in agreement with previous inverse modelling studies, suggesting that the present bottom-up inventories underestimate the anthropogenic CO emissions in the Northern Hemisphere. The magnitude of the optimized NOx global source decreases by 14% with respect to the prior, and amounts to 42.1 Tg N, out of which 22.8 Tg N are due to anthropogenic sources. The NOx emissions increase over Tropical regions, whereas they decrease
Inversion of CO and NOx emissions using the adjoint of the IMAGES model
T. Stavrakou
2004-12-01
Full Text Available We use ground-based observations of CO mixing ratios and vertical column abundances together with tropospheric NO2 columns from the GOME satellite instrument as constraints for improving the global annual emission estimates of CO and NOx for the year 1997. The agreement between concentrations calculated by the global 3-dimensional CTM IMAGES and the observations is optimized using the adjoint modelling technique, which allows to invert for CO and NOx fluxes simultaneously, taking their chemical interactions into account. Our analysis quantifies a total of 39 flux parameters, comprising anthropogenic and biomass burning sources over large continental regions, soil and lightning emissions of NOx, biogenic emissions of CO and non-methane hydrocarbons, as well as the deposition velocities of both CO and NOx. Comparison between observed, prior and optimized CO mixing ratios at NOAA/CMDL sites shows that the inversion performs well at the northern mid- and high latitudes, and that it is less efficient in the Southern Hemisphere, as expected due to the scarsity of measurements over this part of the globe. The inversion, moreover, brings the model much closer to the measured NO2 columns over all regions. Sensitivity tests show that anthropogenic sources exhibit weak sensitivity to changes of the a priori errors associated to the bottom-up inventory, whereas biomass burning sources are subject to a strong variability. Our best estimate for the 1997 global top-down CO source amounts to 2760 Tg CO. Anthropogenic emissions increase by 28%, in agreement with previous inverse modelling studies, suggesting that the present bottom-up inventories underestimate the anthropogenic CO emissions in the Northern Hemisphere. The magnitude of the optimized NOx global source decreases by 14% with respect to the prior, and amounts to 42.1 Tg N, out of which 22.8 Tg N are due to anthropogenic sources. The NOx emissions increase over Tropical regions, whereas they
Galanti, Eli; Kaspi, Yohai
2015-11-01
The nature of the large scale flow on Jupiter below the cloud level is still unknown. The observed surface wind might be confined to the upper layers, or be a manifestation of deep cylindrical flow. Moreover, it is possible that in the case where the observed wind is superficial, there exists deep flow that is completely separated from the surface. To date, all models linking the wind (via the induced density nomalies) to the gravity field to be measured by Juno, consider only wind flow related to the observed could level wind. Some assume full cylindrical flow while others allow for the wind to decay with depth.Here we explore the possibility of complex wind dynamics that include both the upper-layer wind, and a deep flow that is completely detached from the flow above it. The surface flow is based on the observed cloud level flow and is set to decay with depth. The deep flow is constructed synthetically to produce cylindrical structures with variable width and magnitude, thus allowing for a wide range of possible setups of the unknown deep flow. This flow is also set to decay when approaching the surface flow in coordination with the exponential decay rate. The combined 3D flow is then related to the density anomalies via a dynamical model, taking into account oblateness effects as well, and the resulting density field is then used to calculate the gravitational moments. An adjoint inverse model is constructed for the dynamical model, thus allowing backward integration of the dynamical model, from the expected observations of the gravity moments to the parameters controlling the setup of the deep and surface flows. We show that the model can be used for examination of various scenarios, including cases in which the deep flow is dominating over the surface wind. The novelty of our adjoint based inversion approach is in the ability to identify complex dynamics including deep cylindrical flows that have no manifestation in the observed cloud-level wind. Furthermore
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
Santillana, Mauricio
2013-01-01
It is of crucial importance to be able to identify the location of atmospheric pollution sources in our planet. Global models of atmospheric transport in combination with diverse Earth observing systems are a natural choice to achieve this goal. It is shown that the ability to successfully reconstruct the location and magnitude of an instantaneous source in global chemical transport models (CTMs) decreases rapidly as a function of the time interval between the pollution release and the observation time. A simple way to quantitatively characterize this phenomenon is proposed based on the effective -undesired- numerical diffusion present in current Eulerian CTMs and verified using idealized numerical experiments. The approach presented consists of using the adjoint-based optimization method in a state-of-the-art CTM, GEOS-Chem, to reconstruct the location and magnitude of a realistic pollution plume for multiple time scales. The findings obtained from these numerical experiments suggest a time scale of 2 days a...
Fereydooni, Abolhassan; Safapour, Ahmad; Rahimi , Asghar
2012-01-01
The concept of (p,q)-pair frames is generalized to (l,l^*)-pair frames. Adjoint (conjugate) of a pair frames for dual space of a Banach space is introduced and some conditions for the existence of adjoint (conjugate) of pair frames are presented.
A coupled adjoint-sensitivity/kriging approach was used to calibrate a groundwater-flow model to 10 years of human-induced transient hydraulic stresses at the WIPP site in New Mexico, USA. Transmissivity data obtained from local-scale hydraulic tests were first kriged to define an initial transmissivity distribution. Steady-state model calibration was then performed employing adjoint-sensitivity techniques to identify regions where transmissivity changes would improve the model fit to the observed steady-state heads. Subsequent transient calibration to large-scale hydraulic stresses created by shaft construction and long-term pumping tests aided in identifying smaller scale features not detected during steady-state calibration. This transient calibration resulted in a much more reliable and defendable model for use in performance-assessment calculations. Computer codes used: GRASPII; SWIFTII. 7 refs., 7 figs
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.
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
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.
In Part II of this work, the adjoint sensitivity analysis procedure developed in Part I is applied to perform sensitivity analysis of several dynamic reliability models of systems of increasing complexity, culminating with the consideration of the International Fusion Materials Irradiation Facility (IFMIF) accelerator system. Section II presents the main steps of a procedure for the automated generation of Markov chains for reliability analysis, including the abstraction of the physical system, construction of the Markov chain, and the generation and solution of the ensuing set of differential equations; all of these steps have been implemented in a stand-alone computer code system called QUEFT/MARKOMAG-S/MCADJSEN. This code system has been applied to sensitivity analysis of dynamic reliability measures for a paradigm '2-out-of-3' system comprising five components and also to a comprehensive dynamic reliability analysis of the IFMIF accelerator system facilities for the average availability and, respectively, the system's availability at the final mission time. The QUEFT/MARKOMAG-S/MCADJSEN has been used to efficiently compute sensitivities to 186 failure and repair rates characterizing components and subsystems of the first-level fault tree of the IFMIF accelerator system. (authors)
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.
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.
SUSY SU(5)× S 4 GUT flavor model for fermion masses and mixings with adjoint, large θ 13 PMNS
Zhao, Ya; Zhang, Peng-Fei
2016-06-01
We propose an S 4 flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of 10 dimensional representations in SU(5) are all assigned to be 11 of S 4. The second generation of 10 is to be 12 of S 4. Right-handed neutrinos of singlet 1 and three generations of overline{mathbf{5}} are all assigned to be 31 of S 4. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is ˜ λ c . Tri-Bimaximal (TBM) mixing can be produced at both leading order (LO) and next to next to leading order (NNLO) in neutrino sector. All the masses of up-type quarks are obtained at LO. We also get the bottom-tau unification m τ = m b and the popular Georgi-Jarlskog relation m μ = 3 m s as well as a new mass relation {m}_e=8/27{m}_d in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field H 24. The GUT relation leads to a sizable mixing angle θ 12 e ˜ θ c and the correct quark mixing matrix V CKM can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing θ 13 ν in TBM mixing to a large {θ}_{13}^{PMNS}˜eq {θ}_c/√{2} , in excellent agreement with experimental results. A Dirac CP violation phase ϕ 12 ≃ ±π /2 is required to make the deviation from θ 12 ν small. We also present some phenomenological numerical results predicted by the model.
Gates, W. Lawrence
2011-01-01
The design and performance of simple atmospheric models is briefly reviewed as an introduction to the question of energetic consistency. The two-layer model of Lorenz appears to be the simplest fully-consistent formulation, and the freedom of this model from the constraints upon the Coriolis parameter and static stability characteristic of the usual quasi-geostrophic models is felt to be particularly important. As a prelude to actual numerical integration, the baroclinic stability properties ...
A reduced adjoint approach to variational data assimilation
Altaf, Muhammad
2013-02-01
The adjoint method has been used very often for variational data assimilation. The computational cost to run the adjoint model often exceeds several original model runs and the method needs significant programming efforts to implement the adjoint model code. The work proposed here is variational data assimilation based on proper orthogonal decomposition (POD) which avoids the implementation of the adjoint of the tangent linear approximation of the original nonlinear model. An ensemble of the forward model simulations is used to determine the approximation of the covariance matrix and only the dominant eigenvectors of this matrix are used to define a model subspace. The adjoint of the tangent linear model is replaced by the reduced adjoint based on this reduced space. Thus the adjoint model is run in reduced space with negligible computational cost. Once the gradient is obtained in reduced space it is projected back in full space and the minimization process is carried in full space. In the paper the reduced adjoint approach to variational data assimilation is introduced. The characteristics and performance of the method are illustrated with a number of data assimilation experiments in a ground water subsurface contaminant model. © 2012 Elsevier B.V.
Adjoint functors in graph theory
Foniok, Jan; Tardif, Claude
2013-01-01
We survey some uses of adjoint functors in graph theory pertaining to colourings, complexity reductions, multiplicativity, circular colourings and tree duality. The exposition of these applications through adjoint functors unifies the presentation to some extent, and also raises interesting questions.
Wilson, C.; Horsburgh, K. J.; Williams, J. A.
2012-04-01
Adjoint modelling has only been adopted in atmospheric and large-scale ocean modelling within the last few years. For the first time this study applies it to tide-surge modelling in the coastal region to gain new insight into dynamics and predictability. In order to improve the skill of storm surge forecasts, one needs to understand how uncertainty propagates through the dynamical system from its boundary conditions, through physical parameterisations and how it is modified by the system dynamics. Uncertainty can come from many sources. Here, we aim to determine the sensitivity of forecast coastal sea level in a tide-surge model to infinitesimal perturbations of two such sources: wind stress and bottom drag. We aim to answer two key questions: 1. What are the relative roles of uncertainties in wind stress and bottom drag in causing changes in forecast coastal sea level? 2. For such changes, what are the temporal and spatial scales over which the sensitivities are largest? The existing approach to answer these questions is to use forward ensemble experiments to explore the propagation of uncertainty due to small perturbations of each of the parameters at several locations and at several times. However, to cover all parameters, spatial and temporal scales would require an ensemble with many thousands or millions of members in order to produce sensitivity maps and time-series and may still not capture all the sensitivity due to gaps in the choice of perturbation directions. We apply a new technique, adjoint modelling, which can produce sensitivity information with a single model integration. The adjoint of a tide-surge model based on MITgcm is used to examine coastal storm surge sensitivities to wind stress and bottom drag for an extreme event on the northwest European continental shelf on 9th November 2007. The forward model is first validated against the UK operational tide-surge model and observations, and then the adjoint is constructed using algorithmic automatic
Sensitivity analysis via reduced order adjoint method
Notwithstanding the voluminous literature on adjoint sensitivity analysis, it has been generally dismissed by practitioners as cumbersome with limited value in realistic engineering models. This perception reflects two limitations about adjoint sensitivity analysis: a) its most effective application is limited to calculation of first-order variations; when higher order derivatives are required, it quickly becomes computationally inefficient; and b) the number of adjoint model evaluations depends on the number of responses, which renders it ineffective for multi-physics model where entire distributions, such as flux and power distribution, are often transferred between the various physics models. To overcome these challenges, this manuscript employs recent advances in reduced order modeling to re-cast the adjoint model equations into a form that renders its application to real reactor models practical. Past work applied reduced order modeling techniques to render reduction for general nonlinear high dimensional models by identifying mathematical subspaces, called active subspaces, that capture all dominant features of the model, including both linear and nonlinear variations. We demonstrate the application of these techniques to the calculation of first-order derivatives, or as commonly known sensitivity coefficients, for a fuel assembly model with many responses. We show that the computational cost becomes dependent on the physics model itself, via the so-called rank of the active subspace, rather than the number of responses or parameters. (author)
Adjoint-based estimation of plate coupling in a non-linear mantle flow model: theory and examples
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
Adjoint inverse modeling of a CO emission inventory at the city scale: Santiago de Chile's case
Saide, P.; Osses, A.; Gallardo, L.; Osses, M.
2009-03-01
Emission inventories (EIs) are key-tools for air quality management. However, EIs are expensive, and they have uncertainties. A way to improve the accuracy of EIs is data assimilation. Multiple inverse methods have been used at various scales. However, typically, when applying these methods at the city scale, one encounters, in addition to problems related to the precision of the first guess, or the reliability and representativeness of the observations, or the shortcomings of the dispersion model, the problem of co-location of sources and observation sites. The latter problem results in spurious corrections to the a priori EI. Here we present a methodology to improve an EI of carbon monoxide over a city. We use a 3-D variational approach, in which a cost function that includes balanced terms addressing observation and emission errors is minimized to obtain an ameliorated EI. In addition to positivity, the method addresses the co-location of sources and observations by means of a factor that multiplies the emission error covariance matrix. The factor is chosen so that the reliability of the initial inventory is increased at the observation sites, reducing the local influence of the observations, avoiding spurious corrections to the EI and increasing the temporal and spatial extent of the corrections. The method is applied to Santiago de Chile. We find that the a posteriori inventory shows a decrease in total emissions of 8% with respect to the a priori inventory. Nevertheless, locally over 100% changes are found in the eastern area of Santiago during the morning hours.
Double-difference adjoint seismic tomography
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.
Adjoint affine fusion and tadpoles
Urichuk, Andrew; Walton, Mark A.
2016-06-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Adjoint affine fusion and tadpoles
Urichuk, Andrew
2016-01-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows, and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
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
Application of adjoint operators to neural learning
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.
CHENG Qiang; CAO JianWen; WANG Bin; ZHANG HaiBin
2009-01-01
The adjoint code generator (ADG) is developed to produce the adjoint codes, which are used to analytically calculate gradients and the Hessian-vector products with the costs independent of the number of the independent variables. Different from other automatic differentiation tools, the implementation of ADG has advantages of using the least program behavior decomposition method and several static dependence analysis techniques. In this paper we first address the concerned concepts and fundamentals, and then introduce the functionality and the features of ADG. In particular, we also discuss the design architecture of ADG and implementation details including the recomputation and storing strategy and several techniques for code optimization. Some experimental results in several applications are presented at the end.
Nie, Ji; Sobel, Adam H
2016-01-01
Extratropical extreme precipitation events are usually associated with large-scale flow disturbances, strong ascent and large latent heat release. The causal relationships between these factors are often not obvious, however, and the roles of different physical processes in producing the extreme precipitation event can be difficult to disentangle. Here, we examine the large-scale forcings and convective heating feedback in the precipitation events which caused the 2010 Pakistan flood within the Column Quasi-Geostrophic framework. A cloud-revolving model (CRM) is forced with the large-scale forcings (other than large-scale vertical motion) computed from the quasi-geostrophic omega equation with input data from a reanalysis data set, and the large-scale vertical motion is diagnosed interactively with the simulated convection. Numerical results show that the positive feedback of convective heating to large-scale dynamics is essential in amplifying the precipitation intensity to the observed values. Orographic li...
Aerosols Processes in the CMAQ Adjoint
Turner, M.; Henze, D.; Hakami, A.; Zhao, S.; Resler, Jaroslav; Carmichael, G.; Stanier, C.; Baek, J.; Saide, P.; Sandu, A.; Russel, A.; Jeong, G.; Nenes, A.; Capps, S.; Percell, P.; Pinder, R.; Napelenok, S.; Pye, H.; Bash, J.; Chai, T.; Byun, D
Davis: Air Quality Research Center, 2011. [IAMA 2011. International Aerosol Modeling Algorithms Conference /3./. Davis, 30.11.2011-02.12.2011] Institutional research plan: CEZ:AV0Z10300504 Keywords : air pollution * adjoint * aerosols Subject RIV: DG - Athmosphere Sciences, Meteorology http://dl.dropbox.com/u/41967626/IAMApresent/TURNER.pdf
Adjoint affine fusion and tadpoles
Urichuk, Andrew; Walton, Mark A.
2016-01-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-pol...
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.
Southern California Adjoint Source Inversions
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.
Hussein, A.; Krejčiřík, David; Siegl, P.
2015-01-01
Roč. 367, č. 4 (2015), s. 2921-2957. ISSN 0002-9947 R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Laplacians on metric graphs * non-self-adjoint boundary conditions * similarity transforms to self-adjoint operators * Riesz basis Subject RIV: BE - Theoretical Physics Impact factor: 1.122, year: 2014
Martin, Nathan
2014-01-01
This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability to identify the friction coefficient for such methods with a non-linear friction law. The exact adjoint problem is solved, based on second order numerical schemes, and a comparison with the so called "self-adjoint" approximation, neglecting the viscosity dependency to the velocity (leading to an incorrect gradient), common in glaciology, is carried out. For data with a noise of $1\\%$, a lower bound of identifiable wavelengths of $10$ ice thicknesses in the friction coefficient is established, when using the exact adjoint method, while the "self-adjoint" method is limited, even for lower noise, to a minimum of $20$ ice thicknesses wavelengths. The second order exact gradient method therefore provides robustness and reliability for the parameter identification process. In othe...
无
2006-01-01
In the first paper in this series, a variational data assimilation of ideal tropical cyclone (TC) tracks was performed for the statistical-dynamical prediction model SD-90 by the adjoint method, and a prediction of TC tracks was made with good accuracy for tracks containing no sharp turns. In the present paper, the cases of real TC tracks are studied. Due to the complexity of TC motion, attention is paid to the diagnostic research of TC motion. First, five TC tracks are studied. Using the data of each entire TC track, by the adjoint method, five TC tracks are fitted well, and the forces acting on the TCs are retrieved. For a given TC, the distribution of the resultant of the retrieved force and Coriolis force well matches the corresponding TC track, i.e., when a TC turns, the resultant of the retrieved force and Coriolis force acts as a centripetal force, which means that the TC indeed moves like a particle; in particular, for TC 9911, the clockwise looping motion is also fitted well. And the distribution of the resultant appears to be periodic in some cases. Then, the present method is carried out for a portion of the track data for TC 9804, which indicates that when the amount of data for a TC track is sufficient, the algorithm is stable. And finally, the same algorithm is implemented for TCs with a double-eyewall structure, namely Bilis (2000) and Winnie (1997),and the results prove the applicability of the algorithm to TCs with complicated mesoscale structures if the TC track data are obtained every three hours.
Seismic imaging: From classical to adjoint tomography
Liu, Q.; Gu, Y. J.
2012-09-01
Seismic tomography has been a vital tool in probing the Earth's internal structure and enhancing our knowledge of dynamical processes in the Earth's crust and mantle. While various tomographic techniques differ in data types utilized (e.g., body vs. surface waves), data sensitivity (ray vs. finite-frequency approximations), and choices of model parameterization and regularization, most global mantle tomographic models agree well at long wavelengths, owing to the presence and typical dimensions of cold subducted oceanic lithospheres and hot, ascending mantle plumes (e.g., in central Pacific and Africa). Structures at relatively small length scales remain controversial, though, as will be discussed in this paper, they are becoming increasingly resolvable with the fast expanding global and regional seismic networks and improved forward modeling and inversion techniques. This review paper aims to provide an overview of classical tomography methods, key debates pertaining to the resolution of mantle tomographic models, as well as to highlight recent theoretical and computational advances in forward-modeling methods that spearheaded the developments in accurate computation of sensitivity kernels and adjoint tomography. The first part of the paper is devoted to traditional traveltime and waveform tomography. While these approaches established a firm foundation for global and regional seismic tomography, data coverage and the use of approximate sensitivity kernels remained as key limiting factors in the resolution of the targeted structures. In comparison to classical tomography, adjoint tomography takes advantage of full 3D numerical simulations in forward modeling and, in many ways, revolutionizes the seismic imaging of heterogeneous structures with strong velocity contrasts. For this reason, this review provides details of the implementation, resolution and potential challenges of adjoint tomography. Further discussions of techniques that are presently popular in
Chiral transition of fundamental and adjoint quarks
Capdevilla, R. M.; Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil); Natale, A. A.
2014-01-01
The chiral symmetry breaking transition of quarks in the fundamental and adjoint representation is studied in a model where the gap equation contains two contributions, one containing a confining propagator and another corresponding to the exchange of one-dressed dynamically massive gluons. When quarks are in the fundamental representation the confinement effect dominates the chiral symmetry breaking while the gluon exchange is suppressed due to the dynamical gluon mass effect in the propagat...
Double-difference adjoint seismic tomography
Yuan, Yanhua O; Tromp, Jeroen
2016-01-01
We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relat...
Chiral transition of fundamental and adjoint quarks
Capdevilla, R.M. [Instituto de Física Teórica, UNESP – Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070 São Paulo, SP (Brazil); Doff, A., E-mail: agomes@utfpr.edu.br [Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR (Brazil); Natale, A.A., E-mail: natale@ift.unesp.br [Instituto de Física Teórica, UNESP – Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070 São Paulo, SP (Brazil); Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil)
2014-01-20
The chiral symmetry breaking transition of quarks in the fundamental and adjoint representation is studied in a model where the gap equation contains two contributions, one containing a confining propagator and another corresponding to the exchange of one-dressed dynamically massive gluons. When quarks are in the fundamental representation the confinement effect dominates the chiral symmetry breaking while the gluon exchange is suppressed due to the dynamical gluon mass effect in the propagator and in the coupling constant. In this case the chiral and deconfinement transition temperatures are approximately the same. For quarks in the adjoint representation, due to the larger Casimir eigenvalue, the gluon exchange is operative and the chiral transition happens at a larger temperature than the deconfinement one.
Chiral transition of fundamental and adjoint quarks
The chiral symmetry breaking transition of quarks in the fundamental and adjoint representation is studied in a model where the gap equation contains two contributions, one containing a confining propagator and another corresponding to the exchange of one-dressed dynamically massive gluons. When quarks are in the fundamental representation the confinement effect dominates the chiral symmetry breaking while the gluon exchange is suppressed due to the dynamical gluon mass effect in the propagator and in the coupling constant. In this case the chiral and deconfinement transition temperatures are approximately the same. For quarks in the adjoint representation, due to the larger Casimir eigenvalue, the gluon exchange is operative and the chiral transition happens at a larger temperature than the deconfinement one
Lee, Meemong; Weidner, Richard
2016-01-01
In the GEOS-Chem Adjoint (GCA) system, the total (wet) surface pressure of the GEOS meteorology is employed as dry surface pressure, ignoring the presence of water vapor. The Jet Propulsion Laboratory (JPL) Carbon Monitoring System (CMS) research team has been evaluating the impact of the above discrepancy on the CO2 model forecast and the CO2 flux inversion. The JPL CMS research utilizes a multi-mission assimilation framework developed by the Multi-Mission Observation Operator (M2O2) research team at JPL extending the GCA system. The GCA-M2O2 framework facilitates mission-generic 3D and 4D-variational assimilations streamlining the interfaces to the satellite data products and prior emission inventories. The GCA-M2O2 framework currently integrates the GCA system version 35h and provides a dry surface pressure setup to allow the CO2 model forecast to be performed with the GEOS-5 surface pressure directly or after converting it to dry surface pressure.
Inflow and initial conditions for direct numerical simulation based on adjoint data assimilation
Gronskis, A; Heitz, D.; Mémin, E.
2011-01-01
A method for generating inﬂow conditions for direct numerical simulations (DNS) of spatially-developing ﬂows is presented. The proposed method is based on variational data assimilation and adjoint-based optimization. The estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system deﬁned by the adjoint of the discrete scheme associated to the dynamical system. The ap...
Unsteady adjoint of pressure loss for a fundamental transonic turbine vane
Talnikar, Chaitanya; Laskowski, Gregory M
2015-01-01
High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design optimization in these aerodynamic applications. In this paper we present unsteady adjoint solutions using a large eddy simulation model for a vane from VKI using aerothermal objectives. The unsteady adjoint method is effective in capturing the gradient for a short time interval aerothermal objective, whereas the method provides diverging gradients for long time-averaged thermal objectives. As the boundary layer on the suction side near the trailing edge of the vane is turbulent, it poses a challenge for the adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially from the trailing edge region when solved backwards in time. This results in the corruption of the sensitivities obtained from the adjoint solutions. An energy analysis of the unstea...
Deterministic adjoint transport applications for He-3 neutron detector design
This work focuses on the determination of predicted neutron detector response accomplished using neutron importance derived from an adjoint discrete ordinates (SN) transport calculation. A hypothetical detector apparatus, intended to detect fast neutrons, was modeled using He-3 tubes with graphite moderation using the PENTRANTM 3-D multi-group discrete ordinates parallel transport code system. The detector geometry was modeled using z-axis symmetry and discretized into 30,280 3-D Cartesian cells. The material spatial mesh was generated using the PENMSHTM code in the PENTRAN system. The 47-group BUGLE-96 neutron cross section library was used for construction of macroscopic neutron cross sections. Results from an S8 angular quadrature using P3 anisotropy are presented. An adjoint transport source was established in the model using group dependent He-3 response cross sections. Each He-3 tube contained an adjoint source aliased to group He-3 absorption cross sections to permit assessment of detector performance. The spectrally dependent detector response from neutron capture in He-3 tubes from an arbitrary source can, therefore, be readily determined. This response comes from the complete integral of the actual source strength weighted by the adjoint function at the source location for any source distribution scenario. For selected neutron energies, an equivalent forward MCNP Monte Carlo model was used to demonstrate good agreement with the detector response determined from the adjoint calculation. The graphite used in this design has a large impact on detector performance due to the increasing sensitivity inherent in He-3 gas as neutrons thermalize. Computational adjoint results presented here predict a fast neutron detector design that yields efficiencies between 30 and 50% for neutron energies below 3 keV, and up to 30% efficiencies for neutron energies between 3 keV and 1 MeV. Overall, the methodology applied here highlights the elegant nature of an adjoint
Adjoint Functors and Representation Dimensions
Chang Chang XI
2006-01-01
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
Mesh-free adjoint methods for nonlinear filters
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.
Chen, M.; Niu, F.; Liu, Q.; Tromp, J.
2015-12-01
EARA2014 -a 3-D radially anisotropic model of the crust and mantle beneath East Asia down to 900 km depth- is developed by adjoint tomography based on a spectral element method. The data set used for the inversion comprises 1.7 million frequency-dependent traveltime measurements from waveforms of 227 earthquakes recorded by 1869 stations. 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. As part of tectonic interpretations of EARA2014, we investigated the seismic wavespeed anomalies beneath two prominent uplifted regions in East Asia: (1) Hangai Dome, an intra-continental low-relief surface with more than 2 km elevation in central Mongolia, and (2) Tibetan Plateau, a vast continental-margin surface with an average elevation of 4.5 km in west China. We discover beneath Hangai Dome a deep low shear wavespeed (low-V) conduit indicating a slightly warmer (54 K-127 K) upwelling from the transition zone. We propose that the mantle upwelling induced decompression melting in the uppermost mantle and that excess heat associated with melt transport modified the lithosphere that isostatically compensates the surface uplift of Hangai Dome at upper mantle depths (> 80 km). On the other hand, we observe no discernable focused deep mantle upwelling directly beneath Tibetan Plateau, which is instead dominated by a strong high-V structure, appearing below 100 km depth and extending to the bottom of the mantle transition zone. However, we find a very strong and localized low-V anomaly beneath the Tibetan Plateau in the crust and uppermost mantle (at depths of ~50 km and 100 km) mainly confined within the Songpan Ganzi Fold Belt and the northern Qiangtang Block. This low-V anomaly is spatially linked to a low-V anomaly beneath the Chuandian Block in the same depth range, which is fed by a deep mantle upwelling directly beneath Hainan Volcano in south
D. T. Shindell
2008-08-01
Full Text Available Influences of specific sources of inorganic PM2.5 on peak and ambient aerosol concentrations in the US are evaluated using a combination of inverse modeling and sensitivity analysis. First, sulfate and nitrate aerosol measurements from the IMPROVE network are assimilated using the four-dimensional variational (4D-Var method into the GEOS-Chem chemical transport model in order to constrain emissions estimates in four separate month-long inversions (one per season. Of the precursor emissions, these observations primarily constrain ammonia (NH3. While the net result is a decrease in estimated US NH3 emissions relative to the original inventory, there is considerable variability in adjustments made to NH3 emissions in different locations, seasons and source sectors, such as focused decreases in the midwest during July, broad decreases throughout the US~in January, increases in eastern coastal areas in April, and an effective redistribution of emissions from natural to anthropogenic sources. Implementing these constrained emissions, the adjoint model is applied to quantify the influences of emissions on representative PM2.5 air quality metrics within the US. The resulting sensitivity maps display a wide range of spatial, sectoral and seasonal variability in the susceptibility of the air quality metrics to absolute emissions changes and the effectiveness of incremental emissions controls of specific source sectors. NH3 emissions near sources of sulfur oxides (SOx are estimated to most influence peak inorganic PM2.5 levels in the East; thus, the most effective controls of NH3 emissions are often disjoint from locations of peak NH3 emissions. Controls of emissions from industrial sectors of SOx and NOx are estimated to be more effective than surface emissions, and changes to NH3 emissions in regions dominated by natural sources are disproportionately more effective than regions dominated by anthropogenic sources. NOx controls are most effective in
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
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...
Self-adjointness of deformed unbounded operators
Much, Albert [Instituto de Ciencias Nucleares, UNAM, México D.F. 04510 (Mexico)
2015-09-15
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
The genesis and predictability of persistent Pacific–North American anomalies in a model atmosphere
Lin, Hai; DEROME, JACQUES
2011-01-01
The setup process of Pacific–North American (PNA) pattern anomalies that last more than10 days and the role played therein by synoptic-scale transients are investigated using a T21,3-level quasi-geostrophic model. As there is no time-dependent forcing in the model, the lowfrequencyPNA anomalies are generated entirely by the internal dynamics. From a 300-winterintegration, 100 cases of positive PNA anomalies and 118 cases of negative PNA anomalieslasting at least 10 days are identified. The PN...
Self-Adjoint Extension of Symmetric Maps
Friedel, H. N.
2011-01-01
A densely-defined symmetric linear map from/to a real Hilbert space extends to a self-adjoint map. Extension is expressed via Riesz representation. For a case including Friedrichs extension of a strongly monotone map, self-adjoint extension is unique, and equals closure of the given map.
Jacobs, Christian T.; Piggott, Matthew D.; Kramer, Stephan C; Funke, Simon W.
2016-01-01
Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation o...
Adjoint-based sensitivity analysis for reactor accident codes
This paper summarizes a recently completed study that identified and investigated the difficulties and limitations of applying first-order adjoint sensitivity methods to reactor accident codes. The work extends earlier adjoint sensitivity formulations and applications to consider problem/model discontinuities in a general fashion, provide for response (R) formulations required by reactor safety applications, and provide a scheme for accurately handling extremely time-sensitive reactor accident responses. The scheme involves partitioning (dividing) the model into submodels (with spearate defining equations and initial conditions) at the location of discontinuity. Successful partitioning moves the problem dependence on the discontinuity location from the whole model system equations to the initial conditions of the second submodel
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-Based Sensitivity Maps for the Nearshore
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
Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method
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
Automated derivation of the adjoint of high-level transient finite element programs
Farrell, Patrick E; Funke, Simon F; Rognes, Marie E
2012-01-01
In this paper we demonstrate the capability of automatically deriving the discrete adjoint and tangent linear models from a forward model written in the high-level FEniCS finite element computing environment. In contrast to developing a model directly in Fortran or C++, high-level systems allow the developer to express the variational problems to be solved in near-mathematical notation. As such, these systems have a key advantage: since the mathematical structure of the problem is preserved, they are more amenable to automated analysis and manipulation. Our approach to automated adjoint derivation relies on run-time annotation of the temporal structure of the model, and employs the same finite element form compiler to automatically generate the low-level code for the derived models. The approach requires only trivial changes to a large class of forward models, including complicated time-dependent nonlinear models. The adjoint model automatically employs optimal checkpointing schemes to mitigate storage requir...
Optimization of a neutron detector design using adjoint transport simulation
Yi, C.; Manalo, K.; Huang, M.; Chin, M.; Edgar, C.; Applegate, S.; Sjoden, G. [Georgia Inst. of Technology, Gilhouse Boggs Bldg., 770 State St, Atlanta, GA 30332-0745 (United States)
2012-07-01
A synthetic aperture approach has been developed and investigated for Special Nuclear Materials (SNM) detection in vehicles passing a checkpoint at highway speeds. SNM is postulated to be stored in a moving vehicle and detector assemblies are placed on the road-side or in chambers embedded below the road surface. Neutron and gamma spectral awareness is important for the detector assembly design besides high efficiencies, so that different SNMs can be detected and identified with various possible shielding settings. The detector assembly design is composed of a CsI gamma-ray detector block and five neutron detector blocks, with peak efficiencies targeting different energy ranges determined by adjoint simulations. In this study, formulations are derived using adjoint transport simulations to estimate detector efficiencies. The formulations is applied to investigate several neutron detector designs for Block IV, which has its peak efficiency in the thermal range, and Block V, designed to maximize the total neutron counts over the entire energy spectrum. Other Blocks detect different neutron energies. All five neutron detector blocks and the gamma-ray block are assembled in both MCNP and deterministic simulation models, with detector responses calculated to validate the fully assembled design using a 30-group library. The simulation results show that the 30-group library, collapsed from an 80-group library using an adjoint-weighting approach with the YGROUP code, significantly reduced the computational cost while maintaining accuracy. (authors)
Highlights: ► We develop an abstract framework for computing the adjoint to the neutron/nuclide burnup equations posed as a system of differential algebraic equations. ► We validate use of the adjoint for computing both sensitivity to uncertain inputs and for estimating global time discretization error. ► Flexibility of the framework is leveraged to add heat transfer physics and compute its adjoint without a reformulation of the adjoint system. ► Such flexibility is crucial for high performance computing applications. -- Abstract: We develop a general framework for computing the adjoint variable to nuclear engineering problems governed by a set of differential–algebraic equations (DAEs). The nuclear engineering community has a rich history of developing and applying adjoints for sensitivity calculations; many such formulations, however, are specific to a certain set of equations, variables, or solution techniques. Any change or addition to the physics model would require a reformulation of the adjoint problem and substantial difficulties in its software implementation. In this work we propose an abstract framework that allows for the modification and expansion of the governing equations, leverages the existing theory of adjoint formulation for DAEs, and results in adjoint equations that can be used to efficiently compute sensitivities for parametric uncertainty quantification. Moreover, as we justify theoretically and demonstrate numerically, the same framework can be used to estimate global time discretization error. We first motivate the framework and show that the coupled Bateman and transport equations, which govern the time-dependent neutronic behavior of a nuclear reactor, may be formulated as a DAE system with a power constraint. We then use a variational approach to develop the parameter-dependent adjoint framework and apply existing theory to give formulations for sensitivity and global time discretization error estimates using the adjoint
Can Core Flows inferred from Geomagnetic Field Models explain the Earth's Dynamo?
Schaeffer, Nathanaël; Pais, Maria Alexandra
2015-01-01
We test the ability of velocity fields inferred from geomagnetic secular variation data to produce the global magnetic field of the Earth. Our kinematic dynamo calculations use quasi-geostrophic (QG) flows inverted from geomagnetic field models which, as such, incorporate flow structures that are Earth-like and may be important for the geodynamo. Furthermore, the QG hypothesis allows straightforward prolongation of the flow from the core surface to the bulk. As expected from previous studies, we check that a simple quasi-geostrophic flow is not able to sustain the magnetic field against ohmic decay. Additional complexity is then introduced in the flow, inspired by the action of the Lorentz force. Indeed, on centenial timescales, the Lorentz force can balance the Coriolis force and strict quasi-geostrophy may not be the best ansatz. When the columnar flow is modified to account for the action of the Lorentz force, magnetic field is generated for Elsasser numbers larger than 0.25 and magnetic Reynolds numbers l...
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.
System of adjoint P1 equations for neutron moderation
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)
Adjoint-Based Uncertainty Quantification with MCNP
Seifried, Jeffrey E. [Univ. of California, Berkeley, CA (United States)
2011-09-01
This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence in the simulation is acquired.
STUDY ON THE ADJOINT METHOD IN DATA ASSIMILATION AND THE RELATED PROBLEMS
吕咸青; 吴自库; 谷艺; 田纪伟
2004-01-01
It is not reasonable that one can only use the adjoint of model in data assimilation.The simulated numerical experiment shows that for the tidal model,the result of the adjoint of equation is almost the same as that of the adjoint of model:the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°.The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea.For comparison,the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea.The initial guess values of the boundary conditions are given first,and then are adjusted to acquire the simulated results that are as close as possible to the observations.As the boundary conditions contain 72 values,which should be adjusted and how to adjust them can only be partially solved by adjusting them many times.The satisfied results are hard to acquire even gigantic efforts are done.Here,the automation of the treatment of the open boundary conditions is realized.The method is unique and superior to the traditional methods.It is emphasized that if the adjoint of equation is used,tedious and complicated mathematical deduction can be avoided.Therefore the adjoint of equation should attract much attention.
Humbird, Kelli D
2016-01-01
Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a mathematically related set of adjoint equations. The information contained in the equations can be combined to produce sensitivity information in a computationally efficient manner. In this work, sensitivity analyses are performed on systems described by flux-limited radiative diffusion using the adjoint approach. The sensitivities computed are shown to agree with standard perturbation theory, and can be obtained in significantly less computational time.
Solar wind reconstruction from magnetosheath data using an adjoint approach
Nabert, C.; Othmer, C. [Technische Univ. Braunschweig (Germany). Inst. fuer Geophysik und extraterrestrische Physik; Glassmeier, K.H. [Technische Univ. Braunschweig (Germany). Inst. fuer Geophysik und extraterrestrische Physik; Max Planck Institute for Solar System Research, Goettingen (Germany)
2015-07-01
We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradient-based minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.
Solar wind reconstruction from magnetosheath data using an adjoint approach
We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradient-based minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.
Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico
Gopalakrishnan, Ganesh
2013-07-01
Adjoint model sensitivity analyses were applied for the loop current (LC) and its eddy shedding in the Gulf of Mexico (GoM) using the MIT general circulation model (MITgcm). The circulation in the GoM is mainly driven by the energetic LC and subsequent LC eddy separation. In order to understand which ocean regions and features control the evolution of the LC, including anticyclonic warm-core eddy shedding in the GoM, forward and adjoint sensitivities with respect to previous model state and atmospheric forcing were computed using the MITgcm and its adjoint. Since the validity of the adjoint model sensitivities depends on the capability of the forward model to simulate the real LC system and the eddy shedding processes, a 5 year (2004–2008) forward model simulation was performed for the GoM using realistic atmospheric forcing, initial, and boundary conditions. This forward model simulation was compared to satellite measurements of sea-surface height (SSH) and sea-surface temperature (SST), and observed transport variability. Despite realistic mean state, standard deviations, and LC eddy shedding period, the simulated LC extension shows less variability and more regularity than the observations. However, the model is suitable for studying the LC system and can be utilized for examining the ocean influences leading to a simple, and hopefully generic LC eddy separation in the GoM. The adjoint sensitivities of the LC show influences from the Yucatan Channel (YC) flow and Loop Current Frontal Eddy (LCFE) on both LC extension and eddy separation, as suggested by earlier work. Some of the processes that control LC extension after eddy separation differ from those controlling eddy shedding, but include YC through-flow. The sensitivity remains stable for more than 30 days and moves generally upstream, entering the Caribbean Sea. The sensitivities of the LC for SST generally remain closer to the surface and move at speeds consistent with advection by the high-speed core of
Dual of QCD with One Adjoint Fermion
Mojaza, Matin; Nardecchia, Marco; Pica, Claudio;
2011-01-01
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the...
Adjoint P1 equations solution for neutron slowing down
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. The direct and adjoint neutron fluxes resulting from the solution of P1 equations were used to three different weighting processes, to obtain the macrogroup macroscopic cross sections. It was found out noticeable differences among them. (author)
Confinement of a hot temperature patch in the modified SQG model
Garra, Roberto
2016-01-01
In this paper we study the time evolution of a temperature patch in $R^2$ according to the modified Surface Quasi-Geostrophic Equation (SQG) patch equation. In particular we give a temporal estimate on the growth of the support, providing a rigorous proof of the confinement of a hot patch of temperature in absence of external forcing, under the quasi-geostrophic approximation.
Kinetic energy cascades in quasi-geostrophic convection in a spherical shell
Reshetnyak, M.; Hejda, Pavel
Roč. 86, č. 1 ( 2012 ), 018408/1-018408/5. ISSN 0031-8949 Institutional research plan: CEZ:AV0Z30120515 Keywords : magnetohydrodynamic turbulence * magnetic fields * dynamos Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 1.032, year: 2012
Bimetric Gravity From Adjoint Frame Field In Four Dimensions
Guo, Zhi-Qiang
2015-01-01
We provide a novel model of gravity by using adjoint frame fields in four dimensions. It has a natural interpretation as a gravitational theory of a complex metric field, which describes interactions between two real metrics. The classical solutions establish three appealing features. The spherical symmetric black hole solution has an additional hair, which includes the Schwarzschild solution as a special case. The de Sitter solution is realized without introducing a cosmological constant. The constant flat background breaks the Lorentz invariance spontaneously, although the Lorentz breaking effect can be localized to the second metric while the first metric still respects the Lorentz invariance.
Large-N reduction with adjoint Wilson fermions
Bringoltz, Barak; Sharpe, Stephen R
2012-01-01
We analyze the large-N behavior of SU(N) lattice gauge theories with adjoint fermions by studying volume-reduced models, as pioneered by Eguchi and Kawai. We perform simulations on a single-site lattice for Nf = 1 and Nf = 2 Wilson Dirac fermions with values of N up to 53. We show for both values of Nf that in the large-N limit there is a finite region, containing both light and heavy fermions, of unbroken center symmetry where the theory exhibits volume independence. Using large-N reduction we attempt to calculate physical quantities such as the string tension and meson masses.
Highlights: • We present a Monte Carlo method for computing the adjoint-weighted kinetics parameters via the IFP algorithm. • Extensive verification tests are performed on simple models. • Several validation tests are performed on the measured values of effective delayed neutron fraction and Rossi alpha. - Abstract: The analysis of neutron kinetics relies on the knowledge of adjoint-weighted kinetics parameters, which are key to safety issues in the context of transient or accidental reactor behavior. The Iterated Fission Probability (IFP) method allows the adjoint-weighted mean generation time and delayed neutron fraction to be computed within a Monte Carlo power iteration calculation. In this work we describe the specific features of the implementation of the IFP algorithm in the reference Monte Carlo code TRIPOLI-4® developed at CEA. Several verification and validation tests are discussed, and the impact of nuclear data libraries, IFP cycle length and inter-cycle correlations are analyzed in detail
Curbelo, Jesus P.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: jperez@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-Graduacao em Modelagem Computacional; Hernandez, Carlos R.G., E-mail: cgh@instec.cu [Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2015-07-01
The spectral Green's function (SGF) method is a numerical method that is free of spatial truncation errors for slab-geometry fixed-source discrete ordinates (S{sub N}) adjoint problems. The method is based on the standard spatially discretized adjoint S{sub N} balance equations and a nonstandard adjoint auxiliary equation expressing the node-average adjoint angular flux, in each discretization node, as a weighted combination of the node-edge outgoing adjoint fluxes. The auxiliary equation contains parameters which act as Green's functions for the cell-average adjoint angular flux. These parameters are determined by means of a spectral analysis which yields the local general solution of the S{sub N} equations within each node of the discretization grid. In this work a number of advances in the SGF adjoint method are presented: the method is extended to adjoint S{sub N} problems considering linearly anisotropic scattering and non-zero prescribed boundary conditions for the forward source-detector problem. Numerical results to typical model problems are considered to illustrate the efficiency and accuracy of the o offered method. (author)
The spectral Green's function (SGF) method is a numerical method that is free of spatial truncation errors for slab-geometry fixed-source discrete ordinates (SN) adjoint problems. The method is based on the standard spatially discretized adjoint SN balance equations and a nonstandard adjoint auxiliary equation expressing the node-average adjoint angular flux, in each discretization node, as a weighted combination of the node-edge outgoing adjoint fluxes. The auxiliary equation contains parameters which act as Green's functions for the cell-average adjoint angular flux. These parameters are determined by means of a spectral analysis which yields the local general solution of the SN equations within each node of the discretization grid. In this work a number of advances in the SGF adjoint method are presented: the method is extended to adjoint SN problems considering linearly anisotropic scattering and non-zero prescribed boundary conditions for the forward source-detector problem. Numerical results to typical model problems are considered to illustrate the efficiency and accuracy of the o offered method. (author)
Effective freeness of adjoint line bundles
Heier, Gordon
2001-01-01
In this note we establish a new Fujita-type effective bound for the base point freeness of adjoint line bundles on a compact complex projective manifold of complex dimension $n$. The bound we obtain (approximately) differs from the linear bound conjectured by Fujita only by a factor of the cube root of $n$. As an application, a new effective statement for pluricanonical embeddings is derived.
Fast Correlation Greeks by Adjoint Algorithmic Differentiation
Luca Capriotti; Mike Giles
2010-01-01
We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to simultaneously achieve computational efficiency and accurate confidence intervals. We illustrate the method for a copula-based Monte Carlo computation of claims written on a basket of underlying assets, and we test it numerically for Portfolio Default Options. For any...
Nonlinear data-assimilation using implicit models
A. D. Terwisscha van Scheltinga
2005-01-01
Full Text Available We show how the traditional 4D-Var method can be adapted for implicit time-integration and extended for multi-parameter estimation. We present the algorithm for this new method, which we call I4D-Var, and demonstrate its performance using a fully-implicit barotropic quasi-geostrophic model of the wind-driven double-gyre ocean circulation. For the latter model, the different regimes of flow behavior and the regime boundaries (i.e. bifurcation points are well known and hence the parameter estimation problem can be systematically studied. It turns out that I4D-Var is able to correctly estimate parameter values, even when background flow and 'observations' are in different dynamical regimes.
Hybrid Levenberg-Marquardt and weak-constraint ensemble Kalman smoother method
Mandel, J.; Bergou, E.; Gürol, S.; Gratton, S.; Kasanický, I.
2016-03-01
The ensemble Kalman smoother (EnKS) is used as a linear least-squares solver in the Gauss-Newton method for the large nonlinear least-squares system in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble members and no tangent or adjoint operators are needed. Furthermore, adding a regularization term results in replacing the Gauss-Newton method, which may diverge, by the Levenberg-Marquardt method, which is known to be convergent. The regularization is implemented efficiently as an additional observation in the EnKS. The method is illustrated on the Lorenz 63 model and a two-level quasi-geostrophic model.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
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.
Supersymmetric Descendants of Self-Adjointly Extended Quantum Mechanical Hamiltonians
Al-Hashimi, M H; Shalaby, A; Wiese, U -J
2013-01-01
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.
Limitations of Adjoint-Based Optimization for Separated Flows
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.
On the essential self-adjointness of generalized Schroedinger operators
We give a necessary and sufficient condition for the generalized Schroedinger operator to be essentially self-adjoint in L2(Ω; rhodx), under general assumptions on rho and for arbitrary domains Ω in Rsup(n). In particular, if rho is strictly positive and locally Lipschitz continuous on Ω = Rsup(n), then A is essentially self-adjoint. We also give examples of non-essential self-adjointness and a complete discussion of the one-dimensional case. These results have applications to the problem of the essential self-adjointness of quantum Hamiltonians and to the uniqueness problem of Markov processes. (orig./WL)
The Schroedinger differential operator and intrinsic self adjointness
An attempt is made to establish a hermitization procedure for rendering any linear differential operator to be intrinsically self adjoint, independently of any prescribed representation. This is accomplished by introducing an associate differential operator, which is simply a linear combination of all the individual ordinary differential operators belonging to the adjoint of the given linear differential operator, that satisfies the criterion of intrinsic self adjointness. It turns out that the associate differential operator is capable of generating an infinite set of hermitized versions of any arbitrary linear differential operator. Both momentum and kinetic energy differential operators that belong to the Schroedinger wave equation are rendered self adjoint. (author)
Generalized uncertainty principle and self-adjoint operators
Balasubramanian, Venkat, E-mail: vbalasu8@uwo.ca [Department of Applied Mathematics, University of Western Ontario London, Ontario N6A 5B7 (Canada); Das, Saurya, E-mail: saurya.das@uleth.ca [Theoretical Physics Group, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4 (Canada); Vagenas, Elias C., E-mail: elias.vagenas@ku.edu.kw [Theoretical Physics Group, Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)
2015-09-15
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Variability modes in core flows inverted from geomagnetic field models
Pais, Maria A; Schaeffer, Nathanaël
2014-01-01
We use flows that we invert from two geomagnetic field models spanning centennial time periods (gufm1 and COV-OBS), and apply Principal Component Analysis and Singular Value Decomposition of coupled fields to extract the main modes characterizing their spatial and temporal variations. The quasi geostrophic flows inverted from both geomagnetic field models show similar features. However, COV-OBS has a less energetic mean flow and larger time variability. The statistical significance of flow components is tested from analyses performed on subareas of the whole domain. Bootstrapping methods are also used to extract robust flow features required by both gufm1 and COV-OBS. Three main empirical circulation modes emerge, simultaneously constrained by both geomagnetic field models and expected to be robust against the particular a priori used to build them. Mode 1 exhibits three large robust vortices at medium/high latitudes, with opposite circulation under the Atlantic and the Pacific hemispheres. Mode 2 interesting...
A Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0
De Cruz, L; Vannitsem, S
2016-01-01
This paper describes a reduced-order quasi-geostrophic coupled ocean-atmosphere model that allows for an arbitrary number of atmospheric and oceanic modes to be retained in the spectral decomposition. The modularity of this new model allows one to easily modify the model physics. Using this new model, coined "Modular Arbitrary-Order Ocean-Atmosphere Model" (maooam), we analyse the dependence of the model dynamics on the truncation level of the spectral expansion, and unveil spurious behaviour that may exist at low resolution by a comparison with the higher resolution versions. In particular, we assess the robustness of the coupled low-frequency variability when the number of modes is increased. An "optimal" version is proposed for which the ocean resolution is sufficiently high while the total number of modes is small enough to allow for a tractable and extensive analysis of the dynamics.
H. Tanimoto
2008-07-01
Full Text Available Simultaneous ground-based measurements of ozone (O_{3} and carbon monoxide (CO were conducted in March 2005 as part of the East Asian Regional Experiment (EAREX 2005 under the umbrella of the Atmospheric Brown Clouds (ABC project. Multiple air quality monitoring networks were integrated by performing intercomparison of individual calibration standards and measurement techniques to ensure comparability of ambient measurements, along with providing consistently high time-resolution measurements of O_{3} and CO at the surface sites in East Asia. Ambient data collected from eight surface stations were compared with simulation results obtained by a regional chemistry transport model to infer recent changes in CO emissions from East Asia. Our inverse estimates of the CO emissions from China up to 2005 suggested an increase of 16% since 2001, in good agreement with the recent MOPITT satellite observations and the bottom-up estimates up to 2006. The O_{3} enhancement relative to CO in continental pollution plumes traversed in the boundary layer were examined as a function of transport time from the Asian continent to the western Pacific Ocean. The observed ΔO_{3}/ΔCO ratios show increasing tendency during eastward transport events due likely to en-route photochemical O_{3} formation, suggesting that East Asia is an important O_{3} source region during spring.
Local Volatility Calibration Using An Adjoint Proxy
Gabriel TURINICI
2008-11-01
Full Text Available We document the calibration of the local volatility in a framework similar to Coleman, Li and Verma. The quality of a surface is assessed through a functional to be optimized; the specificity of the approach is to separate the optimization (performed with any suitable optimization algorithm from the computation of the functional where we use an adjoint (as in L. Jiang et. al. to obtain an approximation; moreover our main calibration variable is the implied volatility (the procedure can also accommodate the Greeks. The procedure performs well on benchmarks from the literature and on FOREX data.
Symmetries of linearized gravity from adjoint operators
Aksteiner, Steffen
2016-01-01
Using a covariant formulation it is shown that the Teukolsky equation and the Teukolsky-Starobinsky identities for spin-1 and linearized gravity on a vacuum type D background are self-adjoint. This fact is used to construct symmetry operators for each of the four cases. We find both irreducible second order symmetry operators for spin-1, a known fourth order, and a new sixth order symmetry operator for linearized gravity. The results are connected to Hertz and Debye potentials and to the separability of the Teukolsky equation.
An Adjoint-Based Adaptive Ensemble Kalman Filter
Song, Hajoon
2013-10-01
A new hybrid ensemble Kalman filter/four-dimensional variational data assimilation (EnKF/4D-VAR) approach is introduced to mitigate background covariance limitations in the EnKF. The work is based on the adaptive EnKF (AEnKF) method, which bears a strong resemblance to the hybrid EnKF/three-dimensional variational data assimilation (3D-VAR) method. In the AEnKF, the representativeness of the EnKF ensemble is regularly enhanced with new members generated after back projection of the EnKF analysis residuals to state space using a 3D-VAR [or optimal interpolation (OI)] scheme with a preselected background covariance matrix. The idea here is to reformulate the transformation of the residuals as a 4D-VAR problem, constraining the new member with model dynamics and the previous observations. This should provide more information for the estimation of the new member and reduce dependence of the AEnKF on the assumed stationary background covariance matrix. This is done by integrating the analysis residuals backward in time with the adjoint model. Numerical experiments are performed with the Lorenz-96 model under different scenarios to test the new approach and to evaluate its performance with respect to the EnKF and the hybrid EnKF/3D-VAR. The new method leads to the least root-mean-square estimation errors as long as the linear assumption guaranteeing the stability of the adjoint model holds. It is also found to be less sensitive to choices of the assimilation system inputs and parameters.
Coupling of Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences
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
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.
Using adjoint-based optimization to study wing flexibility in flapping flight
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., E-mail: hashimi@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Salman, M., E-mail: msalman@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Shalaby, A., E-mail: amshalab@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Physics Department, Faculty of Science, Mansoura University (Egypt); Wiese, U.-J., E-mail: wiese@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA (United States)
2013-10-15
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
Self-adjointness of the Gaffney Laplacian on Vector Bundles
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
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
Self-adjointness of the Gaffney Laplacian on Vector Bundles
Bandara, Lashi, E-mail: lashi.bandara@chalmers.se [Chalmers University of Technology and University of Gothenburg, Mathematical Sciences (Sweden); Milatovic, Ognjen, E-mail: omilatov@unf.edu [University of North Florida, Department of Mathematics and Statistics (United States)
2015-12-15
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.
The adjoint sensitivity method of global electromagnetic induction for CHAMP magnetic data
Complete text of publication follows. Martinec and McCreadie (2004) developed a time-domain spectral-finite element approach for the forward modelling of electromagnetic induction vector data as measured by the CHAMP satellite. Here, we present a new method of computing the sensitivity of the CHAMP electromagnetic induction data on the Earth's mantle electrical conductivity, which we term the adjoint sensitivity method. The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the specification of prescribed boundary conditions. The respective boundary-value data at the satellite's altitude are the X magnetic component measured by the CHAMP vector magnetometer along satellite tracks for the forward method and the difference between the measured and predicted Z magnetic component for the adjoint method. The squares of these differences summed up over all CHAMP tracks determine the misfit. The sensitivity of the CHAMP data, that is the partial derivatives of the misfit function with respect to mantle conductivity parameters, are then determined by the scalar product of the forward and adjoint solutions, multiplied by the gradient of the conductivity and integrated over all CHAMP tracks. Such exactly determined sensitivities are checked against numerical differentiation of the misfit, and very good agreement is obtained. The attractiveness of the adjoint method lies in the fact that the adjoint sensitivities are calculated for little cost, regardless of the number of conductivity parameters. However, since the adjoint solution proceeds backwards in time, the forward solution must be stored at each time step, leading to memory requirements that are linear with respect to the number of steps undertaken. Having determined the sensitivities, we apply the conjugate gradient method to infer 1-D and 2-D conductivity structures of the Earth based on the CHAMP residual time serie (after the subtraction of static field
Adjoint Monte Carlo simulation of fixed-energy secondary radiation
Fixed energy secondary generation for adjoint Monte Carlo methods constitutes certain difficulties because of zero probability of reaching fixed value from continuous distribution. This paper proposes a possible approach to adjoint Monte Carlo simulation with fixed energy secondary radiation which does not contain any simplifying restriction. This approach uses the introduced before generalized particle concept developed for description of mixed-type radiation transport and allows adjoint Monte Carlo simulation of such processes. It treats particle type as additional discrete coordinate and always considers only one particle even for the interactions with many particles outgoing from the collision. The adjoint fixed energy secondary radiation simulation is performed as local energy estimator through the intermediate state with fixed energy. The proposed algorithm is tested on the example of coupled gamma/electron/positron transport with generation of annihilation radiation. Forward and adjoint simulation according to generalized particle concept show statistically similar results. (orig.)
Measurement of adjoint flux at the RB reactor
The adjoint flux is of the great importance for determination of kinetic parameters of nuclear reactor (ρ, l and βeff) and for the interpretation of experiments with reactivity perturbations. In experimental reactor physics there are a few methods for the adjoint flux measurements. The method of reactivity perturbations with adequate samples is used for thermal reactors. According to the theory of reactivity perturbations the reactivity change due to sample of thermal neutrons absorbing material is proportional to product of flux and adjoint flux of thermal neutrons (Φ2(r)Φ=2(r)). The reactivity change due to fissionable nuclide is proportional to product of thermal neutron flux and adjoint flux of fast neutrons (Φ2(r)Φ=2(r)). The axial distribution of adjoint flux is determined by reactivity measurements and measurements of axial distribution of thermal neutron flux. Thi results of this measurement will be used for interpretation of other experiments with reactivity perturbations at the RB reactor
Mesoscale Eddy Parameterization in an Idealized Primitive Equations Model
Anstey, J.; Zanna, L.
2014-12-01
Large-scale ocean currents such as the Gulf Stream and Kuroshio Extension are strongly influenced by mesoscale eddies, which have spatial scales of order 10-100 km. The effects of these eddies are poorly represented in many state-of-the-art ocean general circulation models (GCMs) due to the inadequate spatial resolution of these models. In this study we examine the response of the large-scale ocean circulation to the rectified effects of eddy forcing - i.e., the role played by surface-intensified mesoscale eddies in sustaining and modulating an eastward jet that separates from an intense western boundary current (WBC). For this purpose a primitive equations ocean model (the MITgcm) in an idealized wind-forced double-gyre configuration is integrated at eddy-resolving resolution to reach a forced-dissipative equilibrium state that captures the essential dynamics of WBC-extension jets. The rectified eddy forcing is diagnosed as a stochastic function of the large-scale state, this being characterized by the manner in which potential vorticity (PV) contours become deformed. Specifically, a stochastic function based on the Laplacian of the material rate of change of PV is examined in order to compare the primitive equations results with those of a quasi-geostrophic model in which this function has shown some utility as a parameterization of eddy effects (Porta Mana and Zanna, 2014). The key question is whether an eddy parameterization based on quasi-geostrophic scaling is able to carry over to a system in which this scaling is not imposed (i.e. the primitive equations), in which unbalanced motions occur.
Infrared regime of SU(2) with one adjoint Dirac flavor
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.
Low-order models of wave interactions in the transition to baroclinic chaos
W.-G. Früh
1996-01-01
Full Text Available A hierarchy of low-order models, based on the quasi-geostrophic two-layer model, is used to investigate complex multi-mode flows. The different models were used to study distinct types of nonlinear interactions, namely wave- wave interactions through resonant triads, and zonal flow-wave interactions. The coupling strength of individual triads is estimated using a phase locking probability density function. The flow of primary interest is a strongly modulated amplitude vacillation, whose modulation is coupled to intermittent bursts of weaker wave modes. This flow was found to emerge in a discontinuous bifurcation directly from a steady wave solution. Two mechanism were found to result in this flow, one involving resonant triads, and the other involving zonal flow-wave interactions together with a strong β-effect. The results will be compared with recent laboratory experiments of multi-mode baroclinic waves in a rotating annulus of fluid subjected to a horizontal temperature gradient.
Global existence for some transport equations with nonlocal velocity
Bae, Hantaek; Granero-Belinchón, Rafael
2014-01-01
In this paper, we study transport equations with nonlocal velocity fields with rough initial data. We address the global existence of weak solutions of an one dimensional model of the surface quasi-geostrophic equation and the incompressible porous media equation, and one dimensional and $n$ dimensional models of the dissipative quasi-geostrophic equations and the dissipative incompressible porous media equation.
In this paper a method to perform sensitivity analysis for a simplified multi-physics problem is presented. The method is based on the Adjoint Sensitivity Analysis Procedure which is used to apply first order perturbation theory to linear and nonlinear problems using adjoint techniques. The multi-physics problem considered includes a neutronic, a thermo-kinetics, and a thermal-hydraulics part and it is used to model the time dependent behavior of a sodium cooled fast reactor. The adjoint procedure is applied to calculate the sensitivity coefficients with respect to the kinetic parameters of the problem for two reference transients using two different model responses, the results obtained are then compared with the values given by a direct sampling of the forward nonlinear problem. Our first results show that, thanks to modern numerical techniques, the procedure is relatively easy to implement and provides good estimation for most perturbations, making the method appealing for more detailed problems. (author)
Gepraegs, R.; Schmitz, G.; Peters, D. [Institut fuer Atmosphaerenphysik, Kuehlungsborn (Germany)
1997-12-31
A 2D version of the ECHAM T21 climate model has been developed. The new model includes an efficient spectral transport scheme with implicit diffusion. Furthermore, photodissociation and chemistry of the NCAR 2D model have been incorporated. A self consistent parametrization scheme is used for eddy heat- and momentum flux in the troposphere. It is based on the heat flux parametrization of Branscome and mixing-length formulation for quasi-geostrophic vorticity. Above 150 hPa the mixing-coefficient K{sub yy} is prescribed. Some of the model results are discussed, concerning especially the impact of aircraft NO{sub x} emission on the model chemistry. (author) 6 refs.
GPU-accelerated adjoint algorithmic differentiation
Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe
2016-03-01
Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the "tape". Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.
First-arrival traveltime tomography for anisotropic media using the adjoint-state method
Waheed, Umair bin
2016-05-27
Traveltime tomography using transmission data has been widely used for static corrections and for obtaining near-surface models for seismic depth imaging. More recently, it is also being used to build initial models for full-waveform inversion. The classic traveltime tomography approach based on ray tracing has difficulties in handling large data sets arising from current seismic acquisition surveys. Some of these difficulties can be addressed using the adjoint-state method, due to its low memory requirement and numerical efficiency. By coupling the gradient computation to nonlinear optimization, it avoids the need for explicit computation of the Fréchet derivative matrix. Furthermore, its cost is equivalent to twice the solution of the forward-modeling problem, irrespective of the size of the input data. The presence of anisotropy in the subsurface has been well established during the past few decades. The improved seismic images obtained by incorporating anisotropy into the seismic processing workflow justify the effort. However, previous literature on the adjoint-state method has only addressed the isotropic approximation of the subsurface. We have extended the adjoint-state technique for first-arrival traveltime tomography to vertical transversely isotropic (VTI) media. Because δ is weakly resolvable from surface seismic alone, we have developed the mathematical framework and procedure to invert for vNMO and η. Our numerical tests on the VTI SEAM model demonstrate the ability of the algorithm to invert for near-surface model parameters and reveal the accuracy achievable by the algorithm.
Neutrino masses in SU(5) x U(1){sub F} with adjoint flavons
Nardi, Enrico [INFN, Laboratori Nazionali di Frascati, C.P. 13, Frascati (Italy); IFT-UAM/CSIC, Madrid (Spain); Universidad Autonoma de Madrid, Departamento de Fisica Teorica, Madrid (Spain); Restrepo, Diego; Velasquez, Mauricio [Universidad de Antioquia, Instituto de Fisica, Medellin (Colombia)
2012-03-15
We present a SU(5) x U(1){sub F} supersymmetric model for neutrino masses and mixings that implements the seesaw mechanism by means of the heavy SU(2) singlets and triplets states contained in three adjoints of SU(5). We discuss how Abelian U(1){sub F} symmetries can naturally yield non-hierarchical light neutrinos even when the heavy states are strongly hierarchical, and how it can also ensure that R-parity arises as an exact accidental symmetry. By assigning two flavons that break U(1){sub F} to the adjoint representation of SU(5) and assuming universality for all the fundamental couplings, the coefficients of the effective Yukawa and Majorana mass operators become calculable in terms of group theoretical quantities. There is a single free parameter in the model, however, at leading order the structure of the light neutrinos mass matrix is determined in a parameter independent way. (orig.)
Jacobs, Christian T; Kramer, Stephan C; Funke, Simon W
2016-01-01
Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation of high-resolution and ideally 3D transient models is generally a very computationally expensive problem. As a result, existing work on the adjoint optimisation of tidal turbine placement has been mostly limited to steady-state simulations in which very high, non-physical values of the background viscosity are required to ensure that a steady-state solution exists. However, such compromises may affect the reliability of the modelled turbines, their wakes and interactions, and thus bring into question the validity of the co...
Plumes, Hotspot & Slabs Imaged by Global Adjoint Tomography
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
Grossman, Bernard
1999-01-01
The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based
Source attribution of particulate matter pollution over North China with the adjoint method
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. (letter)
Source attribution of particulate matter pollution over North China with the adjoint method
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.
Adjoint-based uncertainty quantification and sensitivity analysis for reactor depletion calculations
Stripling, Hayes Franklin
Depletion calculations for nuclear reactors model the dynamic coupling between the material composition and neutron flux and help predict reactor performance and safety characteristics. In order to be trusted as reliable predictive tools and inputs to licensing and operational decisions, the simulations must include an accurate and holistic quantification of errors and uncertainties in its outputs. Uncertainty quantification is a formidable challenge in large, realistic reactor models because of the large number of unknowns and myriad sources of uncertainty and error. We present a framework for performing efficient uncertainty quantification in depletion problems using an adjoint approach, with emphasis on high-fidelity calculations using advanced massively parallel computing architectures. This approach calls for a solution to two systems of equations: (a) the forward, engineering system that models the reactor, and (b) the adjoint system, which is mathematically related to but different from the forward system. We use the solutions of these systems to produce sensitivity and error estimates at a cost that does not grow rapidly with the number of uncertain inputs. We present the framework in a general fashion and apply it to both the source-driven and k-eigenvalue forms of the depletion equations. We describe the implementation and verification of solvers for the forward and ad- joint equations in the PDT code, and we test the algorithms on realistic reactor analysis problems. We demonstrate a new approach for reducing the memory and I/O demands on the host machine, which can be overwhelming for typical adjoint algorithms. Our conclusion is that adjoint depletion calculations using full transport solutions are not only computationally tractable, they are the most attractive option for performing uncertainty quantification on high-fidelity reactor analysis problems.
Topology Optimization of Turbulent Fluid Flow with a Sensitive Porosity Adjoint Method (SPAM)
Philippi, B
2015-01-01
A sensitive porosity adjoint method (SPAM) for optimizing the topology of fluid machines has been proposed. A sensitivity function with respect to the porosity has been developed. In the first step of the optimization process, porous media are introduced into the flow regime according to the sensitivity function. Then the optimized porous media are transformed to solid walls. The turbulent flow in porous media is accounted for by a modified eddy-viscosity based turbulence model. Its influence on the adjoint equations is nevertheless neglected, which refers to the so called frozen turbulence assumption. A test case of application in terms of the turbulent rough wall channel flow shows that a considerable reduction of the objective function can be obtained by this method. The transformation from porous media to solid walls may have important effect on the optimization results.
P. E. Haines
2014-01-01
Full Text Available A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model RETRO-TOM. The Eulerian backtracking method is used, allowing the forward advection scheme (Prather's second-order moments, to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time-symmetric suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux-limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" formulation with the accuracy of an "adjoint of finite difference" formulation.
Self-adjoint Wheeler-DeWitt operators, the problem of time and the wave function of the universe
Feinberg, J; Feinberg, Joshua; Peleg, Yoav
1995-01-01
We discuss minisuperspace aspects of various non empty Robertson-Walker cosmological models. The requirement that the Wheeler-DeWitt (WDW) operator be self adjoint is a key ingredient in constructing the physical Hilbert space of a given model and has non-trivial cosmological implications. We discuss a dust filled Universe and its Schr\\"odinger type WDW operator, as well as a Universe containing scalar field matter and its Klein-Gordon type WDW operator. In the latter case, the issue of self-adjointness is intimately related with the problem of time in quantum cosmology. Namely, if time is parametrized by matter fields we find two types of domains for the self adjoint WDW operator: a non trivial domain is comprised of zero current (Hartle-Hawking type) wave functions and is parametrized by two new parameters, whereas the domain of a self adjoint WDW operator acting on tunneling (Vilenkin type) wave functions is a {\\em single} ray. On the other hand, if time is parametrized by the scale factor both types of wa...
Implementation of Generalized Adjoint Equation Solver for DeCART
In this paper, the generalized adjoint solver based on the generalized perturbation theory is implemented on DeCART and the verification calculations were carried out. As the results, the adjoint flux for the general response coincides with the reference solution and it is expected that the solver could produce the parameters for the sensitivity and uncertainty analysis. Recently, MUSAD (Modules of Uncertainty and Sensitivity Analysis for DeCART) was developed for the uncertainty analysis of PMR200 core and the fundamental adjoint solver was implemented into DeCART. However, the application of the code was limited to the uncertainty to the multiplication factor, keff, because it was based on the classical perturbation theory. For the uncertainty analysis to the general response as like the power density, it is necessary to develop the analysis module based on the generalized perturbation theory and it needs the generalized adjoint solutions from DeCART. In this paper, the generalized adjoint solver is implemented on DeCART and the calculation results are compared with the results by TSUNAMI of SCALE 6.1
Implementation of Generalized Adjoint Equation Solver for DeCART
Han, Tae Young; Cho, Jin Young; Lee, Hyun Chul; Noh, Jae Man [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2013-10-15
In this paper, the generalized adjoint solver based on the generalized perturbation theory is implemented on DeCART and the verification calculations were carried out. As the results, the adjoint flux for the general response coincides with the reference solution and it is expected that the solver could produce the parameters for the sensitivity and uncertainty analysis. Recently, MUSAD (Modules of Uncertainty and Sensitivity Analysis for DeCART) was developed for the uncertainty analysis of PMR200 core and the fundamental adjoint solver was implemented into DeCART. However, the application of the code was limited to the uncertainty to the multiplication factor, k{sub eff}, because it was based on the classical perturbation theory. For the uncertainty analysis to the general response as like the power density, it is necessary to develop the analysis module based on the generalized perturbation theory and it needs the generalized adjoint solutions from DeCART. In this paper, the generalized adjoint solver is implemented on DeCART and the calculation results are compared with the results by TSUNAMI of SCALE 6.1.
Adjoint-based Optimal Flow Control for Compressible DNS
Otero, J Javier; Sandberg, Richard D
2016-01-01
A novel adjoint-based framework oriented to optimal flow control in compressible direct numerical simulations is presented. Also, a new formulation of the adjoint characteristic boundary conditions is introduced, which enhances the stability of the adjoint simulations. The flow configuration chosen as a case study consists of a two dimensional open cavity flow with aspect ratio $L/H=3$ and Reynolds number $Re=5000$. This flow configuration is of particular interest, as the turbulent and chaotic nature of separated flows pushes the adjoint approach to its limit. The target of the flow actuation, defined as cost, is the reduction of the pressure fluctuations at the sensor location. To exploit the advantages of the adjoint method, a large number of control parameters is used. The control consists of an actuating sub-domain where a two-dimensional body force is applied at every point within the sub-volume. This results in a total of $2.256 \\cdot 10^6$ control parameters. The final actuation achieved a successful ...
Adjoint transport methods for radiation-effects testing
Adjoint transport has been exploited for some time for neutral particle calculations. For charged particles, however, production adjoint capability was not available until Morel developed the ability to solve coupled-photon-electron transport problems with production discrete ordinates codes. This represents a significant advance for many problems of interest, such as predicting bremsstrahlung yield from flash X-ray machines, internal electromagnetic pulse (IEMP) for photons incident on printed circuit boards, shielding requirements for electron dosimetry, and dose enhancement from photon irradiation of printed circuit boards. The authors demonstrate here that adjoint photon-electron transport is at least an order of magnitude more efficient than forward transport for optimizing bremsstrahlung yield from flash X-ray machine converters. This problem is particularly interesting since adjoint transport provides a good approximation for a variable geometry in addition to a variable source, due to the highly forward-peaked nature of the electron scattering. Normally, neither forward nor adjoint transport is efficient for studying a variable-geometry problem
One-energy group, two-dimensional computer code was developed to calculate the response of a detector to a vibrating absorber in a reactor core. A concept of local/global components, based on the frequency dependent detector adjoint function, and a nodalization technique were utilized. The frequency dependent detector adjoint functions presented by complex equations were expanded into real and imaginary parts. In the nodalization technique, the flux is expanded into polynomials about the center point of each node. The phase angle and the magnitude of the one-energy group detector adjoint function were calculated for a detector located in the center of a 200x200 cm reactor using a two-dimensional nodalization technique, the computer code EXTERMINATOR, and the analytical solution. The purpose of this research was to investigate the applicability of a polynomial nodal model technique to the calculations of the real and the imaginary parts of the detector adjoint function for one-energy group two-dimensional polynomial nodal model technique. From the results as discussed earlier, it is concluded that the nodal model technique can be used to calculate the detector adjoint function and the phase angle. Using the computer code developed for nodal model technique, the magnitude of one energy group frequency dependent detector adjoint function and the phase angle were calculated for the detector located in the center of a 200x200 cm homogenous reactor. The real part of the detector adjoint function was compared with the results obtained from the EXTERMINATOR computer code as well as the analytical solution based on a double sine series expansion using the classical Green's Function solution. The values were found to be less than 1% greater at 20 cm away from the source region and about 3% greater closer to the source compared to the values obtained from the analytical solution and the EXTERMINATOR code. The currents at the node interface matched within 1% of the average
Adjoint sensitivity analysis of hydrodynamic stability in cyclonic flows
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.
SUPERSTABILITY OF ADJOINTABLE MAPPINGS ON HILBERT C*-MODULES
Mohammad Sal Moslehian
2009-02-01
Full Text Available We define the notion of $varphi$-perturbation of a densely definedadjointable mapping and prove that any such mapping $f$ betweenHilbert ${mathcal A}$-modules over a fixed $C^*$-algebra ${mathcalA}$ with densely defined corresponding mapping $g$ is ${mathcalA}$-linear and adjointable in the classical sense with adjoint $g$.If both $f$ and $g$ are everywhere defined then they are bounded.Our work concerns with the concept of {sc Hyers--Ulam--Rassias} stability originated from the {sc Th.~M.~Rassias}' stability theorem that appeared in his paper [{it On the stability of the linear mapping in Banach spaces}, Proc. Amer. Math. Soc., {f 72} (1978, 297--300]. We also indicate complementary results in the case where the {sc Hilbert} $C^*$-modules admit non-adjointable $C^*$-linear appings
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.
Reconstruction of ocean circulation from sparse data using the adjoint method: LGM and the present
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
Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2
Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)
Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
Nemec, Marian; Aftosmis, Michael J.
2006-01-01
A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design
Adjoint sensitivity of global cloud droplet number to aerosol and dynamical parameters
V. A. Karydis
2012-10-01
Full Text Available We present the development of the adjoint of a comprehensive cloud droplet formation parameterization for use in aerosol-cloud-climate interaction studies. The adjoint efficiently and accurately calculates the sensitivity of cloud droplet number concentration (CDNC to all parameterization inputs (e.g., updraft velocity, water uptake coefficient, aerosol number and hygroscopicity with a single execution. The adjoint is then integrated within three dimensional (3-D aerosol modeling frameworks to quantify the sensitivity of CDNC formation globally to each parameter. Sensitivities are computed for year-long executions of the NASA Global Modeling Initiative (GMI Chemical Transport Model (CTM, using wind fields computed with the Goddard Institute for Space Studies (GISS Global Circulation Model (GCM II', and the GEOS-Chem CTM, driven by meteorological input from the Goddard Earth Observing System (GEOS of the NASA Global Modeling and Assimilation Office (GMAO. We find that over polluted (pristine areas, CDNC is more sensitive to updraft velocity and uptake coefficient (aerosol number and hygroscopicity. Over the oceans of the Northern Hemisphere, addition of anthropogenic or biomass burning aerosol is predicted to increase CDNC in contrast to coarse-mode sea salt which tends to decrease CDNC. Over the Southern Oceans, CDNC is most sensitive to sea salt, which is the main aerosol component of the region. Globally, CDNC is predicted to be less sensitive to changes in the hygroscopicity of the aerosols than in their concentration with the exception of dust where CDNC is very sensitive to particle hydrophilicity over arid areas. Regionally, the sensitivities differ considerably between the two frameworks and quantitatively reveal why the models differ considerably in their indirect forcing estimates.
Lu, A.H.
1991-09-01
The adjoint method is applied to groundwater flow-mass transport coupled equations in variably saturated media. The sensitivity coefficients derived by this method can be calculated by a single execution for each performance measure regardless of the number of parameters in question. The method provides an efficient and effective way to rank the importance of the parameters, so that data collection can be guided in support of site characterization programs. The developed code will facilitate the sensitivity/uncertainty analysis in both model prediction and model calibration/validation. 13 refs., 1 tab.
The adjoint method is applied to groundwater flow-mass transport coupled equations in variably saturated media. The sensitivity coefficients derived by this method can be calculated by a single execution for each performance measure regardless of the number of parameters in question. The method provides an efficient and effective way to rank the importance of the parameters, so that data collection can be guided in support of site characterization programs. The developed code will facilitate the sensitivity/uncertainty analysis in both model prediction and model calibration/validation. 13 refs., 1 tab
Hoteit, Ibrahim
2010-03-02
An eddy-permitting adjoint-based assimilation system has been implemented to estimate the state of the tropical Pacific Ocean. The system uses the Massachusetts Institute of Technology\\'s general circulation model and its adjoint. The adjoint method is used to adjust the model to observations by controlling the initial temperature and salinity; temperature, salinity, and horizontal velocities at the open boundaries; and surface fluxes of momentum, heat, and freshwater. The model is constrained with most of the available data sets in the tropical Pacific, including Tropical Atmosphere and Ocean, ARGO, expendable bathythermograph, and satellite SST and sea surface height data, and climatologies. Results of hindcast experiments in 2000 suggest that the iterated adjoint-based descent is able to significantly improve the model consistency with the multivariate data sets, providing a dynamically consistent realization of the tropical Pacific circulation that generally matches the observations to within specified errors. The estimated model state is evaluated both by comparisons with observations and by checking the controls, the momentum balances, and the representation of small-scale features that were not well sampled by the observations used in the assimilation. As part of these checks, the estimated controls are smoothed and applied in independent model runs to check that small changes in the controls do not greatly change the model hindcast. This is a simple ensemble-based uncertainty analysis. In addition, the original and smoothed controls are applied to a version of the model with doubled horizontal resolution resulting in a broadly similar “downscaled” hindcast, showing that the adjustments are not tuned to a single configuration (meaning resolution, topography, and parameter settings). The time-evolving model state and the adjusted controls should be useful for analysis or to supply the forcing, initial, and boundary conditions for runs of other models.
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
On self-adjointness of singular Floquet Hamiltonians
Duclos, Pierre; Jensen, Arne
2010-01-01
Schrödinger equations with time-dependent interactions are studied. We investigate how to define the Floquet Hamiltonian as a self-adjoint operator, when the interaction is singular in time or space. Using these results we establish the existence of a bounded propagator, by applying a result given...
Large-volume results in SU(2) with adjoint fermions
Del Debbio, Luigi; Lucini, Biagio; Pica, Claudio; Patella, Agostino; Rago, Antonio; Roman, Sabin
2013-01-01
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, and...
The Adjoint of the CMAQ Aqueous Chemistry Module
Baek, J.; Stanier, C.; Saide, P.; Carmichael, G.; Henze, D.; Turner, M.; Zhao, S.; Hakami, A.; Resler, Jaroslav; Sandu, A.; Russell, A. P.; Jeong, G.; Nenes, A.; Capps, S.; Percell, P.; Pinder, R.; Napelenok, S.; Bash, J.; Chai, T.; Byun, D
Chapel Hill : CMAS, 2012. s. 91-92. [Annual CMAS Conference /11./. Chapel Hill, 15.10.2012-17.10.2012] Institutional support: RVO:67985807 Keywords : air pollution * adjoint * aqueous chemistry Subject RIV: DG - Athmosphere Sciences, Meteorology http://www.cmascenter.org/conference/2012/agenda.cfm
Adjoint electron-photon transport Monte Carlo calculations with ITS
A general adjoint coupled electron-photon Monte Carlo code for solving the Boltzmann-Fokker-Planck equation has recently been created. It is a modified version of ITS 3.0, a coupled electronphoton Monte Carlo code that has world-wide distribution. The applicability of the new code to radiation-interaction problems of the type found in space environments is demonstrated
Approximate nonlinear self-adjointness and approximate conservation laws
In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness. (paper)
Non-self-adjoint hamiltonians defined by Riesz bases
Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)
2014-03-15
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
High Order Adjoint Derivatives using ESDIRK Methods for Oil Reservoir Production Optimization
Capolei, Andrea; Stenby, Erling Halfdan; Jørgensen, John Bagterp
2012-01-01
continuous adjoints . The high order integration scheme allows larger time steps and therefore faster solution times. We compare gradient computation by the continuous adjoint method to the discrete adjoint method and the finite-difference method. The methods are implemented for a two phase flow reservoir...... simulator. Computational experiments demonstrate that the accuracy of the sensitivities obtained by the adjoint methods are comparable to the accuracy obtained by the finite difference method. The continuous adjoint method is able to use a different time grid than the forward integration. Therefore, it can...
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.
Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry
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
Adjoint Formulation for an Embedded-Boundary Cartesian Method
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
Two-dimensional QCD with matter in the adjoint representation: What does it teach us?
We analyse the highly excited states in QCD2 (Nc→∞) with adjoint matter by using such general methods as dispersion relations, duality and unitarity. We find the Hagedorn-like spectrum ρ(m) ∝m-aexp (βH m) where the parameters βH and a can be expressed in terms of the asymptotics of the matrix elements fn{k} ∝ left angle 0 vertical stroke Tr(anti ΨΨ)k vertical stroke nk right angle. We argue that the asymptotical values fn{k} do not depend on k (after appropriate normalization). Thus, we obtain βH=(2/π)√(π/g2Nc) and a=-3/2 in the case of Majorana fermions in the adjoint representation. The Hagedorn temperature is the limiting temperature in this case. We also argue that the chiral condensate left angle 0 vertical stroke Tr(anti ΨΨ) vertical stroke 0 right angle is not zero in the model. Contrary to the 't Hooft model, this condensate does not break down any continuous symmetries and can not be considered as an order parameter. Thus, no Goldstone boson appears as a consequence of the condensation. We also discuss a few apparently different but actually tightly related problems: master field, condensate, wee partons and constituent quark model in the light-cone framework. (orig.)
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
Source attribution of PM2.5 pollution over North China using the adjoint method
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.
Refined topological vertex, cylindric partitions and U(1) adjoint theory
We study the partition function of the compactified 5D U(1) gauge theory (in the Ω-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex. We show that this partition function is an example a periodic Schur process and is a refinement of the generating function of cylindric plane partitions. The size of the cylinder is given by the mass of adjoint hypermultiplet and the parameters of the Ω-background. We also show that this partition function can be written as a trace of operators which are generalizations of vertex operators studied by Carlsson and Okounkov. In the last part of the paper we describe a way to obtain (q,t) identities using the refined topological vertex.
Adjoint equation of ADS sub-critical reactor
Compared with the critical reactor, the distributions of source neutron and fission neutron are asymmetric inside ADS (accelerator driven sub-critical system) sub-critical reactor, as well as the importance function is different. The multigroup-diffusion approximation was used to simplify the steady-state transport equation into multigroup equation. Then an adjoint equation normalized by the power of reactor core and an importance function associated with the relative power were derived. The physical significance of neutron importance in the sub-critical reactor was also derived. Finally, two different expressions of multiplication factor for sub-critical reactor with external neutron source were derived based on steady-state adjoint equations. (authors)
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
Adjoint Fokker-Planck equation and runaway electron dynamics
Liu, Chang; Brennan, Dylan P.; Bhattacharjee, Amitava [Princeton University, Princeton, New Jersey 08544 (United States); Boozer, Allen H. [Columbia University, New York, New York 10027 (United States)
2016-01-15
The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.
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
Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle
Peplow, Douglas E. [ORNL; Mosher, Scott W [ORNL; Evans, Thomas M [ORNL
2012-08-01
For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.
Adaptive mesh refinement and adjoint methods in geophysics simulations
Burstedde, Carsten
2013-04-01
It is an ongoing challenge to increase the resolution that can be achieved by numerical geophysics simulations. This applies to considering sub-kilometer mesh spacings in global-scale mantle convection simulations as well as to using frequencies up to 1 Hz in seismic wave propagation simulations. One central issue is the numerical cost, since for three-dimensional space discretizations, possibly combined with time stepping schemes, a doubling of resolution can lead to an increase in storage requirements and run time by factors between 8 and 16. A related challenge lies in the fact that an increase in resolution also increases the dimensionality of the model space that is needed to fully parametrize the physical properties of the simulated object (a.k.a. earth). Systems that exhibit a multiscale structure in space are candidates for employing adaptive mesh refinement, which varies the resolution locally. An example that we found well suited is the mantle, where plate boundaries and fault zones require a resolution on the km scale, while deeper area can be treated with 50 or 100 km mesh spacings. This approach effectively reduces the number of computational variables by several orders of magnitude. While in this case it is possible to derive the local adaptation pattern from known physical parameters, it is often unclear what are the most suitable criteria for adaptation. We will present the goal-oriented error estimation procedure, where such criteria are derived from an objective functional that represents the observables to be computed most accurately. Even though this approach is well studied, it is rarely used in the geophysics community. A related strategy to make finer resolution manageable is to design methods that automate the inference of model parameters. Tweaking more than a handful of numbers and judging the quality of the simulation by adhoc comparisons to known facts and observations is a tedious task and fundamentally limited by the turnaround times
Inverse problem of Ocean Acoustic Tomography (OAT) - A numerical experiment
Murty, T.V.R.; Somayajulu, Y.K.; Mahadevan, R.; Murty, C.S.
the correctness of the solution. In the stochastic inverse case, for random model parameter and data, the vertical structure of the ocean is modeled through the quasi-geostrophic theory while the horizontal structure is assumed to have Gaussian covariance...
Scattering theory for self-adjoint extensions
In this paper a new approach is suggested to the construction of a wide class of exactly solvable quantum-mechanical models of scattering, quantum-mechanical models of solids and an exactly solvable quantum-stochastical model. For most of the models the spectral analysis is performed in an explicit form, for many body problems it is reduced to one-dimensional integral equations. The construction of all models is based on a new version of extension theory, which uses the boundary forms for abstract operators. This version gives a simple and general method to join the pair of operators, one of them abstract, and the other one differential. The solvability of these models is based on Krein's formula for quasiresolvents
Self-Adjoint Extensions of the Pauli Equation in the Presence of a Magnetic Monopole
Karat, Edwin R.; Schulz, Michael B.
1996-01-01
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. However, consistency wi...
Integration of the adjoint gamma quantum transport equation by the Monte Carlo method
Comparative description and analysis of the direct and adjoint algorithms of calculation of gamma-quantum transmission in shielding using the Monte Carlo method have been carried out. Adjoint estimations for a number of monoenergetic sources have been considered. A brief description of ''COMETA'' program for BESM-6 computer reazaling direct and adjoint algorithms is presented. The program is modular-constructed which allows to widen it the new module-units being joined. Results of solution by the adjoint branch of two analog problems as compared to the analytical data are presented. These results confirm high efficiency of ''COMETA'' program
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.
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
The efficiency of geophysical adjoint codes generated by automatic differentiation tools
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
Adjoint optimization of natural convection problems: differentially heated cavity
Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.
2016-06-01
Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here
Running coupling in SU(2) with two adjoint fermions
Rantaharju, Jarno; Rummukainen, Kari; Tuominen, Kimmo
2015-01-01
We study SU(2) gauge theory with two Dirac fermions in the adjoint representation of the gauge group on the lattice. Using clover improved Wilson fermion action with hypercubic truncated stout smearing we perform simulations at larger coupling than earlier. We measure the evolution of the coupling constant using the Schr\\"odinger functional method. Extrapolating our lattice results to the continuum, we confirm the existence of a fixed point in the interval 2.2 $\\lesssim $ $g^{*2}$ $\\lesssim $ 3. We also measure the anomalous dimension and find its value at the fixed point is 0.18 $\\lesssim $ $\\gamma^*$ $\\lesssim $ 0.23.
Self-adjoint dirac equation for a fuzzy potential representation
In the present paper, the dependent-, as well as the independent-variables that belong to a self-adjointed relativistic scattering equation, are properly transformed, for a fuzzy potential representation of Woods and Saxon type, with the purpose of being amenable to analytic solutions. This has been accomplished, in terms of hypergeometric functions that can be analytically continued before-and after-the boundary separating the interior from the exterior. Studies of these analytic solutions about the singular points are performed and the corresponding asymptotic behavior is investigated. The corresponding scattering matrix is extracted, where the resonance energy Eigen-values can be identified
Adjoint Monte Carlo techniques and codes for organ dose calculations
Adjoint Monte Carlo simulations can be effectively used for the estimation of doses in small targets when the sources are extended in large volumes or surfaces. The main features of two computer codes for calculating doses at free points or in organs of an anthropomorphic phantom are described. In the first program (REBEL-3) natural gamma-emitting sources are contained in the walls of a dwelling room; in the second one (POKER-CAMP) the user can specify arbitrary gamma sources with different spatial distributions in the environment: in (or on the surface of) the ground and in the air. 3 figures
Khuat, Quang Huy; Kim, Song Hyun; Kim, Do Hyun; Shin, Chang Ho [Hanyang University, Seoul (Korea, Republic of)
2015-05-15
This technique is known as Consistent Adjoint Driven Importance Sampling (CADIS) method and it is implemented in SCALE code system. In the CADIS method, adjoint transport equation has to be solved to determine deterministic importance functions. Using the CADIS method, a problem was noted that the biased adjoint flux estimated by deterministic methods can affect the calculation efficiency and error. The biases of adjoint function are caused by the methodology, calculation strategy, tolerance of result calculated by the deterministic method and inaccurate multi-group cross section libraries. In this paper, a study to analyze the influence of the biased adjoint functions into Monte Carlo computational efficiency is pursued. In this study, a method to estimate the calculation efficiency was proposed for applying the biased adjoint fluxes in the CADIS approach. For a benchmark problem, the responses and FOMs using SCALE code system were evaluated as applying the adjoint fluxes. The results show that the biased adjoint fluxes significantly affects the calculation efficiencies.
On the Norm Convergence of the Self-Adjoint Trotter–Kato Product Formula with Error Bound
Takashi Ichinose; Hideo Tamura
2002-02-01
The norm convergence of the Trotter–Kato product formula with error bound is shown for the semigroup generated by that operator sum of two nonnegative self-adjoint operators and which is self-adjoint.
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.
Utilisation de sources et d'adjoints dragon pour les calculs TRIPOLI
Camand, Corentin
usually non significant. The second method is to use of the adjoint neutron flux calculated by DRAGON as an importance function for Monte Carlo biaising in TRIPOLI. The objective is to improve the figure of merit of the detector response located far away of the neutron source. The neutron source initialisation of a TRIPOLI calculation required to develop the development of a module in DRAGON that generates a list of sources in the TRIPOLI syntaxe, including for each source, its intensity, its position and the energy domain it covers. We tested our method on a complete 17×17 PWR-UOX assembly and on a reduced 3×3 model. We first verified that the DRAGON and TRIPOLI models were consistent in order to ensure that TRIPOLI receives a coherent source distribution. Then we tested the use of DRAGON sources in TRIPOLI with neutron flux and the effective multiplying coefficient (keff). We observe slightly better standard deviations, of an order of 10 pcm, on keff for simulations using DRAGON sources distributions as compared to simulations with less precise initial sources. Flux convergence is also improved. However some incoherence were also observed in the results, some flux converging slower with DRAGON sources when fewer neutrons per batch are considered. In addition, a very large number of sources is too heavy to insert in TRIPOLI. It seems that our method is perfectible in order to improve implementation and convergence. Study of more complex geometries, with less regular sources distributions (for instance using MOX or irradiated fuel) may provide better performances using our method. For biaising TRIPOLI calculations using the DRAGON adjoint flux we created a module that produces importance maps readable by TRIPOLI. We tested our method on a source-detector shielding problem in one dimension. After checking the coherence of DRAGON and TRIPOLI models, we biaised TRIPOLI simulations using the DRAGON adjoint flux, and using INIPOND, the internal biaising option of TRIPOLI. We
On rational R-matrices with adjoint SU(n) symmetry
Stronks, Laurens; Schuricht, Dirk
2016-01-01
Using the representation theory of Yangians we construct the rational R-matrix which takes values in the adjoint representation of SU(n). From this we derive an integrable SU(n) spin chain with lattice spins transforming under the adjoint representation. However, the resulting Hamiltonian is found to be non-Hermitian.
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2000-07-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)
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
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
Tamás Fülöp
2007-11-01
Full Text Available For a class of singular potentials, including the Coulomb potential (in three and less dimensions and $V(x = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the self-adjoint version chosen. The article discusses how the self-adjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different self-adjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations.
Chen, Han
2016-01-01
Many control applications can be formulated as optimization constrained by conservation laws. Such optimization can be efficiently solved by gradient-based methods, where the gradient is obtained through the adjoint method. Traditionally, the adjoint method has not been able to be implemented in "gray-box" conservation law simulations. In gray-box simulations, the analytical and numerical form of the conservation law is unknown, but the space-time solution of relevant flow quantities is available. Without the adjoint gradient, optimization can be challenging for problems with many control variables. However, much information about the gray-box simulation is contained in its space-time solution, which motivates us to estimate the adjoint gradient by leveraging the space-time solution. This article considers a type of gray-box simulations where the flux function is partially unknown. A method is introduced to estimate the adjoint gradient at a cost independent of the number of control variables. The method firs...
Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow
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
On the Self-adjointness of the Product Operators of Two mth-Order Differential Operators on [0, +∞)
Jian Ye AN; Jiong SUN
2004-01-01
In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, +∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.
F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
Morita, Takeshi
2011-01-01
We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S^3 partition functions computed via localization. An explicit illustration based on the known analytic solution of the Chern-Simons matrix model is presented.
Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks
Catterall, Simon; Sannino, Francesco; Schneible, Joe
2008-01-01
We report on numerical simulations of SU(2) lattice gauge theory with two flavors of light dynamical quarks in the adjoint of the gauge group. The dynamics of this theory is thought to be very different from QCD -- the theory exhibiting conformal or near conformal behavior in the infrared. We make a high resolution survey of the phase diagram of this model in the plane of the bare coupling and quark mass on lattices of size 8^3 \\times 16. Our simulations reveal a line of first order phase transitions extending from beta=0 to beta=beta_c \\sim 2.0. For beta > beta_c the line is no longer first order but continues as the locus of minimum meson mass. For beta > 2.0 we observe the critical pion and rho masses to be light, independent of bare coupling and approximately degenerate. We discuss possible interpretations of these observations and corresponding continuum limits.
Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks
We report on numerical simulations of SU(2) lattice gauge theory with two flavors of light dynamical quarks in the adjoint of the gauge group. The dynamics of this theory is thought to be very different from QCD-the theory exhibiting conformal or near conformal behavior in the infrared. We make a high resolution survey of the phase diagram of this model in the plane of the bare coupling and quark mass on lattices of size 83 x 16. Our simulations reveal a line of first order phase transitions extending from β = 0 to β = βc ∼ 2.0. For β > βc the phase boundary is no longer first order but continues as the locus of minimum meson mass. For β > βc we observe the pion and rho masses along the phase boundary to be light, independent of bare coupling and approximately degenerate. We discuss possible interpretations of these observations and corresponding continuum limits.
Adjoint-based optimization of flapping plates hinged with a trailing-edge flap
Min Xu
2015-01-01
Full Text Available It is important to understand the impact of wing-morphing on aerodynamic performance in the study of flapping-wing flight of birds and insects. We use a flapping plate hinged with a trailing-edge flap as a simplified model for flexible/morphing wings in hovering. The trailing-edge flapping motion is optimized by an adjoint-based approach. The optimized configuration suggests that the trailing-edge flap can substantially enhance the overall lift. Further analysis indicates that the lift enhancement by the trailing-edge flapping is from the change of circulation in two ways: the local circulation change by the rotational motion of the flap, and the modification of vortex shedding process by the relative location between the trailing-edge flap and leading-edge main plate.
We formulate the problem of designing the low-loss cavity for the International Linear Collider (ILC) as an electromagnetic shape optimization problem involving a Maxwell eigenvalue problem. The objective is to maximize the stored energy of a trapped mode in the end cell while maintaining a specified frequency corresponding to the accelerating mode. A continuous adjoint method is presented for computation of the design gradient of the objective and constraint. The gradients are used within a nonlinear optimization scheme to compute the optimal shape for a simplified model of the ILC in a small multiple of the cost of solving the Maxwell eigenvalue problem
K. C. Wells; Millet, D. B.; Bousserez, N.; D. K. Henze; Chaliyakunnel, S.; T. J. Griffis; Luan, Y.; Dlugokencky, E. J.; O'Doherty, S.; R. F. Weiss; G. S. Dutton; Elkins, J. W.; Krummel, P. B.; R. L. Langenfelds; Steele, L.P.
2015-01-01
We describe a new 4D-Var inversion framework for nitrous oxide (N[subscript 2]O) based on the GEOS-Chem chemical transport model and its adjoint, and apply it in a series of observing system simulation experiments to assess how well N[subscript 2]O sources and sinks can be constrained by the current global observing network. The employed measurement ensemble includes approximately weekly and quasi-continuous N[subscript 2]O measurements (hourly averages used) from several long-term monitoring...
Conformal versus confining scenario in SU(2) with adjoint fermions
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 β=4/g02=2.25 for values of the bare fermion mass m0 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.
Adjoint Fokker-Planck equation and runaway electron dynamics
Liu, Chang; Boozer, Allen H; Bhattacharjee, Amitava
2016-01-01
A new method to obtain the runaway probability and the expected slowing-down time for runaway electrons is developed, by solving the adjoint Fokker-Planck equation in momentum space. The runaway probability function has a smooth transition at the runaway separatrix, which can be attributed to the effect of the pitch angle scattering term in the kinetic equation. The expected slowing-down time gives a new way to estimate the runaway current decay time in experiments. The result shows that the decay rate of high energy electron is very slow when E is close to the critical electric field, which helps elucidate the hysteresis effect seen in the runaway electron population. Given the same numerical accuracy, the new method is more efficient than the Monte Carlo simulation.
Complete synchronization of chaotic atmospheric models by connecting only a subset of state space
P. H. Hiemstra
2012-11-01
Full Text Available Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS. In addition, we evaluated whether empirical orthogonal functions (EOF form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5–12 need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables.
Freire, Igor Leite
2010-01-01
In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.
Quantum cosmology of scalar-tensor theories and self-adjointness
Almeida, C R; Fabris, J C; Moniz, P V
2016-01-01
In this paper, the problem of the self-adjointness for the case of a quantum minisuperspace Hamiltonian retrieved from a Brans-Dicke (BD) action is investigated. Our matter content is presented in terms of a perfect fluid, onto which the Schutz's formalism will be applied. We use the von Neumann theorem and the similarity with the Laplacian operator in one of the variables to determine the cases where the Hamiltonian is self-adjoint and if it admits self-adjoint extensions. For the latter, we study which extension is physically more suitable.
Use of adjoint methods in the probabilistic finite element approach to fracture mechanics
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.
Nonlinear Model Predictive Control for Oil Reservoirs Management
Capolei, Andrea
continuous adjoint method to the discrete adjoint method and the finite-difference method. We demonstrate that the optimization algorithm can be accelerated by using the continuous time adjoint equations. This is the first time in the literature that the higher order continuous adjoint and higher order...... optimizer uses gradient-based optimization and the required gradients are computed by the adjoint method. We propose the use of efficient high order implicit time integration methods for the solution of the forward and the adjoint equations of the dynamical model. The Ensemble Kalman filter is used for data...... computationally expensive gradient computation by using high-order ESDIRK (Explicit Singly Diagonally Implicit Runge-Kutta) temporal integration methods and continuous adjoints. The high order integration scheme allows larger time steps and therefore faster solution times. We compare gradient computation by the...
Variational characterizations for eigenfunctions of analytic self-adjoint operator functions
Georgios Katsouleas; John Maroulas
2013-01-01
In this paper we consider Rellich's diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements. As an application, we present a characterization for the eigenvalues of hyperbolic operator polynomials.
Estimation of Adjoint-Weighted Kinetics Parameters in Monte Carlo Wieland Calculations
The effective delayed neutron fraction, βeff, and the prompt neutron generation time, Λ, in the point kinetics equation are weighted by the adjoint flux to improve the accuracy of the reactivity estimate. Recently the Monte Carlo (MC) kinetics parameter estimation methods by using the self-consistent adjoint flux calculated in the MC forward simulations have been developed and successfully applied for the research reactor analyses. However these adjoint estimation methods based on the cycle-by-cycle genealogical table require a huge memory size to store the pedigree hierarchy. In this paper, we present a new adjoint estimation in which the pedigree of a single history is utilized by applying the MC Wielandt method. The effectiveness of the new method is demonstrated in the kinetics parameter estimations for infinite homogeneous two-group problems and the Godiva critical facility
Adjoint Weighted Kinetics Parameter Estimation in the Monte Carlo Wielandt Calculations
Choi, Sung Hoon; Shim, Hyung Jin [Seoul National Univ., Seoul (Korea, Republic of)
2013-10-15
In order to eliminate this huge memory consumption in the current adjoint estimation method, we have developed a new method in which the pedigree of a single history is utilized by applying the MC Wielandt method. The Wielandt method allows the estimations of the adjoint flux and adjoint-weighted parameters within a single cycle neutron simulations. The effectiveness of the new method is demonstrated in the kinetics parameter estimations for an infinite homogeneous two-group problem and the Godiva facility. We have developed an efficient algorithm for the adjoint-weighted kinetics parameter estimation in the MC Wielandt calculations which can significantly reduce the memory usage. From the numerical applications, it is demonstrated that the new method can predict the kinetics parameters with great accuracy.
Estimation of Adjoint-Weighted Kinetics Parameters in Monte Carlo Wieland Calculations
Choi, Sung Hoon; Shim, Hyung Jin [Seoul National Univ., Seoul (Korea, Republic of)
2013-07-01
The effective delayed neutron fraction, β{sub eff}, and the prompt neutron generation time, Λ, in the point kinetics equation are weighted by the adjoint flux to improve the accuracy of the reactivity estimate. Recently the Monte Carlo (MC) kinetics parameter estimation methods by using the self-consistent adjoint flux calculated in the MC forward simulations have been developed and successfully applied for the research reactor analyses. However these adjoint estimation methods based on the cycle-by-cycle genealogical table require a huge memory size to store the pedigree hierarchy. In this paper, we present a new adjoint estimation in which the pedigree of a single history is utilized by applying the MC Wielandt method. The effectiveness of the new method is demonstrated in the kinetics parameter estimations for infinite homogeneous two-group problems and the Godiva critical facility.
Self-adjoint extensions of the Pauli equation in the presence of a magnetic monopole
Karat, E R; Karat, Edwin R; Schulz, Michael B
1996-01-01
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of a magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation.
A SYSTEMATIC FORMULATION OF THE CONTINUOUS ADJOINT METHOD APPLIED TO VISCOUS AERODYNAMIC DESIGN
C. Castro*, C. Lozano**, F. Palacios*** and E. Zuazua****
2009-01-01
Full Text Available A continuous adjoint approach to aerodynamic design for viscous compressible flows on unstructuredgrids is developed, and three important problems raised in the continuous adjoint literature are solved. First, using tools of shape deformation of boundary integrals a generic adjoint formulation is developed withindependence of the kind of mesh used. Then, a systematic way of reducing the 2nd order derivative terms which arise is presented which avoids the need of using higher order numerical solvers to obtain accurateapproximations of the 2nd order derivatives. And finally, the class of admissible optimization functionals isclarified. Several remarks are made concerning the longstanding discrete vs. continuous adjoint dichotomy, with the emphasis not on the advantages or disadvantages of each method, but rather on the well-posedness of the approaches. The accuracy of the sensitivity derivatives is assessed by comparison with finite-difference computations, and the validity of the overall methodology is illustrated with design examples under demanding subsonic conditions.
The effective delayed neutron fraction, βeff, and the prompt neutron generation time, Λ, in the point kinetics equation are weighted by the adjoint flux to improve the accuracy of the reactivity estimate. Recently the Monte Carlo (MC) kinetics parameter estimation methods by using the adjoint flux calculated in the MC forward simulations have been developed and successfully applied for reactor analyses. However these adjoint estimation methods based on the cycle-by-cycle genealogical table require a huge memory size to store the pedigree hierarchy. In this paper, we present a new adjoint estimation method in which the pedigree of a single history is utilized by applying the MC Wielandt method. The algorithm of the new method is derived and its effectiveness is demonstrated in the kinetics parameter estimations for infinite homogeneous two-group problems and critical facilities. (author)
Self-adjoint extensions of the Pauli equation in the presence of a magnetic monopole
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann close-quote s theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. However, consistency with the solutions of the Dirac equation limits the possibilities such that conservation of angular momentum is restored. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation. copyright 1997 Academic Press, Inc
Self-adjoint extensions of the Pauli equation in the presence of a magnetic monopole
Karat, E.; Schulz, M. [Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 (United States)
1997-02-01
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann{close_quote}s theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. However, consistency with the solutions of the Dirac equation limits the possibilities such that conservation of angular momentum is restored. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation. {copyright} 1997 Academic Press, Inc.
MS S4.03.002 - Adjoint-Based Design for Configuration Shaping
Nemec, Marian; Aftosmis, Michael J.
2009-01-01
This slide presentation discusses a method of inverse design for low sonic boom using adjoint-based gradient computations. It outlines a method for shaping a configuration in order to match a prescribed near-field signature.
K. C. Wells; Millet, D. B.; Bousserez, N.; D. K. Henze; Chaliyakunnel, S.; T. J. Griffis; Luan, Y.; Dlugokencky, E. J.; R. G. Prinn; S. O'Doherty; R. F. Weiss; G. S. Dutton; Elkins, J. W.; Krummel, P. B.; Langenfelds, R.
2015-01-01
We describe a new 4D-Var inversion framework for N2O based on the GEOS-Chem chemical transport model and its adjoint, and apply this framework in a series of observing system simulation experiments to assess how well N2O sources and sinks can be constrained by the current global observing network. The employed measurement ensemble includes approximately weekly and quasi-continuous N2O measurements (hourly averages used) from several long-term monitoring netw...
Djath, Bughsin'; Verron, Jacques; Melet, Angelique; Gourdeau, Lionel; Barnier, Bernard; Molines, Jean-Marc
2014-09-01
A high 1/36° resolution numerical model is used to study the ocean circulation in the Solomon Sea. An evaluation of the model with (the few) available observation shows that the 1/36° resolution model realistically simulates the Solomon Sea circulations. The model notably reproduces the high levels of mesoscale eddy activity observed in the Solomon Sea. With regard to previous simulations at 1/12° resolution, the average eddy kinetic energy levels are increased by up to ˜30-40% in the present 1/36° simulation, and the enhancement extends at depth. At the surface, the eddy kinetic energy level is maximum in March-April-May and is minimum in December-January-February. The high subsurface variability is related to the variability of the western boundary current (New Guinea Coastal Undercurrent). Moreover, the emergence of submesoscales is clearly apparent in the present simulations. A spectral analysis is conducted in order to evidence and characterize the modeled submesoscale dynamics and to provide a spectral view of scales interactions. The corresponding spectral slopes show a strong consistency with the Surface Quasi-Geostrophic turbulence theory.
Weighted $L^p$ estimates for the area integral associated to self-adjoint operators
Gong, Ruming; Yan, Lixin
2011-01-01
This article is concerned with some weighted norm inequalities for the so-called horizontal (i.e. involving time derivatives) area integrals associated to a non-negative self-adjoint operator satisfying a pointwise Gaussian estimate for its heat kernel, as well as the corresponding vertical (i.e. involving space derivatives) area integrals associated to a non-negative self-adjoint operator satisfying in addition a pointwise upper bounds for the gradient of the heat kernel. As applications, we...
Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians
Galapon, E A
2002-01-01
We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each characteristic time operator generates an uncountable class of self- adjoint operators canonically conjugate with the same Hamiltonian.
Highlights: ► Successful noise control of a 2D-planejet with DNS resolution and a 3D-planejet with LES-resolution using adjoint method. ► Validation of gradient-information obtained with the continuous-adjoint approach, by comparing gradient with finite differences. ► Extension of control-interval with the receding horizon algorithm. - Abstract: A control optimization technique using the continuous adjoint of the compressible Navier–Stokes equations is implemented for aeroacoustic optimization of plane jet flows. The purpose of the adjoint equations is to provide sensitivity information, which is afterwards used in a gradient-based minimization of a prescribed cost functional, designed to describe the far-field sound pressure level (SPL). The objective of the present paper is to demonstrate the ability to reduce the sound in the near far-field of plane jets. Furthermore, as the continuous adjoint approach can become inaccurate, due to inconsistencies between the continuous and the discretized system, the accuracy of the continuous adjoint approach is investigated. The considered cases exhibit a nozzle exit Reynolds number of Rejet = ρujetD/μ = 2000 and a Mach number of Mjet = 0.9, performed using two-dimensional direct numerical simulation and three-dimensional large-eddy simulation, respectively. A comparison of the obtained gradient via adjoint and finite differences is presented and it is shown, that in order to obtain reliable gradient directions, the length of the optimization time needs to be restricted. Furthermore, a receding horizon optimization for the two-dimensional plane jet simulation is used to obtain a sound reduction over much longer time intervals. The influence of different formulations of the viscosity in the adjoint equations is finally investigated.
Self-adjointness and polarization of the fermionic vacuum in the background of nontrivial topology
Singular configuration of an external static magnetic field in the form of a string polarizes vacuum in the secondly quantized theory on a plane which is orthogonal to the string axis. We consider the most general boundary conditions at the punctured singular point, which are compatible with the self-adjointness of the two-dimensional Dirac Hamiltonian. The dependence of the induced vacuum quantum numbers on the self-adjoint extension parameter and the flux of the string is determined
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.
Fluctuations, Response, and Resonances in a Simple Atmospheric Model
Gritsun, Andrey
2016-01-01
We study the response of a simple quasi-geostrophic barotropic model of the atmosphere to various classes of perturbations affecting its forcing and its dissipation using the formalism of the Ruelle response theory. We investigate the geometry of such perturbations using the covariant Lyapunov vectors on the unperturbed system and discover in one specific case - orographic forcing - a substantial projection of the perturbation onto the stable directions of the flow. As a result, we find a clear violation of the fluctuation-dissipation theorem, in agreement with the basic tenets of nonequilibrium statistical mechanics. This results into a very strong response in the form of a forced Rossby-like wave that has no resemblance to the natural variability in the same range of spatial and temporal scales. We further analyze such a feature and discover it can be interpreted as resonant response to a specific group of rarely visited unstable periodic orbits of the unperturbed system. Our results reinforce the idea of u...
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
Vishnampet, Ramanathan [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Bodony, Daniel J. [Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Freund, Jonathan B., E-mail: jbfreund@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States)
2015-03-15
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that
Adjoint sources, disconnected loops and other fruit of lattice QCD
Foster, M S
1998-01-01
eta' meson mass in full QCD. We introduce related source pairs to minimise the variance of the disconnected loop operators that are employed. We are able to obtain estimates of the mass from a very modest number of gauge configurations and purely local operators. We did not observe any evidence of unquenching from the measurements obtained, though statistical noise dominated the signal in the region where definitive effects would be seen. We undertake a comprehensive study of the gluelump mass spectrum, exploring the spin structure of the state. We use five lattice spacings from which we extract continuum values for the state splittings, with high statistics employed at beta = 6.0. We conduct a low statistics study of a related and previously unexamined lattice state, which we term the adjoint meson. We find that this state is fractionally more massive than the gluelump on the lattices considered, with indications that the splitting is greater than the pion mass at beta = 6.0. We investigate a sum rule approa...
Use of adjoint transport solutions for inverse problems
Inverse problems represent a third major class of transport problems (after criticality-type problems and shielding-type problems). For the purpose of discussion here, an inverse problem is defined to be one in which a medium of interest emits some particular type of radiation, either spontaneously or when exposed to some other type of radiation. From a knowledge of the emitted radiation characteristics, one wishes to infer something about the medium that emits the detected radiation. An important example of a practical inverse problem is the geophysical logging of geological formations to determine the presence of minerals or hydrocarbons in the vicinity of a borehole. Proposals have also been made to detect hidden explosives by these methods. For a complete understanding of the apparatus used to solve inverse problems, it is important to know the characteristic interrogation distance of the method. Phrased more precisely, What is the relative contribution to the detector signal due to radiation particles emitted by different elements of volume in the medium being interrogated? As shown in the paper, it is possible to address this question with a computational procedure that utilizes adjoint transport solutions
Supermodeling With A Global Atmospheric Model
Wiegerinck, Wim; Burgers, Willem; Selten, Frank
2013-04-01
In weather and climate prediction studies it often turns out to be the case that the multi-model ensemble mean prediction has the best prediction skill scores. One possible explanation is that the major part of the model error is random and is averaged out in the ensemble mean. In the standard multi-model ensemble approach, the models are integrated in time independently and the predicted states are combined a posteriori. Recently an alternative ensemble prediction approach has been proposed in which the models exchange information during the simulation and synchronize on a common solution that is closer to the truth than any of the individual model solutions in the standard multi-model ensemble approach or a weighted average of these. This approach is called the super modeling approach (SUMO). The potential of the SUMO approach has been demonstrated in the context of simple, low-order, chaotic dynamical systems. The information exchange takes the form of linear nudging terms in the dynamical equations that nudge the solution of each model to the solution of all other models in the ensemble. With a suitable choice of the connection strengths the models synchronize on a common solution that is indeed closer to the true system than any of the individual model solutions without nudging. This approach is called connected SUMO. An alternative approach is to integrate a weighted averaged model, weighted SUMO. At each time step all models in the ensemble calculate the tendency, these tendencies are weighted averaged and the state is integrated one time step into the future with this weighted averaged tendency. It was shown that in case the connected SUMO synchronizes perfectly, the connected SUMO follows the weighted averaged trajectory and both approaches yield the same solution. In this study we pioneer both approaches in the context of a global, quasi-geostrophic, three-level atmosphere model that is capable of simulating quite realistically the extra
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.
Gopalakrishnan, Ganesh
2013-07-01
An ocean state estimate has been developed for the Gulf of Mexico (GoM) using the MIT general circulation model and its adjoint. The estimate has been tested by forecasting loop current (LC) evolution and eddy shedding in the GoM. The adjoint (or four-dimensional variational) method was used to match the model evolution to observations by adjusting model temperature and salinity initial conditions, open boundary conditions, and atmospheric forcing fields. The model was fit to satellite-derived along-track sea surface height, separated into temporal mean and anomalies, and gridded sea surface temperature for 2 month periods. The optimized state at the end of the assimilation period was used to initialize the forecast for 2 months. Forecasts explore practical LC predictability and provide a cross-validation test of the state estimate by comparing it to independent future observations. The model forecast was tested for several LC eddy separation events, including Eddy Franklin in May 2010 during the deepwater horizon oil spill disaster in the GoM. The forecast used monthly climatological open boundary conditions, atmospheric forcing, and run-off fluxes. The model performance was evaluated by computing model-observation root-mean-square difference (rmsd) during both the hindcast and forecast periods. The rmsd metrics for the forecast generally outperformed persistence (keeping the initial state fixed) and reference (forecast initialized using assimilated Hybrid Coordinate Ocean Model 1/12° global analysis) model simulations during LC eddy separation events for a period of 1̃2 months.
Equilibrium Statistical Mechanics and Energy Partition for the Shallow Water Model
Renaud, A.; Venaille, A.; Bouchet, F.
2016-05-01
The aim of this paper is to use large deviation theory in order to compute the entropy of macrostates for the microcanonical measure of the shallow water system. The main prediction of this full statistical mechanics computation is the energy partition between a large scale vortical flow and small scale fluctuations related to inertia-gravity waves. We introduce for that purpose a semi-Lagrangian discrete model of the continuous shallow water system, and compute the corresponding statistical equilibria. We argue that microcanonical equilibrium states of the discrete model in the continuous limit are equilibrium states of the actual shallow water system. We show that the presence of small scale fluctuations selects a subclass of equilibria among the states that were previously computed by phenomenological approaches that were neglecting such fluctuations. In the limit of weak height fluctuations, the equilibrium state can be interpreted as two subsystems in thermal contact: one subsystem corresponds to the large scale vortical flow, the other subsystem corresponds to small scale height and velocity fluctuations. It is shown that either a non-zero circulation or rotation and bottom topography are required to sustain a non-zero large scale flow at equilibrium. Explicit computation of the equilibria and their energy partition is presented in the quasi-geostrophic limit for the energy-enstrophy ensemble. The possible role of small scale dissipation and shocks is discussed. A geophysical application to the Zapiola anticyclone is presented.
Large-N reduction in QCD-like theories with massive adjoint fermions
Azeyanagi, Tatsuo; /Kyoto U.; Hanada, Masanori; /Weizmann Inst.; Unsal, Mithat; /Weizmann Inst. /SLAC /Stanford U., Phys. Dept.; Yacoby, Ran; /Weizmann Inst.
2010-08-26
Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R3 x S1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1{sup 3} x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.
Comparison of Ensemble and Adjoint Approaches to Variational Optimization of Observational Arrays
Nechaev, D.; Panteleev, G.; Yaremchuk, M.
2015-12-01
Comprehensive monitoring of the circulation in the Chukchi Sea and Bering Strait is one of the key prerequisites of the successful long-term forecast of the Arctic Ocean state. Since the number of continuously maintained observational platforms is restricted by logistical and political constraints, the configuration of such an observing system should be guided by an objective strategy that optimizes the observing system coverage, design, and the expenses of monitoring. The presented study addresses optimization of system consisting of a limited number of observational platforms with respect to reduction of the uncertainties in monitoring the volume/freshwater/heat transports through a set of key sections in the Chukchi Sea and Bering Strait. Variational algorithms for optimization of observational arrays are verified in the test bed of the set of 4Dvar optimized summer-fall circulations in the Pacific sector of the Arctic Ocean. The results of an optimization approach based on low-dimensional ensemble of model solutions is compared against a more conventional algorithm involving application of the tangent linear and adjoint models. Special attention is paid to the computational efficiency and portability of the optimization procedure.
Adjoint-based computation of U.S. nationwide ozone exposure isopleths
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
A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow
Xie, Jin-Han
2014-01-01
Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant role in the slow, large-scale dynamics of the ocean. To analyse this role, we develop a new model of the nondissipative interactions between NIWs and balanced motion. The model is derived using the generalised-Lagrangian-mean (GLM) framework (specifically, the glm variant of Soward & Roberts (2010)), taking advantage of the time-scale separation between the two types of motion to average over the short NIW period. We combine Salmon's (2013) variational formulation of GLM with Whitham averaging to obtain a system of equations governing the joint evolution of NIWs and mean flow. Assuming that the mean flow is geostrophically balanced reduces this system to a simple model coupling Young & Ben Jelloul's (1997) equation for NIWs with a modified quasi-geostrophic equation. In th...
A 24-variable low-order coupled ocean-atmosphere model: OA-QG-WS v2
Vannitsem, S.; De Cruz, L.
2014-04-01
A new low-order coupled ocean-atmosphere model for midlatitudes is derived. It is based on quasi-geostrophic equations for both the ocean and the atmosphere, coupled through momentum transfer at the interface. The systematic reduction of the number of modes describing the dynamics leads to an atmospheric low-order component of 20 ordinary differential equations, already discussed in Reinhold and Pierrehumbert (1982), and an oceanic low-order component of four ordinary differential equations, as proposed by Pierini (2011). The coupling terms for both components are derived and all the coefficients of the ocean model are provided. Its dynamics is then briefly explored, through the analysis of its mean field, its variability and its instability properties. The wind-driven ocean displays a decadal variability induced by the atmospheric chaotic wind forcing. The chaotic behavior of the coupled system is highly sensitive to the ocean-atmosphere coupling for low values of the thermal forcing affecting the atmosphere (corresponding to a weakly chaotic coupled system). But it is less sensitive for large values of the thermal forcing (corresponding to a highly chaotic coupled system). In all the cases explored, the number of positive exponents is increasing with the coupling. Two codes in Fortran and Lua of the model integration are provided as Supplement.
A 24-variable low-order coupled ocean–atmosphere model: OA-QG-WS v2
S. Vannitsem
2014-04-01
Full Text Available A new low-order coupled ocean–atmosphere model for midlatitudes is derived. It is based on quasi-geostrophic equations for both the ocean and the atmosphere, coupled through momentum transfer at the interface. The systematic reduction of the number of modes describing the dynamics leads to an atmospheric low-order component of 20 ordinary differential equations, already discussed in Reinhold and Pierrehumbert (1982, and an oceanic low-order component of four ordinary differential equations, as proposed by Pierini (2011. The coupling terms for both components are derived and all the coefficients of the ocean model are provided. Its dynamics is then briefly explored, through the analysis of its mean field, its variability and its instability properties. The wind-driven ocean displays a decadal variability induced by the atmospheric chaotic wind forcing. The chaotic behavior of the coupled system is highly sensitive to the ocean–atmosphere coupling for low values of the thermal forcing affecting the atmosphere (corresponding to a weakly chaotic coupled system. But it is less sensitive for large values of the thermal forcing (corresponding to a highly chaotic coupled system. In all the cases explored, the number of positive exponents is increasing with the coupling. Two codes in Fortran and Lua of the model integration are provided as Supplement.
Adjoint-based airfoil shape optimization in transonic flow
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.
Assessing the Impact of Observations on Numerical Weather Forecasts Using the Adjoint Method
Gelaro, Ronald
2012-01-01
The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. This talk provides a general overview of the adjoint method, including the theoretical basis and practical implementation of the technique. Results are presented from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. When performed in conjunction with standard observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies may be important for optimizing the use of the current observational network and defining requirements for future observing systems
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
Resonant and quasi-resonant excitation of baroclinic waves in the Eady model
Kalashnik, M. V.
2015-11-01
The structure of baroclinic waves in a geostrophic flow with a constant vertical shear (Eady model) is very consistent with that of atmospheric vortex formations. This paper proposes an approach to describing the generation of these waves by initial perturbations of potential vorticity (PV). Within the framework of the suggested approach, the solution to the initial-value problem for a quasi-geostrophic form of the PV transfer equation is represented as a sum of the wave and vortex components with zero and nonzero PV, respectively. A set of ordinary differential equations with the right-hand side dependent on the vertical PV distribution is formulated using Green functions for the amplitude of the wave component (amplitude of excited baroclinic waves). The solution provides a simple description of the resonant and quasi-resonant baroclinic-wave excitation effects under which the wave amplitude grows according to the linear or logarithmic laws. These types of excitation take place for singular and discontinuous initial PV distributions if the frequencies of the wave and vortex components coincide. Smooth distributions generate finite-amplitude waves.
The adjoint sensitivity method. A contribution to the code uncertainty evaluation
The application of the ASM (Adjoint Sensitivity Method) to thermohydraulic codes, is examined. The advantage of the method is to be very few CPU time consuming in comparison with usual approach requiring one complete code run per sensitivity determination. The mathematical aspects of the problem are first described, and the applicability of the method of the functional-type response of a thermalhydraulic model is demonstrated. On a simple example of non linear hyperbolic equation (Burgers equation) the problem has been analyzed. It is shown that the formalism used in the literature treating this subject is not appropriate. A new mathematical formalism circumventing the problem is proposed. For the discretized form of the problem, two methods are possible: the Continuous ASM and the Discrete ASM. The equivalence of both methods is demonstrated; nevertheless only the DASM constitutes a practical solution for thermalhydraulic codes. The application of the DASM to the thermalhydraulic safety code CATHARE is then presented for two examples. They demonstrate that ASM constitutes an efficient tool for the analysis of code sensitivity. (authors) 7 figs., 5 tabs., 8 refs
The adjoint sensitivity method, a contribution to the code uncertainty evaluation
The application of the ASM (Adjoint Sensitivity Method) to thermohydraulic codes, is examined. The advantage of the method is to be very few CPU time consuming in comparison with usual approach requiring one complete code run per sensitivity determination. The mathematical aspects of the problem are first described, and the applicability of the method of the functional-type response of a thermalhydraulic model is demonstrated. On a simple example of non linear hyperbolic equation (Burgers equation) the problem has been analyzed. It is shown that the formalism used in the literature treating this subject is not appropriate. A new mathematical formalism circumventing the problem is proposed. For the discretized form of the problem, two methods are possible: the Continuous ASM and the Discrete ASM. The equivalence of both methods is demonstrated; nevertheless only the DASM constitutes a practical solution for thermalhydraulic codes. The application of the DASM to the thermalhydraulic safety code CATHARE is then presented for two examples. They demonstrate that ASM constitutes an efficient tool for the analysis of code sensitivity. (authors) 7 figs., 5 tabs., 8 refs
Adjoint optimization scheme for lower hybrid current rampup and profile control in Tokamak
The purpose of this work is to take into account and study the effect of the electric field profiles on the Lower Hybrid (LH) current drive efficiency during transient phases such as rampup. As a complement to the full ray-tracing / Fokker Planck studies, and for the purpose of optimization studies, we developed a simplified 1-D model based on the adjoint Karney-Fisch numerical results. This approach allows us to estimate the LH power deposition profile which would be required for ramping the current with prescribed rate, total current density profile (q-profile) and surface loop voltage. For rampup optimization studies, we can therefore scan the whole parameter space and eliminate a posteriori those scenarios which correspond to unrealistic deposition profiles. We thus obtain the time evolution of the LH power, minor radius of the plasma, volt-second consumption and total energy dissipated. Optimization can thus be performed with respect to any of those criteria. This scheme is illustrated by some numerical simulations performed with TORE-SUPRA and NET/ITER parameters. We conclude with a derivation of a simple and general scaling law for the flux consumption during the rampup phase
Decomposition of the adjoint representation of the small quantum sl$_{2}$
Ostrik, V
1997-01-01
Given a finite type root datum and a primitive root of unity q=\\sqrt[l]{1}, G.~Lusztig has defined in [Lu] a remarkable finite dimensional Hopf algebra \\fu over the cyclotomic field {\\Bbb Q}(\\sqrt[l]{1}). In this note we study the adjoint representation \\ad of \\fu in the simplest case of the root datum sl_2. The semisimple part of this representation is of big importance in the study of local systems of conformal blocks in WZW model for \\hat{sl}_2 at level l-2 in arbitrary genus. The problem of distinguishing the semisimple part is closely related to the problem of integral representation of conformal blocks (see [BFS]). We find all the indecomposable direct summands of \\ad with multiplicities. It appears that \\ad is isomorphic to a direct sum of simple and projective modules. It can be lifted to a module over the (infinite dimensional) quantum universal enveloping algebra with divided powers U_q(sl_2) which is also a direct sum of simples and projectives.
Adjoint-based sensitivity and uncertainty analysis of lattice physics calculations with CASMO-4
The topic of this paper is the development of sensitivity and uncertainty analysis capability to the reactor physics code CASMO-4 in the UAM (Uncertainty Analysis in Best-Estimate Modelling for Design, Operation and Safety Analysis of LWRs) benchmark. The developed calculation system enables the uncertainty analysis of homogenized multi-group cross-sections, diffusion coefficients and pin powers with respect to nuclear data. The uncertainty analysis methodology is deterministic, meaning that the sensitivity profiles of the responses are computed first, after which uncertainty is propagated by combining the sensitivity profiles with the covariance matrices of the uncertain nuclear data. The sensitivity analysis is based on perturbation theory which enables computing the sensitivity profiles efficiently by solving one generalized adjoint system for each response. The mathematical background of this work is reviewed and the main conclusions related to the implementation are summarized. Special emphasis is placed on the sensitivity analysis of two-group homogenized diffusion coefficients which require some modifications to the standard equations of generalized perturbation theory. Numerical results are presented and analyzed for a PWR fuel assembly with control rods out and inserted. The computational efficiency of the calculations is discussed. (author)
Experience with Monte Carlo variance reduction using adjoint solutions in HYPER neutronics analysis
The variance reduction techniques using adjoint solutions are applied to the Monte Carlo calculation of the HYPER(HYbrid Power Extraction Reactor) core neutronics. The applied variance reduction techniques are the geometry splitting and the weight windows. The weight bounds and the cell importance needed for these techniques are generated from an adjoint discrete ordinate calculation by the two-dimensional TWODANT code. The flux distribution variances of the Monte Carlo calculations by these variance reduction techniques are compared with the results of the standard Monte Carlo calculations. It is shown that the variance reduction techniques using adjoint solutions to the HYPER core neutronics result in a decrease in the efficiency of the Monte Carlo calculation
An adjoint-based approach for finding invariant solutions of Navier-Stokes equations
Farazmand, Mohammad
2015-01-01
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and traveling wave solutions of the Navier--Stokes equations. Using the adjoint equations, arbitrary initial conditions evolve to the vicinity of a (relative) equilibrium at which point a few Newton-type iterations yield the desired (relative) equilibrium solution. We apply this adjoint-based method to a chaotic two-dimensional Kolmogorov flow. A convergence rate of 100% is observed, leading to the discovery of 21 new steady state and traveling wave solutions at Reynolds number Re=40. Some of the new invariant solutions have spatially localized structures that were previously believed to only exist on domains with large aspect ratios. We show that one of the newly found steady state solutions underpins the temporal intermittencies, i.e., high energy dissipation episodes of the flo...
Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics
Tavener, Simon
2013-01-01
In this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjoint problems within each subdomain. The primal subdomains are discretized using either an interior penalty discontinuous Galerkin method or a continuous Galerkin method with weakly imposed Dirichlet conditions. The mixed subdomains are discretized using Raviart- Thomas mixed finite elements. The a posteriori error estimate also accounts for the errors due to adjoint-inconsistent subdomain discretizations. The coupling between the subdomain discretizations is achieved via a mortar space. We show that the numerical discretization error can be broken down into subdomain and mortar components which may be used to drive adaptive refinement.Copyright © by SIAM.
The adjoint method of data assimilation used operationally for shelf circulation
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.
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.
Vannitsem, Stephane
2015-01-01
We study a simplified coupled atmosphere-ocean model using the formalism of covariant Lyapunov vectors (CLVs), which link physically-based directions of perturbations to growth/decay rates. The model is obtained via a severe truncation of quasi-geostrophic equations for the two fluids, and includes a simple yet physically meaningful representation of their dynamical/thermodynamical coupling. The model has 36 degrees of freedom, and the parameters are chosen so that a chaotic behaviour is observed. One finds two positive Lyapunov exponents (LEs), sixteen negative LEs, and eighteen near-zero LEs. The presence of many near-zero LEs results from the vast time-scale separation between the characteristic time scales of the two fluids, and leads to nontrivial error growth properties in the tangent space spanned by the corresponding CLVs, which are geometrically very degenerate. Such CLVs correspond to two different classes of ocean/atmosphere coupled modes. The tangent space spanned by the CLVs corresponding to the ...
Bounds on variation of spectral subspaces under J-self-adjoint perturbations
Albeverio, S.; Motovilov, A. K.; Shkalikov, A. A.
2008-01-01
Let $A$ be a self-adjoint operator on a Hilbert space $\\fH$. Assume that the spectrum of $A$ consists of two disjoint components $\\sigma_0$ and $\\sigma_1$. Let $V$ be a bounded operator on $\\fH$, off-diagonal and $J$-self-adjoint with respect to the orthogonal decomposition $\\fH=\\fH_0\\oplus\\fH_1$ where $\\fH_0$ and $\\fH_1$ are the spectral subspaces of $A$ associated with the spectral sets $\\sigma_0$ and $\\sigma_1$, respectively. We find (optimal) conditions on $V$ guaranteeing that the pertur...
The features and the algorithm of the program to calculate adjoint neutron cross sections on the basis of the continuous energy neutron cross sections as well as energy and angular distributions are described. The calculated adjoint cross sections are intended for Monte Carlo investigation of the nonuniform adjoint Boltzmann equation. 16 refs
Seismic structure of the European upper mantle based on adjoint tomography
Zhu, Hejun; Bozdağ, Ebru; Tromp, Jeroen
2015-04-01
We use adjoint tomography to iteratively determine seismic models of the crust and upper mantle beneath the European continent and the North Atlantic Ocean. Three-component seismograms from 190 earthquakes recorded by 745 seismographic stations are employed in the inversion. Crustal model EPcrust combined with mantle model S362ANI comprise the 3-D starting model, EU00. Before the structural inversion, earthquake source parameters, for example, centroid moment tensors and locations, are reinverted based on global 3-D Green's functions and Fréchet derivatives. This study consists of three stages. In stage one, frequency-dependent phase differences between observed and simulated seismograms are used to constrain radially anisotropic wave speed variations. In stage two, frequency-dependent phase and amplitude measurements are combined to simultaneously constrain elastic wave speeds and anelastic attenuation. In these two stages, long-period surface waves and short-period body waves are combined to simultaneously constrain shallow and deep structures. In stage three, frequency-dependent phase and amplitude anomalies of three-component surface waves are used to simultaneously constrain radial and azimuthal anisotropy. After this three-stage inversion, we obtain a new seismic model of the European curst and upper mantle, named EU60. Improvements in misfits and histograms in both phase and amplitude help us to validate this three-stage inversion strategy. Long-wavelength elastic wave speed variations in model EU60 compare favourably with previous body- and surface wave tomographic models. Some hitherto unidentified features, such as the Adria microplate, naturally emerge from the smooth starting model. Subducting slabs, slab detachments, ancient suture zones, continental rifts and backarc basins are well resolved in model EU60. We find an anticorrelation between shear wave speed and anelastic attenuation at depths global attenuation studies. Furthermore, enhanced
Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators
Jefferies, Brian [University of New South Wales, School of Mathematics (Australia)], E-mail: b.jefferies@unsw.edu.au; Johnson, Gerald W. [333 Avery Hall, University of Nebraska, Lincoln, Department of Mathematics (United States)], E-mail: gjohnson@math.unl.edu; Nielsen, Lance [Creighton University, Department of Mathematics (United States)], E-mail: lnielsen@creighton.edu
2007-02-15
The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A{sub 1},..., A{sub n} and associated continuous Borel probability measures {mu}{sub 1}, ?, {mu}{sub n} on [0,1]. Fix A{sub 1},..., A{sub n}. Then each choice of an n-tuple ({mu}{sub 1},...,{mu}{sub n}) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A{sub 1}, ..., A{sub n} are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi.
Popov, A. V., E-mail: Popov.Barnaul@mail.ru [Polzunov Altai State Technical University (Russian Federation)
2016-01-15
Metallic lithium is used to demonstrate the possibilities of applying non-self-adjoint operators for quantitative description of orbital excitations of electrons in crystals. It is shown that, the nonequilibrium distribution function can be calculated when solving the spectral problem; therefore, the kinetic properties of a material can also be described with the unified band theory.
Möbius invariant BFKL equation for the adjoint representation in N=4 SUSY
Fadin, V.S., E-mail: fadin@inp.nsk.su [Budker Institute of Nuclear Physics of SD RAS, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, 630090 Novosibirsk (Russian Federation); Fiore, R., E-mail: roberto.fiore@cs.infn.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, Arcavacata di Rende, I-87036 Cosenza (Italy); Lipatov, L.N., E-mail: lipatov@thd.pnpi.spb.ru [Petersburg Nuclear Physics Institute and St. Petersburg State University, Gatchina, 188300 St. Petersburg (Russian Federation); Papa, A., E-mail: alessandro.papa@cs.infn.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, Arcavacata di Rende, I-87036 Cosenza (Italy)
2013-09-01
It is shown that in the next-to-leading approximation of N=4 SUSY the BFKL equation for two-gluon composite states in the adjoint representation of the gauge group can be reduced to a form which is invariant under Möbius transformation in the momentum space. The corresponding similarity transformation of its integral kernel is constructed in an explicit way.
On a class of non-self-adjoint periodic boundary value problems with discrete real spectrum
Boulton, Lyonell; Levitin, Michael; Marletta, Marco
2010-01-01
In [arXiv:0801.0172] we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.
Theory of Loops and Strings with Matter in the Adjoint Representation
Maharana, Jnanadeva; Singh, Lambodhar P.
1994-01-01
We have presented canonical and path integral formulations of a theory of loops and closed strings with the matter field quanta transforming in the adjoint representation of the SU(N) gauge group. The physical processes arising out of the interactions of loops and closed strings are discussed.
On the Finite Volume Element Method for Self-Adjoint Parabolic Integrodifferential Equations
Mohamed Bahaj; Anas Rachid
2013-01-01
Finite volume element schemes for non-self-adjoint parabolic integrodifferential equations are derived and stated. For the spatially discrete scheme, optimal-order error estimates in , , and , norms for are obtained. In this paper, we also study the lumped mass modification. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived.
Adjoint sensitivity in PDE constrained least squares problems as a multiphysics problem
Lahaye, D.; Mulckhuyse, W.F.W.
2012-01-01
Purpose - The purpose of this paper is to provide a framework for the implementation of an adjoint sensitivity formulation for least-squares partial differential equations constrained optimization problems exploiting a multiphysics finite elements package. The estimation of the diffusion coefficient
Brane Configurations for Nonsupersymmetric Meta-Stable Vacua in SQCD with Adjoint Matter
Ahn, C
2006-01-01
We present the configurations of intersecting branes in type IIA string theory corresponding to the meta-stable supersymmetry breaking vacua(hep-th/0608063) in the four-dimensional N}=1 supersymmetric Yang-Mills theory coupled massive flavors with adjoint matter where the superpotential has three deformed terms.
Intensity-modulated radiation therapy (IMRT) is a new technique for administering external beam radiation therapy. This technology modulates the intensity and shape of the treatment beam as a function of source position and patient anatomy. This process of conforming the source to the patient requires the optimization of the independent variables of the source field. In this study, adjoint Monte Carlo methods were used to compute the sensitivity field that corresponds to a prescribed dose distribution. Given these data, linear and nonlinear optimization models were constructed with a simplified geometry to compute an optimized set of beams to deliver a desired dose distribution. The dose delivered to voxel i by beam j (Dij) influence matrix may be obtained from solutions to the adjoint transport equation. These solutions provide the sensitivity of the prescribed dose at a single point in the patient to all possible points in the source field. For this investigation, the source field consisted of 36 possible positions along a circular gantry. Each position had 21 possible directions to aim at the patient. Beam weights could vary continuously, and beam energy spectra matched that of a hospital-based linear accelerator. The MCNP Monte Carlo code was used to transport adjoint particles from each patient voxel to the 36 possible source locations where they were binned by direction and energy. The patient voxels (1 cm3) were defined within the central slice of a block phantom (31 x 31 x 11 cm) of unit-density water. The adjoint source for each voxel was the flux-to-dose conversion factor for tissue. The bin structures for the tallies matched the direction and energy structure of the forward source. Figure 1 shows the dose volume histograms (DVHs) for the optimized dose distributions for a ring-shaped tumor surrounding a sensitive structure. The DVH reports the fraction of each tissue type that is raised to each dose level. The lower dose limit prescribed for TU was 2
K. C. Wells; Millet, D. B.; Bousserez, N.; D. K. Henze; Chaliyakunnel, S.; T. J. Griffis; Luan, Y.; Dlugokencky, E. J.; R. G. Prinn; S. O'Doherty; R. F. Weiss; G. S. Dutton; Elkins, J. W.; Krummel, P. B.; Langenfelds, R.
2015-01-01
We describe a new 4D-Var inversion framework for nitrous oxide (N2O) based on the GEOS-Chem chemical transport model and its adjoint, and apply it in a series of observing system simulation experiments to assess how well N2O sources and sinks can be constrained by the current global observing network. The employed measurement ensemble includes approximately weekly and quasi-continuous N2O measurements (hourly averages used) from several long-term monitoring networks, N2O mea...
CMT Source Inversions for Massive Data Assimilation in Global Adjoint Tomography
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
Galanti, Eli
2016-01-01
During 2016-17 the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. This data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus allowing only calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model, is developed to relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for examination of various scenarios, simulating cases in which the depth of the wind depends...
Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods
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
Deconfinement and chiral symmetry restoration in an SU(3) gauge theory with adjoint fermions
We analyze the finite temperature phase diagram of QCD with fermions in the adjoint representation. The simulations performed with four dynamical Majorana fermions show that the deconfinement and chiral phase transitions occur at two distinct temperatures. While the deconfinement transition is first-order at Td we find evidence for a continuous chiral transition at a higher temperature Tc ≅ 8 Td. We observe a rapid change of bulk thermodynamic observables at Td which reflects the increase in the number of degrees of freedom. However, these show little variation at Tc, where the fermion condensate vanishes. We also analyze the potential between static fundamental and adjoint charges in all three phases and extract the corresponding screening masses above Td
Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems
Asner, Liya
2012-01-01
We consider time-dependent parabolic problem s coupled across a common interface which we formulate using a Lagrange multiplier construction and solve by applying a monolithic solution technique. We derive an adjoint-based a posteriori error representation for a quantity of interest given by a linear functional of the solution. We establish the accuracy of our error representation formula through numerical experimentation and investigate the effect of error in the adjoint solution. Crucially, the error representation affords a distinction between temporal and spatial errors and can be used as a basis for a blockwise time-space refinement strategy. Numerical tests illustrate the efficacy of the refinement strategy by capturing the distinctive behavior of a localized traveling wave solution. The saddle point systems considered here are equivalent to those arising in the mortar finite element technique for parabolic problems. © 2012 Society for Industrial and Applied Mathematics.
Weyl theorems for the polluted set of self-adjoint operators in Galerkin approximations
Boulton, Lyonell; Lewin, Mathieu
2010-01-01
Let A be a self-adjoint operator on a separable Hilbert space H and let (L_n) be a sequence of finite dimensional subspaces of the domain of A, approximating H in the large n limit. Denote by A_n the compression of A to L_n. In general the spectrum of A is only a subset of the limit of the spectra of A_n and the latter might differ from the former in a non-trivial "polluted set". In this paper we show that this polluted set is determined by the existence of particular Weyl sequences of singular type. This characterization allows us to identify verifiable conditions on self-adjoint perturbations B, ensuring that the polluted set of B is identical to that of A. The results reported are illustrated by means of several canonical examples and they reveal the many subtleties involved in the systematic study of spectral pollution.
Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
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.
Method of tallying adjoint fluence and calculating kinetics parameters in Monte Carlo codes
A method of using iterated fission probability to estimate the adjoint fluence during particles simulation, and using it as the weighting function to calculate kinetics parameters βeff and A in Monte Carlo codes, was introduced in this paper. Implements of this method in continuous energy Monte Carlo code MCNP and multi-group Monte Carlo code MCMG are both elaborated. Verification results show that, with regardless additional computing cost, using this method, the adjoint fluence accounted by MCMG matches well with the result computed by ANISN, and the kinetics parameters calculated by MCNP agree very well with benchmarks. This method is proved to be reliable, and the function of calculating kinetics parameters in Monte Carlo codes is carried out effectively, which could be the basement for Monte Carlo codes' utility in the analysis of nuclear reactors' transient behavior. (authors)
Adjoint Airfoil Optimization of Darrieus-Type Vertical Axis Wind Turbine
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.
Efficient optimization for Model Predictive Control in reservoir models
Borgesen, Jørgen Frenken
2009-01-01
The purpose of this thesis was to study the use of adjoint methods for gradient calculations in Model Predictive Control (MPC) applications. The goal was to find and test efficient optimization methods to use in MPC on oil reservoir models. Handling output constraints in the optimization problem has been studied closer since they deteriorate the efficiency of the MPC applications greatly. Adjoint- and finite difference approaches for gradient calculations was tested on reservoir models to de...
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.
Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
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
The Adjoint Monte Carlo - a viable option for efficient radiotherapy treatment planning
In cancer therapy using collimated beams of photons, the radiation oncologist must determine a set of beams that delivers the required dose to each point in the tumor and minimizes the risk of damage to the healthy tissue and vital organs. Currently, the oncologist determines these beams iteratively, by using a sequence of dose calculations using approximate numerical methods. In this paper, a more accurate and potentially faster approach, based on the Adjoint Monte Carlo method, is presented (authors)
Adjoint gradient-based approach for aerodynamic optimization of transport aircraft
Ilic, Caslav
2013-01-01
Aerodynamic design of transport aircraft has been steadily improved over past several decades, to the point where today highly-detailed shape control is needed to achieve further improvements. Aircraft manufacturers are therefore increasingly looking into formal optimization methods, driving high-fidelity CFD analysis of finely-parametrized candidate designs. We present an adjoint gradient-based approach for maximizing the aerodynamic performance index relevant to cruise-climb mission segment...
Spectrum of SU(2) gauge theory with two fermions in the adjoint representation
Hietanen, Ari; Rantaharju, Jarno; Rummukainen, Kari; Tuominen, Kimmo
2008-01-01
We present preliminary results of lattice simulations of SU(2) gauge theory with two Wilson fermions in the adjoint representation. This theory has recently attracted considerable attention because it might possess an infrared fixed point (or an almost-fixed-point), and hence be a candidate for a walking technicolor theory. In this work we study the particle spectrum of the theory, and compare it with more familiar spectrum of the theory with SU(2) gauge fields and two flavors of fundamental ...
Serre's reduction of linear systems of partial differential equations with holonomic adjoints
Cluzeau, Thomas; Quadrat, Alban
2010-01-01
Given a linear functional system (e.g., ordinary/partial di erential system, di erential time-delay system, di erence system), Serre's reduction aims at nding an equivalent linear functional system which contains fewer equations and fewer unknowns. The purpose of this paper is to study Serre's reduction of underdetermined linear systems of partial di erential equations with either polynomial, formal power series or analytic coe cients and with holonomic adjoints in the sense of algebraic anal...
Adjoint BFKL at finite coupling: a short-cut from the collinear limit
Basso, Benjamin; Sever, Amit
2014-01-01
In the high energy Regge limit, the six gluons scattering amplitude is controlled by the adjoint BFKL eigenvalue and impact factor. In this paper we determine these two building blocks at any value of the 't Hooft coupling in planar $\\cal{N}$=4 SYM theory. This is achieved by means of analytic continuations from the collinear limit, where similar all loops expressions were recently established. We check our predictions against all available data at weak and strong coupling.
Scattering and self-adjoint extensions of the Aharonov-Bohm Hamiltonian
De Oliveira, Cesar R [Departamento de Matematica-UFSCar, Sao Carlos, Sao Paulo 13560-970 (Brazil); Pereira, Marciano, E-mail: marciano@uepg.b [Departamento de Matematica e EstatIstica-UEPG, Ponta Grossa, Parana 84030-900 (Brazil)
2010-09-03
We consider the Hamiltonian operator associated with planar sections of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space H{sup 2}, we characterize all generalized boundary conditions on the solenoid border compatible with quantum mechanics, i.e. the boundary conditions, so that the corresponding Hamiltonian operators are self-adjoint. Then we study and compare the scattering of the most usual boundary conditions, that is, Dirichlet, Neumann and Robin.
Adjoint Monte Carlo calculation of charged plasma particle flux to wall
Äkäslompolo, Simppa
2015-01-01
This manuscript describes an adjoint/reverse Monte Carlo method to calculate the flux of charged plasma particles to the wall of e.g. a tokamak. Two applications are described: a fusion product activation probe and a neutral beam injection prompt loss measurement with a fast ion loss diagnostic. In both cases, the collisions of the particles with the background plasma can be omitted.
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2016-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet is demonstrated.
Methods of Monte Carlo biasing using two-dimensional discrete ordinates adjoint flux
Tang, J.S.; Stevens, P.N.; Hoffman, T.J.
1976-06-01
Methods of biasing three-dimensional deep penetration Monte Carlo calculations using importance functions obtained from a two-dimensional discrete ordinates adjoint calculation have been developed. The important distinction was made between the applications of the point value and the event value to alter the random walk in Monte Carlo analysis of radiation transport. The biasing techniques developed are the angular probability biasing which alters the collision kernel using the point value as the importance function and the path length biasing which alters the transport kernel using the event value as the importance function. Source location biasings using the step importance function and the scalar adjoint flux obtained from the two-dimensional discrete ordinates adjoint calculation were also investigated. The effects of the biasing techniques to Monte Carlo calculations have been investigated for neutron transport through a thick concrete shield with a penetrating duct. Source location biasing, angular probability biasing, and path length biasing were employed individually and in various combinations. Results of the biased Monte Carlo calculations were compared with the standard Monte Carlo and discrete ordinates calculations.
An adjoint-based approach for finding invariant solutions of Navier–Stokes equations
Farazmand, M.
2016-05-01
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and traveling wave solutions of the Navier--Stokes equations. Using the adjoint equations, arbitrary initial conditions evolve to the vicinity of a (relative) equilibrium at which point a few Newton-type iterations yield the desired (relative) equilibrium solution. We apply this adjoint-based method to a chaotic two-dimensional Kolmogorov flow. A convergence rate of 100% is observed, leading to the discovery of 21 new steady state and traveling wave solutions at Reynolds number Re=40. Some of the new invariant solutions have spatially localized structures that were previously believed to only exist on domains with large aspect ratios. We show that one of the newly found steady state solutions underpins the temporal intermittencies, i.e., high energy dissipation episodes of the flow. More precisely, it is shown that each intermittent episode of a generic turbulent trajectory corresponds to its close passage to this equilibrium solution.
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.
Adjoint-based deviational Monte Carlo methods for phonon transport calculations
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.
Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time
Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)
1999-01-01
A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.
Adjoint sensitivity analysis of the RELAPS/MOD3.2 two-fluid thermal-hydraulic code system
This work presents the implementation of the Adjoint Sensitivity Analysis Procedure (ASAP) for the non-equilibrium, non-homogeneous two-fluid model, including boron concentration and non-condensable gases, of the RELAP5/MOD3.2 code. The end-product of this implementation is the Adjoint Sensitivity Model (ASM-REL/TF), which is derived for both the differential and discretized equations underlying the two-fluid model with non-condensable(s). The consistency requirements between these two representations are also highlighted. The validation of the ASM-REL/TF has been carried out by using sample problems involving: (i) liquid-phase only, (ii) gas-phase only, and (iii) two-phase mixture (of water and steam). Thus the 'Two-Loops with Pumps' sample problem supplied with RELAP5/MOD3.2 has been used to verify the accuracy and stability of the numerical solution of the ASM-REL/TF when only the liquid-phase is present. Furthermore, the 'Edwards Pipe' sample problem, also supplied with RELAP5/MOD3.2, has been used to verify the accuracy and stability of the numerical solution of the ASM-REL/TF when both (i.e., liquid and gas) phases are present. In addition, the accuracy and stability of the numerical solution of the ASM-REL/TF have been verified when only the gas-phase is present by using modified 'Two-Loops with Pumps' and the 'Edwards Pipe' sample problems in which the liquid and two-phase fluids, respectively, were replaced by pure steam. The results obtained for these sample problems depict typical sensitivities of junction velocities and volume-averaged pressures to perturbations in initial conditions, and indicate that the numerical solution of the ASM-REL/TF is as robust, stable, and accurate as the original RELAP5/MOD3.2 calculations. In addition, the solution of the ASM-REL/TF has been used to calculate sample sensitivities of volume-averaged pressures to variations in the pump head. (orig.)
Forecasting turbulent modes with nonparametric diffusion models: Learning from noisy data
Berry, Tyrus; Harlim, John
2016-04-01
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the availability of a noise-free training data set observing the full state space of the dynamics, in real applications we often have only partial observations which are corrupted by noise. To alleviate these practical issues, following the theory of embedology, the diffusion model is built using the delay-embedding coordinates of the data. We show that this delay embedding biases the geometry of the data in a way which extracts the most stable component of the dynamics and reduces the influence of independent additive observation noise. The resulting diffusion forecast model approximates the semigroup solutions of the generator of the underlying dynamics in the limit of large data and when the observation noise vanishes. As in any standard forecasting problem, the forecasting skill depends crucially on the accuracy of the initial conditions. We introduce a novel Bayesian method for filtering the discrete-time noisy observations which works with the diffusion forecast to determine the forecast initial densities. Numerically, we compare this nonparametric approach with standard stochastic parametric models on a wide-range of well-studied turbulent modes, including the Lorenz-96 model in weakly chaotic to fully turbulent regimes and the barotropic modes of a quasi-geostrophic model with baroclinic instabilities. We show that when the only available data is the low-dimensional set of noisy modes that are being modeled, the diffusion forecast is indeed competitive to the perfect model.
Asorey, M.; Ibort, A.; Marmo, G.
2015-06-01
The theory of self-adjoint extensions of first- and second-order elliptic differential operators on manifolds with boundary is studied via its most representative instances: Dirac and Laplace operators. The theory is developed by exploiting the geometrical structures attached to them and, by using an adapted Cayley transform on each case, the space {M} of such extensions is shown to have a canonical group composition law structure. The obtained results are compared with von Neumann's theorem characterizing the self-adjoint extensions of densely defined symmetric operators on Hilbert spaces. The 1D case is thoroughly investigated. The geometry of the submanifold of elliptic self-adjoint extensions {M}ellip is studied and it is shown that it is a Lagrangian submanifold of the universal Grassmannian Gr. The topology of {M}ellip is also explored and it is shown that there is a canonical cycle whose dual is the Maslov class of the manifold. Such cycle, called the Cayley surface, plays a relevant role in the study of the phenomena of topology change. Self-adjoint extensions of Laplace operators are discussed in the path integral formalism, identifying a class of them for which both treatments leads to the same results. A theory of dissipative quantum systems is proposed based on this theory and a unitarization theorem for such class of dissipative systems is proved. The theory of self-adjoint extensions with symmetry of Dirac operators is also discussed and a reduction theorem for the self-adjoint elliptic Grassmannian is obtained. Finally, an interpretation of spontaneous symmetry breaking is offered from the point of view of the theory of self-adjoint extensions.
It is noted that the analog Monte Carlo method has low calculation efficiency at deep penetration problems such as radiation shielding analysis. In order to increase the calculation efficiency, variance reduction techniques have been introduced and applied for the shielding calculation. To optimize the variance reduction technique, the hybrid Monte Carlo method was introduced. For the determination of the parameters using the hybrid Monte Carlo method, the adjoint flux should be calculated by the deterministic methods. In this study, the collision probability method is applied to calculate adjoint flux. The solution of integration transport equation in the collision probability method is modified to calculate the adjoint flux approximately even for complex and arbitrary geometries. For the calculation, C++ program is developed. By using the calculated adjoint flux, importance parameters of each cell in shielding material are determined and used for variance reduction of transport calculation. In order to evaluate calculation efficiency with the proposed method, shielding calculations are performed with MCNPX 2.7. In this study, a method to calculate the adjoint flux in using the Monte Carlo variance reduction was proposed to improve Monte Carlo calculation efficiency of thick shielding problem. The importance parameter for each cell of shielding material is determined by calculating adjoint flux with the modified collision probability method. In order to calculate adjoint flux with the proposed method, C++ program is developed. The results show that the proposed method can efficiently increase the FOM of transport calculation. It is expected that the proposed method can be utilize for the calculation efficiency in thick shielding calculation
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.
M. Kopacz
2010-02-01
Full Text Available We combine CO column measurements from the MOPITT, AIRS, SCIAMACHY, and TES satellite instruments in a full-year (May 2004–April 2005 global inversion of CO sources at 4°×5° spatial resolution and monthly temporal resolution. The inversion uses the GEOS-Chem chemical transport model (CTM and its adjoint applied to MOPITT, AIRS, and SCIAMACHY. Observations from TES, surface sites (NOAA/GMD, and aircraft (MOZAIC are used for evaluation of the a posteriori solution. Using GEOS-Chem as a common intercomparison platform shows global consistency between the different satellite datasets and with the in situ data. Differences can be largely explained by different averaging kernels and a priori information. The global CO emission from combustion as constrained in the inversion is 1350 Tg a^{−1}. This is much higher than current bottom-up emission inventories. A large fraction of the correction results from a seasonal underestimate of CO sources at northern mid-latitudes in winter and suggests a larger-than-expected CO source from vehicle cold starts and residential heating. Implementing this seasonal variation of emissions solves the long-standing problem of models underestimating CO in the northern extratropics in winter-spring. A posteriori emissions also indicate a general underestimation of biomass burning in the GFED2 inventory. However, the tropical biomass burning constraints are not quantitatively consistent across the different datasets.
WANG Caixia; Paola Malanotte-Rizzoli
2014-01-01
The linkage between physical and biological processes, particularly the effect of the circulation field on the distribution of phytoplankton, is studied by applying a two-dimensional model and an adjoint data assimilation approach to the Gulf of Maine-Georges Bank region. The model results, comparing well with observation data, reveal seasonal and geographic variations of phytoplankton concentration and verify that the seasonal cycles of phytoplankton are controlled by both biological sources and ad-vection processes which are functions of space and time and counterbalance each other. Although advective flux divergences have greater magnitudes on Georges Bank than in the coastal region of the western Gulf of Maine, advection control over phytoplankton concentration is more significant in the coastal region of the western Gulf of Maine. The model results also suggest that the two separated populations in the coastal regions of the western Gulf of Maine and on Georges Bank are self-sustaining.
Adjoint-based sensitivity and feedback control of noise emission
Airiau, Christophe
2013-01-01
A LQR control is performed on a reduce order model built from Direct Numerical Simulation of an open cavity flow, for a 2D geometry, and in the aim of controlling noise emission. A -10 dB achievement is demonstrated
Adjoint sensitivity in Electrical Impedance Tomography using COMSOL Multiphysics
Mulckhuyse, W.F.W.; Lahaye, D.; Belitskaya, A.
2012-01-01
In 3D reconstruction problems the number of design variables is large and the forward model is typically computationally expensive. Reconstruction using gradient-based optimization algorithms requires many gradient computations. For such problems the computational cost of a finite difference approac
Cacuci, Dan G.
2015-03-01
This work presents an illustrative application of the second-order adjoint sensitivity analysis methodology (2nd-ASAM) to a paradigm neutron diffusion problem, which is sufficiently simple to admit an exact solution, thereby making transparent the underlying mathematical derivations. The general theory underlying 2nd-ASAM indicates that, for a physical system comprising Nα parameters, the computation of all of the first- and second-order response sensitivities requires (per response) at most (2Nα + 1) "large-scale" computations using the first-level and, respectively, second-level adjoint sensitivity systems (1st-LASS and 2nd-LASS). Very importantly, however, the illustrative application presented in this work shows that the actual number of adjoint computations needed for computing all of the first- and second-order response sensitivities may be significantly less than (2Nα + 1) per response. For this illustrative problem, four "large-scale" adjoint computations sufficed for the complete and exact computations of all 4 first- and 10 distinct second-order derivatives. Furthermore, the construction and solution of the 2nd-LASS requires very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first-order sensitivities. Very significantly, only the sources on the right-sides of the diffusion (differential) operator needed to be modified; the left-side of the differential equations (and hence the "solver" in large-scale practical applications) remained unchanged. All of the first-order relative response sensitivities to the model parameters have significantly large values, of order unity. Also importantly, most of the second-order relative sensitivities are just as large, and some even up to twice as large as the first-order sensitivities. In the illustrative example presented in this work, the second-order sensitivities contribute little to the response variances and covariances. However, they have the
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.
Non-self-adjoint Hamiltonians with complex eigenvalues
Bagarello, F.
2016-05-01
Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime.
On the Spectra and Pseudospectra of a Class of Non-Self-Adjoint Random Matrices and Operators
Chandler-Wilde, Simon N; Lindner, Marko
2011-01-01
In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E.B.Davies (Commun. Math. Phys. 216 (2001), 687-704). As a major application to illustrate our methods we focus on the "hopping sign model" introduced by J.Feinberg and A.Zee (Phys. Rev. E 59 (1999), 6433-6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random $\\pm 1$'s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and $p$-norm $\\eps$-pseudospectra ($\\eps>0$, $p\\in [1,\\infty]$) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite ma...
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.
Wave propagational inverse problems arise in several applications including medical imaging and geophysical exploration. In these problems, one is interested in obtaining the parameters describing the medium from its response to excitations. The problems are characterized by their large size, and by the hyperbolic equation which models the physical phenomena. The inverse problems are often posed as a nonlinear data-fitting where the unknown parameters are found by minimizing the misfit between the predicted data and the actual data. In order to solve the problem numerically using a gradient-type approach, one must calculate the action of the Jacobian and its adjoint on a given vector. In this paper, the authors explore the use of automatic differentiation (AD) to develop codes that perform these calculations. They show that by exploiting structure at 2 scales, they can arrive at a very efficient code whose main components are produced by AD. In the first scale they exploit the time-stepping nature of the hyperbolic solver by using the Extended Jacobian framework. In the second (finer) scale, they exploit the finite difference stencil in order to make explicit use of the sparsity in the dependence of the output variables to the input variables. The main ideas in this work are illustrated with a simpler, one-dimensional version of the problem. Numerical results are given for both one- and two-dimensional problems. They present computational templates that can be used in conjunction with optimization packages to solve the inverse problem
Size-resolved adjoint inversion of Asian dust
Yumimoto, K.; Uno, I.; Sugimoto, N.; Shimizu, A.; Hara, Y.; Takemura, T.
2012-12-01
We expanded the variational assimilation system of a regional dust model by using size-resolved inversion. Dust emissions and particle-size distributions of a severe dust and sandstorm (DSS) in April 2005 were inversely optimized with optical measurements by the National Institute for Environmental Studies lidar network. The inversion results successfully compensated underestimates by the original model and increased the Ångström exponent around the DSS core by 13-17%, shifting the particle-size distribution to finer. The a posteriori size distribution was distinctly different between eastern and western source regions. In the western regions, dust emissions in the 3.19 and 5.06μm size bins increased considerably, and the peak size shifted from 5.06 to 3.19 μm, whereas in the eastern regions, emissions of finer particles (bins 0.82-2.01 μm) increased. Differences in vegetation and soil type and moisture between eastern and western regions might explain the characteristics of the inverted size distribution.
Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds
T. Mine
2010-01-01
Full Text Available We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in terms of the boundary conditions. The result is an extension of the former results by Dabrowski-Šťoviček and Exner-Šťoviček-Vytřas.
On Maximal Abelian Self-adjoint Subalgebras of Factors of Type Ⅱ1
Li Guang WANG
2005-01-01
In this note, we show that if (N) is a proper subfactor of a factor (M) of type Ⅱ1 with finite Jones index, then there is a maximal abelian self-adjoint subalgebra (masa) (A) of (N) that is not a masa in (M). Popa showed that there is a proper subfactor (R)O of the hyperfinite type Ⅱ1 factor (R) such that each masa in (R)O is also a masa in (R). We shall give a detailed proof of Popa's result.
Self-adjointness and the Casimir effect with confined quantized spinor matter
Sitenko, Yurii A
2015-01-01
A generalization of the MIT bag boundary condition for spinor matter is proposed basing on the requirement that the Dirac hamiltonian operator be self-adjoint. An influence of a background magnetic field on the vacuum of charged spinor matter confined between two parallel material plates is studied. Employing the most general set of boundary conditions at the plates in the case of the uniform magnetic field directed orthogonally to the plates, we find the pressure from the vacuum onto the plates. In physically plausible situations, the Casimir effect is shown to be repulsive, independently of a choice of boundary conditions and of a distance between the plates.
Infrared fixed point in SU(2) gauge theory with adjoint fermions
We apply Schroedinger-functional techniques to the SU(2) lattice gauge theory with Nf=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* where 1/g*2=0.20(4)(3). At the fixed point, we find a mass anomalous dimension γm(g*)=0.31(6).
Infrared fixed point in SU(2) gauge theory with adjoint fermions
DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
2011-01-01
We apply Schrodinger-functional techniques to the SU(2) lattice gauge theory with N_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* where 1/g*^2 = 0.20(4)(3). At the fixed point, we find a mass anomalous dimension gamma_m(g*) = 0.31(6).
Self-adjointness and the Casimir effect with confined quantized spinor matter
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.
The adjoint equation method for constructing first integrals of difference equations
A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation. The method is based on a newly established identity which links symmetries of the underlying discrete equations, solutions of the discrete adjoint equations and first integrals. The method is applied to an invariant mapping and to discretizations of second order and third order ordinary differential equations. In examples the set of independent first integrals makes it possible to find the general solution of the discrete equations. (paper)
On linear operators with s-nuclear adjoints: $0< s \\le 1$
Reinov, O. I.
2013-01-01
If $ s\\in (0,1]$ and $ T$ is a linear operator with $ s$-nuclear adjoint from a Banach space $ X$ to a Banach space $ Y$ and if one of the spaces $ X^*$ or $ Y^{***}$ has the approximation property of order $s,$ $AP_s,$ then the operator $ T$ is nuclear. The result is in a sense exact. For example, it is shown that for each $r\\in (2/3, 1]$ there exist a Banach space $Z_0$ and a non-nuclear operator $ T: Z_0^{**}\\to Z_0$ so that $Z_0^{**}$ has a Schauder basis, $ Z_0^{***}$ has the $AP_s$ for ...
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.
Hilbert-Schmidt Inner Product for an Adjoint Representation of the Quantum Algebra U⌣Q(SU2)
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.
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 S16 or higher
Eguchi-Kawai reduction with one flavor of adjoint Möbius fermion
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.
Radiation source reconstruction with known geometry and materials using the adjoint
We present a method to estimate an unknown isotropic source distribution, in space and energy, using detector measurements when the geometry and material composition are known. The estimated source distribution minimizes the difference between the measured and computed responses of detectors located at a selected number of points within the domain. In typical methods, a forward flux calculation is performed for each source guess in an iterative process. In contrast, we use the adjoint flux to compute the responses. Potential applications of the proposed method include determining the distribution of radio-contaminants following a nuclear event, monitoring the flow of radioactive fluids in pipes to determine hold-up locations, and retroactive reconstruction of radiation fields using workers' detectors' readings. After presenting the method, we describe a numerical test problem to demonstrate the preliminary viability of the method. As expected, using the adjoint flux reduces the number of transport solves to be proportional to the number of detector measurements, in contrast to methods using the forward flux that require a typically larger number proportional to the number of spatial mesh cells. (author)
Aerodynamic Optimization of the Nose Shape of a Train Using the Adjoint Method
Jorge Munoz-Paniagua
2015-01-01
Full Text Available The adjoint method is used in this paper for the aerodynamic optimization of the nose shape of a train. This method has been extensively applied in aircraft or ground vehicle aerodynamic optimization, but is still in progress in train aerodynamics. Here we consider this innovative optimization method and present its application to reduce the aerodynamic drag when the train is subjected to front wind. The objective of this paper is to demonstrate the effectiveness of the method, highlighting the requirements, limitations and capabilities of it. Furthermore, a significant reduction of the aerodynamic drag in a short number of solver calls is aimed as well. The independence of the computational cost with respect to the number of design variables that define the optimal candidate is stressed as the most interesting characteristic of the adjoint method. This behavior permits a more complete modification of the shape of the train nose because the number of design variables is not a constraint anymore. The information obtained from the sensitivity field permits determining the regions of the geometry where a small modification of the nose shape might introduce a larger improvement of the train performance. A good agreement between this information and the successive geometry modifications is observed here.
A generalized albedo option for forward and adjoint Monte Carlo calculations
The advisability of using the albedo procedure for the Monte Carlo solution of deep-penetration shielding problems which have ducts and other penetrations is investigated. It is generally accepted that the use of albedo data can dramatically improve the computational efficiency of certain Monte Carlo calculations - however the accuracy of these results may be unacceptable because of lost information during the albedo event and serious errors in the available differential albedo data. This study was done to evaluate and appropriate modify the MORSE/BREESE package, to develop new methods for generating the required albedo data, and to extend the adjoint capability to the albedo-modified calculations. The major modifications include an option to save for further use information that would be lost at the albedo event, an option to displace the emergent point during an albedo event, and an option to read spatially-dependent albedo data for both forward and adjoint calculations - which includes the emergent point as a new random variable to be selected during an albedo reflection event. The theoretical basis for using TORT-generated forward albedo information to produce adjuncton albedos is derived
Adjoint sensitivity theory for steady-state ground-water flow
In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady-state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah and the Wolcamp carbonate/sandstone aquifer of the Palo Duro Basin in the Texas Panhandle. Two performance measures are evaluated, local heads and velocity in the vicinity of potential high-level nuclear waste repositories. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Local velocity-related performance measures are more sensitive to hydraulic conductivities. The uncertainty in the performance measure is a function of the parameter sensitivity, parameter variance and the correlation between parameters. Given a parameter covariance matrix, the uncertainty of the performance measure can be calculated. Although no results are presented here, the implications of uncertainty calculations for the two studies are discussed. 18 references, 25 figures
Abhyankar, Shrirang [Argonne National Lab. (ANL), Argonne, IL (United States); Anitescu, Mihai [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil [Argonne National Lab. (ANL), Argonne, IL (United States); Zhang, Hong [Argonne National Lab. (ANL), Argonne, IL (United States)
2016-03-31
Sensitivity analysis is an important tool to describe power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this work, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating trajectory sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as DC exciters, by deriving and implementing the adjoint jump conditions that arise from state and time-dependent discontinuities. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach.
Fadin, V.S. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Budker Nuclear Physics Institute, Novosibirsk (Russian Federation); Novosibirskij Gosudarstvennyj Univ., Novosibirsk (Russian Federation); Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); St. Petersburg State Univ., Gatchina (Russian Federation)
2011-12-15
We calculate the eigenvalues of the next-to-leading kernel for the BFKL equation in the adjoint representation of the gauge group SU(N{sub c}) in the N=4 supersymmetric Yang-Mills model. These eigenvalues are used to obtain the high energy behavior of the remainder function for the 6-point scattering amplitude with the maximal helicity violation in the kinematical regions containing the Mandelstam cut contribution. The leading and next-to-leading singularities of the corresponding collinear anomalous dimension are calculated in all orders of perturbation theory. We compare our result with the known collinear limit and with the recently suggested ansatz for the remainder function in three loops and obtain the full agreement providing that the numerical parameters in this anzatz are chosen in an appropriate way.
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
Can core flows inferred from geomagnetic field models explain the Earth's dynamo?
Schaeffer, N.; Silva, E. Lora; Pais, M. A.
2016-02-01
We test the ability of large-scale velocity fields inferred from geomagnetic secular variation data to produce the global magnetic field of the Earth. Our kinematic dynamo calculations use quasi-geostrophic (QG) flows inverted from geomagnetic field models which, as such, incorporate flow structures that are Earth-like and may be important for the geodynamo. Furthermore, the QG hypothesis allows straightforward prolongation of the flow from the core surface to the bulk. As expected from previous studies, we check that a simple QG flow is not able to sustain the magnetic field against ohmic decay. Additional complexity is then introduced in the flow, inspired by the action of the Lorentz force. Indeed, on centennial timescales, the Lorentz force can balance the Coriolis force and strict quasi-geostrophy may not be the best ansatz. When our columnar flow is modified to account for the action of the Lorentz force, magnetic field is generated for Elsasser numbers larger than 0.25 and magnetic Reynolds numbers larger than 100. This suggests that our large-scale flow captures the relevant features for the generation of the Earth's magnetic field and that the invisible small-scale flow may not be directly involved in this process. Near the threshold, the resulting magnetic field is dominated by an axial dipole, with some reversed flux patches. Time dependence is also considered, derived from principal component analysis applied to the inverted flows. We find that time periods from 120 to 50 yr do not affect the mean growth rate of the kinematic dynamos. Finally, we note that the footprint of the inner core in the magnetic field generated deep in the bulk of the shell, although we did not include one in our computations.
P. D. Williams
2004-01-01
Full Text Available We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.
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.
Hietanen, A.; Narayanan, R.
2012-01-01
We use a single site lattice in four dimensions to study the scaling of large N Yang-Mills field coupled to a single massless Dirac fermion in the adjoint representation. We use the location of the strong to the weak coupling transition defined through the eigenvalues of the folded Wilson loop...
Bondarenko, S
2015-01-01
We revisit the next-to-leading order~(NLO) correction to the eigenvalue of the BFKL equation in the adjoint representation and investigate its properties in analogy with the singlet BFKL in planar $\\mathcal{N}=4$ super Yang-Mills Theory~(SYM). We show that the adjoint NLO BFKL eigenvalue is needed to be slightly modified in order to have a property of hermitian separability present for the singlet BFKL. After this modification the adjoint NLO BFKL eigenvalue is expressed through holomorphic and antiholomophic parts of the leading order eigenvalue and their derivatives. The proposed choice of the modified NLO expression is supported by the fact that it is possible to obtain the same result in a relatively straightforward way directly from the singlet NLO BFKL eigenvalue replacing alternating series by series of constant sign. This transformation corresponds to changing cylindrical topology of the singlet BFKL to the planar topology of the adjoint BFKL. We believe that the original NLO calculation of Fadin and ...
Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland;
2014-01-01
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...
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.
A relatively new technique for achieving the right dose to the right tissue, is intensity modulated radiation therapy (IMRT). In this technique, a megavoltage x-ray beam is rotated around a patient, and the intensity and shape of the beam is modulated as a function of source position and patient anatomy. The relationship between beam-let intensity and patient dose can be expressed under a matrix form where the matrix Dij represents the dose delivered to voxel i by beam-let j per unit fluence. The Dij influence matrix is the key element that enables this approach. In this regard, sensitivity theory lends itself in a natural way to the process of computing beam weights for treatment planning. The solution of the adjoint form of the Boltzmann equation is an adjoint function that describes the importance of particles throughout the system in contributing to the detector response. In this case, adjoint methods can provide the sensitivity of the dose at a single point in the patient with respect to all points in the source field. The purpose of this study is to investigate the feasibility of using the adjoint method and Monte Carlo transport for radiation therapy treatment planning
Slices to sums of adjoint orbits, the Atiyah-Hitchin manifold, and Hilbert schemes of points
Bielawski, Roger
2015-01-01
We show that the regular Slodowy slice to the sum of two semisimple adjoint orbits of $GL(n,C)$ is isomorphic to the deformation of the $D_2$-singularity if $n=2$, the Dancer deformation of the double cover of the Atiyah-Hitchin manifold if $n=3$, and to the Atiyah-Hitchin manifold itself if $n=4$. For higher $n$, such slices to the sum of two orbits, each having only two distinct eigenvalues, are either empty or biholomorphic to open subsets of the Hilbert scheme of points on of one the above surfaces. In particular, these open subsets of Hilbert schemes of points carry complete hyperk\\"ahler metrics, which in the case of the Atiyah-Hitchin manifold turns out to be the natural $L^2$-metric on a hyperk\\"ahler submanifold of the monopole moduli space.
Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours
An SU(2) gauge theory with two fermions transforming under the adjoint representation of the gauge group may appear conformal or almost conformal in the infrared. We use lattice simulations to study the spectrum of this theory and present results on the masses of several gauge singlet states as a function of the physical quark mass determined through the axial Ward identity and find indications of a change from chiral symmetry breaking to a phase consistent with conformal behaviour at βL ∼ 2. However, the measurement of the spectrum is not alone sufficient to decisively confirm the existence of conformal fixed point in this theory as we show by comparing to similar measurements with fundamental fermions. Based on the results we sketch a possible phase diagram of this lattice theory and discuss the applicability and importance of these results for the future measurement of the evolution of the coupling constant.
Multi-objective optimization strategies using adjoint method and game theory in aerodynamics
Zhili Tang
2006-01-01
There are currently three different game strategies originated in economics:(1) Cooperative games (Pareto front),(2)Competitive games (Nash game) and (3)Hierarchical games (Stackelberg game).Each game achieves different equilibria with different performance,and their players play different roles in the games.Here,we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multicriteria aerodynamic optimization problems.The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments.We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method.The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front.Non-dominated Pareto front solutions are obtained,however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.
Confining vs. conformal scenario for SU(2) with 2 adjoint fermions. Gluonic observables
Del Debbio, Luigi; Lucini, Biagio; Patella, Agostino; Pica, Claudio; Rago, Antonio
2010-01-01
Walking technicolor is a mechanism for electroweak symmetry breaking without Higgs field. The Higgs mechanism is provided by chiral symmetry breaking in the technicolor theory. An essential ingredient is the vicinity to an IR fixed point, which could reconcile technicolor with the electroweak...... signal for the existence of an IR fixed point in this theory can be obtained by comparing the mesonic and gluonic sectors. We review some technical details of our calculations. Possible systematic errors are discussed....... precision tests. SU(2) gauge theory with two Dirac adjoint fermions has been proposed as a candidate for walking technicolor. Understanding whether this theory is confining or IR-conformal is a challenging problem, which can be addressed by means of numerical simulations. We have pointed out that a clean...
The 2-loop partition function of large N gauge theories with adjoint matter on S^3
Mussel, Matan
2009-01-01
We compute the 2-loop thermal partition function of Yang-Mills theory on a small 3-sphere, in the large N limit with weak 't Hooft coupling. We include N_s scalars and N_f chiral fermions in the adjoint representation of the gauge group (S)U(N), with arbitrary Yukawa and quartic scalar couplings, assuming only commutator interactions. From this computation one can extract information on the perturbative corrections to the spectrum of the theory, and the correction to its Hagedorn temperature. Furthermore, the computation of the 2-loop partition function is a necessary step towards determining the order of the deconfinement phase transition at weak coupling, for which a 3-loop computation is needed.
On the product of self-adjoint Sturm-Liouville differential operators in direct sum spaces
Sobhy El-Sayed Ibrahim
2006-03-01
Full Text Available In this paper, the second-order symmetric Sturm-Liouville differential expressions $ \\tau_1,\\tau_2, \\ldots, \\tau_n $, with real coefficients on any finite number of intervals are studied in the setting of the direct sum of the $ L_w^2 $-spaces of functions defined on each of the separate intervals. It is shown that the characterization of singular self-adjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, it is an exact parallel of that in the regular case. This characterization is an extension of those obtained in [6], [7], [8], [9], [12], [14] and [15].
Focus Point Gauge Mediation with Incomplete Adjoint Messengers and Gauge Coupling Unification
Bhattacharyya, Gautam; Yokozaki, Norimi
2015-01-01
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 $\\Delta=$ 60-150. Interestingly, even in the presence of incomplete messenger multiplet...
One-loop adjoint masses for non-supersymmetric intersecting branes
Anastasopoulos, P. [Technische Univ., Vienna (Austria). 1. Inst. fuer Theoretische Physik; Antoniadis, I. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Benakli, K. [CNRS, UPMC Univ. Paris (France). Lab. de Physique Theorique et Haute Energies; Goodsell, M.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Vichi, A. [Institute de Theorie des Phenomenes Physiques, EPFL, Lausanne (Switzerland)
2011-05-15
We consider breaking of supersymmetry in intersecting D-brane configurations by slight deviation of the angles from their supersymmetric values. We compute the masses generated by radiative corrections for the adjoint scalars on the brane world-volumes. In the open string channel, the string two-point function receives contributions only from the infrared and the ultraviolet limits. The latter is due to tree-level closed string uncanceled NS-NS tadpoles, which we explicitly reproduce from the effective Born-Infeld action. On the other hand, the infrared region reproduces the one-loop mediation of supersymmetry breaking in the effective gauge theory, via messengers and their Kaluza-Klein excitations. In the toroidal set-up considered here, it receives contributions only from N {approx} 4 and N {approx} 2 supersymmetric configurations, and thus always leads at leading order to a tachyonic direction, in agreement with effective field theory expectations. (orig.)
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Koshmanenko, Volodymyr; Koshmanenko, Nataliia
2016-01-01
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...
Solution of the self-adjoint radiative transfer equation on hybrid computer systems
Gasilov, V. A.; Kuchugov, P. A.; Olkhovskaya, O. G.; Chetverushkin, B. N.
2016-06-01
A new technique for simulating three-dimensional radiative energy transfer for the use in the software designed for the predictive simulation of plasma with high energy density on parallel computers is proposed. A highly scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is developed based on the solution of a second-order equation with a self-adjoint operator. A distinctive feature of this algorithm is a preliminary transformation of rotation to eliminate mixed derivatives with respect to the spatial variables, simplify the structure of the difference operator, and accelerate the convergence of the iterative solution of the equation. It is shown that the proposed method correctly reproduces the limiting cases—isotropic radiation and the directed radiation with a δ-shaped angular distribution.
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.
SO(N) Higgs problem with adjoint + vector representations and non-linear potentials
Using the recently devised geometrical method, we analyze the quartic Higgs potential for SO(N) adjoint + vector representations. The minimum energy solutions are found to correspond to maxi-maximal little groups, but not all such groups are used. However, in the complete orbit space (including invariants not employed in the Higgs potential) we find that their strata have somewhat equal geometrical status of being low dimensional singular subspaces, i.e., cusps, edge curves, two-dimensional surfaces, etc. We also consider simple scalar potentials which are nonlinear with respect to orbit parameters and show that the directional extremum often, though not always, remains monotonic in orbit parameters within the orbit space and consequently the absolute extremum is likely to occur on the most protrudent portions of the orbit space boundary. Thus we clarify the range of validity of the Michel-Radicati conjecture and the Gell-Mann-Slansky conjecture. (orig.)
Discrete Adjoint-Based Design for Unsteady Turbulent Flows On Dynamic Overset Unstructured Grids
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.
The asymptotic behaviour of the spectrum of a self-adjoint second-order differential operator on the axis is investigated. The coefficients of this operator depend on rapid and slow variables and are periodic in the rapid variable. The period of oscillations in the rapid variable is a small parameter. The dependence of the coefficients on the rapid variable is localized, and they stop depending on it at infinity. Asymptotic expansions for the eigenvalues and the eigenfunctions of the operator in question are constructed. It is shown that, apart from eigenvalues convergent to eigenvalues of the homogenized operator as the small parameter converges to zero, the perturbed operator can also have an eigenvalue convergent to the boundary of the continuous spectrum. Necessary and sufficient conditions for the existence of such an eigenvalue are obtained. Bibliography: 22 titles.
Pingen, Georg; Evgrafov, Anton; Maute, Kurt
2009-01-01
We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion of...... generalized geometry optimization formulation and derive the corresponding sensitivity analysis for the single relaxation LBM for both topology and shape optimization applications. Using numerical examples, we verify the accuracy of the analytical sensitivity analysis through a comparison with finite...... differences. In addition, we show that for fluidic topology optimization a scaled volume constraint should be used to obtain the desired "0-1" optimal solutions. (C) 2008 Elsevier Ltd. All rights reserved....
Chandler-Wilde, Simon; Lindner, Marko
2010-01-01
The purpose of this paper is to prove that the spectrum of the non-self-adjoint one-particle Hamiltonian proposed by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433--6443) has interior points. We do this by first recalling that the spectrum of this random operator is the union of the set of $\\ell^\\infty$ eigenvalues of all infinite matrices with the same structure. We then construct an infinite matrix of this structure for which every point of the open unit disk is an $\\ell^\\infty$ eigenvalue, this following from the fact that the components of the eigenvector are polynomials in the spectral parameter whose non-zero coefficients are $\\pm 1$'s, forming the pattern of an infinite discrete Sierpinski triangle.
The 'adjoint transport equation in its integro-differential form' is derived for the radiation damage produced by atoms injected into solids. We reduce it to the one-dimensional form and prepare it for a numerical solution by: --discretizing the continuous variables energy, space and direction, --replacing the partial differential quotients by finite differences and --evaluating the collision integral by a double sum. By a proper manipulation of this double sum the adjoint transport equation turns into a (very large) set of linear equations with tridiagonal matrix which can be solved by a special (simple and fast) algorithm. The solution of this set of linear equations contains complete information on a specified damage type (e.g. the energy deposited in a volume V) in terms of the function D(i,E,c,x) which gives the damage produced by all particles generated in a cascade initiated by a particle of type i starting at x with energy E in direction c. It is essential to remark that one calculation gives the damage function D for the complete ranges of the variables {i,E,c and x} (for numerical reasons of course on grid-points in the {E,c,x}-space). This is most useful to applications where a general source-distribution S(i,E,c,x) of particles is given by the experimental setup (e.g. beam-window and and target in proton accelerator work. The beam-protons along their path through the window--or target material generate recoil atoms by elastic collisions or nuclear reactions. These recoil atoms form the particle source S). The total damage produced then is eventually given by: D = (Σ)i ∫ ∫ ∫ S(i, E, c, x)*D(i, E, c, x)*dE*dc*dx A Fortran-77 program running on a PC-486 was written for the overall procedure and applied to some problems
Feng, Jie; Ding, Ruiqiang; Li, Jianping; Liu, Deqiang
2016-09-01
The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors (BVs) are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector (NLLV) scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more components in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random perturbation (RP) technique, and the BV method, as well as its improved version—the ensemble transform Kalman filter (ETKF) method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.
K. C. Wells
2015-07-01
Full Text Available We describe a new 4D-Var inversion framework for N2O based on the GEOS-Chem chemical transport model and its adjoint, and apply this framework in a series of observing system simulation experiments to assess how well N2O sources and sinks can be constrained by the current global observing network. The employed measurement ensemble includes approximately weekly and quasi-continuous N2O measurements (hourly averages used from several long-term monitoring networks, N2O measurements collected from discrete air samples aboard a commercial aircraft (CARIBIC, and quasi-continuous measurements from an airborne pole-to-pole sampling campaign (HIPPO. For a two-year inversion, we find that the surface and HIPPO observations can accurately resolve a uniform bias in emissions during the first year; CARIBIC data provide a somewhat weaker constraint. Variable emission errors are much more difficult to resolve given the long lifetime of N2O, and major parts of the world lack significant constraints on the seasonal cycle of fluxes. Current observations can largely correct a global bias in the stratospheric sink of N2O if emissions are known, but do not provide information on the temporal and spatial distribution of the sink. However, for the more realistic scenario where source and sink are both uncertain, we find that simultaneously optimizing both would require unrealistically small errors in model transport. Regardless, a bias in the magnitude of the N2O sink would not affect the a posteriori N2O emissions for the two-year timescale used here, given realistic initial conditions, due to the timescale required for stratosphere–troposphere exchange (STE. The same does not apply to model errors in the rate of STE itself, which we show exerts a larger influence on the tropospheric burden of N2O than does the chemical loss rate over short (2O emissions. There, averaging kernels are highly smeared spatially and extend even to the midlatitudes, so that tropical
Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame
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.
Ali Sirma
2015-07-01
Full Text Available In this work, we generalize so called Green's functional concept in literature to second-order linear integro-differential equation with nonlocal conditions. According to this technique, a linear completely nonhomogeneous nonlocal problem for a second-order integro-differential equation is reduced to one and one integral equation to identify the Green's solution. The coefficients of the equation are assumed to be generally nonsmooth functions satisfying some general properties such as p-integrability and boundedness. We obtain new adjoint system and Green's functional for second-order linear integro-differential equation with nonlocal conditions. An application illustrate the adjoint system and the Green's functional. Another application shows when the Green's functional does not exist.
Verch, R
1996-01-01
We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a one-parametric family of scalar products canonically associated with the initially given one, among them being its ``purification''. As a typical example we consider a scalar field on a globally hyperbolic spacetime governed by the Klein-Gordon equation; the classical system is described by a symplectic space and the temporal evolution by symplectomorphisms (which are symplectically adjoint to their inverses). A natural scalar product is that inducing the classical energy norm, and an application of the above result yields that its ``purification'' induces on the one-particle space of the quantized system a topology which coincides with that given by the two-point functions of quasifree Hadamard states...
Multi-point Adjoint-Based Design of Tilt-Rotors in a Noninertial Reference Frame
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.
Large-N reduction in QCD with two adjoint Dirac fermions
Bringoltz, Barak; Sharpe, Stephen R
2011-01-01
We use lattice simulations to study the single-site version of SU(N) lattice gauge theory with two flavors of Wilson-Dirac fermions in the adjoint representation, a theory whose large volume correspondent is expected to be conformal or nearly conformal. Working with N as large as 53, we map out the phase diagram in the plane of bare `t Hooft coupling, g^2 N, and of the lattice quark mass, a*m, and look for the region where the Z_N^4 center symmetry of the theory is intact. In this region one expects the large-N equivalence of the single site and infinite volume theories to be valid. As for the N_f=1 case (see Phys. Rev. D80: 065031), we find that the center-symmetric region is large and includes both light fermion masses and masses at the cutoff scale. We study the N-dependence of the width of this region and, while we cannot rule out that it shrinks to zero at infinite N, the bulk of the evidence suggests that it remains of finite width. Simulating with couplings as small as g^2 N = 0.005, we find that the w...
Äkäslompolo, Simppa; Tardini, Giovanni; Kurki-Suonio, Taina
2015-01-01
The activation probe is a robust tool to measure flux of fusion products from a magnetically confined plasma. A carefully chosen solid sample is exposed to the flux, and the impinging ions transmute the material makig it radioactive. Ultra-low level gamma-ray spectroscopy is used post mortem to measure the activity and, thus, the number of fusion products. This contribution presents the numerical analysis of the first measurement in the ASDEX Upgrade tokamak, which was also the first experiment to measure a single discharge. The ASCOT suite of codes was used to perform adjoint/reverse Monte-Carlo calculations of the fusion products. The analysis facilitated, for the first time, a comparison of numerical and experimental values for absolutely calibrated flux. The results agree to within 40%, which can be considered remarkable considering the fact that all features of the plasma cannot be accounted in the simulations. Also an alternative probe orientation was studied. The results suggest that a better optimized...
Discrete SLn-connections and self-adjoint difference operators on 2-dimensional manifolds
The programme of discretization of famous completely integrable systems and associated linear operators was launched in the 1990s. In particular, the properties of second-order difference operators on triangulated manifolds and equilateral triangular lattices have been studied by Novikov and Dynnikov since 1996. This study included Laplace transformations, new discretizations of complex analysis, and new discretizations of GLn-connections on triangulated n-dimensional manifolds. A general theory of discrete GLn-connections 'of rank one' has been developed (see the Introduction for definitions). The problem of distinguishing the subclass of SLn-connections (and unimodular SLn± -connections, which satisfy detA = ±1) has not been solved. In the present paper it is shown that these connections play an important role (which is similar to the role of magnetic fields in the continuous case) in the theory of self-adjoint Schrödinger difference operators on equilateral triangular lattices in ℝ2. In Appendix 1 a complete characterization is given of unimodular SLn± -connections of rank 1 for all n > 1, thus correcting a mistake (it was wrongly claimed that they reduce to a canonical connection for n > 2). With the help of a communication from Korepanov, a complete clarification is provided of how the classical theory of electrical circuits and star-triangle transformations is connected with the discrete Laplace transformations on triangular lattices. Bibliography: 29 titles
Finite volume phases of large-N gauge theories with massive adjoint fermions
The phase structure of QCD-like gauge theories with fermions in various representations is an interesting but generally analytically intractable problem. One way to ensure weak coupling is to define the theory in a small finite volume, in this case S3 x S1. Genuine phase transitions can then occur in the large N theory. Here, we use this technique to investigate SU(N) gauge theory with a number Nf of massive adjoint-valued Majorana fermions having non-thermal boundary conditions around S1. For Nf = 1 we find a line of transitions that separate the weak-coupling analogues of the confined and de-confined phases for which the density of eigenvalues of the Wilson line transform from the uniform distribution to a gapped distribution. However, the situation for Nf > 1 is much richer and a series of weak-coupling analogues of partially-confined phases appear which leave unbroken a Zp subgroup of the centre symmetry. In these Zp phases the eigenvalue density has p gaps and they are separated from the confining phase and from one-another by first order phase transitions. We show that for small enough mR (the mass of the fermions times the radius of the S3) only the confined phase exists. The large N phase diagram is consistent with the finite N result and with other approaches based on R3 x S1 calculations and lattice simulations.
Laboure, Vincent M; Wang, Yaqi
2016-01-01
In this paper, we derive a method for the second-order form of the transport equation that is both globally conservative and compatible with voids, using Continuous Finite Element Methods (CFEM). The main idea is to use the Least-Squares (LS) form of the transport equation in the void regions and the Self-Adjoint Angular Flux (SAAF) form elsewhere. While the SAAF formulation is globally conservative, the LS formulation need a correction in void. The price to pay for this fix is the loss of symmetry of the bilinear form. We first derive this Conservative LS (CLS) formulation in void. Second we combine the SAAF and CLS forms and end up with an hybrid SAAF-CLS method, having the desired properties. We show that extending the theory to near-void regions is a minor complication and can be done without affecting the global conservation of the scheme. Being angular discretization agnostic, this method can be applied to both discrete ordinates (SN) and spherical harmonics (PN) methods. However, since a globally conse...
Komatitsch, Dimitri; Bozdag, Ebru; de Andrade, Elliott Sales; Peter, Daniel B; Liu, Qinya; Tromp, Jeroen
2016-01-01
We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the $K_\\alpha$ sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersi...
Highlights: • Performance estimation of nuclear-data benchmark was investigated. • Point detector contribution played a benchmark role not only to the neutron producing the detector contribution but also equally to all the upstream transport neutrons. • New functions were defined to give how well the contribution could be interpreted for benchmarking. • Benchmark performance could be evaluated only by a forward Monte Carlo calculation. -- Abstract: The author's group has been investigating how the performance estimation of nuclear-data benchmark using experiment and its analysis by Monte Carlo code should be carried out especially at 14 MeV. We have recently found that a detector contribution played a benchmark role not only to the neutron producing the detector contribution but also equally to all the upstream neutrons during the neutron history. This result would propose that the benchmark performance could be evaluated only by a forward Monte Carlo calculation. In this study, we thus defined new functions to give how well the contribution could be utilized for benchmarking using the point detector, and described that it was deeply related to the newly introduced “partial adjoint contribution”. By preparing these functions before benchmark experiments, one could know beforehand how well and for which nuclear data the experiment results could do benchmarking in forward Monte Carlo calculations
Focus point gauge mediation with incomplete adjoint messengers and gauge coupling unification
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.
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
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W. [North Carolina State Univ., Raleigh, NC (United States)
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation.
This work presents the implementation of the Adjoint Sensitivity Analysis Procedure (ASAP) for the Continuous Time, Discrete Space Markov chains (CTMC), as an alternative to the other computational expensive methods. In order to develop this procedure as an end product in reliability studies, the reliability of the physical systems is analyzed using a coupled Fault-Tree - Markov chain technique, i.e. the abstraction of the physical system is performed using as the high level interface the Fault-Tree and afterwards this one is automatically converted into a Markov chain. The resulting differential equations based on the Markov chain model are solved in order to evaluate the system reliability. Further sensitivity analyses using ASAP applied to CTMC equations are performed to study the influence of uncertainties in input data to the reliability measures and to get the confidence in the final reliability results. The methods to generate the Markov chain and the ASAP for the Markov chain equations have been implemented into the new computer code system QUEFT/MARKOMAGS/MCADJSEN for reliability and sensitivity analysis of physical systems. The validation of this code system has been carried out by using simple problems for which analytical solutions can be obtained. Typical sensitivity results show that the numerical solution using ASAP is robust, stable and accurate. The method and the code system developed during this work can be used further as an efficient and flexible tool to evaluate the sensitivities of reliability measures for any physical system analyzed using the Markov chain. Reliability and sensitivity analyses using these methods have been performed during this work for the IFMIF Accelerator System Facilities. The reliability studies using Markov chain have been concentrated around the availability of the main subsystems of this complex physical system for a typical mission time. The sensitivity studies for two typical responses using ASAP have been
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.
Interstitial diffuse optical tomography using an adjoint model with linear sources
Zhou, Xiaodong; Zhu, Timothy C.
2008-01-01
An improved interstitial diffuse optical tomography (iDOT) system has been developed to characterize the optical properties of prostate gland during the photodynamic therapy (PDT). Multiple cylindrical light diffusers with different lengths (instead of point sources used in an earlier version) and isotropic detectors are introduced interstitially in the prostate gland in-vivo. During the data acquisition, linear sources and detectors are stepping into prostate sequentially controlled by a mot...
Bred vectors, singular vectors, and Lyapunov vectors in simple and complex models
Norwood, Adrienne
We compute and compare three types of vectors frequently used to explore the instability properties of dynamical models, Lyapunov vectors (LVs), singular vectors (SVs), and bred vectors (BVs). The first model is the Lorenz (1963) three-variable model. We find BVs align with the locally fastest growing LV, which is often the second fastest growing global LV. The growth rates of the three types of vectors reveal all predict regime changes and durations of new regimes, as shown for BVs by Evans et al. (2004). The second model is the toy 'atmosphere-ocean model' developed by Pena and Kalnay (2004) coupling three Lorenz (1963) models with different time scales to test the effects of fast and slow modes of growth on the dynamical vectors. A fast 'extratropical atmosphere' is weakly coupled to a fast 'tropical atmosphere' which is strongly coupled to a slow 'ocean' system, the latter coupling imitating the tropical El Nino--Southern Oscillation. BVs separate the fast and slow modes of growth through appropriate selection of the breeding parameters. LVs successfully separate the fast 'extratropics' but cannot completely decouple the 'tropics' from the 'ocean,' leading to 'coupled' LVs that are affected by both systems but mainly dominated by one. SVs identify the fast modes but cannot capture the slow modes until the fast 'extratropics' are replaced with faster 'convection.' The dissimilar behavior of the three types of vectors degrades the similarities of the subspaces they inhabit (Norwood et al. 2013). The third model is a quasi-geostrophic channel model (Rotunno and Bao 1996) that is a simplification of extratropical synoptic-scale motions with baroclinic instabilities only. We were unable to successfully compute LVs for it. However, randomly initialized BVs quickly converge to a single vector that is the leading LV. The last model is the SPEEDY model created by Molteni (2003). It is a simplified general atmospheric circulation model with several types of instabilities
Description of the Earth system model of intermediate complexity LOVECLIM version 1.2
H. Goosse
2010-03-01
Full Text Available The main characteristics of the new version 1.2 of the three-dimensional Earth system model of intermediate complexity LOVECLIM are briefly described. LOVECLIM 1.2 includes representations of the atmosphere, the ocean and sea ice, the land surface (including vegetation, the ice sheets, the icebergs and the carbon cycle. The atmospheric component is ECBilt2, a T21, 3-level quasi-geostrophic model. The oceanic component is CLIO3, which is made up of an ocean general circulation model coupled to a comprehensive thermodynamic-dynamic sea-ice model. Its horizontal resolution is 3° by 3°, and there are 20 levels in the ocean. ECBilt-CLIO is coupled to VECODE, a vegetation model that simulates the dynamics of two main terrestrial plant functional types, trees and grasses, as well as desert. VECODE also simulates the evolution of the carbon cycle over land while the oceanic carbon cycle is represented in LOCH, a comprehensive model that takes into account both the solubility and biological pumps. The ice sheet component AGISM is made up of a three-dimensional thermomechanical model of the ice sheet flow, a visco-elastic bedrock model and a model of the mass balance at the ice-atmosphere and ice ocean interfaces. For both the Greenland and Antarctic ice sheets, calculations are made on a 10 km by 10 km resolution grid with 31 sigma levels. LOVECLIM 1.2 reproduces well the major characteristics of the observed climate both for present-day conditions and for key past periods such as the last millennium, the mid-Holocene and the Last Glacial Maximum. However, despite some improvements compared to earlier versions, some biases are still present in the model. The most serious ones are mainly located at low latitudes with an overestimation of the temperature there, a too symmetric distribution of precipitation between the two hemispheres, an overestimation of precipitation and vegetation cover in the subtropics. In addition, the atmospheric circulation is
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.
Permanent radioactive seed implantation (interstitial brachytherapy) is becoming the preferred method of treating prostate cancers. The main goal of the treatment is to deliver a conformal dose to the tumor while simultaneously minimizing the dose to the normal tissue and sensitive tissue structures. The treatment plan determines the number of seeds, their embedded positions, and the dose delivered to the tissue by photons emitted from the seeds. This study adopts the adjoint method to calculate dose and mixed integer programming (MIP) to optimize the dose to regions of interest for the permanent implantation of 125I radioactive source seeds for prostate cancers. DANTSYS, a discrete ordinates transport code, is utilized to compute the adjoint flux at all fine meshes (voxels) within a geometric model of the prostate image taken by a Transrectal Ultrasound probe. A broad 3-group-photon cross-section library was generated from the lowest three energy groups of the FENDL-2 42-group cross-section library. The first group spans the energy range 20 to 30 keV in which the photons emitted by 125I lie. The second and third groups span the energy ranges 10 to 20 keV and 1 to 10 keV, respectively. The flux-to-dose rate conversion factors for the broad 3-group-photon library are computed using the methodology described in Ref. 2. These factors are used as the adjoint source for the adjoint calculations. The adjoint flux obtained is then used to compute the absorbed dose rate in the regions of interest. The MIP solver is used to optimize seed placements for the treatment plan. MIP is well suited for the optimization problem of brachytherapy because the binary integer variable can represent yes/no decisions as to the placement or non-placement of seeds. The prescribed dose Dp to the tumor in our study is 150 Gy.We set the lower dose constraint, lDtu, for the tumor and the upper dose constraints, uDur and uDno, for the urethra and the normal tissue. The objective function we
Sampling strategies based on singular vectors for assimilated models in ocean forecasting systems
Fattorini, Maria; Brandini, Carlo; Ortolani, Alberto
2016-04-01
Meteorological and oceanographic models do need observations, not only as a ground truth element to verify the quality of the models, but also to keep model forecast error acceptable: through data assimilation techniques which merge measured and modelled data, natural divergence of numerical solutions from reality can be reduced / controlled and a more reliable solution - called analysis - is computed. Although this concept is valid in general, its application, especially in oceanography, raises many problems due to three main reasons: the difficulties that have ocean models in reaching an acceptable state of equilibrium, the high measurements cost and the difficulties in realizing them. The performances of the data assimilation procedures depend on the particular observation networks in use, well beyond the background quality and the used assimilation method. In this study we will present some results concerning the great impact of the dataset configuration, in particular measurements position, on the evaluation of the overall forecasting reliability of an ocean model. The aim consists in identifying operational criteria to support the design of marine observation networks at regional scale. In order to identify the observation network able to minimize the forecast error, a methodology based on Singular Vectors Decomposition of the tangent linear model is proposed. Such a method can give strong indications on the local error dynamics. In addition, for the purpose of avoiding redundancy of information contained in the data, a minimal distance among data positions has been chosen on the base of a spatial correlation analysis of the hydrodynamic fields under investigation. This methodology has been applied for the choice of data positions starting from simplified models, like an ideal double-gyre model and a quasi-geostrophic one. Model configurations and data assimilation are based on available ROMS routines, where a variational assimilation algorithm (4D-var) is
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
A user`s manual for MASH 1.0: A Monte Carlo Adjoint Shielding Code System
Johnson, J.O. [ed.
1992-03-01
The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the ``dose importance`` of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user`s manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.
A user's manual for MASH 1. 0: A Monte Carlo Adjoint Shielding Code System
Johnson, J.O. (ed.)
1992-03-01
The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the dose importance'' of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.
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. - Highlights: • Blueprint for 3D remote sensing of the atmosphere and surface. • Procedure for adjusting thousands of parameters with millions of data
Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF. (authors)
On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators
Kemppainen, Mikko
2014-01-01
In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1. The holomorphic functional calculus of L is also shown to be bounded on the associated Hardy space H^1_L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent spac...
Ardhuin, Fabrice; Rawat, Arshad; Aucan, Jerome
2014-05-01
The spectral wave model WAVEWATCH III is extended from the windsea and swell band to lower frequencies, in order to represent free waves in the infragravity (IG) wave band. This extension is based on an empirical source of IG energy, which is defined along shorelines from the significant wave height and a mean period. The empirical proportionality factor is found to reproduce accurately the variations of free IG wave energy in coastal areas, where it was calibrated, and also has a good skill at global scales. In the open ocean, the model is particularly verified for frequencies in the range 5 to 14 mHz for which ocean bottom records are sensitive to the IG signal. The model captures between 30% and 80% of the variance in IG wave heights, depending on location, and reproduces the mean IG energies within 50%. Where the model reproduces best the IG variability, it can be used to fill in the gaps between recording stations, providing a first view of the global IG wave field. Our first application is the estimation of the surface gravity wave contribution to the surface elevation spectra that will be measured by the Surface Water Ocean Topography (SWOT) satellite mission. The actual contribution of IG waves on measured along-track wavenumber spectra varies with the cross-track averaging method. Typically, the strongest IG signal is expected to occur for wavelengths between 2 and 10 km. For a given region, the spectral level at 10 km wavelength are not very sensitive to the local depth in the range 200 to 5000 m. At this wavelength, and on the east side of all mid-latitude ocean basins, the median spectral density associated to free IG waves is of the order of 0.4 cm2/(cycle/km), equal to the expected quasi-geostrophic signature of surface currents. IG spectra rise above 4 times this level for 16% of the time. Even at 20 km wavelength, spectral levels above 1 cm2/(cycle/km) are likely to occur more that 10% of the time for some oceanic regions.
Variational asymptotics for rotating shallow water near geostrophy: a transformational approach
Oliver, Marcel
2006-03-01
We introduce a unified variational framework in which the classical balance models for nearly geostrophic shallow water as well as several new models can be derived. Our approach is based on consistently truncating an asymptotic expansion of a near-identity transformation of the rotating shallow-water Lagrangian. Model reduction is achieved by imposing either degeneracy (for models in a semi-geostrophic scaling) or incompressibility (for models in a quasi-geostrophic scaling) with respect to the new coordinates.
Anisotropic models are unitary: A rejuvenation of standard quantum cosmology
Pal, Sridip
2016-01-01
The present work proves that the folk-lore of the pathology of non-conservation of probability in quantum anisotropic models is wrong. It is shown in full generality that all operator ordering can lead to a Hamiltonian with a self-adjoint extension as long as it is constructed to be a symmetric operator, thereby making the problem of non-unitarity in context of anisotropic homogeneous model a ghost. Moreover, it is indicated that the self-adjoint extension is not unique and this non-uniqueness is suspected not to be a feature of Anisotropic model only, in the sense that there exists operator orderings such that Hamiltonian for an isotropic homogeneous cosmological model does not have unique self-adjoint extension, albeit for isotropic model, there is a special unique extension associated with quadratic form of Hamiltonian i.e {\\it Friedrichs extension}. Details of calculations are carried out for a Bianchi III model.
王兴涛
2002-01-01
Control equation and adjoint equation are established by using block-pulse functions, which trans-forms the linear time-varying systems with time delays into a system of algebraic equations and the optimal con-trol problems are transformed into an optimization problem of multivariate functions thereby achieving the opti-mal control of linear systems with time delays.
Weiss, M.; Vermeulen, A.; Bos, J.; Bucco, D.
2011-01-01
The Adjoint Method is a well establised tool for assessement of guidance loops in conceptual design studies. It allows one to perform quick assessments of the performance both in deterministic settings, to determine a nominal or average miss distance, and in stochastic settings, to determine the sta
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 (TRIPOLI-4® by using the eigenvalue difference method. This "direct" method has shown limitations in the evaluation of very small reactivity effects because it needs to reach a very small variance associated to the reactivity in both states. To answer this problem, it has been decided to implement the exact perturbation theory in TRIPOLI-4® and, consequently, to calculate a continuous-energy adjoint flux. The Iterated Fission Probability (IFP) method was chosen because it has shown great results in some other Monte Carlo codes. The IFP method uses a forward calculation to compute the adjoint flux, and consequently, it does not rely on complex code modifications but on the physical definition of the adjoint flux as a phase-space neutron importance. In the first part of this paper, the IFP method implemented in TRIPOLI-4® is described. To illustrate the effciency of the method, several adjoint fluxes are calculated and compared with their equivalent obtained by the deterministic code APOLLO-2. The new implementation can calculate angular adjoint flux. In the second part, a procedure to carry out an exact perturbation calculation is described. A single cell benchmark has been used to test the accuracy of the method, compared with the "direct" estimation of the perturbation. Once again the method based on the IFP shows good agreement for a calculation time far more inferior to the "direct" method. The main advantage of the method is that the relative accuracy of the reactivity variation does not depend on the magnitude of the variation itself, which allows us to calculate very small reactivity perturbations with high precision. Other applications of this perturbation method are presented and tested like the calculation of exact kinetic parameters (βeff, Λeff) or sensitivity parameters.
Remarks on rotating shallow-water magnetohydrodynamics
Zeitlin, V.
2013-01-01
We show how the rotating shallow-water MHD model, which was proposed in the solar tachocline context, may be systematically derived by vertical averaging of the full MHD equations for the rotating magneto fluid under the influence of gravity. The procedure highlights the main approximations and the domain of validity of the model, and allows for multi-layer generalizations and, hence, inclusion of the baroclinic effects. A quasi-geostrophic version of the model, both in barotropic and in baro...
Finlay, Christopher C.; Olsen, Nils; Kotsiaros, Stavros; Gillet, Nicolas; Tøffner-Clausen, Lars
2016-07-01
We use more than 2 years of magnetic data from the Swarm mission, and monthly means from 160 ground observatories as available in March 2016, to update the CHAOS time-dependent geomagnetic field model. The new model, CHAOS-6, provides information on time variations of the core-generated part of the Earth's magnetic field between 1999.0 and 2016.5. We present details of the secular variation (SV) and secular acceleration (SA) from CHAOS-6 at Earth's surface and downward continued to the core surface. At Earth's surface, we find evidence for positive acceleration of the field intensity in 2015 over a broad area around longitude 90°E that is also seen at ground observatories such as Novosibirsk. At the core surface, we are able to map the SV up to at least degree 16. The radial field SA at the core surface in 2015 is found to be largest at low latitudes under the India-South-East Asia region, under the region of northern South America, and at high northern latitudes under Alaska and Siberia. Surprisingly, there is also evidence for significant SA in the central Pacific region, for example near Hawaii where radial field SA is observed on either side of a jerk in 2014. On the other hand, little SV or SA has occurred over the past 17 years in the southern polar region. Inverting for a quasi-geostrophic core flow that accounts for this SV, we obtain a prominent planetary-scale, anti-cyclonic, gyre centred on the Atlantic hemisphere. We also find oscillations of non-axisymmetric, azimuthal, jets at low latitudes, for example close to 40°W, that may be responsible for localized SA oscillations. In addition to scalar data from Ørsted, CHAMP, SAC-C and Swarm, and vector data from Ørsted, CHAMP and Swarm, CHAOS-6 benefits from the inclusion of along-track differences of scalar and vector field data from both CHAMP and the three Swarm satellites, as well as east-west differences between the lower pair of Swarm satellites, Alpha and Charlie. Moreover, ground observatory SV
Cagnetti, Filippo
2013-11-01
We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞ norm and O(h) in terms of the L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper. © 2013 IMACS.
Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter
Başar, Gökçe; Dienes, Keith R; McGady, David A
2015-01-01
In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and $(-1)^F$-twisted partition functions, and collectively suggest that the spectra of large-$N$ confining gauge theories are organized by the symmetries of two-dimensional conformal field theories.
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation
The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions. Bibliography: 23 titles
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
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.
Conventional collapsing for group cross sections used in multigroup nuclear reactor calculations is usually performed using normal (real; direct) flux weighting. The application of more advanced collapsing procedures using in an appropriate manner real, adjoint and bilinear weighting was in the past restricted in general to fundamental mode problems. Although the principles have been published for more than ten years, there seems to exist little recent experience on the merits and possible difficulties of these improved procedures for multidimensional diffusion problems for practical purposes, e.g. in the nuclear design and analysis of large Liquid Metal Fast Breeder Reactors (LMFBRs). The present work indicates the nature of the problems which could possibly be encountered in applying these procedures by tracing them back to the known close correspondence between group collapsing and synthesis methods. It tries to explain certain somewhat unusual features of the collapsed group constants obtained by adjoint and bilinear weighting and describes the experience gained in representative 1-dim. and 2-dim. test cases. It could be shown for criticality and perturbation calculations that in general it is advantageous to apply these improved collapsing methods if the necessary precautions are taken. Compared to the conventional collapsing procedures these improved procedures are especially useful for multidimensional problems because their application is well suited for that purpose. In the present study it could be proven that they are favorable with respect to computer time and storage needed due to the fact that the necessary number of coarse groups can be kept fairly small without deteriorating too much the accuracy and reliability of the coarse group results compared to reference results of corresponding fine group calculations with uncollapsed group constants. (orig.)
Zang, X.; Malanotte-Rizzoli, P.
2003-01-01
The goal of this study is to compare the performances of the ensemble Kalman filter and a reduced-rank extended Kalman filter when applied to different dynamic regimes. Data assimilation experiments are performed using an eddy-resolving quasi-geostrophic model of the wind-driven ocean circulation. By changing eddy viscosity, this model exhibits two qualitatively distinct behaviors: strongly chaotic for the low viscosity case and quasi-peri...
Kushner, P.J.; Shepherd, T.G. [Univ. of Toronto, Toronto (Canada)
1995-05-01
A study of the semi-geostrophic (SG) geophysical fluid dynamics is presented. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. An invariant for the semi-geostrophic equations is derived and use it to obtain: (1) a linear stability theorem analogous to Arnold`s first theorem; and (2) a small-amplitude local conservation law for invariant, obeying the group-velocity in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. 23 refs.
Kushner, Paul J.; Shepherd, Theodore G.
1995-05-01
A study of the semi-geostrophic (SG) geophysical fluid dynamics is presented. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. An invariant for the semi-geostrophic equations is derived and use it to obtain: (1) a linear stability theorem analogous to Arnold's first theorem; and (2) a small-amplitude local conservation law for invariant, obeying the group-velocity in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number.
A study of surface semi-geostrophic turbulence: freely decaying dynamics
Ragone, Francesco
2015-01-01
In this study we give a characterization of semi-geostrophic turbulence by performing freely decaying simulations of the semi-geostrophic equations for the case of constant uniform potential vorticity, a set of equations known as surface semi-geostrophic approximation. The equations are formulated as conservation laws for potential temperature and potential vorticity, with a nonlinear Monge-Amp\\'{e}re type inversion equation for the streamfunction, expressed in a transformed coordinate system that follows the geostrophic flow. We perform model studies of turbulent surface semi-geostrophic flows in a doubly-periodic domain in the horizontal limited in the vertical by two rigid lids, allowing for variations of potential temperature at one of the boundaries, and we compare them with the corresponding surface quasi-geostrophic case. Results show that, while surface quasi-geostrophic dynamics is dominated by a symmetric population of cyclones-anticyclones, surface semi-geostrophic dynamics features a prominent rol...
Regularity and blow up for active scalars
Kiselev, Alexander
2010-01-01
We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall what is known about the possibility of finite time blow up in the supercritical regime.
Scaling laws for parametrizations of subgrid interactions in simulations of oceanic circulations
Kitsios, V.; J. S. Frederiksen; Zidikheri, M. J.
2014-01-01
Parametrizations of the subgrid eddy–eddy and eddy–meanfield interactions are developed for the simulation of baroclinic ocean circulations representative of an idealized Antarctic Circumpolar Current. Benchmark simulations are generated using a spectral spherical harmonic quasi-geostrophic model with maximum truncation wavenumber of T=504, which is equivalent to a resolution of 0.24° globally. A stochastic parametrization is used for the eddy–eddy interactions, and a linear deterministic par...
The Halting Effect of Baroclinicity in Vortex Merging
Masina, S.; Istituto per lo studio delle Metodologie Geofisiche e Ambientali, CNR, Modena, Italy.; Pinardi, N.; Istituto per lo studio delle Metodologie Geofisiche e Ambientali, CNR, Modena, Italy.
1993-01-01
We study the quasi-geostrophic merging dynamics of axisymmetric baroclinic vortices to understand how baroclinicity affects merging rates and the development of the nonlinear cascade of enstrophy. The initial vortices are taken to simulate closely the horizontal' and vertical structure of Gulf Stream rings. A quasigeostrophic model is set with a horizontal resolution of 9 km and 6 vertical levels to resolve the mean stratification of the Gulf Stream region. The results show th...
Kushner, Paul J.; Shepherd, Theodore G.
1995-01-01
There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, lik...
Sensitivity of African easterly waves to boundary layer conditions
A. Lenouo; Mkankam Kamga, F.
2008-01-01
A linearized version of the quasi-geostrophic model (QGM) with an explicit Ekman layer and observed static stability parameter and profile of the African easterly jet (AEJ), is used to study the instability properties of the environment of the West African wave disturbances. It is found that the growth rate, the propagation velocity and the structure of the African easterly waves (AEW) can be well simulated. Two different lower boundary conditions are applied. One assumes a lack of vertical g...
Stochastic flow modeling : Quasi-Geostrophy, Taylor state and torsional wave excitation
Gillet, Nicolas; Jault, D.; Finlay, Chris
observed geomagnetic series. We account for errors of representativeness (subgrid processes associated with the unresolved field at small length-scales) that are correlated in space and time, using an iterative scheme. An ensemble approach allows us to measure the uncertainties within the recovered motions...... interpret this as an evidence for quasi-geostrophic rapid flow changes, and the consequence of a too loose data constraint during the oldest period. We manage to retrieve rapid flow changes over the past 60 yrs, and in particular modulated torsional waves predicting correctly interannual length-of day...
Galapon, E A
1999-01-01
Pauli's well known theorem (W. Pauli, Hanbuch der Physik vol. 5/1, ed. S. Flugge, (1926) p.60) asserts that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian implies that the time operator and the Hamitlonian posses completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate to a Hamiltonian with a spectrum which is a proper subspace of the real line. But we challenge this conclusion. We show rigourously the consitency of assuming a bounded, self-adjoint time operator conjugate to a Hamiltonian with an unbounded, or semibounded, or finitely countable point spectrum. Pauli implicitly assumed unconditionally that the domain of the Hamiltonian is invariant under the action of $U_\\beta=\\exp(-i\\beta T)$, where $T$ is the time operator, for arbitrary real number $\\betaA$. But we show that the $\\beta$'s are at most the differences of the eigenvalues of the Hamiltonian. And this happens, under some ...
Maria Malejki
2007-01-01
Full Text Available We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space \\(l^2(\\mathbb{N}\\ by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator is bounded from below with compact resolvent. In our research we estimate the asymptotics (with \\(n\\to \\infty\\ of the joint error of approximation for the first \\(n\\ eigenvalues and eigenvectors of the operator by the eigenvalues and eigenvectors of the finite submatrix of order \\(n \\times n\\. The method applied in our research is based on the Rayleigh-Ritz method and Volkmer's results included in [H. Volkmer, Error Estimates for Rayleigh-Ritz Approximations of Eigenvalues and Eigenfunctions of the Mathieu and Spheroidal Wave Equation, Constr. Approx. 20 (2004, 39-54]. We extend the method to cover a class of infinite symmetric Jacobi matrices with three diagonals satisfying some polynomial growth estimates.
Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach
Magri, Luca
2013-01-01
We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We ...
A novel approach is proposed for charged particle transport calculations using a recently developed second-order, self-adjoint angular flux (SAAF) form of the Boltzmann transport equation with continuous slowing-down. A finite element discretization that is linear continuous in space and linear discontinuous (LD) in energy is described and implemented in a one-dimensional, planar geometry, multigroup, discrete ordinates code for charged particle transport. The cross-section generating code CEPXS is used to generate the electron and photon transport cross sections employed in this code. The discrete ordinates SAAF transport equation is solved using source iteration in conjunction with an inner iteration acceleration scheme and an outer iteration acceleration scheme. Outer iterations are required with the LD energy discretization scheme because the two angular flux unknowns within each group are coupled, which gives rise to effective upscattering. The inner iteration convergence is accelerated using diffusion synthetic acceleration, and the outer iteration convergence is accelerated using a diamond difference approximation to the LD energy discretization. Computational results are given that demonstrate the effectiveness of our convergence acceleration schemes and the accuracy of our discretized SAAF equation
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.
The goal of this project is to investigate the use of the adjoint method, commonly used in the reactor physics community, for the optimization of radiation therapy patient treatment plans. Two different types of radiation therapy are being examined, interstitial brachytherapy and radiotherapy. In brachytherapy radioactive sources are surgically implanted within the diseased organ such as the prostate to treat the cancerous tissue. With radiotherapy, the x-ray source is usually located at a distance of about 1-meter from the patient and focused on the treatment area. For brachytherapy the optimization phase of the treatment plan consists of determining the optimal placement of the radioactive sources, which delivers the prescribed dose to the disease tissue while simultaneously sparing (reducing) the dose to sensitive tissue and organs. For external beam radiation therapy the optimization phase of the treatment plan consists of determining the optimal direction and intensity of beam, which provides complete coverage of the tumor region with the prescribed dose while simultaneously avoiding sensitive tissue areas. For both therapy methods, the optimal treatment plan is one in which the diseased tissue has been treated with the prescribed dose and dose to the sensitive tissue and organs has been kept to a minimum
GRASP (GRound-Water Adjunct Senstivity Program) computes measures of the behavior of a ground-water system and the system's performance for waste isolation, and estimates the sensitivities of these measures to system parameters. The computed measures are referred to as ''performance measures'' and include weighted squared deviations of computed and observed pressures or heads, local Darcy velocity components and magnitudes, boundary fluxes, and travel distance and time along travel paths. The sensitivities are computed by the adjoint method and are exact derivatives of the performance measures with respect to the parameters for the modeled system, taken about the assumed parameter values. GRASP presumes steady-state, saturated grondwater flow, and post-processes the results of a multidimensional (1-D, 2-D, 3-D) finite-difference flow code. This document describes the mathematical basis for the model, the algorithms and solution techniques used, and the computer code design. The implementation of GRASP is verified with simple one- and two-dimensional flow problems, for which analytical expressions of performance measures and sensitivities are derived. The linkage between GRASP and multidimensional finite-difference flow codes is described. This document also contains a detailed user's manual. The use of GRASP to evaluate nuclear waste disposal issues has been emphasized throughout the report. The performance measures and their sensitivities can be employed to assist in directing data collection programs, expedite model calibration, and objectively determine the sensitivity of projected system performance to parameters
Automating sensitivity analysis of computer models using computer calculus
An automated procedure for performing sensitivity analysis has been developed. The procedure uses a new FORTRAN compiler with computer calculus capabilities to generate the derivatives needed to set up sensitivity equations. The new compiler is called GRESS - Gradient Enhanced Software System. Application of the automated procedure with direct and adjoint sensitivity theory for the analysis of non-linear, iterative systems of equations is discussed. Calculational efficiency consideration and techniques for adjoint sensitivity analysis are emphasized. The new approach is found to preserve the traditional advantages of adjoint theory while removing the tedious human effort previously needed to apply this theoretical methodology. Conclusions are drawn about the applicability of the automated procedure in numerical analysis and large-scale modelling sensitivity studies
Automating sensitivity analysis of computer models using computer calculus
An automated procedure for performing sensitivity analyses has been developed. The procedure uses a new FORTRAN compiler with computer calculus capabilities to generate the derivatives needed to set up sensitivity equations. The new compiler is called GRESS - Gradient Enhanced Software System. Application of the automated procedure with ''direct'' and ''adjoint'' sensitivity theory for the analysis of non-linear, iterative systems of equations is discussed. Calculational efficiency consideration and techniques for adjoint sensitivity analysis are emphasized. The new approach is found to preserve the traditional advantages of adjoint theory while removing the tedious human effort previously needed to apply this theoretical methodology. Conclusions are drawn about the applicability of the automated procedure in numerical analysis and large-scale modelling sensitivity studies. 24 refs., 2 figs
Non-Self-Adjoint Operators in Quantum Physics: Ideas, People, and Trends
Znojil, Miloslav
Vol. 1. New Jersey: John Wiley & Sons, Inc., 2015, s. 7-50. ISBN 978-1-118-85528-7 Institutional support: RVO:61389005 Keywords : quantum mechanics * cryptohermitian model of dynamics * cryptounitary evolution equations Subject RIV: BE - Theoretical Physics
Chae, Dongho; Constantin, Peter; Wu, Jiahong
2014-09-01
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.
Source-resolved fine particulate matter (PM) concentrations are needed at high spatial and temporal resolutions for epidemiological studies aimed at identifying more- and less-harmful types of PM. Building on recent advances in air quality modeling, data assimilation, and s...
Low Boom Configuration Analysis with FUN3D Adjoint Simulation Framework
Park, Michael A.
2011-01-01
Off-body pressure, forces, and moments for the Gulfstream Low Boom Model are computed with a Reynolds Averaged Navier Stokes solver coupled with the Spalart-Allmaras (SA) turbulence model. This is the first application of viscous output-based adaptation to reduce estimated discretization errors in off-body pressure for a wing body configuration. The output adaptation approach is compared to an a priori grid adaptation technique designed to resolve the signature on the centerline by stretching and aligning the grid to the freestream Mach angle. The output-based approach produced good predictions of centerline and off-centerline measurements. Eddy viscosity predicted by the SA turbulence model increased significantly with grid adaptation. Computed lift as a function of drag compares well with wind tunnel measurements for positive lift, but predicted lift, drag, and pitching moment as a function of angle of attack has significant differences from the measured data. The sensitivity of longitudinal forces and moment to grid refinement is much smaller than the differences between the computed and measured data.
Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir
Capolei, Andrea; Völcker, Carsten; Frydendall, Jan;
2012-01-01
injections and oil production such that ow is uniform in a given geological structure. Even in the case of conventional water ooding, feedback based optimal control technologies may enable higher oil recovery than with conventional operational strategies. The optimal control problems that must be solved are......Conventional recovery techniques enable recovery of 10-50% of the oil in an oil eld. Advances in smart well technology and enhanced oil recovery techniques enable signicant larger recovery. To realize this potential, feedback model-based optimal control technologies are needed to manipulate the...... sensitivity computation. We demonstrate the procedure on a water ooding example with conventional injectors and producers....
This two part study introduces new developments in frequency domain optical tomography to take into account the collimated source direction in the computation of both the forward and the adjoint models. The solution method is based on the least square finite element method associated to the discrete ordinates method where no empirical stabilization is needed. In this first part of the study, the solution method of the forward model is highlighted with an easy handling of complex boundary condition through a penalization method. Gradient computation from an adjoint method is developed rigorously in a continuous manner through a lagrangian formalism for the deduction of the adjoint equation and the gradient of the objective function. The proposed formulation can be easily generalized to stationary and time domain optical tomography by keeping the same expressions.
Fadin, V. S.; Fiore, R.
2016-05-01
We analyze a modification of the BFKL kernel for the adjoint representation of the color group in the maximally supersymmetric (N=4) Yang-Mills theory in the limit of a large number of colors, related to the modification of the eigenvalues of the kernel suggested by Bondarenko and Prygarin in order to obtain Hermitian separability of the eigenvalues. We restore the modified kernel in the momentum space. It turns out that the modification is related only to the real part of the kernel and that the correction to the kernel cannot be presented by a single analytic function in the entire momentum region, which contradicts the known properties of the kernel.
Krejčiřík, David; Siegl, Petr; Železný, Jakub
2014-01-01
Roč. 8, č. 1 (2014), s. 255-281. ISSN 1661-8254 R&D Projects: GA MŠk LC06002; GA MŠk LC527; GA ČR GAP203/11/0701 Grant ostatní: GA ČR(CZ) GD202/08/H072 Institutional support: RVO:61389005 Keywords : Sturm-Liouville operators * non-symmetric Robin boundary conditions * similarity to normal or self-adjoint operators * discrete spectral operator * complex symmetric operator * PT-symmetry * metric operator * C operator * Hilbert-Schmidt operators Subject RIV: BE - Theoretical Physics Impact factor: 0.545, year: 2014
王建丰; 黄琼湘; 刘儒英; 冶成福
2008-01-01
For a graph G,let h(G;x)=h(G)and[G]h denote the adjoint polynomial and the adjoint equivalence class of G,respectively.In this paper,a new application of[G]h is given.Making use of[G]h,we give a necessary and suffcient condition for adjoint uniqueness of the graph H such that H≠G,where H=(Ui∈APi)U(Uj∈BUj),A(∈)A'={1,2,3,5}U{2n|n∈N,n≥3},B(∈)B'={7,2n|n∈N,n(>)5)and G=a p1UaoP2Ua1P3Ua2P5U(U(n i)=3aiP2i).
Development of a High-Order Space-Time Matrix-Free Adjoint Solver
Ceze, Marco A.; Diosady, Laslo T.; Murman, Scott M.
2016-01-01
The growth in computational power and algorithm development in the past few decades has granted the science and engineering community the ability to simulate flows over complex geometries, thus making Computational Fluid Dynamics (CFD) tools indispensable in analysis and design. Currently, one of the pacing items limiting the utility of CFD for general problems is the prediction of unsteady turbulent ows.1{3 Reynolds-averaged Navier-Stokes (RANS) methods, which predict a time-invariant mean flowfield, struggle to provide consistent predictions when encountering even mild separation, such as the side-of-body separation at a wing-body junction. NASA's Transformative Tools and Technologies project is developing both numerical methods and physical modeling approaches to improve the prediction of separated flows. A major focus of this e ort is efficient methods for resolving the unsteady fluctuations occurring in these flows to provide valuable engineering data of the time-accurate flow field for buffet analysis, vortex shedding, etc. This approach encompasses unsteady RANS (URANS), large-eddy simulations (LES), and hybrid LES-RANS approaches such as Detached Eddy Simulations (DES). These unsteady approaches are inherently more expensive than traditional engineering RANS approaches, hence every e ort to mitigate this cost must be leveraged. Arguably, the most cost-effective approach to improve the efficiency of unsteady methods is the optimal placement of the spatial and temporal degrees of freedom (DOF) using solution-adaptive methods.