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...
A BAROTROPIC QUASI-GEOSTROPHIC MODEL WITH LARGE-SCALE TOPOGRAPHY, FRICTION AND HEATING
Institute of Scientific and Technical Information of China (English)
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.
Stochastic modelling of primitive equation and quasi-geostrophic subgrid turbulence
Frederiksen, Jorgen; Kitsios, Vassili; Dix, Martin; Osbrough, Stacey
2016-04-01
A general method for stochastic and deterministic modelling of subgrid scale turbulence is presented and applied to primitive equation and quasi-geostrophic models of atmospheric and oceanic flows. Dynamical and thermodynamical subgrid-scale parameterisations of eddy drain, net dissipation and stochastic backscatter are calculated for a multi-level primitive equation atmospheric general circulation model. The parameterisations have only moderate variability with height and a cusp behaviour with peaks near the largest retained wavenumber. They are compared with corresponding results for quasi-geostrophic models of the atmosphere and ocean for which the parameterisations are shown to satisfy scaling laws. Large-eddy simulations (LES) with the subgrid terms very closely reproduce the results of higher resolution direct numerical simulations. The method is shown to produce parameterisations and LES with similar skill for three-dimensional turbulence in boundary layer channel flow.
Schubert, Sebastian; Lucarini, Valerio
2016-04-01
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 quasi-geostrophic flow. 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 ΔT . We explore three settings of ΔT , representative of relatively weak turbulence, well-developed turbulence, and intermediate conditions. We construct the Lorenz energy cycle for each CLV describing the energy exchanges with the background state. A positive baroclinic conversion rate is a necessary but not sufficient condition of instability. Barotropic instability is present only for few very unstable CLVs for large values of ΔT. Slowly growing and decaying hydrodynamic Lyapunov modes closely mirror the properties of the background flow. Following classical necessary conditions for barotropic/baroclinic instability, we find a clear relationship between the properties of the eddy fluxes of a CLV and its instability. CLVs with positive baroclinic conversion seem to form a set of modes for constructing a reduced model of the atmosphere dynamics.
A quasi-geostrophic wavelet-spectrum model for barotropic atmosphere and its numerical solution
Institute of Scientific and Technical Information of China (English)
DAI Xingang; WANG Ping; CHOU Jifan
2004-01-01
A quasi-geostrophic wavelet-spectrum model of barotropic atmosphere has been constructed by wavelet-Galerkin method with the periodic orthogonal wavelet bases. In this study a wavelet grid-spectrum transform method is designed to decrease the tremendous computation of the nonlinear interaction term in the model, and a two-dimensional Helmholtz equation from the model in a wavelet spectrum form is derived, and a solution with high precision under the periodic boundary condition is obtained. The numerical investigation manifests that the wavelet-spectrum model (WSM) could keep on running for a long time under the forcing of heating and topography. Although its numerical solution is compatible with the grid model (GM), the WSM is of a higher precision and faster convergence rate than GM's. A stationary solution comes forth when the model is forced only by the surface heating, whereas a quasi-periodic oscillation with a period about 15 days appears as considering the topography in the model. The latter oscillation, to some extent, is very similar to the Rossby index cycle of atmosphere over middle and high latitudes.
Extreme events statistics in a two-layer quasi-geostrophic atmospheric model
Galfi, Vera Melinda; Bodai, Tamas; Lucarini, Valerio
2016-04-01
Extreme events statistics provides a theoretical framework to analyze and predict extreme events based on the convergence of the distribution of the extremes to some limiting distribution. In this work we analyze the convergence of the distribution of extreme events to the Generalized Extreme Value (GEV) distribution and to the Generalized Pareto Distribution (GPD), using a two-layer quasi-geostrophic atmospheric model, and compare our results with theoretical findings from the field of extreme value theory for dynamical systems. We study the behavior of the GEV shape parameter by increasing the block size and of the GPD shape parameter by increasing the threshold, and compare the inferred parameters with a theoretical shape parameter that depends only on the geometrical properties of the attractor. The main objective is to find out whether this theoretical shape parameter can be used to evaluate extreme event analysis based on model output. For this, we perform very long simulations. We run our system with two different levels of forcing determined by two different meridional temperature gradients, one inducing a medium level of chaos and the other one a high level of chaos. We analyze in both cases extremes of energy variables.
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
Energy Technology Data Exchange (ETDEWEB)
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
Directory of Open Access Journals (Sweden)
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...
Williams, Paul; Read, Peter; Haine, Thomas
2010-05-01
We compare laboratory observations of equilibrated baroclinic waves in the rotating two-layer annulus, with numerical simulations from a quasi-geostrophic model. The laboratory experiments lie well outside the quasi-geostrophic regime: the Rossby number reaches unity; the depth-to-width aspect ratio is large; and the fluid contains ageostrophic inertia-gravity waves. Despite being formally inapplicable, the quasi-geostrophic model captures the laboratory flows reasonably well. The model displays several systematic biases, which are consequences of its treatment of boundary layers and neglect of interfacial surface tension, and which may be explained without invoking the dynamical effects of the moderate Rossby number, large aspect ratio or inertia-gravity waves. We conclude that quasi-geostrophic theory appears to continue to apply well outside its formal bounds. This is an unexpected and intriguing result that could not have been predicted from the existing literature. It is also potentially useful, for example by permitting the use of a low-order quasi-geostrophic model to easily map out the bifurcation structure - which would be very difficult with a primitive equations model - followed by the use of a primitive equations model for more quantitative agreement in specific cases. Reference Williams, PD, PL Read and TWN Haine (2010) Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime. Journal of Fluid Mechanics, in press.
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...
AVERAGING PRINCIPLE FOR QUASI-GEOSTROPHIC MOTION UNDER RAPIDLY OSCILLATING FORCING
Institute of Scientific and Technical Information of China (English)
高洪俊; 段金桥
2005-01-01
A class of large scale geophysical fluid flows are modelled by the quasigeostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating( non-autonomous ) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions.Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.
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...
Large-scale quasi-geostrophic magnetohydrodynamics
International Nuclear Information System (INIS)
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.
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 ...
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
2016-05-01
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.
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.
On Nonlinear Stability Theorems of 3D Quasi-geostrophic Flow
Institute of Scientific and Technical Information of China (English)
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=\
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...
GLOBAL REGULARITY FOR MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
杨婉蓉; 酒全森
2014-01-01
We consider the n-dimensional modified quasi-geostrophic (SQG) equations∂tθ+u ·∇θ+κΛαθ=0, u=Λα−1R⊥θwithκ>0,α∈(0, 1] andθ0∈W 1,∞(Rn). In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu [5], who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case. The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol [2].
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...
SIMULATION OF EDDIES AFFECTED BY TOPOGRAPHY IN A BAROTROPICAL QUASI-GEOSTROPHIC FLUID
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Based upon the quasi-geostrophic barotropic equation, taking into account the effect of seabed topography, analytical solutions and simulated eddies associated with different topographies are obtained. Through exhibiting the shape of various eddies we have found some interesting phenomena and had a better understanding of the importance of seabed topography to the eddy shape.
Chen, Zhi-Min
2016-10-01
It is shown that the non-homogeneous dissipative quasi-geostrophic equation ∂θ∂t+uṡ∇θ+κ(-Δ)αθ=sinx2, u=(-∂x2, ∂x1)(-Δ)-β/2θ with α =0 and β >1 losses stability at a critical value {κc}>0 and this instability gives rise to a circle of steady-state solutions.
THE DISSIPATIVE QUASI-GEOSTROPHIC EQUATION IN SPACES ADMITTING SINGULAR SOLUTIONS
Institute of Scientific and Technical Information of China (English)
2007-01-01
This paper studies the Cauchy problem of the dissipative quasi-geostrophic equation in pseudomeasure space PMn+1-2α(Rn) or Lorentz space Ln/2α-1, ∞(Rn), which admit the singular solutions. The global well-posedness is established provided initial dataθ0 (x) are small enough in these spaces. Moreover, the asymptotic stability of solutions in pseudomeasure space is proved. In particular, if the initial data are homogeneous functions of degree 1-2α, the self-similar solutions are also obtained.
Similarity Reductions of Barotropic and Quasi-geostrophic Potential Vorticity Equation
Institute of Scientific and Technical Information of China (English)
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.
Model adjointization and its cost
Institute of Scientific and Technical Information of China (English)
CHENG Qiang; ZHANG Linbo; WANG Bin
2004-01-01
In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) and in tools design, and does not require programs to be evenly separable but the cost in terms of operations count and memory is similar to methods using checkpointing. This article starts by summarizing the rules of adjointization and then presents the implementation of LPBD. Next, the definition of the separable program space, based on the fundamental assumptions (FA) of automatic differentiation, is given and the differentiation cost functions are derived. Also,two constants of fundamental importance in AD, σ and μ, are derived under FA. Under the assumption of even separability, the adjoint cost of simple and deep decomposition is subsequently discussed quantitatively using checkpointing. Finally, the adjoint costs in terms of operations count and memory through the LPBD method are shown to be uniformly dependent on the depth of structure or decomposition.
ADGEN: ADjoint GENerator for computer models
Energy Technology Data Exchange (ETDEWEB)
Worley, B.A.; Pin, F.G.; Horwedel, J.E.; Oblow, E.M.
1989-05-01
This paper presents the development of a FORTRAN compiler and an associated supporting software library called ADGEN. ADGEN reads FORTRAN models as input and produces and enhanced version of the input model. The enhanced version reproduces the original model calculations but also has the capability to calculate derivatives of model results of interest with respect to any and all of the model data and input parameters. The method for calculating the derivatives and sensitivities is the adjoint method. Partial derivatives are calculated analytically using computer calculus and saved as elements of an adjoint matrix on direct assess storage. The total derivatives are calculated by solving an appropriate adjoint equation. ADGEN is applied to a major computer model of interest to the Low-Level Waste Community, the PRESTO-II model. PRESTO-II sample problem results reveal that ADGEN correctly calculates derivatives of response of interest with respect to 300 parameters. The execution time to create the adjoint matrix is a factor of 45 times the execution time of the reference sample problem. Once this matrix is determined, the derivatives with respect to 3000 parameters are calculated in a factor of 6.8 that of the reference model for each response of interest. For a single 3000 for determining these derivatives by parameter perturbations. The automation of the implementation of the adjoint technique for calculating derivatives and sensitivities eliminates the costly and manpower-intensive task of direct hand-implementation by reprogramming and thus makes the powerful adjoint technique more amenable for use in sensitivity analysis of existing models. 20 refs., 1 fig., 5 tabs.
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...
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
Adjoint method for hybrid guidance loop state-space models
Weiss, M.; Bucco, D.
2015-01-01
A framework is introduced to develop the theory of the adjoint method for models including both continuous and discrete dynamics. The basis of this framework consists of the class of impulsive linear dynamic systems. It allows extension of the adjoint method to more general models that include multi
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.
Institute of Scientific and Technical Information of China (English)
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.
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.
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
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.
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.
Serakos, Demetrios
2015-01-01
This book defines and develops the generalized adjoint of an input-output system. It is the result of a theoretical development and examination of the generalized adjoint concept and the conditions under which systems analysis using adjoints is valid. Results developed in this book are useful aids for the analysis and modeling of physical systems, including the development of guidance and control algorithms and in developing simulations. The generalized adjoint system is defined and is patterned similarly to adjoints of bounded linear transformations. Next the elementary properties of the generalized adjoint system are derived. For a space of input-output systems, a generalized adjoint map from this space of systems to the space of generalized adjoints is defined. Then properties of the generalized adjoint map are derived. Afterward the author demonstrates that the inverse of an input-output system may be represented in terms of the generalized adjoint. The use of generalized adjoints to determine bounds for ...
Water flooding optimization with adjoint model under control constraints
Institute of Scientific and Technical Information of China (English)
张凯; 张黎明; 姚军; 陈玉雪; 路然然
2014-01-01
The oil recovery enhancement is a major technical issue in the development of oil and gas fields. The smart oil field is an effective way to deal with the issue. It can achieve the maximum profits in the oil production at a minimum cost, and represents the future direction of oil fields. This paper discusses the core of the smart field theory, mainly the real-time optimization method of the injection-production rate of water-oil wells in a complex oil-gas filtration system. Computing speed is considered as the primary prerequisite because this research depends very much on reservoir numerical simulations and each simulation may take several hours or even days. An adjoint gradient method of the maximum theory is chosen for the solution of the optimal control variables. Conven-tional solving method of the maximum principle requires two solutions of time series: the forward reservoir simulation and the backward adjoint gradient calculation. In this paper, the two processes are combined together and a fully implicit reservoir simulator is developed. The matrixes of the adjoint equation are directly obtained from the fully implicit reservoir simulation, which accelera-tes the optimization solution and enhances the efficiency of the solving model. Meanwhile, a gradient projection algorithm combined with the maximum theory is used to constrain the parameters in the oil field development, which make it possible for the method to be applied to the water flooding optimization in a real oil field. The above theory is tested in several reservoir cases and it is shown that a better development effect of the oil field can be achieved.
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...
The state-space approach to the method of adjoints for hybrid guidance loop models
Weiss, M.; Bucco, D.
2009-01-01
A framework is introduced to develop the theory of the Adjoint Method for models including both continuous and discrete dynamics. The basis of this framework consists of the class of impulsive linear dynamical systems. It allows extension of the Adjoint Method to more general models that include mul
Adjoint Assimilation in Marine Ecosystem Models and an Example of Application
Institute of Scientific and Technical Information of China (English)
XU Qing; LIU Yuguang; L(U) Xianqing
2005-01-01
This paper aims at a review of the work carried out to date on the adjoint assimilation of data in marine ecosystem models since 1995. The structure and feature of the adjoint assimilation in marine ecosystem models are also introduced.To illustrate the application of the adjoint technique and its merits, a 4-variable ecosystem model coupled with a 3-D physical model is established for the Bohai Sea and the Yellow Sea. The chlorophyll concentration data derived from the SeaWiFS ocean colour data are assimilated in the model with the technique. Some results are briefly presented.
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...
A self-adjoint arrival time operator inspired by measurement models
International Nuclear Information System (INIS)
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
Adjoint inversion modeling of Asian dust emission using lidar observations
Directory of Open Access Journals (Sweden)
K. Yumimoto
2008-06-01
Full Text Available A four-dimensional variational (4D-Var data assimilation system for a regional dust model (RAMS/CFORS-4DVAR; RC4 is applied to an adjoint inversion of a heavy dust event over eastern Asia during 20 March–4 April 2007. The vertical profiles of the dust extinction coefficients derived from NIES Lidar network are directly assimilated, with validation using observation data. Two experiments assess impacts of observation site selection: Experiment A uses five Japanese observation sites located downwind of dust source regions; Experiment B uses these and two other sites near source regions. Assimilation improves the modeled dust extinction coefficients. Experiment A and Experiment B assimilation results are mutually consistent, indicating that observations of Experiment A distributed over Japan can provide comprehensive information related to dust emission inversion. Time series data of dust AOT calculated using modeled and Lidar dust extinction coefficients improve the model results. At Seoul, Matsue, and Toyama, assimilation reduces the root mean square differences of dust AOT by 35–40%. However, at Beijing and Tsukuba, the RMS differences degrade because of fewer observations during the heavy dust event. Vertical profiles of the dust layer observed by CALIPSO are compared with assimilation results. The dense dust layer was trapped at potential temperatures (θ of 280–300 K and was higher toward the north; the model reproduces those characteristics well. Latitudinal distributions of modeled dust AOT along the CALIPSO orbit paths agree well with those of CALIPSO dust AOT, OMI AI, and MODIS coarse-mode AOT, capturing the latitude at which AOTs and AI have high values. Assimilation results show increased dust emissions over the Gobi Desert and Mongolia; especially for 29–30 March, emission flux is about 10 times greater. Strong dust uplift fluxes over the Gobi Desert and Mongolia cause the heavy dust event. Total optimized dust emissions are 57
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.
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.
Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Dimitrakopoulos, G.; Giannakoglou, K. C.
2015-11-01
In this article, the gradient of aerodynamic objective functions with respect to design variables, in problems governed by the incompressible Navier-Stokes equations coupled with the k-ω SST turbulence model, is computed using the continuous adjoint method, for the first time. Shape optimization problems for minimizing drag, in external aerodynamics (flows around isolated airfoils), or viscous losses in internal aerodynamics (duct flows) are considered. Sensitivity derivatives computed with the proposed adjoint method are compared to those computed with finite differences or a continuous adjoint variant based on the frequently used assumption of frozen turbulence; the latter proves the need for differentiating the turbulence model. Geometries produced by optimization runs performed with sensitivities computed by the proposed method and the 'frozen turbulence' assumption are also compared to quantify the gain from formulating and solving the adjoint to the turbulence model equations.
Michalak, Anna M.; Kitanidis, Peter K.
2004-08-01
As the incidence of groundwater contamination continues to grow, a number of inverse modeling methods have been developed to address forensic groundwater problems. In this work the geostatistical approach to inverse modeling is extended to allow for the recovery of the antecedent distribution of a contaminant at a given point back in time, which is critical to the assessment of historical exposure to contamination. Such problems are typically strongly underdetermined, with a large number of points at which the distribution is to be estimated. To address this challenge, the computational efficiency of the new method is increased through the application of the adjoint state method. In addition, the adjoint problem is presented in a format that allows for the reuse of existing groundwater flow and transport codes as modules in the inverse modeling algorithm. As demonstrated in the presented applications, the geostatistical approach combined with the adjoint state method allow for a historical multidimensional contaminant distribution to be recovered even in heterogeneous media, where a numerical solution is required for the forward problem.
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.
The Adjoint Method Formulation for an Inverse Problem in the Generalized Black-Scholes Model
Directory of Open Access Journals (Sweden)
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.
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
Using Adjoint Methods to Improve 3-D Velocity Models of Southern California
Liu, Q.; Tape, C.; Maggi, A.; Tromp, J.
2006-12-01
We use adjoint methods popular in climate and ocean dynamics to calculate Fréchet derivatives for tomographic inversions in southern California. The Fréchet derivative of an objective function χ(m), where m denotes the Earth model, may be written in the generic form δχ=int Km(x) δln m(x) d3x, where δln m=δ m/m denotes the relative model perturbation. For illustrative purposes, we construct the 3-D finite-frequency banana-doughnut kernel Km, corresponding to the misfit of a single traveltime measurement, by simultaneously computing the 'adjoint' wave field s† forward in time and reconstructing the regular wave field s backward in time. The adjoint wave field is produced by using the time-reversed velocity at the receiver as a fictitious source, while the regular wave field is reconstructed on the fly by propagating the last frame of the wave field saved by a previous forward simulation backward in time. The approach is based upon the spectral-element method, and only two simulations are needed to produce density, shear-wave, and compressional-wave sensitivity kernels. This method is applied to the SCEC southern California velocity model. Various density, shear-wave, and compressional-wave sensitivity kernels are presented for different phases in the seismograms. We also generate 'event' kernels for Pnl, S and surface waves, which are the Fréchet kernels of misfit functions that measure the P, S or surface wave traveltime residuals at all the receivers simultaneously for one particular event. Effectively, an event kernel is a sum of weighted Fréchet kernels, with weights determined by the associated traveltime anomalies. By the nature of the 3-D simulation, every event kernel is also computed based upon just two simulations, i.e., its construction costs the same amount of computation time as an individual banana-doughnut kernel. One can think of the sum of the event kernels for all available earthquakes, called the 'misfit' kernel, as a graphical
Comparison of adjoint and nudging methods to initialise ice sheet model basal conditions
Mosbeux, Cyrille; Gillet-Chaulet, Fabien; Gagliardini, Olivier
2016-07-01
Ice flow models are now routinely used to forecast the ice sheets' contribution to 21st century sea-level rise. For such short term simulations, the model response is greatly affected by the initial conditions. Data assimilation algorithms have been developed to invert for the friction of the ice on its bedrock using observed surface velocities. A drawback of these methods is that remaining uncertainties, especially in the bedrock elevation, lead to non-physical ice flux divergence anomalies resulting in undesirable transient effects. In this study, we compare two different assimilation algorithms based on adjoints and nudging to constrain both bedrock friction and elevation. Using synthetic twin experiments with realistic observation errors, we show that the two algorithms lead to similar performances in reconstructing both variables and allow the flux divergence anomalies to be significantly reduced.
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
Ito, Shin-Ichi; Nagao, Hiromichi; Yamanaka, Akinori; Tsukada, Yuhki; Koyama, Toshiyuki; Inoue, Junya
Phase field (PF) method, which phenomenologically describes dynamics of microstructure evolutions during solidification and phase transformation, has progressed in the fields of hydromechanics and materials engineering. How to determine, based on observation data, an initial state and model parameters involved in a PF model is one of important issues since previous estimation methods require too much computational cost. We propose data assimilation (DA), which enables us to estimate the parameters and states by integrating the PF model and observation data on the basis of the Bayesian statistics. The adjoint method implemented on DA not only finds an optimum solution by maximizing a posterior distribution but also evaluates the uncertainty in the estimations by utilizing the second order information of the posterior distribution. We carried out an estimation test using synthetic data generated by the two-dimensional Kobayashi's PF model. The proposed method is confirmed to reproduce the true initial state and model parameters we assume in advance, and simultaneously estimate their uncertainties due to quality and quantity of the data. This result indicates that the proposed method is capable of suggesting the experimental design to achieve the required accuracy.
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.
Zheng, Xiangyang; Mayerle, Roberto; Xing, Qianguo; Fernández Jaramillo, José Manuel
2016-08-01
In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.
Adjoint LMS (ALMS Algorithm Based Active Noise Control with Feedback Path Modeling
Directory of Open Access Journals (Sweden)
U Ramachandraiah,
2010-12-01
Full Text Available In active noise control (ANC systems, there exists an inherent feedback from the loudspeaker to the primary microphone. Adjoint least mean square (ALMS algorithm is known to be an alternative to the widely used filtered x LMS (FxLMS for reducing the computational complexity and memory requirements, especially in the case of multi-channel systems. Further FxLMS algorithm is based on the assumptionthat the order of the weighing filter and secondary path can be commuted which is not always true in practice. Though ALMS do not make such an assumption, neither FxLMS nor the ALMS algorithms onsider the feedback path effect that is inherent in ANC systems.We propose a feedback ANC system based on ALMS algorithm which is analogous to the system based on FxLMS. Detailed computational complexity analysis for addition and multiplication requirements ispresented and are compared with those of its counterpart to establish its usefulness. Simulation results show the convergence characteristics of the ALMS based ANC with feedback path modeling is on par with that based on FxLMS.
Directory of Open Access Journals (Sweden)
R. H. Moore
2012-08-01
Full Text Available We use the Global Modeling Initiative (GMI chemical transport model with a cloud droplet parameterization adjoint to quantify the sensitivity of cloud droplet number concentration to uncertainties in predicting CCN concentrations. Published CCN closure prediction uncertainties for six different sets of simplifying compositional and mixing state assumptions are used as proxies for modeled CCN uncertainty arising from application of those scenarios. It is found that cloud droplet number concentrations are fairly insensitive to CCN-active aerosol number concentrations over the continents (∂Nd/∂N_{a} ~ 10–30%, but the sensitivities exceed 70% in pristine regions such as the Alaskan Arctic and remote oceans. Since most of the anthropogenic indirect forcing is concentrated over the continents, this work shows that the application of Köhler theory and attendant simplifying assumptions in models is not a major source of uncertainty in predicting cloud droplet number or anthropogenic aerosol indirect forcing for the liquid, stratiform clouds simulated in these models. However, it does highlight the sensitivity of some remote areas to pollution brought into the region via long-range transport (e.g. biomass burning or from seasonal biogenic sources (e.g. phytoplankton as a source of dimethylsulfide in the southern oceans. Since these transient processes are not captured well by the climatological emissions inventories employed by current large-scale models, the uncertainties in aerosol-cloud interactions during these events could be much larger than those uncovered here. This finding motivates additional measurements in these pristine regions, which have recieved little attention to date, in order to quantify the impact of, and uncertainty associated with, transient processes in effecting changes in cloud properties.
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
Baroclinic flow and the Lorenz-84 model
Veen, Lennaert van
2002-01-01
The bifurcation diagram of a truncation to six degrees of freedom of the equations for quasi-geostrophic, baroclinic flow is investigated. Period doubling cascades and Shil'nikov bifurcations lead to chaos in this model. The low dimension of the chaotic attractor suggests the possibility to reduce t
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.
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
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
T. Stavrakou
2004-12-01
Full Text Available We use ground-based observations of CO mixing ratios and vertical column abundances together with tropospheric NO2 columns from the GOME satellite instrument as constraints for improving the global annual emission estimates of CO and NOx for the year 1997. The agreement between concentrations calculated by the global 3-dimensional CTM IMAGES and the observations is optimized using the adjoint modelling technique, which allows to invert for CO and NOx fluxes simultaneously, taking their chemical interactions into account. Our analysis quantifies a total of 39 flux parameters, comprising anthropogenic and biomass burning sources over large continental regions, soil and lightning emissions of NOx, biogenic emissions of CO and non-methane hydrocarbons, as well as the deposition velocities of both CO and NOx. Comparison between observed, prior and optimized CO mixing ratios at NOAA/CMDL sites shows that the inversion performs well at the northern mid- and high latitudes, and that it is less efficient in the Southern Hemisphere, as expected due to the scarsity of measurements over this part of the globe. The inversion, moreover, brings the model much closer to the measured NO2 columns over all regions. Sensitivity tests show that anthropogenic sources exhibit weak sensitivity to changes of the a priori errors associated to the bottom-up inventory, whereas biomass burning sources are subject to a strong variability. Our best estimate for the 1997 global top-down CO source amounts to 2760 Tg CO. Anthropogenic emissions increase by 28%, in agreement with previous inverse modelling studies, suggesting that the present bottom-up inventories underestimate the anthropogenic CO emissions in the Northern Hemisphere. The magnitude of the optimized NOx global source decreases by 14% with respect to the prior, and amounts to 42.1 Tg N, out of which 22.8 Tg N are due to anthropogenic sources. The NOx emissions increase over Tropical regions, whereas they
Double-Difference Adjoint Tomography
Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen
2016-04-01
We introduce a double-difference method for the inversion of seismic wavespeed structure by adjoint tomography. Differences between seismic observations and model-based predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby largely canceling out the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher-resolution) structural variations in areas close to the stations. Whereas in conventional tomography, a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography, one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.
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...
Lu, Xianqing; Zhang, Jicai
2006-10-01
Based on the simulation of M2 tide in the Bohai Sea, the Yellow Sea and the East China Sea, TOPEX/Poseidon altimeter data are assimilated into a 2D tidal model to study the spatially varying bottom friction coefficient (BFC) by using the adjoint method. In this study, the BFC at some grid points are selected as the independent BFC, while the BFC at other grid points can be obtained through linear interpolation with the independent BFC. Two strategies for selecting the independent BFC are discussed. In the first strategy, one independent BFC is uniformly selected from each 1°×1° area. In the second one, the independent BFC are selected based on the spatial distribution of water depth. Twin and practical experiments are carried out to compare the two strategies. In the twin experiments, the adjoint method has a strong ability of inverting the prescribed BFC distributions combined with the spatially varying BFC. In the practical experiments, reasonable simulation results can be obtained by optimizing the spatially varying independent BFC. In both twin and practical experiments, the simulation results with the second strategy are better than those with the first one. The BFC distribution obtained from the practical experiment indicates that the BFC in shallow water are larger than those in deep water in the Bohai Sea, the North Yellow Sea, the South Yellow Sea and the East China Sea individually. However, the BFC in the East China Sea are larger than those in the other areas perhaps because of the large difference of water depth or bottom roughness. The sensitivity analysis indicates that the model results are more sensitive to the independent BFC near the land.
Hot QCD, k-strings and the adjoint monopole gas model
Altes, C P K; Altes, Chris P. Korthals; Meyer, Harvey B.
2005-01-01
When the magnetic sector of hot QCD, 3D SU(N) Yang-Mills theory, is described as a dilute gas of non-Abelian monopoles in the adjoint representation of the magnetic group, Wilson loops of N-ality k are known to obey a periodic k(N-k) law. Lattice simulations have confirmed this prediction to a few percent for N=4 and 6. We describe in detail how the magnetic flux of the monopoles produces different area laws for spatial Wilson k-loops. A simple physical argument is presented, why the predicted and observed Casimir scaling is allowed in the large-N limit by usual power-counting arguments. The same scaling is also known to hold in two-loop perturbation theory for the spatial 't Hooft loop, which measures the electric flux. We then present new lattice data for 3D N=8 k-strings as long as 3`fm' that provide further confirmation. Finally we suggest new tests in theories with spontaneous breaking and in SO(4n+2) gauge groups.
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.
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.
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.
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 ...
Sensitivity analysis via reduced order adjoint method
International Nuclear Information System (INIS)
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 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.
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.
Double-difference adjoint seismic tomography
Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen
2016-09-01
We introduce a `double-difference' method for the inversion for seismic wave speed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings and systematic uncertainties. To alleviate the corresponding non-uniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and practically. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher resolution) structural variations in areas close to the stations. Whereas in conventional tomography a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.
Institute of Scientific and Technical Information of China (English)
CHENG Qiang; CAO JianWen; WANG Bin; ZHANG HaiBin
2009-01-01
The adjoint code generator (ADG) is developed to produce the adjoint codes, which are used to analytically calculate gradients and the Hessian-vector products with the costs independent of the number of the independent variables. Different from other automatic differentiation tools, the implementation of ADG has advantages of using the least program behavior decomposition method and several static dependence analysis techniques. In this paper we first address the concerned concepts and fundamentals, and then introduce the functionality and the features of ADG. In particular, we also discuss the design architecture of ADG and implementation details including the recomputation and storing strategy and several techniques for code optimization. Some experimental results in several applications are presented at the end.
The compressible adjoint equations in geodynamics: equations and numerical assessment
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
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...
Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores
DEFF Research Database (Denmark)
Canet, E.; Finlay, Chris; Fournier, A.
2014-01-01
by the magnitude of the Elsasser number), we find that slow magnetic modes weakly modified by diffusion exhibit a distinctive spiralling planform. When magnetic diffusion is significant (Elsasser number much smaller than unity), we find quasi-free decay slow magnetic modes whose decay time scale is comparable to...
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...
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.
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...
Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method
Directory of Open Access Journals (Sweden)
Khaled Gamal Eltohamy
2015-12-01
Full Text Available In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In the first paper in this series, a variational data assimilation of ideal tropical cyclone (TC) tracks was performed for the statistical-dynamical prediction model SD-90 by the adjoint method, and a prediction of TC tracks was made with good accuracy for tracks containing no sharp turns. In the present paper, the cases of real TC tracks are studied. Due to the complexity of TC motion, attention is paid to the diagnostic research of TC motion. First, five TC tracks are studied. Using the data of each entire TC track, by the adjoint method, five TC tracks are fitted well, and the forces acting on the TCs are retrieved. For a given TC, the distribution of the resultant of the retrieved force and Coriolis force well matches the corresponding TC track, i.e., when a TC turns, the resultant of the retrieved force and Coriolis force acts as a centripetal force, which means that the TC indeed moves like a particle; in particular, for TC 9911, the clockwise looping motion is also fitted well. And the distribution of the resultant appears to be periodic in some cases. Then, the present method is carried out for a portion of the track data for TC 9804, which indicates that when the amount of data for a TC track is sufficient, the algorithm is stable. And finally, the same algorithm is implemented for TCs with a double-eyewall structure, namely Bilis (2000) and Winnie (1997),and the results prove the applicability of the algorithm to TCs with complicated mesoscale structures if the TC track data are obtained every three hours.
Chiral phases of fundamental and adjoint quarks
Energy Technology Data Exchange (ETDEWEB)
Natale, A. A. [Centro de Ciências Naturais e Humanas, Universidade Federal do ABC 09210-170, Santo André, SP (Brazil); Instituto de Física Teórica - UNESP Rua Dr. Bento T. Ferraz, 271, Bl.II - 01140-070, São Paulo, SP (Brazil)
2016-01-22
We consider a QCD chiral symmetry breaking model where the gap equation contains an effective confining propagator and a dressed gluon propagator with a dynamically generated mass. This model is able to explain the ratios between the chiral transition and deconfinement temperatures in the case of fundamental and adjoint quarks. It also predicts the recovery of the chiral symmetry for a large number of quarks (n{sub f} ≈ 11 – 13) in agreement with lattice data.
Adjoint method for the optimum planning of industrial pollutant sources
Institute of Scientific and Technical Information of China (English)
LIU Feng; HU Fei; ZHU Jiang
2005-01-01
The optimum planning of industrial pollutant sources, which optimizes the economic object without violating environmental constraints, is an important and hard task to be conquered. In this paper, an adjoint method is developed to solve the problem. The penalty function is introduced to deal with the environmental inequality constraints, and Lagrange function is constructed to derive the adjoint equation and the gradient of the object function. In this means, the gradient of the object function can be calculated by solving the adjoint equation, and the information from the gradient is used to make the object function descend and approach to an optimal solution after some iterations. A two-dimensional, simplified model is used for numerical experiments. The theoretical derivations are verified by the results of the experiments. Furthermore, the adjoint method is shown to be of excellent convergence and efficiency, which is adaptive to the fast development of air quality numerical models and super computers.
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...
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...
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.
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...
Adjoint Functors and Representation Dimensions
Institute of Scientific and Technical Information of China (English)
Chang Chang XI
2006-01-01
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
Tracking down the ENSO delayed oscillator with an adjoint OGCM
Van Oldenborgh, G J; Venzke, S; Eckert, C; Giering, R; Oldenborgh, Geert Jan van; Burgers, Gerrit; Venzke, Stephan; Eckert, Christian; Giering, Ralf
1997-01-01
The adjoint of an ocean general circulation model is used as a tool for investigating the causes of changes in ENSO SST indices. We identify adjoint Kelvin and Rossby waves in the sensitivities to sea level and wind stress at earlier times, which can be traced back for more than a year through western and weak eastern boundary reflections. Depending on the thermocline depth the first and second baroclinic modes are excited. The sensitivities to the heat flux and SST are local and decay in about a month. The sensitivities to the fluxes are converted into the influence of SST using the adjoint of a statistical atmosphere model. Focusing on SST perturbations in the index region itself, we recover, up to a scale factor, the delayed oscillator concept.
Adjoint method for solid-oxide fuel cell simulations
Energy Technology Data Exchange (ETDEWEB)
Kapadia, S.; Anderson, W.K.; Elliott, L.; Burdyshaw, C. [University of Tennessee SimCenter at Chattanooga, 701 East M.L. King Boulevard, Chattanooga, TN 37403 (United States)
2007-04-15
Adjoint methods suitable for obtaining sensitivity derivatives for numerical simulations of solid-oxide fuel cells are presented. The adjoint method is derived, and the implementation is discussed, including a methodology for accurately obtaining all the linearizations necessary for correct implementation. Results are included for a one-dimensional anode model that includes diffusion, permeation, and relevant chemical reactions. Using this model, the accuracy of the sensitivity derivatives is demonstrated for design variables describing geometric and material properties of the anode. Finally, the adjoint method is demonstrated for a three-dimensional fuel cell geometry where sensitivity derivatives are obtained for approximately 180,000 design variables. The results are used to modify the upper and lower walls of the plenum to obtain significantly improved distribution of fluid amongst the channels. (author)
Directory of Open Access Journals (Sweden)
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
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
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
Energy Technology Data Exchange (ETDEWEB)
Much, Albert [Instituto de Ciencias Nucleares, UNAM, México D.F. 04510 (Mexico)
2015-09-15
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
A simple model for the interaction between vertical eddy heat fluxes and static stability
Gutowski, W. J., Jr.
1985-01-01
A numerical model for studying the interaction of vertical eddy heat fluxes and vertical temperature structure in midlatitude regions is described. The temperature profile for the model was derived from calculations of the equilibrium among heating rates in simplified representations of large-scale vertical eddy heat flux, moist convection and radiation. An eddy flux profile is calculated based on the quasi-geostrophic, liner baroclinic instability of a single wave. Model equilibrium states for summer and winter conditions are compared with observations, and the results are discussed in detail.
Adjoint Error Estimation for Linear Advection
Energy Technology Data Exchange (ETDEWEB)
Connors, J M; Banks, J W; Hittinger, J A; Woodward, C S
2011-03-30
An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.
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
International Nuclear Information System (INIS)
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.
Local fibred right adjoints are polynomial
DEFF Research Database (Denmark)
Kock, Anders; Kock, Joachim
2013-01-01
For any locally cartesian closed category E, we prove that a local fibred right adjoint between slices of E is given by a polynomial. The slices in question are taken in a well known fibred sense......For any locally cartesian closed category E, we prove that a local fibred right adjoint between slices of E is given by a polynomial. The slices in question are taken in a well known fibred sense...
The adjoint neutron transport equation and the statistical approach for its solution
Saracco, Paolo; Ravetto, Piero
2016-01-01
The adjoint equation was introduced in the early days of neutron transport and its solution, the neutron importance, has ben used for several applications in neutronics. The work presents at first a critical review of the adjoint neutron transport equation. Afterwards, the adjont model is constructed for a reference physical situation, for which an analytical approach is viable, i.e. an infinite homogeneous scattering medium. This problem leads to an equation that is the adjoint of the slowing-down equation that is well-known in nuclear reactor physics. A general closed-form analytical solution to such adjoint equation is obtained by a procedure that can be used also to derive the classical Placzek functions. This solution constitutes a benchmark for any statistical or numerical approach to the adjoint equation. A sampling technique to evaluate the adjoint flux for the transport equation is then proposed and physically interpreted as a transport model for pseudo-particles. This can be done by introducing appr...
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
Energy Technology Data Exchange (ETDEWEB)
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)
International Nuclear Information System (INIS)
Highlights: ► We develop an abstract framework for computing the adjoint to the neutron/nuclide burnup equations posed as a system of differential algebraic equations. ► We validate use of the adjoint for computing both sensitivity to uncertain inputs and for estimating global time discretization error. ► Flexibility of the framework is leveraged to add heat transfer physics and compute its adjoint without a reformulation of the adjoint system. ► Such flexibility is crucial for high performance computing applications. -- Abstract: We develop a general framework for computing the adjoint variable to nuclear engineering problems governed by a set of differential–algebraic equations (DAEs). The nuclear engineering community has a rich history of developing and applying adjoints for sensitivity calculations; many such formulations, however, are specific to a certain set of equations, variables, or solution techniques. Any change or addition to the physics model would require a reformulation of the adjoint problem and substantial difficulties in its software implementation. In this work we propose an abstract framework that allows for the modification and expansion of the governing equations, leverages the existing theory of adjoint formulation for DAEs, and results in adjoint equations that can be used to efficiently compute sensitivities for parametric uncertainty quantification. Moreover, as we justify theoretically and demonstrate numerically, the same framework can be used to estimate global time discretization error. We first motivate the framework and show that the coupled Bateman and transport equations, which govern the time-dependent neutronic behavior of a nuclear reactor, may be formulated as a DAE system with a power constraint. We then use a variational approach to develop the parameter-dependent adjoint framework and apply existing theory to give formulations for sensitivity and global time discretization error estimates using the adjoint
Adjoint variational methods in nonconservative stability problems.
Prasad, S. N.; Herrmann, G.
1972-01-01
A general nonself-adjoint eigenvalue problem is examined and it is shown that the commonly employed approximate methods, such as the Galerkin procedure, the method of weighted residuals and the least square technique lack variational descriptions. When used in their previously known forms they do not yield stationary eigenvalues and eigenfunctions. With the help of an adjoint system, however, several analogous variational descriptions may be developed and it is shown in the present study that by properly restating the method of least squares, stationary eigenvalues may be obtained. Several properties of the adjoint eigenvalue problem, known only for a restricted group, are shown to exist for the more general class selected for study.
System of adjoint P1 equations for neutron moderation
International Nuclear Information System (INIS)
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
Energy Technology Data Exchange (ETDEWEB)
Seifried, Jeffrey E. [Univ. of California, Berkeley, CA (United States)
2011-09-01
This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence in the simulation is acquired.
Process-theoretic characterisation of the Hermitian adjoint
Selby, John; Coecke, Bob
2016-01-01
We show that the physical principle "the adjoint associates to each state a `test' for that state" fully characterises the Hermitian adjoint for pure quantum theory, therefore providing the adjoint with operational meaning beyond its standard mathematical definition. Also, we show that for general process theories, which all admit a diagrammatic representation, this physical principle induces a reflection operation.
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...
STUDY ON THE ADJOINT METHOD IN DATA ASSIMILATION AND THE RELATED PROBLEMS
Institute of Scientific and Technical Information of China (English)
吕咸青; 吴自库; 谷艺; 田纪伟
2004-01-01
It is not reasonable that one can only use the adjoint of model in data assimilation.The simulated numerical experiment shows that for the tidal model,the result of the adjoint of equation is almost the same as that of the adjoint of model:the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°.The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea.For comparison,the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea.The initial guess values of the boundary conditions are given first,and then are adjusted to acquire the simulated results that are as close as possible to the observations.As the boundary conditions contain 72 values,which should be adjusted and how to adjust them can only be partially solved by adjusting them many times.The satisfied results are hard to acquire even gigantic efforts are done.Here,the automation of the treatment of the open boundary conditions is realized.The method is unique and superior to the traditional methods.It is emphasized that if the adjoint of equation is used,tedious and complicated mathematical deduction can be avoided.Therefore the adjoint of equation should attract much attention.
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.
Self-adjoint Extensions for the Neumann Laplacian and Applications
Institute of Scientific and Technical Information of China (English)
S. A. NAZAROV; J. SOKO(L)OWSKI
2006-01-01
A new technique is proposed for the analysis of shape optimization problems. The technique uses the asymptotic analysis of boundary value problems in singularly perturbed geometrical domains. The asymptotics of solutions are derived in the framework of compound and matched asymptotics expansions. The analysis involves the so-called interior topology variations. The asymptotic expansions are derived for a model problem, however the technique applies to general elliptic boundary value problems. The self-adjoint extensions of elliptic operators and the weighted spaces with detached asymptotics are exploited for the modelling of problems with small defects in geometrical domains. The error estimates for proposed approximations of shape functionals are provided.
Dual of QCD with One Adjoint Fermion
DEFF Research Database (Denmark)
Mojaza, Matin; Nardecchia, Marco; Pica, Claudio;
2011-01-01
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound...
Solar wind reconstruction from magnetosheath data using an adjoint approach
International Nuclear Information System (INIS)
We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradient-based minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.
Solar wind reconstruction from magnetosheath data using an adjoint approach
Energy Technology Data Exchange (ETDEWEB)
Nabert, C.; Othmer, C. [Technische Univ. Braunschweig (Germany). Inst. fuer Geophysik und extraterrestrische Physik; Glassmeier, K.H. [Technische Univ. Braunschweig (Germany). Inst. fuer Geophysik und extraterrestrische Physik; Max Planck Institute for Solar System Research, Goettingen (Germany)
2015-07-01
We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradient-based minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.
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
Adjoint P1 equations solution for neutron slowing down
International Nuclear Information System (INIS)
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)
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Curbelo, Jesus P.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: jperez@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-Graduacao em Modelagem Computacional; Hernandez, Carlos R.G., E-mail: cgh@instec.cu [Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2015-07-01
The spectral Green's function (SGF) method is a numerical method that is free of spatial truncation errors for slab-geometry fixed-source discrete ordinates (S{sub N}) adjoint problems. The method is based on the standard spatially discretized adjoint S{sub N} balance equations and a nonstandard adjoint auxiliary equation expressing the node-average adjoint angular flux, in each discretization node, as a weighted combination of the node-edge outgoing adjoint fluxes. The auxiliary equation contains parameters which act as Green's functions for the cell-average adjoint angular flux. These parameters are determined by means of a spectral analysis which yields the local general solution of the S{sub N} equations within each node of the discretization grid. In this work a number of advances in the SGF adjoint method are presented: the method is extended to adjoint S{sub N} problems considering linearly anisotropic scattering and non-zero prescribed boundary conditions for the forward source-detector problem. Numerical results to typical model problems are considered to illustrate the efficiency and accuracy of the o offered method. (author)
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.
Essential self-adjointness of the graph-Laplacian
Jorgensen, Palle E. T.
2008-07-01
We study the operator theory associated with such infinite graphs G as occur in electrical networks, in fractals, in statistical mechanics, and even in internet search engines. Our emphasis is on the determination of spectral data for a natural Laplace operator associated with the graph in question. This operator Δ will depend not only on G but also on a prescribed positive real valued function c defined on the edges in G. In electrical network models, this function c will determine a conductance number for each edge. We show that the corresponding Laplace operator Δ is automatically essential self-adjoint. By this we mean that Δ is defined on the dense subspace D (of all the real valued functions on the set of vertices G0 with finite support) in the Hilbert space l2(G0). The conclusion is that the closure of the operator Δ is self-adjoint in l2(G0), and so, in particular, that it has a unique spectral resolution, determined by a projection valued measure on the Borel subsets of the infinite half-line. We prove that generically our graph Laplace operator Δ =Δc will have continuous spectrum. For a given infinite graph G with conductance function c, we set up a system of finite graphs with periodic boundary conditions such the finite spectra, for an ascending family of finite graphs, will have the Laplace operator for G as its limit.
Virtual Seismometer and Adjoint Methods for Induced Seismicity Monitoring
Morency, C.; Matzel, E.
2014-12-01
Induced seismicity is associated with subsurface fluid injection, and puts at risk efforts to develop geologic carbon sequestration and enhanced geothermal systems. We are developing methods to monitor the microseismically active zone so that we can identify faults at risk of slipping. We are using the Virtual Seismometer Method (VSM), which is an interferometric technique that is very sensitive to the source parameters (location, mechanism and magnitude) and to the earth structure in the source region. Given an ideal geometry, that is, when two quakes are roughly in line with a recording station, the correlation of their waveforms provide a precise estimate of the Green's function between them, modified by their source mechanisms. When measuring microseismicity, this geometry is rarely ideal and we need to account for variations in the geometry as well. In addition, we also investigate the adjoint method to calculate sensitivity kernels, which define the sensitivity of an observable to model parameters. Classically, adjoint tomography relies on the interaction between a forward waveform, from the source to the recording station, and a backpropagated waveform, from the recorded station to the source. By combining the two approaches we can focus on properties directly between induced micro events, and doing so, monitor the evolution of the seismicity and precisely image potential fault zones. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
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.
On the essential self-adjointness of generalized Schroedinger operators
International Nuclear Information System (INIS)
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)
Nonlinear data-assimilation using implicit models
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
J. J. Guerrette
2015-02-01
Full Text Available Here we present the online meteorology and chemistry adjoint and tangent linear model, WRFPLUS-Chem, which incorporates modules to treat boundary layer mixing, emission, aging, dry deposition, and advection of black carbon aerosol. We also develop land surface and surface layer adjoints to account for coupling between radiation and vertical mixing. Model performance is verified against finite difference derivative approximations. A second order checkpointing scheme is created to reduce computational costs and enable simulations longer than six hours. The adjoint is coupled to WRFDA-Chem, in order to conduct a sensitivity study of anthropogenic and biomass burning sources throughout California during the 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS field campaign. A cost function weighting scheme was devised to increase adjoint sensitivity robustness in future inverse modeling studies. Results of the sensitivity study show that, for this domain and time period, anthropogenic emissions are over predicted, while wildfire emissions are under predicted. We consider the diurnal variation in emission sensitivities to determine at what time sources should be scaled up or down. Also, adjoint sensitivities for two choices of land surface model indicate that emission inversion results would be sensitive to forward model configuration. The tools described here are the first step in conducting four-dimensional variational data assimilation in a coupled meteorology-chemistry model, which will potentially provide new constraints on aerosol precursor emissions and their distributions. Such analyses will be invaluable to assessments of particulate matter health and climate impacts.
Elementary operators on self-adjoint operators
Molnar, Lajos; Semrl, Peter
2007-03-01
Let H be a Hilbert space and let and be standard *-operator algebras on H. Denote by and the set of all self-adjoint operators in and , respectively. Assume that and are surjective maps such that M(AM*(B)A)=M(A)BM(A) and M*(BM(A)B)=M*(B)AM*(B) for every pair , . Then there exist an invertible bounded linear or conjugate-linear operator and a constant c[set membership, variant]{-1,1} such that M(A)=cTAT*, , and M*(B)=cT*BT, .
Local Volatility Calibration Using An Adjoint Proxy
Directory of Open Access Journals (Sweden)
Gabriel TURINICI
2008-11-01
Full Text Available We document the calibration of the local volatility in a framework similar to Coleman, Li and Verma. The quality of a surface is assessed through a functional to be optimized; the specificity of the approach is to separate the optimization (performed with any suitable optimization algorithm from the computation of the functional where we use an adjoint (as in L. Jiang et. al. to obtain an approximation; moreover our main calibration variable is the implied volatility (the procedure can also accommodate the Greeks. The procedure performs well on benchmarks from the literature and on FOREX data.
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.
Directory of Open Access Journals (Sweden)
Z. Tan
2015-11-01
Full Text Available Understanding methane emissions from the Arctic, a fast warming carbon reservoir, is important for projecting changes in the global methane cycle under future climate scenarios. Here we optimize Arctic methane emissions with a nested-grid high-resolution inverse model by assimilating both high-precision surface measurements and column-average SCIAMACHY satellite retrievals of methane mole fraction. For the first time, methane emissions from lakes are integrated into an atmospheric transport and inversion estimate, together with prior wetland emissions estimated by six different biogeochemical models. We find that, the global methane emissions during July 2004–June 2005 ranged from 496.4 to 511.5 Tg yr−1, with wetland methane emissions ranging from 130.0 to 203.3 Tg yr−1. The Arctic methane emissions during July 2004–June 2005 were in the range of 14.6–30.4 Tg yr−1, with wetland and lake emissions ranging from 8.8 to 20.4 Tg yr−1 and from 5.4 to 7.9 Tg yr−1 respectively. Canadian and Siberian lakes contributed most of the estimated lake emissions. Due to insufficient measurements in the region, Arctic methane emissions are less constrained in northern Russia than in Alaska, northern Canada and Scandinavia. Comparison of different inversions indicates that the distribution of global and Arctic methane emissions is sensitive to prior wetland emissions. Evaluation with independent datasets shows that the global and Arctic inversions improve estimates of methane mixing ratios in boundary layer and free troposphere. The high-resolution inversions provide more details about the spatial distribution of methane emissions in the Arctic.
NEW METHOD FOR LOW ORDER SPECTRAL MODEL AND ITS APPLICATION
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In order to overcome the deficiency in classical method of low order spectral model, a new method for low order spectral model was advanced. Through calculating the multiple correlation coefficients between combinations of different functions and the recorded data under the least square criterion, the truncated functions which can mostly reflect the studied physical phenomenon were objectively distilled from these data. The new method overcomes the deficiency of artificially selecting the truncated functions in the classical low order spectral model. The new method being applied to study the inter-annual variation of summer atmospheric circulation over Northern Hemisphere, the truncated functions were obtained with the atmospheric circulation data of June 1994 and June 1998. The mechanisms for the two-summer atmospheric circulation variations over Northern Hemisphere were obtained with two-layer quasi-geostrophic baroclinic equation.
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...
Directory of Open Access Journals (Sweden)
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.
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.
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
International Nuclear Information System (INIS)
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
Energy Technology Data Exchange (ETDEWEB)
Bandara, Lashi, E-mail: lashi.bandara@chalmers.se [Chalmers University of Technology and University of Gothenburg, Mathematical Sciences (Sweden); Milatovic, Ognjen, E-mail: omilatov@unf.edu [University of North Florida, Department of Mathematics and Statistics (United States)
2015-12-15
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Al-Hashimi, M.H., E-mail: hashimi@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Salman, M., E-mail: msalman@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Shalaby, A., E-mail: amshalab@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Physics Department, Faculty of Science, Mansoura University (Egypt); Wiese, U.-J., E-mail: wiese@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA (United States)
2013-10-15
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
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.
Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator
Weir, John
2008-01-01
We prove that the eigenvalues of a certain highly non-self-adjoint operator correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many eigenvalues which accumulate only at infinity.
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.
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.
International Nuclear Information System (INIS)
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)
Numerical tests of efficiency of the retrospective time integration scheme in the self-memory model
Institute of Scientific and Technical Information of China (English)
GU Xiangqian; YOU Xingtian; ZHU He; CAO Hongxing
2004-01-01
A set of numerical tests was carried out to compare the retrospective time integral scheme in a self-memory model,whose dynamic kernel is the barotropical quasi-geostrophic model, with the ordinary centered difference scheme in the barotropical quasigeostrophic model. The Rossby-Haurwitz wave function was taken as the initial fields for both schemes. The results show that in comparison with the ordinary centered difference scheme, the retrospective time integral scheme reduces by 2 orders of magnitude the forecast error, and the forecast error increases very little with lengthening of the time-step. Therefore, the retrospective time integral scheme has advantages of improving the forecast accuracy, extending the predictable duration and reducing the computation amount.
Low-order models of wave interactions in the transition to baroclinic chaos
Directory of Open Access Journals (Sweden)
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.
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.
Energy Technology Data Exchange (ETDEWEB)
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.
Neutrino masses in SU(5) x U(1){sub F} with adjoint flavons
Energy Technology Data Exchange (ETDEWEB)
Nardi, Enrico [INFN, Laboratori Nazionali di Frascati, C.P. 13, Frascati (Italy); IFT-UAM/CSIC, Madrid (Spain); Universidad Autonoma de Madrid, Departamento de Fisica Teorica, Madrid (Spain); Restrepo, Diego; Velasquez, Mauricio [Universidad de Antioquia, Instituto de Fisica, Medellin (Colombia)
2012-03-15
We present a SU(5) x U(1){sub F} supersymmetric model for neutrino masses and mixings that implements the seesaw mechanism by means of the heavy SU(2) singlets and triplets states contained in three adjoints of SU(5). We discuss how Abelian U(1){sub F} symmetries can naturally yield non-hierarchical light neutrinos even when the heavy states are strongly hierarchical, and how it can also ensure that R-parity arises as an exact accidental symmetry. By assigning two flavons that break U(1){sub F} to the adjoint representation of SU(5) and assuming universality for all the fundamental couplings, the coefficients of the effective Yukawa and Majorana mass operators become calculable in terms of group theoretical quantities. There is a single free parameter in the model, however, at leading order the structure of the light neutrinos mass matrix is determined in a parameter independent way. (orig.)
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
Ibragimov, Nail H
2011-01-01
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.
Self-Adjointness Criterion for Operators in Fock Spaces
Energy Technology Data Exchange (ETDEWEB)
Falconi, Marco, E-mail: marco.falconi@univ-rennes1.fr [Université de Rennes I, IRMAR and Centre Henri Lebesgue (France)
2015-12-15
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.
Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
Mironov, A
2015-01-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SU_N) and Kauffman (SO_N) polynomials. For E_8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6x6 case. The adjoint polynomials do not distinguish between mutant...
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.
ADJOINT METHOD OF PARAMETER IDENTIFICATION FOR SOME NON- LINEAR REACTION-DIFFUSION SYSTEMS
Institute of Scientific and Technical Information of China (English)
JIANG Cheng-shun; LIU Chao; SHEN Yong-ming
2005-01-01
This paper deals with the problem of determining two unknown parameters of some nonlinear reaction-diffusion models. These reaction-diffusion models are derived from applications in the groundwater flow transport, environmental sciences, gas dynamics, heat and mass transfer, industrial automatization and some other engineering technological fields. The adjoint method based on the variational principle is a relatively new optimal control method. It is used in the identification of the unknown diffusion coefficient, and some coefficients of the nonlinear sink or source terms in these systems. At first, the problem is transferred into an optimization problem of minimizing a functional, and the adjoint equations of the governing equations are derived from the adjoint method. Then, the formulas are given to calculate the gradient of the objective function with respect to the couple of unknown parameters. At last, an iterative gradient-based optimization algorithm is presented for solving the optimization problem. A numerical example is offered in the end. It shows the effectiveness of the proposed approach.
SUSY SU(5) with singlet plus adjoint matter and A{sub 4} family symmetry
Energy Technology Data Exchange (ETDEWEB)
Cooper, Iain K., E-mail: ikc1g08@soton.ac.u [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); King, Stephen F., E-mail: sfk@hep.phys.soton.ac.u [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Luhn, Christoph, E-mail: christoph.luhn@soton.ac.u [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom)
2010-06-28
We propose a supersymmetric (SUSY) SU(5) Grand Unified Theory (GUT) including a single right-handed neutrino singlet and an adjoint matter representation below the GUT scale and extend this model to include an A{sub 4} family symmetry and a gauged anomaly-free Abelian group. In our approach hierarchical neutrino masses result from a combined type I and type III seesaw mechanism, and the A{sub 4} symmetry leads to tri-bimaximal mixing which arises indirectly. The mixing between the single right-handed neutrino and the matter in the adjoint is forbidden by excluding an adjoint Higgs, leading to a diagonal heavy Majorana sector as required by constrained sequential dominance. The model also reproduces a realistic description of quark and charged lepton masses and quark mixings, including the Georgi-Jarlskog relations and the leptonic mixing sum rules s=rcos{delta} and a=-r{sup 2}/4 with r={theta}{sub C}/3.
Directory of Open Access Journals (Sweden)
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.
Big Data Challenges in Global Seismic 'Adjoint Tomography' (Invited)
Tromp, J.; Bozdag, E.; Krischer, L.; Lefebvre, M.; Lei, W.; Smith, J.
2013-12-01
The challenge of imaging Earth's interior on a global scale is closely linked to the challenge of handling large data sets. The related iterative workflow involves five distinct phases, namely, 1) data gathering and culling, 2) synthetic seismogram calculations, 3) pre-processing (time-series analysis and time-window selection), 4) data assimilation and adjoint calculations, 5) post-processing (pre-conditioning, regularization, model update). In order to implement this workflow on modern high-performance computing systems, a new seismic data format is being developed. The Adaptable Seismic Data Format (ASDF) is designed to replace currently used data formats with a more flexible format that allows for fast parallel I/O. The metadata is divided into abstract categories, such as "source" and "receiver", along with provenance information for complete reproducibility. The structure of ASDF is designed keeping in mind three distinct applications: earthquake seismology, seismic interferometry, and exploration seismology. Existing time-series analysis tool kits, such as SAC and ObsPy, can be easily interfaced with ASDF so that seismologists can use robust, previously developed software packages. ASDF accommodates an automated, efficient workflow for global adjoint tomography. Manually managing the large number of simulations associated with the workflow can rapidly become a burden, especially with increasing numbers of earthquakes and stations. Therefore, it is of importance to investigate the possibility of automating the entire workflow. Scientific Workflow Management Software (SWfMS) allows users to execute workflows almost routinely. SWfMS provides additional advantages. In particular, it is possible to group independent simulations in a single job to fit the available computational resources. They also give a basic level of fault resilience as the workflow can be resumed at the correct state preceding a failure. Some of the best candidates for our particular workflow
Adjoint transport methods for radiation-effects testing
International Nuclear Information System (INIS)
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
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 ...
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...
SUPERSTABILITY OF ADJOINTABLE MAPPINGS ON HILBERT C*-MODULES
Directory of Open Access Journals (Sweden)
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
Energy Technology Data Exchange (ETDEWEB)
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.
Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2
International Nuclear Information System (INIS)
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
Directory of Open Access Journals (Sweden)
V. A. Karydis
2012-10-01
Full Text Available We present the development of the adjoint of a comprehensive cloud droplet formation parameterization for use in aerosol-cloud-climate interaction studies. The adjoint efficiently and accurately calculates the sensitivity of cloud droplet number concentration (CDNC to all parameterization inputs (e.g., updraft velocity, water uptake coefficient, aerosol number and hygroscopicity with a single execution. The adjoint is then integrated within three dimensional (3-D aerosol modeling frameworks to quantify the sensitivity of CDNC formation globally to each parameter. Sensitivities are computed for year-long executions of the NASA Global Modeling Initiative (GMI Chemical Transport Model (CTM, using wind fields computed with the Goddard Institute for Space Studies (GISS Global Circulation Model (GCM II', and the GEOS-Chem CTM, driven by meteorological input from the Goddard Earth Observing System (GEOS of the NASA Global Modeling and Assimilation Office (GMAO. We find that over polluted (pristine areas, CDNC is more sensitive to updraft velocity and uptake coefficient (aerosol number and hygroscopicity. Over the oceans of the Northern Hemisphere, addition of anthropogenic or biomass burning aerosol is predicted to increase CDNC in contrast to coarse-mode sea salt which tends to decrease CDNC. Over the Southern Oceans, CDNC is most sensitive to sea salt, which is the main aerosol component of the region. Globally, CDNC is predicted to be less sensitive to changes in the hygroscopicity of the aerosols than in their concentration with the exception of dust where CDNC is very sensitive to particle hydrophilicity over arid areas. Regionally, the sensitivities differ considerably between the two frameworks and quantitatively reveal why the models differ considerably in their indirect forcing estimates.
Energy Technology Data Exchange (ETDEWEB)
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.
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
Non-self-adjoint hamiltonians defined by Riesz bases
Energy Technology Data Exchange (ETDEWEB)
Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)
2014-03-15
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
Adjoint electron-photon transport Monte Carlo calculations with ITS
International Nuclear Information System (INIS)
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
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
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.
Two-dimensional QCD with matter in the adjoint representation: What does it teach us?
International Nuclear Information System (INIS)
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
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
Volume reduction in large-N lattice gauge theories [with adjoint fermions
Koren, Mateusz
2013-01-01
This work covers volume reduction in quantum field theories on a lattice at large $N$ (number of colors), as first described by Eguchi and Kawai in 1982. The volume reduction (or volume independence) means that the theory defined on an arbitrarily small lattice is equivalent in the large-$N$ limit to the theory on an infinite lattice with the same bare parameters. We analyze the volume reduction by means of Monte Carlo simulations using the lattice model on a single site (or a small fixed number of sites) with Wilson fermions in the adjoint representation, using $N$ up to 60. Most of the results focus on two flavours of Dirac fermions and the single fermionic flavour is also discussed where there is a significant difference of behaviour. We find that the $(Z_N)^4$ center symmetry, necessary for the realization of volume reduction, is unbroken in the reduced model for a large range of parameters and, in particular, that the maximum admissible value of the adjoint fermion mass is non-zero in the large-$N$ limit...
Hybrid Active Noise Control using Adjoint LMS Algorithms
Energy Technology Data Exchange (ETDEWEB)
Nam, Hyun Do; Hong, Sik Ki [Dankook University (Korea, Republic of)
1998-07-01
A multi-channel hybrid active noise control(MCHANC) is derived by combining hybrid active noise control techniques and adjoint LMS algorithms, and this algorithm is applied to an active noise control system in a three dimensional enclosure. A MCHANC system uses feed forward and feedback filters simultaneously to cancel noises in an enclosure. The adjoint LMs algorithm, in which the error is filtered through an adjoint filter of the secondary channel, is also used to reduce the computational burden of adaptive filters. The overall attenuation performance and convergence characteristics of MCHANC algorithm is better than both multiple-channel feed forward algorithms and multiple-channel feedback algorithms. In a large enclosure, the acoustic reverberation can be very long, which means a very high order feed forward filter must be used to cancel the reverberation noises. Strong reverberation noises are generally narrow band and low frequency, which can be effectively predicted and canceled by a feedback adaptive filters. So lower order feed forward filter taps can be used in MCHANC algorithm which combines advantages of fast convergence and small excess mean square error. In this paper, computer simulations and real time implementations is carried out on a TMS320C31 processor to evaluate the performance of the MCHANC systems. (author). 11 refs., 11 figs., 1 tab.
Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle
Energy Technology Data Exchange (ETDEWEB)
Peplow, Douglas E. [ORNL; Mosher, Scott W [ORNL; Evans, Thomas M [ORNL
2012-08-01
For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.
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
Nonself-Adjoint Second-Order Difference Operators in Limit-Circle Cases
Directory of Open Access Journals (Sweden)
Bilender P. Allahverdiev
2012-01-01
Full Text Available We consider the maximal dissipative second-order difference (or discrete Sturm-Liouville operators acting in the Hilbert space ℓ2(ℤ (ℤ:={0,±1,±2,…}, that is, the extensions of a minimal symmetric operator with defect index (2,2 (in the Weyl-Hamburger limit-circle cases at ±∞. We investigate two classes of maximal dissipative operators with separated boundary conditions, called “dissipative at −∞” and “dissipative at ∞.” In each case, we construct a self-adjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also establish a functional model of the maximal dissipative operator and determine its characteristic function through the Titchmarsh-Weyl function of the self-adjoint operator. We prove the completeness of the system of eigenvectors and associated vectors of the maximal dissipative operators.
On adjoint symmetry equations, integrating factors and solutions of nonlinear ODEs
Energy Technology Data Exchange (ETDEWEB)
Guha, Partha [Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig (Germany); Choudhury, A Ghose [Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta-700 009 (India); Khanra, Barun [Sailendra Sircar Vidyalaya, 62A Shyampukur Street, Calcutta-700 004 (India)], E-mail: partha.guha@mis.mpg.de, E-mail: a_ghosechoudhury@rediffmail.com, E-mail: barunkhanra@rediffmail.com
2009-03-20
We consider the role of the adjoint equation in determining explicit integrating factors and first integrals of nonlinear ODEs. In Chandrasekar et al (2006 J. Math. Phys. 47 023508), the authors have used an extended version of the Prelle-Singer method for a class of nonlinear ODEs of the oscillator type. In particular, we show that their method actually involves finding a solution of the adjoint symmetry equation. Next, we consider a coupled second-order nonlinear ODE system and derive the corresponding coupled adjoint equations. We illustrate how the coupled adjoint equations can be solved to arrive at a first integral.
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
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 Monte Carlo techniques and codes for organ dose calculations
International Nuclear Information System (INIS)
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
A self-adjoint decomposition of the radial momentum operator
Liu, Q. H.; Xiao, S. F.
2015-12-01
With acceptance of the Dirac's observation that the canonical quantization entails using Cartesian coordinates, we examine the operator erPr rather than Pr itself and demonstrate that there is a decomposition of erPr into a difference of two self-adjoint but noncommutative operators, in which one is the total momentum and another is the transverse one. This study renders the operator Pr indirectly measurable and physically meaningful, offering an explanation of why the mean value of Pr over a quantum mechanical state makes sense and supporting Dirac's claim that Pr "is real and is the true momentum conjugate to r".
Neutrino masses in $SU(5)\\times U(1)_F$ with adjoint flavons
Nardi, Enrico; Velasquez, Mauricio
2011-01-01
We present a $SU(5)\\times U(1)_F$ supersymmetric model for neutrino masses and mixings that includes three heavy singlet neutrinos and two flavons. We discuss how Abelian $U(1)_F$ symmetries can naturally yield non-hierarchical light neutrinos even when the heavy states are strongly hierarchical, and how it can also ensure that $R$--parity arises as an exact accidental symmetry. By assigning flavons to the adjoint representation of SU(5) and assuming universality for all the fundamental couplings, the coefficients of the effective Yukawa and Majorana mass operators become calculable in terms of group theoretical quantities. There is a single free parameter in the model, however, at leading order the structure of the light neutrinos mass matrix is determined in a parameter independent way.
On the Norm Convergence of the Self-Adjoint Trotter–Kato Product Formula with Error Bound
Indian Academy of Sciences (India)
Takashi Ichinose; Hideo Tamura
2002-02-01
The norm convergence of the Trotter–Kato product formula with error bound is shown for the semigroup generated by that operator sum of two nonnegative self-adjoint operators and which is self-adjoint.
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.
Nonlinear Hilbert Adjoints : Properties and Applications to Hankel Singular Value Analysis
Gray, W. Steven; Scherpen, Jacquelien M.A.
2001-01-01
The notion of an adjoint operator for a nonlinear mapping has few interpretations in the literature. In this paper a new nonlinear Hilbert adjoint operator is proposed. It is shown to unite several existing concepts and provides an essential tool for singular value analysis of nonlinear Hankel opera
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.
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
Energy Technology Data Exchange (ETDEWEB)
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2000-07-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)
High Order Adjoint Derivatives using ESDIRK Methods for Oil Reservoir Production Optimization
DEFF Research Database (Denmark)
Capolei, Andrea; Stenby, Erling Halfdan; Jørgensen, John Bagterp
2012-01-01
and continuous adjoints . The high order integration scheme allows larger time steps and therefore faster solution times. We compare gradient computation by the continuous adjoint method to the discrete adjoint method and the finite-difference method. The methods are implemented for a two phase flow reservoir......In production optimization, computation of the gradients is the computationally expensive step. We improve the computational efficiency of such algorithms by improving the gradient computation using high-order ESDIRK (Explicit Singly Diagonally Implicit Runge-Kutta) temporal integration methods...... 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...
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...
Self-adjoint oscillator operator from a modified factorization
Energy Technology Data Exchange (ETDEWEB)
Reyes, Marco A. [Departamento de Fisica, DCI Campus Leon, Universidad de Guanajuato, Apdo. Postal E143, 37150 Leon, Gto. (Mexico); Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Gutierrez, M. Ranferi [Departamento de Fisica, DCI Campus Leon, Universidad de Guanajuato, Apdo. Postal E143, 37150 Leon, Gto. (Mexico)
2011-05-30
By using an alternative factorization, we obtain a self-adjoint oscillator operator of the form L{sub δ}=d/(dx) (p{sub δ}(x)d/(dx) )-((x{sup 2})/(p{sub δ}(x)) +p{sub δ}(x)-1), where p{sub δ}(x)=1+δe{sup -x{sup 2}}, with δ element of (-1,∞) an arbitrary real factorization parameter. At positive values of δ, this operator interpolates between the quantum harmonic oscillator Hamiltonian for δ=0 and a scaled Hermite operator at high values of δ. For the negative values of δ, the eigenfunctions look like deformed quantum mechanical Hermite functions. Possible applications are mentioned. -- Highlights: → We present a generalization of the Mielnik factorization. → We study the case of linear relationship between the factorization coefficients. → We introduce a new one-parameter self-adjoint oscillator operator. → We show its properties depending on the values of the parameter.
On the Self-adjointness of the Product Operators of Two mth-Order Differential Operators on [0, +∞)
Institute of Scientific and Technical Information of China (English)
Jian Ye AN; Jiong SUN
2004-01-01
In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, +∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.
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.
Adjoint-based optimization of flapping plates hinged with a trailing-edge flap
Directory of Open Access Journals (Sweden)
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.
Finite volume effects in SU(2) with two adjoint fermions
DEFF Research Database (Denmark)
Del Debbio, Luigi; Lucini, Biagio; Patella, Agostino;
2011-01-01
Many evidences from lattice simulations support the idea that SU(2) with two Dirac flavors in the adjoint representation (also called Minimal Walking Technicolor) is IR conformal. A possible way to see this is through the behavior of the spectrum of the mass-deformed theory. When fermions...... are massive, a mass-gap is generated and the theory is confined. IR-conformality is recovered in the chiral limit: masses of particles vanish in the chiral limit, while their ratios stay finite. In order to trust this analysis one has to relay on the infinite volume extrapolation. We will discuss the finite...... volume effects on the mesonic spectrum, investigated by varying the size of the lattice and by changing the boundary conditions for the fields....
Adjoint operators and perturbation theory of black holes
Cartas-Fuentevilla, R
2000-01-01
We present a new approach for finding conservation laws in the perturbation theory of black holes which applies for the more general cases of non-Hermitian equations governing the perturbations. The approach is based on a general result which establishes that a covariantly conserved current can be obtained from a solution of any system of homogeneous linear differential equations and a solution of the adjoint system. It is shown that the results obtained from the present approach become essentially the same (with some diferences) to those obtained by means of the traditional methods in the simplest black hole geometry corresponding to the Schwarzschild space-time. The future applications of our approach for studying the perturbations of black hole space-time in string theory is discussed.
Adjoint Fokker-Planck equation and runaway electron dynamics
Liu, Chang; Boozer, Allen H; Bhattacharjee, Amitava
2016-01-01
A new method to obtain the runaway probability and the expected slowing-down time for runaway electrons is developed, by solving the adjoint Fokker-Planck equation in momentum space. The runaway probability function has a smooth transition at the runaway separatrix, which can be attributed to the effect of the pitch angle scattering term in the kinetic equation. The expected slowing-down time gives a new way to estimate the runaway current decay time in experiments. The result shows that the decay rate of high energy electron is very slow when E is close to the critical electric field, which helps elucidate the hysteresis effect seen in the runaway electron population. Given the same numerical accuracy, the new method is more efficient than the Monte Carlo simulation.
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.
Directory of Open Access Journals (Sweden)
Mehdi Delkhosh
2012-01-01
Full Text Available Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011. In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefited from the solution of numerical Self-adjoint equations (Mohynl-Din, 2009; Allame and Azal, 2011; Borhanifar et al. 2011; Sweilam and Nagy, 2011; Gülsu et al. 2011; Mohyud-Din et al. 2010; and Li et al. 1996.
Global Regularity for Several Incompressible Fluid Models with Partial Dissipation
Wu, Jiahong; Xu, Xiaojing; Ye, Zhuan
2016-09-01
This paper examines the global regularity problem on several 2D incompressible fluid models with partial dissipation. They are the surface quasi-geostrophic (SQG) equation, the 2D Euler equation and the 2D Boussinesq equations. These are well-known models in fluid mechanics and geophysics. The fundamental issue of whether or not they are globally well-posed has attracted enormous attention. The corresponding models with partial dissipation may arise in physical circumstances when the dissipation varies in different directions. We show that the SQG equation with either horizontal or vertical dissipation always has global solutions. This is in sharp contrast with the inviscid SQG equation for which the global regularity problem remains outstandingly open. Although the 2D Euler is globally well-posed for sufficiently smooth data, the associated equations with partial dissipation no longer conserve the vorticity and the global regularity is not trivial. We are able to prove the global regularity for two partially dissipated Euler equations. Several global bounds are also obtained for a partially dissipated Boussinesq system.
Complete synchronization of chaotic atmospheric models by connecting only a subset of state space
Directory of Open Access Journals (Sweden)
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.
A SYSTEMATIC FORMULATION OF THE CONTINUOUS ADJOINT METHOD APPLIED TO VISCOUS AERODYNAMIC DESIGN
Directory of Open Access Journals (Sweden)
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.
Self-adjoint extensions of the Pauli equation in the presence of a magnetic monopole
Karat, E R; Karat, Edwin R; Schulz, Michael B
1996-01-01
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of a magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation.
Self-adjoint extensions of the Pauli equation in the presence of a magnetic monopole
International Nuclear Information System (INIS)
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
Energy Technology Data Exchange (ETDEWEB)
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
Cheng Yongcun; Lu Xianqing; Liu Yuguang; Xu Qing
2007-01-01
Considering the interaction of different tidal waves, an adjoint numerical model is developed to simulate M2, S2, K1 and O1 tidal waves in the Bohai Sea, the Yellow Sea and the East China Sea(B-Y-E) simultaneously. Compared with previous researches, by using the adjoint assimilation technique to inverse open boundary conditions and bottom friction coefficients based on altimetric data from TOPEX/Poseidon (T/P)and tidal gauges data, the precision of the numerical simulation is significantly improved. Selecting 14 days of simulated results after t11e initial warming run to conduct harmonic analysis, the results can show the characteristics of M2, S2, K1 and O1 tidal wave systems perfectly in B-Y-E. Compared with 9 current stations, the calculated harmonic constants of tidal currents for M2 and K1 are in good agreement With the observed ones.
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...
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.
2015-03-01
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space-time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge-Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
Energy Technology Data Exchange (ETDEWEB)
Vishnampet, Ramanathan [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Bodony, Daniel J. [Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Freund, Jonathan B., E-mail: jbfreund@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States)
2015-03-15
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that
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...
Fernández-López, Sheila; Carrera, Jesús; Ledo, Juanjo; Queralt, Pilar; Luquot, Linda; Martínez, Laura; Bellmunt, Fabián
2016-04-01
Seawater intrusion in aquifers is a complex phenomenon that can be characterized with the help of electric resistivity tomography (ERT) because of the low resistivity of seawater, which underlies the freshwater floating on top. The problem is complex because of the need for joint inversion of electrical and hydraulic (density dependent flow) data. Here we present an adjoint-state algorithm to treat electrical data. This method is a common technique to obtain derivatives of an objective function, depending on potentials with respect to model parameters. The main advantages of it are its simplicity in stationary problems and the reduction of computational cost respect others methodologies. The relationship between the concentration of chlorides and the resistivity values of the field is well known. Also, these resistivities are related to the values of potentials measured using ERT. Taking this into account, it will be possible to define the different resistivities zones from the field data of potential distribution using the basis of inverse problem. In this case, the studied zone is situated in Argentona (Baix Maresme, Catalonia), where the values of chlorides obtained in some wells of the zone are too high. The adjoint-state method will be used to invert the measured data using a new finite element code in C ++ language developed in an open-source framework called Kratos. Finally, the information obtained numerically with our code will be checked with the information obtained with other codes.
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.
The drag-adjoint field of a circular cylinder wake at Reynolds numbers 20, 100 and 500
Wang, Qiqi
2012-01-01
This paper analyzes the adjoint solution of the Navier-Stokes equation. We focus on flow across a circular cylinder at three Reynolds numbers, ReD = 20, 100 and 500. The objective function in the adjoint formulation is the drag on the cylinder. We use classical fluid mechanics approaches to analyze the adjoint solution, which is a vector field similar to a flow field. Production and dissipation of kinetic energy of the adjoint field is discussed. We also derive the evolution of circulation of the adjoint field along a closed material contour. These analytical results are used to explain three numerical solutions of the adjoint equations presented in this paper: The adjoint solution at ReD = 20, a viscous steady state flow, exhibits a downstream suction and an upstream jet, opposite of expected behavior of a flow field. The adjoint solution at ReD = 100, a periodic 2D unsteady flow, exhibits periodic, bean shaped circulation the near wake region. The adjoint solution at ReD = 500, a turbulent 3D unsteady flow,...
Haydock’s recursive solution of self-adjoint problems. Discrete spectrum
Energy Technology Data Exchange (ETDEWEB)
Moroz, Alexander, E-mail: wavescattering@yahoo.com
2014-12-15
Haydock’s recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber’s quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock’s recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials (p{sub n}(E)) in energy variable E. The polynomials (p{sub n}(E)) are orthonormal with respect to the density of states n{sub 0}(E) and energy eigenstate |E〉 is the generating function of (p{sub n}(E)). The generality of Haydock’s recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.
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
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
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.
Damage Detection of Bridges Using Vibration Data by Adjoint Variable Method
Directory of Open Access Journals (Sweden)
Akbar Mirzaee
2014-01-01
Full Text Available This research entails a theoretical and numerical study on a new damage detection method for bridges, using response sensitivity in time domain. This method, referred to as “adjoint variable method,” is a finite element model updating sensitivity based method. Governing equation of the bridge-vehicle system is established based on finite element formulation. In the inverse analysis, the new approach is presented to identify elemental flexural rigidity of the structure from acceleration responses of several measurement points. The computational cost of sensitivity matrix is the main concern associated with damage detection by these methods. The main advantage of the proposed method is the inclusion of an analytical method to augment the accuracy and speed of the solution. The reliable performance of the method to precisely identify the location and intensity of all types of predetermined single, multiple, and random damages over the whole domain of moving vehicle speed is shown. A comparison study is also carried out to demonstrate the relative effectiveness and upgraded performance of the proposed method in comparison to the similar ordinary sensitivity analysis methods. Moreover, various sources of errors including the effects of noise and primary errors on the numerical stability of the proposed method are discussed.
The adjoint method for general EEG and MEG sensor-based lead field equations
Energy Technology Data Exchange (ETDEWEB)
Vallaghe, Sylvain; Papadopoulo, Theodore; Clerc, Maureen [INRIA, Projet Odyssee, Sophia Antipolis (France)], E-mail: Sylvain.Vallaghe@sophia.inria.fr
2009-01-07
Most of the methods for the inverse source problem in electroencephalography (EEG) and magnetoencephalography (MEG) use a lead field as an input. The lead field is the function which relates any source in the brain to its measurements at the sensors. For complex geometries, there is no analytical formula of the lead field. The common approach is to numerically compute the value of the lead field for a finite number of point sources (dipoles). There are several drawbacks: the model of the source space is fixed (a set of dipoles), and the computation can be expensive for as much as 10 000 dipoles. The common idea to bypass these problems is to compute the lead field from a sensor point of view. In this paper, we use the adjoint method to derive general EEG and MEG sensor-based lead field equations. Within a simple framework, we provide a complete review of the explicit lead field equations, and we are able to extend these equations to non-pointlike sensors.
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
Directory of Open Access Journals (Sweden)
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 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.
Bucco, D.; Weiss, M.
2007-01-01
The COVariance and ADjoint Analysis Tool (COVAD) is a specially designed software tool, written for the Matlab/Simulink environment, which allows the user the capability to carry out system analysis and simulation using the adjoint, covariance or Monte Carlo methods. This paper describes phase one o
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.
Institute of Scientific and Technical Information of China (English)
DUAN Anmin; WU Guoxiong; LIANG Xiaoyun
2008-01-01
A series of numerical experiments are carried out by using the Spectral Atmospheric Model of State Key Laboratory of Numerical Modeling Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics (SAMIL) to investigate how the Tibetan Plateau (TP) mechanical and thermal forcing affect the circulation and climate patterns over subtropical Asia. It is shown that, compared to mechanical forcing, the thermal forcing of TP plays a dominant role in determining the large-scale circulation in summer. Both the sensible heating and the latent heating over TP tend to generate a surface cyclonic circulation and a gigantic anticyclonic circulation in the mid- and upper layers, whereas the direct effect of the latter is much more significant. Following a requirement of the time-mean quasi-geostrophic vorticity equation for large-scale air motion in the subtropics, convergent flow and vigorous ascending motion must appear to the east of TP. Hence the summer monsoon in East China is reinforced efficiently by TP. In contrast, the atmosphere to the west of TP is characterized by divergent flow and downward motion, which induces the arid climate in Mid-Asia.
International Nuclear Information System (INIS)
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
Dirac lattices, zero-range potentials, and self-adjoint extension
Bordag, M.; Muñoz-Castañeda, J. M.
2015-03-01
We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches handling these: the self-adjoint extension, regularization/renormalization and the zero range potential methods. Their close interrelations are discussed in detail and compared with the electrostatic approach which drops the contributions from the self fields. For a homogeneous two dimensional lattice of dipoles we write down the complete solutions, which allow, for example, for an easy numerical treatment of the scattering of the electromagnetic field on the lattice or for investigating plasmons. Using these formulas, we consider the limiting case of vanishing lattice spacing, i.e., the transition to a continuous sheet. For a scalar field and for the TE polarization of the electromagnetic field this transition is smooth and results in the results known from the continuous sheet. Especially for the TE polarization, we reproduce the results known from the hydrodynamic model describing a two dimensional electron gas. For the TM polarization, for polarizability parallel and perpendicular to the lattice, in both cases, the transition is singular. For the parallel polarizability this is surprising and different from the hydrodynamic model. For perpendicular polarizability this is what was known in literature. We also investigate the case when the transition is done with dipoles described by smeared delta function, i.e., keeping a regularization. Here, for TM polarization for parallel polarizability, when subsequently doing the limit of vanishing lattice spacing, we reproduce the result known from the hydrodynamic model. In case of perpendicular polarizability we need an additional renormalization to reproduce the result obtained previously by stepping back from the dipole approximation.
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 ...
Towards magnetic sounding of the Earth's core by an adjoint method
Li, K.; Jackson, A.; Livermore, P. W.
2013-12-01
Earth's magnetic field is generated and sustained by the so called geodynamo system in the core. Measurements of the geomagnetic field taken at the surface, downwards continued through the electrically insulating mantle to the core-mantle boundary (CMB), provide important constraints on the time evolution of the velocity, magnetic field and temperature anomaly in the fluid outer core. The aim of any study in data assimilation applied to the Earth's core is to produce a time-dependent model consistent with these observations [1]. Snapshots of these ``tuned" models provide a window through which the inner workings of the Earth's core, usually hidden from view, can be probed. We apply a variational data assimilation framework to an inertia-free magnetohydrodynamic system (MHD) [2]. Such a model is close to magnetostrophic balance [3], to which we have added viscosity to the dominant forces of Coriolis, pressure, Lorentz and buoyancy, believed to be a good approximation of the Earth's dynamo in the convective time scale. We chose to study the MHD system driven by a static temperature anomaly to mimic the actual inner working of Earth's dynamo system, avoiding at this stage the further complication of solving for the time dependent temperature field. At the heart of the models is a time-dependent magnetic field to which the core-flow is enslaved. In previous work we laid the foundation of the adjoint methodology, applied to a subset of the full equations [4]. As an intermediate step towards our ultimate vision of applying the techniques to a fully dynamic mode of the Earth's core tuned to geomagnetic observations, we present the intermediate step of applying the adjoint technique to the inertia-free Navier-Stokes equation in continuous form. We use synthetic observations derived from evolving a geophysically-reasonable magnetic field profile as the initial condition of our MHD system. Based on our study, we also propose several different strategies for accurately
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
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E. [Department of Physics, University of San Francisco, San Francisco, CA 94117-1080 (United States)]. E-mail: camblong@usfca.edu; Epele, Luis N. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Fanchiotti, Huner [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Garcia Canal, Carlos A. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Ordonez, Carlos R. [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States); World Laboratory Center for Pan-American Collaboration in Science and Technology, University of Houston Center, Houston, TX 77204-5506 (United States)
2007-05-14
A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian.
Blind range influence on guidance loop performance: An adjoint-based analysis
Bucco, D.; Weiss, M.
2013-01-01
In this paper, we investigate the use of adjoint simulation for assessing the miss distance performance of a generic guidance system under the influence of a blind range condition. The term "blind range" refers to that final portion of the missile trajectory for which sensor data are not available.
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.
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
Energy Technology Data Exchange (ETDEWEB)
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.
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.
DEFF Research Database (Denmark)
Pingen, Georg; Evgrafov, Anton; Maute, Kurt
2009-01-01
We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion...
International Nuclear Information System (INIS)
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
Stochastic flow modeling : Quasi-Geostrophy, Taylor state and torsional wave excitation
DEFF Research Database (Denmark)
Gillet, Nicolas; Jault, D.; Finlay, Chris
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...
Bretaudeau, F.; Metivier, L.; Brossier, R.; Virieux, J.
2013-12-01
Traveltime tomography algorithms generally use ray tracing. The use of rays in tomography may not be suitable for handling very large datasets and perform tomography in very complex media. Traveltime maps can be computed through finite-difference approach (FD) and avoid complex ray-tracing algorithm for the forward modeling (Vidale 1998, Zhao 2004). However, rays back-traced from receiver to source following the gradient of traveltime are still used to compute the Fréchet derivatives. As a consequence, the sensitivity information computed using back-traced rays is not numerically consistent with the FD modeling used (the derivatives are only a rough approximation of the true derivatives of the forward modeling). Leung & Quian (2006) proposed a new approach that avoid ray tracing where the gradient of the misfit function is computed using the adjoint-state method. An adjoint-state variable is thus computed simultaneously for all receivers using a numerical method consistent with the forward modeling, and for the computational cost of one forward modeling. However, in their formulation, the receivers have to be located at the boundary of the investigated model, and the optimization approach is limited to simple gradient-based method (i.e. steepest descent, conjugate gradient) as only the gradient is computed. However, the Hessian operator has an important role in gradient-based reconstruction methods, providing the necessary information to rescale the gradient, correct for illumination deficit and remove artifacts. Leung & Quian (2006) uses LBFGS, a quasi-Newton method that provides an improved estimation of the influence of the inverse Hessian. Lelievre et al. (2011) also proposed a tomography approach in which the Fréchet derivatives are computed directly during the forward modeling using explicit symbolic differentiation of the modeling equations, resulting in a consistent Gauss-Newton inversion. We are interested here in the use of a new optimization approach
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...
Energy Technology Data Exchange (ETDEWEB)
Yoo, S.; Henderson, D.L. [Dept. of Medical Physics, Madison, WI (United States); Thomadsen, B.R. [Dept. of Medical Physics and Dept. of Human Oncology, Madison (United States)
2001-07-01
Interstitial brachytherapy is a type of radiation in which radioactive sources are implanted directly into cancerous tissue. Determination of dose delivered to tissue by photons emitted from implanted seeds is an important step in the treatment plan process. In this paper we will investigate the use of the discrete ordinates method and the adjoint method to calculate absorbed dose in the regions of interest. MIP (mixed-integer programming) is used to determine the optimal seed distribution that conforms the prescribed dose to the tumor and delivers minimal dose to the sensitive structures. The patient treatment procedure consists of three steps: (1) image acquisition with the transrectal ultrasound (TRUS) and assessing the region of interest, (2) adjoint flux computation with discrete ordinate code for inverse dose calculation, and (3) optimization with the MIP branch-and-bound method.
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.
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.
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.
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
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.
Scattering and self-adjoint extensions of the Aharonov-Bohm Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
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.
The Adjoint Monte Carlo - a viable option for efficient radiotherapy treatment planning
International Nuclear Information System (INIS)
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)
Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
International Nuclear Information System (INIS)
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
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.
Adjoint representation of the graded Lie algebra osp(2/1; C) and its exponentiation
Ilyenko, K
2003-01-01
We construct explicitly the grade star Hermitian adjoint representation of osp(2/1; C) graded Lie algebra. Its proper Lie subalgebra, the even part of the graded Lie algebra osp(2/1; C), is given by su(2) compact Lie algebra. The Baker-Campbell-Hausdorff formula is considered and reality conditions for the Grassman-odd transformation parameters, which multiply the pair of odd generators of the graded Lie algebra, are clarified.
Methods of Monte Carlo biasing using two-dimensional discrete ordinates adjoint flux
Energy Technology Data Exchange (ETDEWEB)
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.
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.
Zhang, Lin; Shao, Jingyuan; Lu, Xiao; Zhao, Yuanhong; Hu, Yongyun; Henze, Daven K; Liao, Hong; Gong, Sunling; Zhang, Qiang
2016-08-16
The stringent emission controls during the APEC 2014 (the Asia-Pacific Economic Cooperation Summit; November 5-11, 2014) offer a unique opportunity to quantify factors affecting fine particulate matter (PM2.5) pollution over North China. Here we apply a four-dimensional variational data assimilation system using the adjoint model of GEOS-Chem to address this issue. Hourly surface measurements of PM2.5 and SO2 for October 15-November 14, 2014 are assimilated into the model to optimize daily aerosol primary and precursor emissions over North China. Measured PM2.5 concentrations in Beijing average 50.3 μg m(-3) during APEC, 43% lower than the mean concentration (88.2 μg m(-3)) for the whole period including APEC. Model results attribute about half of the reduction to meteorology due to active cold surge occurrences during APEC. Assimilation of surface measurements largely reduces the model biases and estimates 6%-30% lower aerosol emissions in the Beijing-Tianjin-Hebei region during APEC than in late October. We further demonstrate that high PM2.5 events in Beijing during this period can be occasionally contributed by natural mineral dust, but more events show large sensitivities to inorganic aerosol sources, particularly emissions of ammonia (NH3) and nitrogen oxides (NOx) reflecting strong formation of aerosol nitrate in the fall season. PMID:27434821
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.
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
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
Institute of Scientific and Technical Information of China (English)
WANG Caixia; Paola Malanotte-Rizzoli
2014-01-01
The linkage between physical and biological processes, particularly the effect of the circulation field on the distribution of phytoplankton, is studied by applying a two-dimensional model and an adjoint data assimilation approach to the Gulf of Maine-Georges Bank region. The model results, comparing well with observation data, reveal seasonal and geographic variations of phytoplankton concentration and verify that the seasonal cycles of phytoplankton are controlled by both biological sources and ad-vection processes which are functions of space and time and counterbalance each other. Although advective flux divergences have greater magnitudes on Georges Bank than in the coastal region of the western Gulf of Maine, advection control over phytoplankton concentration is more significant in the coastal region of the western Gulf of Maine. The model results also suggest that the two separated populations in the coastal regions of the western Gulf of Maine and on Georges Bank are self-sustaining.
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.
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.
Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds
Directory of Open Access Journals (Sweden)
T. Mine
2010-01-01
Full Text Available We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in terms of the boundary conditions. The result is an extension of the former results by Dabrowski-Šťoviček and Exner-Šťoviček-Vytřas.
Non-consistent approximations of self-adjoint eigenproblems: Application to the supercell method
Cancès, Eric; Maday, Yvon
2012-01-01
In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eigenvalues laying in spectral gaps. We first provide a priori error estimates on the eigenvalues and eigenvectors in the absence of spectral pollution. We then show that the supercell method for perturbed periodic Schr\\"odinger operators falls into the scope of our study. We prove that this method is spectral pollution free, and we derive optimal convergence rates for the planewave discretization method, taking numerical integration errors into account. Some numerical illustrations are provided.
One-loop adjoint masses for branes at non-supersymmetric angles
Anastasopoulos, P; Benakli, K; Goodsell, M D; Vichi, A
2012-01-01
This proceeding is based on arXiv:1110.5359 [hep-th] where 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 limits of N~4 and N~2 supersymmetric configurations, via messengers and their Kaluza-Klein excitations, and leads at leading order to tachyonic directions.
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.
Adjoint backtracking for the verification of the Comprehensive Test Ban Treaty
Directory of Open Access Journals (Sweden)
J.-P. Issartel
2002-11-01
Full Text Available An international monitoring system is being built as a verification tool for the Comprehensive Test Ban Treaty. Forty stations will measure on a worldwide daily basis the concentration of radioactive noble gases. The paper introduces, by handling preliminary real data, a new approach of backtracking for the identification of sources after positive measurements. When several measurements are available the ambiguity about possible sources is reduced significantly. As an interesting side result it is shown that diffusion in the passive tracer dispersion equation is necessarily a self-adjoint operator.
On Maximal Abelian Self-adjoint Subalgebras of Factors of Type Ⅱ1
Institute of Scientific and Technical Information of China (English)
Li Guang WANG
2005-01-01
In this note, we show that if (N) is a proper subfactor of a factor (M) of type Ⅱ1 with finite Jones index, then there is a maximal abelian self-adjoint subalgebra (masa) (A) of (N) that is not a masa in (M). Popa showed that there is a proper subfactor (R)O of the hyperfinite type Ⅱ1 factor (R) such that each masa in (R)O is also a masa in (R). We shall give a detailed proof of Popa's result.
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Nakshatrala, Praveen B.; Tortorelli, Daniel A.
2014-01-01
Gradient-based topology optimization typically involves thousands or millions of design variables. This makes efficient sensitivity analysis essential and for this the adjoint variable method (AVM) is indispensable. For transient problems it has been observed that the traditional AVM, based...... on a differentiate-then-discretize approach, may lead to inconsistent sensitivities. Herein this effect is explicitly demonstrated for a single dof system and the source of inconsistency is identified. Additionally, we outline an alternative discretize-then-differentiate AVM that inherently produces consistent...
Diagonalization of a self-adjoint operator acting on a Hilbert module
Directory of Open Access Journals (Sweden)
Parfeny P. Saworotnow
1985-01-01
Full Text Available For each bounded self-adjoint operator T on a Hilbert module H over an H*-algebra A there exists a locally compact space m and a certain A-valued measure μ such that H is isomorphic to L2(μ⊗A and T corresponds to a multiplication with a continuous function. There is a similar result for a commuting family of normal operators. A consequence for this result is a representation theorem for generalized stationary processes.
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Energy Technology Data Exchange (ETDEWEB)
Galanti, Eli; Kaspi, Yohai, E-mail: eli.galanti@weizmann.ac.il [Weizmann Institute of Science, Rehovot (Israel)
2016-04-01
During 2016–17, the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. These data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus only allowing the calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model is developed to relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for the examination of various scenarios, simulating cases in which the depth of the wind depends on latitude. We show that it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn, also taking into account measurement errors. Calculating the solution uncertainties, we show that the wind depth can be determined more precisely in the low-to-mid-latitudes. In addition, the gravitational moments are found to be particularly sensitive to flows at the equatorial intermediate depths. Therefore, we expect that if deep winds exist on these planets they will have a measurable signature by Juno and Cassini.
Duivesteijn, G.F.; Bijl, H.; Koren, B.; Brummelen, E.H. van
2005-01-01
This work compares a numerical and analytical adjoint equation method with respect to boundary condition treatments applied to the quasi-1D Euler equations. The effect of strong and weak boundary conditions and the effect of flux evaluators on the numerical adjoint solution near the boundaries are d
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.
Ibort, A
2012-01-01
In these three lectures we will discuss some fundamental aspects of the theory of self-adjoint extensions of the covariant Laplace-Beltrami and Dirac operators on compact Riemannian manifolds with smooth boundary emphasizing the relation with the theory of global boundary conditions. Self-adjoint extensions of symmetric operators, specially of the Laplace-Beltrami and Dirac operators, are fundamental in Quantum Physics as they determine either the energy of quantum systems and/or their unitary evolution. The well-known von Neumann's theory of self-adjoint extensions of symmetric operators is not always easily applicable to differential operators, while the description of extensions in terms of boundary conditions constitutes a more natural approach. Thus an effort is done in offering a description of self-adjoint extensions in terms of global boundary conditions showing how an important family of self-adjoint extensions for the Laplace-Beltrami and Dirac operators are easily describable in this way. Moreover ...
Aerodynamic Optimization of the Nose Shape of a Train Using the Adjoint Method
Directory of Open Access Journals (Sweden)
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.
Radiation source reconstruction with known geometry and materials using the adjoint
Energy Technology Data Exchange (ETDEWEB)
Hykes, Joshua M.; Azmy, Yousry Y., E-mail: jmhykes@ncsu.edu, E-mail: yyazmy@ncsu.gov [Department of Nuclear Engineering, North Carolina State University, Raleigh, NC (United States)
2011-07-01
We present a method to estimate an unknown isotropic source distribution, in space and energy, using detector measurements when the geometry and material composition are known. The estimated source distribution minimizes the difference between the measured and computed responses of detectors located at a selected number of points within the domain. In typical methods, a forward flux calculation is performed for each source guess in an iterative process. In contrast, we use the adjoint flux to compute the responses. Potential applications of the proposed method include determining the distribution of radio-contaminants following a nuclear event, monitoring the flow of radioactive fluids in pipes to determine hold-up locations, and retroactive reconstruction of radiation fields using workers' detectors' readings. After presenting the method, we describe a numerical test problem to demonstrate the preliminary viability of the method. As expected, using the adjoint flux reduces the number of transport solves to be proportional to the number of detector measurements, in contrast to methods using the forward flux that require a typically larger number proportional to the number of spatial mesh cells. (author)
Energy Technology Data Exchange (ETDEWEB)
Abhyankar, Shrirang [Argonne National Lab. (ANL), Argonne, IL (United States); Anitescu, Mihai [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil [Argonne National Lab. (ANL), Argonne, IL (United States); Zhang, Hong [Argonne National Lab. (ANL), Argonne, IL (United States)
2016-03-31
Sensitivity analysis is an important tool to describe power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this work, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating trajectory sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as DC exciters, by deriving and implementing the adjoint jump conditions that arise from state and time-dependent discontinuities. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach.
A generalized albedo option for forward and adjoint Monte Carlo calculations
International Nuclear Information System (INIS)
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
Yu, Jia; Ji, Lucheng; Li, Weiwei; Yi, Weilin
2016-06-01
Adjoint method is an important tool for design refinement of multistage compressors. However, the radial static pressure distribution deviates during the optimization procedure and deteriorates the overall performance, producing final designs that are not well suited for realistic engineering applications. In previous development work on multistage turbomachinery blade optimization using adjoint method and thin shear-layer N-S equations, the entropy production is selected as the objective function with given mass flow rate and total pressure ratio as imposed constraints. The radial static pressure distribution at the interfaces between rows is introduced as a new constraint in the present paper. The approach is applied to the redesign of a five-stage axial compressor, and the results obtained with and without the constraint on the radial static pressure distribution at the interfaces between rows are discussed in detail. The results show that the redesign without the radial static pressure distribution constraint (RSPDC) gives an optimal solution that shows deviations on radial static pressure distribution, especially at rotor exit tip region. On the other hand, the redesign with the RSPDC successfully keeps the radial static pressure distribution at the interfaces between rows and make sure that the optimization results are applicable in a practical engineering design.
Radiation source reconstruction with known geometry and materials using the adjoint
International Nuclear Information System (INIS)
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)
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.
Adjoint sensitivity theory for steady-state ground-water flow
International Nuclear Information System (INIS)
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
Energy Technology Data Exchange (ETDEWEB)
Fadin, V.S. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Budker Nuclear Physics Institute, Novosibirsk (Russian Federation); Novosibirskij Gosudarstvennyj Univ., Novosibirsk (Russian Federation); Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); St. Petersburg State Univ., Gatchina (Russian Federation)
2011-12-15
We calculate the eigenvalues of the next-to-leading kernel for the BFKL equation in the adjoint representation of the gauge group SU(N{sub c}) in the N=4 supersymmetric Yang-Mills model. These eigenvalues are used to obtain the high energy behavior of the remainder function for the 6-point scattering amplitude with the maximal helicity violation in the kinematical regions containing the Mandelstam cut contribution. The leading and next-to-leading singularities of the corresponding collinear anomalous dimension are calculated in all orders of perturbation theory. We compare our result with the known collinear limit and with the recently suggested ansatz for the remainder function in three loops and obtain the full agreement providing that the numerical parameters in this anzatz are chosen in an appropriate way.
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.
DEFF Research Database (Denmark)
Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland;
2014-01-01
, in the case of classical low-order FE methods, we show numerically that we achieve long-time stability for both forward and adjoint problems both for the convolution and the ADE formulations. In the case of higher order Legendre spectral-element methods, we show that weak numerical instabilities can appear...
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.
Directory of Open Access Journals (Sweden)
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.
Lemke, Mathias; Reiss, Julius; Sesterhenn, Jörn
2016-06-01
Particle image velocimetry (PIV) is one of the major tools to measure velocity fields in experiments. However, other flow properties like density or pressure are often of vital interest, but usually cannot be measured non-intrusively. There are many approaches to overcome this problem, but none is fully satisfactory. Here the computational method of an adjoint based data assimilation for this purpose is discussed. A numerical simulation of a flow is adapted to given velocity data. After successful adaption, previously unknown quantities can be taken from the - necessarily complete - simulation data. The main focus of this work is the efficient implementation of this approach by boundary driven optimisation. Synthetic test cases are presented to allow an assessment of the method.
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.
Adjoint Variable Method for the Study of Combined Active and Passive Magnetic Shielding
Directory of Open Access Journals (Sweden)
Peter Sergeant
2008-01-01
Full Text Available For shielding applications that cannot sufficiently be shielded by only a passive shield, it is useful to combine a passive and an active shield. Indeed, the latter does the “finetuning” of the field reduction that is mainly caused by the passive shield. The design requires the optimization of the geometry of the passive shield, the position of all coils of the active shield, and the real and imaginary components of the currents (when working in the frequency domain. As there are many variables, the computational effort for the optimization becomes huge. An optimization using genetic algorithms is compared with a classical gradient optimization and with a design sensitivity approach that uses an adjoint system. Several types of active and/or passive shields with constraints are designed. For each type, the optimization was carried out by all three techniques in order to compare them concerning CPU time and accuracy.
Chiba, G.; Tsuji, M.; Narabayashi, T.
2014-04-01
In order to better predict a kinetic behavior of a nuclear fission reactor, an improvement of the delayed neutron parameters is essential. The present paper specifies important nuclear data for a reactor kinetics: Fission yield and decay constant data of 86Ge, some bromine isotopes, 94Rb, 98mY and some iodine isotopes. Their importance is quantified as sensitivities with a help of the adjoint kinetic equation, and it is found that they are dependent on an inserted reactivity (or a reactor period). Moreover, dependence of sensitivities on nuclear data files is also quantified using the latest files. Even though the currently evaluated data are used, there are large differences among different data files from a view point of the delayed neutrons.
One-loop adjoint masses for non-supersymmetric intersecting branes
Anastasopoulos, P; Benakli, K; Goodsell, M D; Vichi, A
2011-01-01
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 broken N=4 and N=2 supersymmetric configurations, and thus always leads at leading order to a tachyonic direction, in agreement with effective field theory expectations.
Partial breakdown of center symmetry in large-N QCD with adjoint Wilson fermions
Bringoltz, Barak
2009-01-01
We study the one-loop potential of large-N QCD with adjoint Dirac fermions. Space-time is a discretization of R^3 x S^1 where the compact direction consists of a single lattice site. We use Wilson fermions with different values of the quark mass m and set the lattice spacings in the compact and non-compact directions to be a_t and a_s respectively. Extending the results of JHEP 0906:091,2009, we prove that if the ratio xi = a_s/a_t obeys 0> 1, while for large masses K ~ O(1). Despite certain UV sensitivities of the lattice one-loop potential, this phase structure is similar to the one obtained in the continuum works of Kovtun-Unsal-Yaffe, Myers-Ogilvie, and Hollowood-Myers. We explain the physical origin of the cascade of transitions and its relation to the embedding of space-time into color space.
International Nuclear Information System (INIS)
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.
Spectral properties and self-adjoint extensions of the third power of the radial Laplace operator
Bolokhov, T A
2014-01-01
We consider self-adjoint extensions of differential operators of the type $ (-\\frac{d^2}{dr^2} + \\frac{l(l+1)}{r^2})^3 $ on the real semi-axis for l=1,2 with two kinds of boundary conditions: first that nullify the value of a function and its first derivative and second that nullify the 4th (l=1) or the 3rd (l=2) derivative. We calculate the expressions for the correponding resolvents and derive spectral decompositions. These types of boundary conditions are interesting from the physical point of view, especially the second ones, which give an example of emergence of long-range action in exchange for a singularity at the origin.
The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours
Bergner, Georg; Montvay, Istvan; Münster, Gernot; Piemonte, Stefano
2016-01-01
In this work we present the results of our investigation of SU(2) gauge theory with two Dirac fermions in the adjoint representation, also known as Minimal Walking Technicolour. We have done numerical lattice simulations of this theory at two different values of the gauge coupling and several fermion masses. Our results include the particle spectrum and the mass anomalous dimension. The spectrum contains so far unconsidered states, a fermion-gluon state and flavour singlet mesons. The mass anomalous dimension is determined from the scaling of the masses and the mode number. The remnant dependence of the universal mass ratios and mass anomalous dimension on the gauge coupling indicates the relevance of scaling corrections.
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.
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...
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.
Multi-objective optimization strategies using adjoint method and game theory in aerodynamics
Institute of Scientific and Technical Information of China (English)
Zhili Tang
2006-01-01
There are currently three different game strategies originated in economics:(1) Cooperative games (Pareto front),(2)Competitive games (Nash game) and (3)Hierarchical games (Stackelberg game).Each game achieves different equilibria with different performance,and their players play different roles in the games.Here,we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multicriteria aerodynamic optimization problems.The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments.We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method.The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front.Non-dominated Pareto front solutions are obtained,however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.
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...
One-loop adjoint masses for non-supersymmetric intersecting branes
Energy Technology Data Exchange (ETDEWEB)
Anastasopoulos, P. [Technische Univ., Vienna (Austria). 1. Inst. fuer Theoretische Physik; Antoniadis, I. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Benakli, K. [CNRS, UPMC Univ. Paris (France). Lab. de Physique Theorique et Haute Energies; Goodsell, M.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Vichi, A. [Institute de Theorie des Phenomenes Physiques, EPFL, Lausanne (Switzerland)
2011-05-15
We consider breaking of supersymmetry in intersecting D-brane configurations by slight deviation of the angles from their supersymmetric values. We compute the masses generated by radiative corrections for the adjoint scalars on the brane world-volumes. In the open string channel, the string two-point function receives contributions only from the infrared and the ultraviolet limits. The latter is due to tree-level closed string uncanceled NS-NS tadpoles, which we explicitly reproduce from the effective Born-Infeld action. On the other hand, the infrared region reproduces the one-loop mediation of supersymmetry breaking in the effective gauge theory, via messengers and their Kaluza-Klein excitations. In the toroidal set-up considered here, it receives contributions only from N {approx} 4 and N {approx} 2 supersymmetric configurations, and thus always leads at leading order to a tachyonic direction, in agreement with effective field theory expectations. (orig.)
Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators
Directory of Open Access Journals (Sweden)
Wen Zhang
2014-01-01
Full Text Available Let A1 and A2 be standard real Jordan algebras of self-adjoint operators on complex Hilbert spaces H1 and H2, respectively. For k≥2, let (i1,…,im be a fixed sequence with i1,…,im∈{1,…,k} and assume that at least one of the terms in (i1,…,im appears exactly once. Define the generalized Jordan product T1∘T2∘⋯∘Tk=Ti1Ti2⋯Tim+Tim⋯Ti2Ti1 on elements in Ai. Let Φ:A1→A2 be a map with the range containing all rank-one projections and trace zero-rank two self-adjoint operators. We show that Φ satisfies that σπ(Φ(A1∘⋯∘Φ(Ak=σπ(A1∘⋯∘Ak for all A1,…,Ak, where σπ(A stands for the peripheral spectrum of A, if and only if there exist a scalar c∈{-1,1} and a unitary operator U:H1→H2 such that Φ(A=cUAU* for all A∈A1, or Φ(A=cUAtU* for all A∈A1, where At is the transpose of A for an arbitrarily fixed orthonormal basis of H1. Moreover, c=1 whenever m is odd.
Near-horizon states of black holes and Calogero models
Indian Academy of Sciences (India)
B Basu-Mallick; Pijush K Ghosh; Kumar S Gupta
2004-03-01
We find self-adjoint extensions of the rational Calogero model in the presence of the harmonic interaction. The corresponding eigenfunctions may describe the near-horizon quantum states of certain types of black holes.
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.
Mineev, V S
2003-01-01
In the paper the one-dimensional one-center scattering problem with the initial potential $\\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as necessary conditions in the singular point alongside with account of the analytical structure of fundamental solutions, it allows us to receive exact expressions for the wave functions (i.e. for the boundary conditions), scattering coefficients and the singular corrections to the potential, as well as the corresponding bound state spectrum. It turns out that the point $\\delta$-shaped correction to the potential should be present without fail at any choice of the allowable self-adjoint extension, moreover a form of these corrections corresponds to the form of renormalization terms obtained in quantum electrodynamics. Thus, the proposed method shows the unequivocal connection among the boundary conditions, scattering coefficients and $\\delta$-shaped additions to the potential. Ta...
Directory of Open Access Journals (Sweden)
K. C. Wells
2015-07-01
Full Text Available We describe a new 4D-Var inversion framework for N2O based on the GEOS-Chem chemical transport model and its adjoint, and apply this framework in a series of observing system simulation experiments to assess how well N2O sources and sinks can be constrained by the current global observing network. The employed measurement ensemble includes approximately weekly and quasi-continuous N2O measurements (hourly averages used from several long-term monitoring networks, N2O measurements collected from discrete air samples aboard a commercial aircraft (CARIBIC, and quasi-continuous measurements from an airborne pole-to-pole sampling campaign (HIPPO. For a two-year inversion, we find that the surface and HIPPO observations can accurately resolve a uniform bias in emissions during the first year; CARIBIC data provide a somewhat weaker constraint. Variable emission errors are much more difficult to resolve given the long lifetime of N2O, and major parts of the world lack significant constraints on the seasonal cycle of fluxes. Current observations can largely correct a global bias in the stratospheric sink of N2O if emissions are known, but do not provide information on the temporal and spatial distribution of the sink. However, for the more realistic scenario where source and sink are both uncertain, we find that simultaneously optimizing both would require unrealistically small errors in model transport. Regardless, a bias in the magnitude of the N2O sink would not affect the a posteriori N2O emissions for the two-year timescale used here, given realistic initial conditions, due to the timescale required for stratosphere–troposphere exchange (STE. The same does not apply to model errors in the rate of STE itself, which we show exerts a larger influence on the tropospheric burden of N2O than does the chemical loss rate over short (2O emissions. There, averaging kernels are highly smeared spatially and extend even to the midlatitudes, so that tropical
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.
Curvature Theory for Point-Path and Plane-Envelope in Spherical Kinematics by New Adjoint Approach
Institute of Scientific and Technical Information of China (English)
WANG Wei; WANG Delun
2014-01-01
Planar kinematics has been studied systematically based on centrodes, however axodes are underutilized to set up the curvature theories in spherical and spatial kinematics. Through a spherical adjoint approach, an axode-based theoretical system of spherical kinematics is established. The spherical motion is re-described by the adjoint approach and vector equation of spherical instant center is concisely derived. The moving and fixed axodes for spherical motion are mapped onto a unit sphere to obtain spherical centrodes, whose kinematic invariants totally reflect the intrinsic property of spherical motion. Based on the spherical centrodes, the curvature theories for a point and a plane of a rigid body in spherical motion are revealed by spherical fixed point and plane conditions. The Euler-Savary analogue for point-path is presented. Tracing points with higher order curvature features are located in the moving body by means of algebraic equations. For plane-envelope, the construction parameters are obtained. The osculating conditions for plane-envelope and circular cylindrical surface or circular conical surface are given. A spherical four-bar linkage is taken as an example to demonstrate the spherical adjoint approach and the curvature theories. The research proposes systematic spherical curvature theories with the axode as logical starting-point, and sets up a bridge from the centrode-based planar kinematics to the axode-based spatial kinematics.
Adjoint-based shape optimization of fin geometry for enhanced solid/liquid phase-change process
Morimoto, Kenichi; Suzuki, Yuji
2015-11-01
In recent years, the control of heat transfer processes, which play a critical role in various engineering devices/systems, has gained renewed attention. The present study aims to establish an adjoint-based shape optimization method for high-performance heat transfer processes involving phase-change phenomena. A possible example includes the application to the thermal management technique using phase-change material. Adjoint-based shape optimization scheme is useful to optimal shape design and optimal control of systems, for which the base function of the solution is unknown and the solution includes an infinite number of degrees of freedom. Here we formulate the shape-optimization scheme based on adjoint heat conduction analyses, focusing on the shape optimization of fin geometry. In the computation of the developed scheme, a meshless local Petrov-Galerkin (MLPG) method that is suited for dealing with complex boundary geometry is employed, and the enthalpy method is adopted for analyzing the motion of the phase-change interface. We examine in detail the effect of the initial geometry and the node distribution in the MLPG analysis upon the final solution of the shape optimization. Also, we present a new strategy for the computation using bubble mesh.
Sensitivity analysis for solid oxide fuel cells using a three-dimensional numerical model
Energy Technology Data Exchange (ETDEWEB)
Kapadia, S.; Anderson, W.K. [University of Tennessee SimCenter at Chattanooga, 701, East M.L. King Boulevard, Chattanooga, TN 37403 (United States)
2009-04-15
A three-dimensional numerical solver is developed to model complex transport processes inside all components of a solid oxide fuel cell (SOFC). An initial assessment of the accuracy of the model is made by comparing a numerically generated polarization curve with experimental results. Sensitivity derivatives of objective functions representing the cell voltage and the concentration polarization are obtained with respect to the material properties of the anode and the cathode using discrete adjoint method. Implementation of the discrete adjoint method is validated by comparing sensitivity derivatives obtained using the adjoint technique with results obtained using direct-differentiation and finite-difference methods. (author)
Discrete SLn-connections and self-adjoint difference operators on 2-dimensional manifolds
Grinevich, P. G.; Novikov, S. P.
2013-10-01
The programme of discretization of famous completely integrable systems and associated linear operators was launched in the 1990s. In particular, the properties of second-order difference operators on triangulated manifolds and equilateral triangular lattices have been studied by Novikov and Dynnikov since 1996. This study included Laplace transformations, new discretizations of complex analysis, and new discretizations of 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.
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...
Komatitsch, Dimitri
2016-06-13
We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.
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...
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.
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...
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.
International Nuclear Information System (INIS)
The activation probe is a robust tool to measure flux of fusion products from a magnetically confined plasma. A carefully chosen solid sample is exposed to the flux, and the impinging ions transmute the material making it radioactive. Ultra-low level gamma-ray spectroscopy is used post mortem to measure the activity and, thus, the number of fusion products. This contribution presents the numerical analysis of the first measurement in the ASDEX Upgrade tokamak, which was also the first experiment to measure a single discharge. The ASCOT suite of codes was used to perform adjoint/reverse Monte Carlo calculations of the fusion products. The analysis facilitates, for the first time, a comparison of numerical and experimental values for absolutely calibrated flux. The results agree to within a factor of about two, which can be considered a quite good result considering the fact that all features of the plasma cannot be accounted in the simulations.Also an alternative to the present probe orientation was studied. The results suggest that a better optimized orientation could measure the flux from a significantly larger part of the plasma. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
Adjoint $QCD_{1+1}$ in Light-cone Gauge, Quantized at Equal Time
Vianello, E
2004-01-01
SU(2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with "twisted" boundary conditions, periodic for one color component (the diagonal 3- component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-color component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the fr...
Nonperturbative Effects from Perturbation Theory in Adjoint QCD_{1+1}
Vianello, E
2004-01-01
SU(2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with "twisted" boundary conditions, periodic for one colour component (the diagonal 3- component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-colour component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the ...
Sikarwar, Nidhi
multiple experiments or numerical simulations. Alternatively an inverse design method can be used. An adjoint optimization method can be used to achieve the optimum blowing rate. It is shown that the method works for both geometry optimization and active control of the flow in order to deflect the flow in desirable ways. An adjoint optimization method is described. It is used to determine the blowing distribution in the diverging section of a convergent-divergent nozzle that gives a desired pressure distribution in the nozzle. Both the direct and adjoint problems and their associated boundary conditions are developed. The adjoint method is used to determine the blowing distribution required to minimize the shock strength in the nozzle to achieve a known target pressure and to achieve close to an ideally expanded flow pressure. A multi-block structured solver is developed to calculate the flow solution and associated adjoint variables. Two and three-dimensional calculations are performed for internal and external of the nozzle domains. A two step MacCormack scheme based on predictor- corrector technique is was used for some calculations. The four and five stage Runge-Kutta schemes are also used to artificially march in time. A modified Runge-Kutta scheme is used to accelerate the convergence to a steady state. Second order artificial dissipation has been added to stabilize the calculations. The steepest decent method has been used for the optimization of the blowing velocity after the gradients of the cost function with respect to the blowing velocity are calculated using adjoint method. Several examples are given of the optimization of blowing using the adjoint method.
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.
International Nuclear Information System (INIS)
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
Virieux, J.; Bretaudeau, F.; Metivier, L.; Brossier, R.
2013-12-01
Simultaneous inversion of seismic velocities and source parameters have been a long standing challenge in seismology since the first attempts to mitigate trade-off between very different parameters influencing travel-times (Spencer and Gubbins 1980, Pavlis and Booker 1980) since the early development in the 1970s (Aki et al 1976, Aki and Lee 1976, Crosson 1976). There is a strong trade-off between earthquake source positions, initial times and velocities during the tomographic inversion: mitigating these trade-offs is usually carried empirically (Lemeur et al 1997). This procedure is not optimal and may lead to errors in the velocity reconstruction as well as in the source localization. For a better simultaneous estimation of such multi-parametric reconstruction problem, one may take benefit of improved local optimization such as full Newton method where the Hessian influence helps balancing between different physical parameter quantities and improving the coverage at the point of reconstruction. Unfortunately, the computation of the full Hessian operator is not easily computed in large models and with large datasets. Truncated Newton (TCN) is an alternative optimization approach (Métivier et al. 2012) that allows resolution of the normal equation H Δm = - g using a matrix-free conjugate gradient algorithm. It only requires to be able to compute the gradient of the misfit function and Hessian-vector products. Traveltime maps can be computed in the whole domain by numerical modeling (Vidale 1998, Zhao 2004). The gradient and the Hessian-vector products for velocities can be computed without ray-tracing using 1st and 2nd order adjoint-state methods for the cost of 1 and 2 additional modeling step (Plessix 2006, Métivier et al. 2012). Reciprocity allows to compute accurately the gradient and the full Hessian for each coordinates of the sources and for their initial times. Then the resolution of the problem is done through two nested loops. The model update Δm is
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...
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
Directory of Open Access Journals (Sweden)
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
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
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
Institute of Scientific and Technical Information of China (English)
王兴涛
2002-01-01
Control equation and adjoint equation are established by using block-pulse functions, which trans-forms the linear time-varying systems with time delays into a system of algebraic equations and the optimal con-trol problems are transformed into an optimization problem of multivariate functions thereby achieving the opti-mal control of linear systems with time delays.
Morency, C.; Tromp, J.
2008-12-01
successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.
Mullen, Steven L.
1986-07-01
Blocking anticyclones that appear in perpetual January simulations of a spectral general circulation model are examined. Blocks in three geographical regions are studied: the North Pacific, the North Atlantic and western North America. Local time-averaged balances of vorticity and heat are evaluated for composite cases of blocking. The following common relationships emerged from these budgets.The time-mean divergence term is, in general, a flat-order term in the vorticity balance throughout the troposphere and its pattern over severe orography is closely related to the underlying topography. Above the surface layer, the horizontal advection of time-mean absolute vorticity by the mean wind mainly balances the divergence term with the net effect of the time-mean vorticity forcing being a tendency for the blocking pattern to propagate downstream. The transient eddy vorticity transports act to shift the block upstream and hence they mainly offset the downstream tendency due to the time-mean flow; the magnitude of the eddy vorticity term is typically one-third to one-half that of the divergence or advection terms alone. Frictional dissipation is negligible everywhere except near the ground where it primarily offsets the divergence term.The horizontal advection of the time-mean temperature field by the mean wind throughout the troposphere is a first-order term in the beat balance and is mainly responsible for maintaining the block's thermal perturbations; it is predominately balanced by adiabatic heating in the free troposphere and by diabatic heating near the surface. Transient eddy heat transports act to dissipate the block's thermal perturbations at all levels, while diabatic heating does not exhibit a systematic relationship with the temperature field at any level.A quasi-geostrophic diagnosis of the ageostrophic motion field suggests that dynamical processes which strongly affect the vorticity balance may be more important to the maintenance of model blocks than
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.
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.
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
Energy Technology Data Exchange (ETDEWEB)
C. O. Slater; J. M. Barnes; J. O. Johnson; J.D. Drischler
1998-10-01
The Monte Carlo ~djoint ~ielding Code System, MASH, calculates neutron and gamma- ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air- over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system includes the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. The current version, MASH v 1.5, is the successor to the original MASH v 1.0 code system initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the "dose importance" of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response as a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem.
International Nuclear Information System (INIS)
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.)
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
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...
Energy Technology Data Exchange (ETDEWEB)
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.
Nonlinear Model Predictive Control for Oil Reservoirs Management
DEFF Research Database (Denmark)
Capolei, Andrea
, the research community is working on improving current feedback model-based optimal control technologies. The topic of this thesis is production optimization for water flooding in the secondary phase of oil recovery. We developed numerical methods for nonlinear model predictive control (NMPC) of an oil field...... gradient-based optimization and the required gradients are computed by the adjoint method. We propose the use of efficient high order implicit time integration methods for the solution of the forward and the adjoint equations of the dynamical model. The Ensemble Kalman filter is used for data assimilation...... expensive gradient computation by using high-order ESDIRK (Explicit Singly Diagonally Implicit Runge-Kutta) temporal integration methods and continuous adjoints. The high order integration scheme allows larger time steps and therefore faster solution times. We compare gradient computation by the continuous...
Krejcirik, D; Zelezny, J
2011-01-01
We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.
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.
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...
Directory of Open Access Journals (Sweden)
Vjacheslav Yurko
2011-08-01
Full Text Available Non-self-adjoint Sturm-Liouville differential operators on the half-line with a boundary condition depending polynomially on the spectral parameter are studied. We investigate the inverse problem of recovering the operator from the Weyl function. For this inverse problem we provide necessary and suffcient conditions for its solvability along with a procedure for constructing its solution by the method of spectral mappings.
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 ...
Veneziani, M.; Edwards, C.; Moore, A.
2008-12-01
We use the Regional Ocean Modeling System (ROMS) to model the circulation of the California Current System (CCS) using ECCO-GODAE products to force the model at the open boundaries of the domain. We investigate the impact that lateral boundary forcing (and the boundary region in general) has on particular metrics of the interior circulation by adopting both an adjoint model and a traditional sensitivity approach. Adjoint methods are naturally suited to sensitivity studies as they provide the direct dependencies of circulation metrics on uncertainties of the model initial conditions, surface and lateral external forcing, and model parameters, but their results are only valid within the time scale during which the linearity assumption underlying adjoint models can be considered to hold. More traditional sensitivity studies must be conducted to investigate longer time scales. We describe the adjoint model results for two metrics that represent the upwelling processes of the Central California region and the mean sea level field of the coastal circulation, respectively. The spatial distribution of the adjoint sensitivity fields allows us to quantify the contribution of the boundary regions over a biweekly time scale. We investigate longer time scales by adopting two methods: 1) apply different ECCO products at the open boundaries and evaluate mean stratification changes in the CalCOFI coastal region; 2) release passive tracers at the boundaries and calculate ventilation time scales and pathways from the boundary areas to the CCS interior.
Smith, P. J.
1985-01-01
An important component of the research was a continuing investigation of the impact of latent release on extratropical cyclone development. Previous efforts to accomplish this task have focused on the energy balance and the vertical motion field of an intense winter extratropical cyclone over the United States. During this fiscal year researchers turned their attention to a more fundamental diagnostic variable, the height tendency. Central to this effort is the use of a modified form of the quasi-geostrophic height tendency equation, in which geostrophic wind components have been replaced by observed winds and a latent heat release term has been added. This methodology was adopted to produce a simple diagnostic model which retains the essential mechanisms of quasi-geostrophic theory but more faithfully describes observed wave development when the Rossby Number approaches and exceeds 0.5. Results to date indicate that the new model yields height tendencies that are superior to those obtained from the quasi-geostrophic formulation and are sufficiently close to the observed tendencies to be a useful tool for diagnosing the principle large-scale forcing mechanisms in th e700-300 mb layer. Of the three forcing terms included in the new model, vortity advection is in general dominant. The most persistent challenge to this dominance is made by the thermal advection. On the whole, latent heat release plays a secondary role. Finally, during the rapid intensification observed for this cyclone, all three processes complement each other in forcing height falls.
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.
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 ...
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
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
Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir
DEFF Research Database (Denmark)
Capolei, Andrea; Völcker, Carsten; Frydendall, Jan;
2012-01-01
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 i...... for sensitivity computation. We demonstrate the procedure on a water ooding example with conventional injectors and producers....
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...
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.
MCRG study of 12 fundamental flavors with mixed fundamental-adjoint gauge action
Hasenfratz, Anna
2011-01-01
I discuss the infrared behavior of the SU(3) gauge model with 12 fundamental fermions. Using a Monte Carlo renormalization group technique I investigate the fixed point structure in the chiral limit and show that this system has an infrared fixed point and consequently conformal infrared dynamics. I am able to reach the FP by using a new analysis method for the 2-lattice matching MCRG technique that significantly reduces finite volume effects and by choosing a lattice action that avoids a spurious ultraviolet fixed point created by strong coupling lattice artifacts.
Martin, William G.; Cairns, Brian; Bal, Guillaume
2014-01-01
This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth?s atmosphere.
Energy Technology Data Exchange (ETDEWEB)
Fadin, V.S. [Budker Institute of Nuclear Physics, SD RAS, Novosibirsk (Russian Federation); Novosibirsk State University, Novosibirsk (Russian Federation); Fiore, R. [Universita della Calabria, Dipartimento di Fisica, Cosenza (Italy); Istituto Nazionale di Fisica, Nucleare Gruppo Collegato di Cosenza (Italy)
2016-05-15
We analyze a modification of the BFKL kernel for the adjoint representation of the color group in the maximally supersymmetric (N = 4) Yang-Mills theory in the limit of a large number of colors, related to the modification of the eigenvalues of the kernel suggested by Bondarenko and Prygarin in order to obtain Hermitian separability of the eigenvalues. We restore the modified kernel in the momentum space. It turns out that the modification is related only to the real part of the kernel and that the correction to the kernel cannot be presented by a single analytic function in the entire momentum region, which contradicts the known properties of the kernel. (orig.)
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.
International Nuclear Information System (INIS)
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.
Institute of Scientific and Technical Information of China (English)
王建丰; 黄琼湘; 刘儒英; 冶成福
2008-01-01
For a graph G,let h(G;x)=h(G)and[G]h denote the adjoint polynomial and the adjoint equivalence class of G,respectively.In this paper,a new application of[G]h is given.Making use of[G]h,we give a necessary and suffcient condition for adjoint uniqueness of the graph H such that H≠G,where H=(Ui∈APi)U(Uj∈BUj),A(∈)A'={1,2,3,5}U{2n|n∈N,n≥3},B(∈)B'={7,2n|n∈N,n(>)5)and G=a p1UaoP2Ua1P3Ua2P5U(U(n i)=3aiP2i).
Mazaheri, K.; Nejati, A.; Chaharlang Kiani, K.; Taheri, R.
2015-08-01
A shock control bump (SCB) is a flow control method which uses local small deformations in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, we have used a multi-point adjoint optimization scheme to optimize shape and location of the SCB. Practically, this introduces transonic airfoils equipped with the SCB which are simultaneously optimized for different off-design transonic flight conditions. Here, we use this optimization algorithm to enhance and optimize the performance of SCBs in two benchmark airfoils, i.e., RAE-2822 and NACA-64A010, over a wide range of off-design Mach numbers. All results are compared with the usual single-point optimization. We use numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm to find the optimum location and shape of the SCB. We show that the application of SCBs may increase the aerodynamic performance of an RAE-2822 airfoil by 21.9 and by 22.8 % for a NACA-64A010 airfoil compared to the no-bump design in a particular flight condition. We have also investigated the simultaneous usage of two bumps for the upper and the lower surfaces of the airfoil. This has resulted in a 26.1 % improvement for the RAE-2822 compared to the clean airfoil in one flight condition.
Simon, Moritz
2014-11-14
© 2014, Springer Science+Business Media New York. With the target of optimizing CO
Stratification and energy fluxes in the anelastic convection model
Hejda, Pavel; Reshetnyak, Maxim
2013-04-01
convection substantially, shifting maximum of convection to the inner part of the liquid core. Similar to the Boussinesq model the both direct and inverse cascades of the kinetic energy as well as the direct cascade of the specific entropy in the wave space occur. Reshetnyak, M. and Hejda, P., 2008. Direct and inverse cascades in the geodynamo. Nonlin. Proc. Geophys. 15, 873-880. Hejda, P. and Reshetnyak, M., 2009. Effect of anisotropy in the geostrophic turbulence. Phys. Earth Planet. Inter. 177, 152-160, doi: 10.1016/j.pepi.2009.08.006. Reshetnyak, M. and Hejda, P., 2012. Kinetic energy cascades in quasi-geostrophic convection in a spherical shell. Physica Scripta 86, article No. 018408, doi: 10.1088/0031-8949/86/01/018408.
Efficient transfer of sensitivity information in multi-component models
International Nuclear Information System (INIS)
In support of adjoint-based sensitivity analysis, this manuscript presents a new method to efficiently transfer adjoint information between components in a multi-component model, whereas the output of one component is passed as input to the next component. Often, one is interested in evaluating the sensitivities of the responses calculated by the last component to the inputs of the first component in the overall model. The presented method has two advantages over existing methods which may be classified into two broad categories: brute force-type methods and amalgamated-type methods. First, the presented method determines the minimum number of adjoint evaluations for each component as opposed to the brute force-type methods which require full evaluation of all sensitivities for all responses calculated by each component in the overall model, which proves computationally prohibitive for realistic problems. Second, the new method treats each component as a black-box as opposed to amalgamated-type methods which requires explicit knowledge of the system of equations associated with each component in order to reach the minimum number of adjoint evaluations. (author)
Vich, M.; Romero, R.; Richard, E.; Arbogast, P.; Maynard, K.
2010-09-01
Heavy precipitation events occur regularly in the western Mediterranean region. These events often have a high impact on the society due to economic and personal losses. The improvement of the mesoscale numerical forecasts of these events can be used to prevent or minimize their impact on the society. In previous studies, two ensemble prediction systems (EPSs) based on perturbing the model initial and boundary conditions were developed and tested for a collection of high-impact MEDEX cyclonic episodes. These EPSs perturb the initial and boundary potential vorticity (PV) field through a PV inversion algorithm. This technique ensures modifications of all the meteorological fields without compromising the mass-wind balance. One EPS introduces the perturbations along the zones of the three-dimensional PV structure presenting the local most intense values and gradients of the field (a semi-objective choice, PV-gradient), while the other perturbs the PV field over the MM5 adjoint model calculated sensitivity zones (an objective method, PV-adjoint). The PV perturbations are set from a PV error climatology (PVEC) that characterizes typical PV errors in the ECMWF forecasts, both in intensity and displacement. This intensity and displacement perturbation of the PV field is chosen randomly, while its location is given by the perturbation zones defined in each ensemble generation method. Encouraged by the good results obtained by these two EPSs that perturb the PV field, a new approach based on a manual perturbation of the PV field has been tested and compared with the previous results. This technique uses the satellite water vapor (WV) observations to guide the correction of initial PV structures. The correction of the PV field intents to improve the match between the PV distribution and the WV image, taking advantage of the relation between dark and bright features of WV images and PV anomalies, under some assumptions. Afterwards, the PV inversion algorithm is applied to run
Bondarenko, Sergey
2016-01-01
We discuss a residual freedom of the next-to-leading BFKL eigenvalue that originates from ambiguity in redistributing the next-to-leading~(NLO) corrections between the adjoint BFKL eigenvalue and eigenfunctions in planar $\\mathcal{N}=4$ super-Yang-Mills~(SYM) Theory. In terms of the remainder function of the Bern-Dixon-Smirnov~(BDS) amplitude this freedom is translated to reshuffling correction between the eigenvalue and the impact factors in the multi-Regge kinematics~(MRK) in the next-to-leading logarithm approximation~(NLA). We show that the modified NLO BFKL eigenvalue suggested by the authors can be introduced in the MRK expression for the remainder function by shifting the anomalous dimension in the impact factor in such a way that the two and three loop remainder function is left unchanged to the NLA accuracy.
Bondarenko, Sergey; Prygarin, Alex
2016-07-01
We discuss a residual freedom of the next-to-leading BFKL eigenvalue that originates from ambiguity in redistributing the next-to-leading (NLO) corrections between the adjoint BFKL eigenvalue and eigenfunctions in planar {N}=4 super-Yang-Mills (SYM) Theory. In terms of the remainder function of the Bern-Dixon-Smirnov (BDS) amplitude this freedom is translated to reshuffling correction between the eigenvalue and the impact factors in the multi-Regge kinematics (MRK) in the next-to-leading logarithm approximation (NLA). We show that the modified NLO BFKL eigenvalue suggested by the authors in ref. [1] can be introduced in the MRK expression for the remainder function by shifting the anomalous dimension in the impact factor in such a way that the two and three loop remainder function is left unchanged to the NLA accuracy.
Gesztesy, Fritz; Tkachenko, Vadim
Under the assumption that V∈L2([0,π];dx), we derive necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrödinger operators -d2/dx2+V in L2([0,π];dx) with periodic and antiperiodic boundary conditions to possess a Riesz basis of root vectors (i.e., eigenvectors and generalized eigenvectors spanning the range of the Riesz projection associated with the corresponding periodic and antiperiodic eigenvalues). We also discuss the case of a Schauder basis for periodic and antiperiodic Schrödinger operators -d2/dx2+V in Lp([0,π];dx), p∈(1,∞).
Fadin, V S
2015-01-01
We analyze a modification of the BFKL kernel for the adjoint representation of the colour group in the maximally supersymmetric (N=4) Yang-Mills theory in the limit of a large number of colours, related to the modification of the eigenvalues of the kernel suggested by S. Bondarenko and A. Prygarin in order to reach the 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 can not be presented by a single analytic function in the entire momentum region, which contradicts the known properties of the kernel.
Energy Technology Data Exchange (ETDEWEB)
Endres, Sebastian; Steiner, Frank, E-mail: sebastian.endres@uni-ulm.d, E-mail: frank.steiner@uni-ulm.d [Institut fuer Theoretische Physik, Universitaet Ulm Albert-Einstein-Allee 11, 89081 Ulm (Germany)
2010-03-05
The Berry-Keating operator H{sub BK} := -i h-bar (x d/dx + 1/2) (Berry and Keating 1999 SIAM Rev. 41 236) governing the Schroedinger dynamics is discussed in the Hilbert space L{sup 2}(R{sub >},dx) and on compact quantum graphs. It has been proved that the spectrum of H{sub BK} defined on L{sup 2}(R{sub >},dx) is purely continuous and thus this quantization of H{sub BK} cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of H{sub BK} acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of H{sub BK}. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the 'squared' Berry-Keating operator H{sub BK}{sup 2} := -x{sup 2} d{sup 2}/dx{sup 2} -2x d/dx - 1/4 which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for H{sup 2}{sub BK} on compact quantum graphs. While the spectra of both H{sub BK} and H{sup 2}{sub BK} on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither H{sub BK} nor H{sup 2}{sub BK} can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.
Endres, Sebastian; Steiner, Frank
2010-03-01
The Berry-Keating operator H_{BK}:= -i\\hbar \\big(x\\frac{d}{dx}+\\frac{1}{2}\\big) (Berry and Keating 1999 SIAM Rev. 41 236) governing the Schrödinger dynamics is discussed in the Hilbert space L^2({\\mathbb R}_\\gt,dx) and on compact quantum graphs. It has been proved that the spectrum of HBK defined on L^2({\\mathbb R}_\\gt,dx) is purely continuous and thus this quantization of HBK cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of HBK acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of HBK. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the 'squared' Berry-Keating operator H_{BK}^2:= -x^2\\frac{d^2}{dx^2}-2x\\frac{d}{dx}-\\frac{1}{4} which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for H2BK on compact quantum graphs. While the spectra of both HBK and H2BK on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither HBK nor H2BK can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.
International Nuclear Information System (INIS)
The Berry-Keating operator HBK := -i h-bar (x d/dx + 1/2) (Berry and Keating 1999 SIAM Rev. 41 236) governing the Schroedinger dynamics is discussed in the Hilbert space L2(R>,dx) and on compact quantum graphs. It has been proved that the spectrum of HBK defined on L2(R>,dx) is purely continuous and thus this quantization of HBK cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of HBK acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of HBK. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the 'squared' Berry-Keating operator HBK2 := -x2 d2/dx2 -2x d/dx - 1/4 which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for H2BK on compact quantum graphs. While the spectra of both HBK and H2BK on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither HBK nor H2BK can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.
Data assimilation using a hybrid ice flow model
Directory of Open Access Journals (Sweden)
D. N. Goldberg
2010-10-01
Full Text Available Hybrid models, or depth-integrated flow models that include the effect of both longitudinal stresses and vertical shearing, are becoming more prevalent in dynamical ice modeling. Under a wide range of conditions they closely approximate the well-known First Order stress balance, yet are of computationally lower dimension, and thus require less intensive resources. Concomitant with the development and use of these models is the need to perform inversions of observed data. Here, an inverse control method is extended to use a hybrid flow model as a forward model. We derive an adjoint of a hybrid model and use it for inversion of ice-stream basal traction from observed surface velocities. A novel aspect of the adjoint derivation is a retention of non-linearities in Glen's flow law. Experiments show that including those nonlinearities is advantageous in minimization of the cost function, yielding a more efficient inversion procedure.
The Nonlinear Interaction Process in the Wave Assimilation Model and Its Experiments
Institute of Scientific and Technical Information of China (English)
杨永增; 纪永刚; 袁业立
2003-01-01
This paper presents a composite interaction formula based on the discrete-interactionoperator of wave-wave nonlinear interaction for deriving its adjoint source function in the wave assimilation model. Assimilation experiments were performed using the significant wave heights observed by the TOPES/POSEIDON satellite, and the gradient distribution in the physical space wasalso analyzed preliminarily.
Smooth spaces versus continuous spaces in models for synthetic differential geometry
Reyes, G.E.; Moerdijk, I.
1984-01-01
In topos models for synthetic differential geometry we study connections between smooth spaces (which interpret synthetic calculus) and continuous spaces (which interpret intuitionistic analysis). Our main tools are adjoint retractions of toposes and the standard map from the smooth reals to the con
Model of tunnelling through periodic array of quantum dots in a magnetic field
Institute of Scientific and Technical Information of China (English)
I.Yu.Popov; S.A.Osipov
2012-01-01
A two-dimensional periodic array of quantum dots with two laterally coupled leads in a magnetic field is considered.The model of electron transport through the system based on the theory of self-adjoint extensions of symmetric operators is suggested.We obtain the formula for the transmission coefficient and investigate its dependence on the magnetic field.
Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics
Agoshkov, V. I.; Zalesny, V. B.
2012-03-01
Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of Numerical Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and space coordinates. Numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples. These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean dynamics model with an observed data assimilation procedure.
Ohta, Yuji
1999-01-01
Instanton correction of prepotential of one-dimensional SL(2) Ruijsenaars model is presented with the help of Picard-Fuchs equation of Pakuliak-Perelomov type. It is shown that the instanton induced prepotential reduces to that of the SU(2) gauge theory coupled with a massive adjoint hypermultiplet.
Institute of Scientific and Technical Information of China (English)
王志敬; 李丽君
2011-01-01
研究了二阶奇型J-对称微分算子辛几何刻画问题,通过构造商空间,应用辛几何的方法讨论了二阶J-对称微分算子的自共轭扩张问题.给出了与二阶微分算子自共轭域相对应的完全J-Lagrangian子流型的分类与描述.%The symplectic geometry characterization of second order singular J - symmetric differential operators was investigated. By constructing different quotient spaces, self-adjoint extensions of second order J - symmetric differential operators were studied using the method of symplectic geometry. Then classification and description of complete J - Lagrangian submanifold corresponding with self-adjoint domains of second order differential operators were obtained.
New Calculations in Dirac Gaugino Models: Operators, Expansions, and Effects
Carpenter, Linda M
2015-01-01
In this work we calculate important one loop SUSY-breaking parameters in models with Dirac gauginos, which are implied by the existence of heavy messenger fields. We find that these SUSY-breaking effects are all related by a small number of parameters, thus the general theory is tightly predictive. In order to make the most accurate analyses of one loop effects, we introduce calculations using an expansion in SUSY breaking messenger mass, rather than relying on postulating the forms of effective operators. We use this expansion to calculate one loop contributions to gaugino masses, non-holomorphic SM adjoint masses, new A-like and B-like terms, and linear terms. We also test the Higgs potential in such models, and calculate one loop contributions to the Higgs mass in certain limits of R-symmetric models, finding a very large contribution in many regions of the $\\mu$-less MSSM, where Higgs fields couple to standard model adjoint fields.
Kushner, Paul J.; Shepherd, Theodore G.
1995-01-01
This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. 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. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of distur...
Endres, Sebastian
2009-01-01
The Berry-Keating operator $H_{\\mathrm{BK}}:= -\\ui\\hbar(x\\frac{\\ud\\phantom{x}}{\\ud x}+{1/2})$ [M. V. Berry and J. P. Keating, SIAM Rev. 41 (1999) 236] governing the Schr\\"odinger dynamics is discussed in the Hilbert space $L^2(\\rz_>,\\ud x)$ and on compact quantum graphs. It is proved that the spectrum of $H_{\\mathrm{BK}}$ defined on $L^2(\\rz_>,\\ud x)$ is purely continuous and thus this quantization of $H_{\\mathrm{BK}}$ cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of $H_{\\mathrm{BK}}$ acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of $H_{\\mathrm{BK}}$. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the ``squared'' Berry-Keating operator $H_{\\mathrm{BK}}^2:= -x^2\\frac{\\ud^2...
Healy, R.W.; Russell, T.F.
1998-01-01
We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.
Institute of Scientific and Technical Information of China (English)
YUAN Jin-nan; HUANG Yan-yan; LIU Chun-xia; WAN Qi-lin
2008-01-01
A quasi-geostrophic barotropic vorticity equation model is used to simulate the influences of topographic forcing and land friction on landfall tropical cyclone track and intensity. The simulation results show that tropical cyclone track may have sudden deflection when the action of topographic friction dissipation is considered, and sudden deflection of the track is easy to happen and sudden change of tropical cyclone intensity is not clear when the intensity of tropical cyclone is weak and the land friction is strong.The land friction may be an important factor that causes sudden deflection of tropical cyclone track around landfall.
Two possible mechanisms for vortex self-organization
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The vortex self-organization is investigated in this paper by four groups of numerical experiments within the framework of quasi-geostrophic model, and based on the experimental results two types of possible mechanisms for vortex self-organization are suggested. The meso-scale topography may enable separated vortices to merge into a larger scale vortex; and the interaction of meso-γand meso-β scale systems may make separated vortices to self organize a typhoon-like vortex circulation.
The Ising model and special geometries
International Nuclear Information System (INIS)
We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals χ(n) of the magnetic susceptibility of the Ising model (n ⩽ 6) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms is equivalent to the feature of their symmetric squares, or their exterior squares, having rational solutions. The differential Galois groups are in the special orthogonal, or symplectic, groups. This self-adjoint (up to operator equivalence) property means that the factor operators that we already know to be derived from geometry are special globally nilpotent operators: they correspond to ‘special geometries’. Beyond the small order factor operators (occurring in the linear differential operators associated with χ(5) and χ(6)), and, in particular, those associated with modular forms, we focus on the quite large order-12 and order-23 operators. We show that the order-12 operator has an exterior square which annihilates a rational solution. Then, its differential Galois group is in the symplectic group Sp(12, C). The order-23 operator is shown to factorize into an order-2 operator and an order-21 operator. The symmetric square of this order-21 operator has a rational solution. Its differential Galois group is, thus, in the orthogonal group SO(21, C). (paper)
Adjoint Methed Analysis of Hypersonic Vehicle Separation Interference%高超声速飞行器分离干扰的伴随方法分析
Institute of Scientific and Technical Information of China (English)
凡雪灵; 陈凯
2013-01-01
The hypersonic vehicle stage separation process in the atmosphere is researched.Adjoint method is introduced and the way to get the analytical solution of angle of attack caused by impact force and aerodynamic interference torque.Using the above solution,the angle of attack instantaneous change curve is obtained which is caused by separation interference.The results show that impact force and aerodynamic interference torque have certain effect on angle of attack and increase with the increase of the interference in the beginning of the hypersonic vehicle stage separation 0.4 seconds.This study has realized the predicted for the process of the hypersonic vehicle stage separation risk and provided a theoretical basis for the strategy formulation of the hypersonic vehicle separation interference.%以大气层内高超声速飞行器级间分离过程为研究对象,采用伴随方法得到了由冲击力和气动干扰力矩引起的攻角的解析解.利用该解析解,得到了分离干扰引起的攻角的瞬时变化曲线.结果表明,在高超声速飞行器级间分离开始0.4s内,冲击力和气动干扰力矩对攻角有一定的影响,并且随干扰的增大而增大.本研究实现了预示高超声速飞行器分离过程风险的目的,对高超声速飞行器分离干扰策略的制定提供了理论依据.
A light neutralino in hybrid models of supersymmetry breaking
Dudas, Emilian; Parmentier, Jeanne
2008-01-01
We show that in gauge mediation models where heavy messenger masses are provided by the adjoint Higgs field of an underlying SU(5) theory, a generalized gauge mediation spectrum arises with the characteristic feature of having a neutralino much lighter than in the standard gauge or gravity mediation schemes. This naturally fits in a hybrid scenario where gravity mediation, while subdominant with respect to gauge mediation, provides mu and B mu parameters in the TeV range.
Semenoff, Gordon W; Semenoff, Gordon W; Szabo, Richard J
1996-01-01
We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them with their bosonic counterparts which are the more familiar Hermitian matrix models. We derive and solve the complete sets of loop equations for the correlators of these models and use these equations to examine critical behaviour. The topological large-N expansions are also constructed and their relation to other aspects of modern string theory such as integrable hierarchies is discussed. We use these connections to discuss the applications of these matrix models to string theory and induced gauge theories. We argue that as such the fermionic matrix models may provide a novel generalization of the discretized random surface representation of quantum gravity in which the genus sum alternates and the sums over genera for correlators have better convergence properties than thei...
Outline of a superunification model
Towe, J
2007-01-01
Tensor products of standard model bosons and fermions form a spin-2 self-realization of SU(5), and because every quark can be interpreted as a lepton that has coupled to an appropriate element of this adjoint representation, and inversely, SUGRA GUT interactions between proposed spin-2 elements and baryons of spin 3/2, can exist as residual manifestations of quark-lepton transitions that occur within baryonic domains of asymptotic freedom. It is argued that these interactions preserve baryonic structure and continually re-establish a locally SUSY version of broken SU(5), indicating a recurring inflation event that addresses the large scale.
PWR Facility Dose Modeling Using MCNP5 and the CADIS/ADVANTG Variance-Reduction Methodology
Energy Technology Data Exchange (ETDEWEB)
Blakeman, Edward D [ORNL; Peplow, Douglas E. [ORNL; Wagner, John C [ORNL; Murphy, Brian D [ORNL; Mueller, Don [ORNL
2007-09-01
The feasibility of modeling a pressurized-water-reactor (PWR) facility and calculating dose rates at all locations within the containment and adjoining structures using MCNP5 with mesh tallies is presented. Calculations of dose rates resulting from neutron and photon sources from the reactor (operating and shut down for various periods) and the spent fuel pool, as well as for the photon source from the primary coolant loop, were all of interest. Identification of the PWR facility, development of the MCNP-based model and automation of the run process, calculation of the various sources, and development of methods for visually examining mesh tally files and extracting dose rates were all a significant part of the project. Advanced variance reduction, which was required because of the size of the model and the large amount of shielding, was performed via the CADIS/ADVANTG approach. This methodology uses an automatically generated three-dimensional discrete ordinates model to calculate adjoint fluxes from which MCNP weight windows and source bias parameters are generated. Investigative calculations were performed using a simple block model and a simplified full-scale model of the PWR containment, in which the adjoint source was placed in various regions. In general, it was shown that placement of the adjoint source on the periphery of the model provided adequate results for regions reasonably close to the source (e.g., within the containment structure for the reactor source). A modification to the CADIS/ADVANTG methodology was also studied in which a global adjoint source is weighted by the reciprocal of the dose response calculated by an earlier forward discrete ordinates calculation. This method showed improved results over those using the standard CADIS/ADVANTG approach, and its further investigation is recommended for future efforts.
Institute of Scientific and Technical Information of China (English)
杨倩; 吕莉莉; 张丽美; 孙蓉
2011-01-01
Objective To offer experimental basement for the elucidation of dependablity between "toxicity-efficacy" by researching the adjoint toxical and side effects of anti-inflammatory effect of water and alcohol extract from Fructus Bruceae. Methods The model of ear swelling by croton oil and granuloma by agar were made and model mice were administrated with water and alcohol extract from Fructus Bruceae of high, middle and low dosage 3/7 days continually. The activities of serum ALT, AST and contents of Cr, BUN were detected while the ratio of liver and kidney to body was measured. Results Both ear swelling by croton oil and granuloma by agar can be inhibited by multiple intragastric administration of water and alcohol extract from Fructus Bruceae. The swelling depressive rate of water extract was higher than that of alcohol extract and showed a well "dose-effect" relationship. The activities of serum ALT, AST and ratio of liver to body showed little change, but both the contents of Cr and BUN and ratio of kidney to body increased significantly with doses and time. Conclusion Both water and alcohol extract from Fructus Bruceae at effective dosage could efficiently inhibit acute and chronic inflammation. At the same time some toxical and side effects can be caused to kidney, however, the occurrence mechanism of its toxical and side effects still need further study.%目的 对鸦胆子水提、醇提组分发挥抗炎药效剂量下出现的伴随毒副作用进行观察与研究,为阐明其"毒性-功效"相关性提供实验依据.方法 建立小鼠巴豆油耳肿胀模型和琼脂肉芽肿模型,并分别给小鼠灌胃高、中、低不同剂量的鸦胆子水提、醇提组分连续3天和7天,末次给药后取血检测血清丙氨酸氨基转移酶(ALT)、天门冬氨酸氨基转移酶(AST)活性及肌Of(Cr)、尿素氮(BUN)含量变化并取肝、肾称重计算脏体比值.结果 连续多次给小鼠灌胃药效剂量的鸦胆子水提和醇提组分均可明
Jault, Dominique
2013-04-01
Understanding the main magnetic field variations has been hindered by the discrepancy between the periods (from months to years) of the simplest linear wave phenomena and the relatively long time intervals (10 to 100 years) over which magnetic field changes can be confidently monitored. A theoretical description of short-period waves within the Earth's fluid core is at hand. Quasi-geostrophic inertial waves (akin to Rossby waves in the atmosphere) are slightly modified in the presence of magnetic fields and torsional oscillations consist of differential motion between coaxial rigid cylindrical annuli. Torsional oscillations are sensitive to the whole magnetic field that they shear in the course of their propagation. From their modelling, we have thus gained an estimate for the magnetic field strength in the core interior. There is now ongoing work to extend the theoretical framework to longer times. Furthermore, data collected from the Swarm constellation of three satellites to be launched this year by ESA will permit to better separate the internal and external magnetic signals. We may thus dream to detect quasi-geostrophic inertial waves. As the spectral ranges of theoretical models and observations begin to overlap, we can now go beyond the understanding of the magnetic field variations as the juxtaposition of partial models, arranged as a set of nested Matryoshka dolls. This talk will give illustrations for this statement, among which the question of induction in the lower mantle.
Plaut, E.; Lebranchu, Y.; Simitev, R.; Busse, F. H.
A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds-Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found.
Network Analysis of Atmospheric Rossby Wave Patterns in the Northern Midlatitudes
Martin, P.; Stolbova, V.; Kurths, J.
2015-12-01
Rossby waves, the primary contributors to weather and storms in the midlatitudes, are a major phenomenon in the upper atmosphere, and play a large role in poleward heat transport. Understanding the mechanism and features of Rossby waves are crucial for millions of people, especially due to the extreme events caused by Rossby Waves such as the Russian Heat Wave and the flood in Pakistan, both occurring in 2010. In this study, we use an idealized, regional, quasi-geostrophic, coupled ocean-atmosphere model (The Quasi-Geostrophic Coupled Model, or QGCM) to create Rossby waves in the northern hemisphere. We analyze these waves using the emerging technique of climate networks - a useful statistical tool for a range of complex systems, which has proven to be extremely useful in giving new insight into the climate system's behavior. Here, we create networks using different climatic variables, and investigate the properties of Rossby waves, including propagation speed and energy transport. We look at network measures, such as degree and link length, to determine the major features of Rossby waves. Finally, we compare our results to observed data, and show how our findings provide a better understanding of the different regimes of Rossby Waves, their features, and mechanisms of their propagation, which is crucial for forecasting on short and long-range time scales.
Patrice Loïez
2005-01-01
The exhibition"La France au CERN" was inaugurated by Danièle Hulin, Directrice adjointe Secteur Physique, Chimie, Sciences pour l'Ingénieur (PCSI), Ministère délégué à l'Enseignement supérieur et à la recherche.
Simple Models of Superconformal Flavor
Craig, Nathaniel
2010-01-01
The observed hierarchy of fermion masses and mixings may be generated by renormalization group flow if the Standard Model is coupled to a near-conformal sector at high energies. If the conformal sector is supersymmetric, these effects are rendered calculable by a combination of superconformal symmetry and a-maximization. The viability of such models depends on whether they generate the observed fermion mass hierarchy before the Standard Model gauge couplings hit a Landau pole. Here we construct a variety of simple vector-like models of superconformal flavor, including both ten-centered and democratic variations. We discuss in detail the subtleties of applying the a-maximization procedure to determine anomalous dimensions of Standard Model fields. We find that a wide range of models based on SU(N) or Sp(2N) SQCD with fundamental and adjoint matter are viable theories of superconformal flavor.
Directory of Open Access Journals (Sweden)
Daniel Holdaway
2015-09-01
Full Text Available The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5. All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have non-linear behaviour. The piecewise parabolic method (PPM with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.
Holdaway, Daniel; Kent, James
2015-01-01
The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.
Optimizing chemotherapy in an HIV model
Directory of Open Access Journals (Sweden)
K. Renee Fister
1998-12-01
Full Text Available We examine an ordinary differential system modeling the interaction of the HIV virus and the immune system of the human body. The optimal control represents a percentage effect the chemotherapy has on the interaction of the CD4$^+$T cells with the virus. We maximize the benefit based on the T cell count and minimize the systemic cost based on the percentage of chemotherapy given. Existence of an optimal control is proven, and the optimal control is uniquely characterized in terms of the solution of the optimality system, which is the state system coupled with the adjoint system. In addition, numerical examples are given for illustration.
Ding-Iohara-Miki symmetry of network matrix models
Mironov, A; Zenkevich, Y
2016-01-01
Ward identities in the most general "network matrix model" can be described in terms of the Ding-Iohara-Miki algebras (DIM). This confirms an expectation that such algebras and their various limits/reductions are the relevant substitutes/deformations of the Virasoro/W-algebra for (q,t) and (q_1,q_2,q_3) deformed network matrix models. Exhaustive for these purposes should be the Pagoda triple-affine elliptic DIM, which corresponds to networks associated with 6d gauge theories with adjoint matter (double elliptic systems). We provide some details on elliptic qq-characters.
Shang, Linyuan; Zhao, Guozhong
2016-06-01
This article investigates topology optimization of a bi-material model for acoustic-structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic-structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic-structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC.
New data assimilation system DNDAS for high-dimensional models
Qun-bo, Huang; Xiao-qun, Cao; Meng-bin, Zhu; Wei-min, Zhang; Bai-nian, Liu
2016-05-01
The tangent linear (TL) models and adjoint (AD) models have brought great difficulties for the development of variational data assimilation system. It might be impossible to develop them perfectly without great efforts, either by hand, or by automatic differentiation tools. In order to break these limitations, a new data assimilation system, dual-number data assimilation system (DNDAS), is designed based on the dual-number automatic differentiation principles. We investigate the performance of DNDAS with two different optimization schemes and subsequently give a discussion on whether DNDAS is appropriate for high-dimensional forecast models. The new data assimilation system can avoid the complicated reverse integration of the adjoint model, and it only needs the forward integration in the dual-number space to obtain the cost function and its gradient vector concurrently. To verify the correctness and effectiveness of DNDAS, we implemented DNDAS on a simple ordinary differential model and the Lorenz-63 model with different optimization methods. We then concentrate on the adaptability of DNDAS to the Lorenz-96 model with high-dimensional state variables. The results indicate that whether the system is simple or nonlinear, DNDAS can accurately reconstruct the initial condition for the forecast model and has a strong anti-noise characteristic. Given adequate computing resource, the quasi-Newton optimization method performs better than the conjugate gradient method in DNDAS. Project supported by the National Natural Science Foundation of China (Grant Nos. 41475094 and 41375113).
Huang, M.; G. R. Carmichael; S. N. Spak; B. Adhikary; Kulkarni, S; Cheng, Y. F.; Wei, C.; Tang, Y.; A. D'Allura; Wennberg, P.O.; G. L. Huey; Dibb, J. E.; Jimenez, J. L.; M. J. Cubison; A. J. Weinheimer
2011-01-01
Chronic high surface ozone (O_{3}) levels and the increasing sulfur oxides (SO_{x} = SO_{2}+SO_{4}) ambient concentrations over South Coast (SC) and other areas of California (CA) are affected by both local emissions and long-range transport. In this paper, multi-scale tracer, full-chemistry and adjoint simulations using the STEM atmospheric chemistry model are conducted to assess the contribution of local emissio...
Scale invariant behavior in a large N matrix model
Narayanan, Rajamani; Neuberger, Herbert
2016-01-01
Eigenvalue distributions of properly regularized Wilson-loop operators are used to study the transition from UV behavior to IR behavior in gauge theories coupled to matter that potentially have an IR fixed point. We numerically demonstrate the emergence of scale invariance in a matrix model that describes S U (N ) gauge theory coupled to two flavors of massless adjoint fermions in the large N limit. The eigenvalue distribution of Wilson loops of varying sizes cannot be described by a universal lattice beta function connecting the UV to the IR.
Null controllability in a fluid-solid structure model
Raymond, J.-P.; Vanninathan, M.
We consider a system coupling the Stokes equations in a two-dimensional domain with a structure equation which is a system of ordinary differential equations corresponding to a finite dimensional approximation of equations modeling deformations of an elastic body or vibrations of a rigid body. For that system we establish a null controllability result for localized distributed controls acting only in the fluid equations and there is no control in the solid part. This controllability result follows from a Carleman inequality that we prove for the adjoint system.
Scale invariant behavior in a large N matrix model
Narayanan, Rajamani
2016-01-01
Eigenvalue distributions of properly regularized Wilson loop operators are used to study the transition from ultra-violet (UV) behavior to infra-red (IR) behavior in gauge theories coupled to matter that potentially have an IR fixed point (FP). We numerically demonstrate emergence of scale invariance in a matrix model that describes $SU(N)$ gauge theory coupled to two flavors of massless adjoint fermions in the large $N$ limit. The eigenvalue distribution of Wilson loops of varying sizes cannot be described by a universal lattice beta-function connecting the UV to the IR.
New calculations in Dirac gaugino models: operators, expansions, and effects
Carpenter, Linda M.; Goodman, Jessica
2015-07-01
In this work we calculate important one loop SUSY-breaking parameters in models with Dirac gauginos, which are implied by the existence of heavy messenger fields. We find that these SUSY-breaking effects are all related by a small number of parameters, thus the general theory is tightly predictive. In order to make the most accurate analyses of one loop effects, we introduce calculations using an expansion in SUSY breaking messenger mass, rather than relying on postulating the forms of effective operators. We use this expansion to calculate one loop contributions to gaugino masses, non-holomorphic SM adjoint masses, new A-like and B-like terms, and linear terms. We also test the Higgs potential in such models, and calculate one loop contributions to the Higgs mass in certain limits of R-symmetric models, finding a very large contribution in many regions of the [InlineMediaObject not available: see fulltext.], where Higgs fields couple to standard model adjoint fields.
Remarks on rotating shallow-water magnetohydrodynamics
Directory of Open Access Journals (Sweden)
V. Zeitlin
2013-10-01
Full Text Available 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 baroclinic cases, is derived in the limit of strong rotation. The basic properties of the model(s are sketched, including the stabilizing role of magnetic fields in the baroclinic version.
Zhang, Jicai; Lu, Xianqing; Wang, Ping; Wang, Ya Ping
2011-04-01
Data assimilation technique (adjoint method) is applied to study the similarities and the differences between the Ekman (linear) and the Quadratic (nonlinear) bottom friction parameterizations for a two-dimensional tidal model. Two methods are used to treat the bottom friction coefficient (BFC). The first method assumes that the BFC is a constant in the entire computation domain, while the second applies the spatially varying BFCs. The adjoint expressions for the linear and the nonlinear parameterizations and the optimization formulae for the two BFC methods are derived based on the typical Largrangian multiplier method. By assimilating the model-generated 'observations', identical twin experiments are performed to test and validate the inversion ability of the presented methodology. Four experiments, which employ the linear parameterization, the nonlinear parameterizations, the constant BFC and the spatially varying BFC, are carried out to simulate the M 2 tide in the Bohai Sea and the Yellow Sea by assimilating the TOPEX/Poseidon altimetry and tidal gauge data. After the assimilation, the misfit between model-produced and observed data is significantly decreased in the four experiments. The simulation results indicate that the nonlinear Quadratic parameterization is more accurate than the linear Ekman parameterization if the traditional constant BFC is used. However, when the spatially varying BFCs are used, the differences between the Ekman and the Quadratic approaches diminished, the reason of which is analyzed from the viewpoint of dissipation rate caused by bottom friction. Generally speaking, linear bottom friction parameterizations are often used in global tidal models. This study indicates that they are also applicable in regional ocean tidal models with the combination of spatially varying parameters and the adjoint method.
基于伴随算子的气动布局优化技术及其在大飞机机翼减阻中的应用%Wing optimization of large airplane by adjoint method
Institute of Scientific and Technical Information of China (English)
吴文华; 陶洋; 陈德华; 王元靖; 黄勇
2011-01-01
为了提高大型飞机机翼的气动性能,发展了基于Bezier-Bernstein曲线的机翼气动布局参数化技术和网格变形技术,以及基于Navier-Stokes方程的流场解算器、伴随算子解算器和二次规划寻优算法,形成了气动布局优化软件.通过改变约束条件、设计参数范围和初始点,对机翼进行了一系列的极多参数和多约束的气动布局精细优化设计,得到了良好的优化结果,优化结果表明该优化方法是高效和可靠的.%The optimization software was developed to improve the performance of the wing of large airplane. This software include the three main techniques： the aerodynamic configuration parameterization and grid update technique based on Bezier-Bernstein curve parameterization method; the flow solver and adjoint solver based on three-dimensional （3 D） Reynolds averaged Navier-Stokes equations; the optimization method based on sequential quadratic programming algorithm. This paper did series optimization for a wing with many design variables and different constraints and get some excellent results, The analysis to the result shows the optimization method is reliable and efficient.
Towards high resolution mapping of 3-D mesoscale dynamics from observations
Directory of Open Access Journals (Sweden)
B. Buongiorno Nardelli
2012-10-01
Full Text Available The MyOcean R&D project MESCLA (MEsoSCaLe dynamical Analysis through combined model, satellite and in situ data was devoted to the high resolution 3-D retrieval of tracer and velocity fields in the oceans, based on the combination of in situ and satellite observations and quasi-geostrophic dynamical models. The retrieval techniques were also tested and compared with the output of a primitive equation model, with particular attention to the accuracy of the vertical velocity field as estimated through the Q vector formulation of the omega equation. The project focused on a test case, covering the region where the Gulf Stream separates from the US East Coast. This work demonstrated that innovative methods for the high resolution mapping of 3-D mesoscale dynamics from observations can be used to build the next generations of operational observation-based products.
Variational estimation of process parameters in a simplified atmospheric general circulation model
Lv, Guokun; Koehl, Armin; Stammer, Detlef
2016-04-01
Parameterizations are used to simulate effects of unresolved sub-grid-scale processes in current state-of-the-art climate model. The values of the process parameters, which determine the model's climatology, are usually manually adjusted to reduce the difference of model mean state to the observed climatology. This process requires detailed knowledge of the model and its parameterizations. In this work, a variational method was used to estimate process parameters in the Planet Simulator (PlaSim). The adjoint code was generated using automatic differentiation of the source code. Some hydrological processes were switched off to remove the influence of zero-order discontinuities. In addition, the nonlinearity of the model limits the feasible assimilation window to about 1day, which is too short to tune the model's climatology. To extend the feasible assimilation window, nudging terms for all state variables were added to the model's equations, which essentially suppress all unstable directions. In identical twin experiments, we found that the feasible assimilation window could be extended to over 1-year and accurate parameters could be retrieved. Although the nudging terms transform to a damping of the adjoint variables and therefore tend to erases the information of the data over time, assimilating climatological information is shown to provide sufficient information on the parameters. Moreover, the mechanism of this regularization is discussed.
Scaling of saturation amplitudes in baroclinic instability
International Nuclear Information System (INIS)
By using finite-amplitude conservation laws for pseudomomentum and pseudoenergy, rigorous upper bounds have been derived on the saturation amplitudes in baroclinic instability for layered and continuously-stratified quasi-geostrophic models. Bounds have been obtained for both the eddy energy and the eddy potential enstrophy. The bounds apply to conservative (inviscid, unforced) flow, as well as to forced-dissipative flow when the dissipation is proportional to the potential vorticity. This approach provides an efficient way of extracting an analytical estimate of the dynamical scalings of the saturation amplitudes in terms of crucial non-dimensional parameters. A possible use is in constructing eddy parameterization schemes for zonally-averaged climate models. The scaling dependences are summarized, and compared with those derived from weakly-nonlinear theory and from baroclinic-adjustment estimates
Mathematical modeling of growth processes in nature and engineering: A variational approach
Energy Technology Data Exchange (ETDEWEB)
Manzhirov, A V; Lychev, S A, E-mail: manzh@ipmnet.r [Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Vernadsky Ave 101 Bldg 1, Moscow, 119526 (Russian Federation)
2009-08-01
We present a variational approach to the mathematical theory of accreted solids. One main point in this approach is that the operator of the accretion problem proves to be self-adjoint with respect to an appropriately modified convolution bilinear form, and it is this linear form that we use in the construction of the variational functional. Our growing solid model can be efficiently applied to describe processes such as concreting, pyrolytic deposition, laser spraying, electrolytic deposition, polymerization, solidification of melts, crystal growth, glacier and ice cover freezing, sedimentary and volcanic rock forming, and biological tissue growth. These applications will be considered elsewhere.
Error Estimation for Reduced Order Models of Dynamical Systems
Energy Technology Data Exchange (ETDEWEB)
Homescu, C; Petzold, L; Serban, R
2004-01-22
The use of reduced order models to describe a dynamical system is pervasive in science and engineering. Often these models are used without an estimate of their error or range of validity. In this paper we consider dynamical systems and reduced models built using proper orthogonal decomposition. We show how to compute estimates and bounds for these errors, by a combination of small sample statistical condition estimation and error estimation using the adjoint method. Most importantly, the proposed approach allows the assessment of regions of validity for reduced models, i.e., ranges of perturbations in the original system over which the reduced model is still appropriate. Numerical examples validate our approach: the error norm estimates approximate well the forward error while the derived bounds are within an order of magnitude.
Sensitivity of a Shallow-Water Model to Parameters
Kazantsev, Eugene
2011-01-01
An adjoint based technique is applied to a shallow water model in order to estimate the influence of the model's parameters on the solution. Among parameters the bottom topography, initial conditions, boundary conditions on rigid boundaries, viscosity coefficients Coriolis parameter and the amplitude of the wind stress tension are considered. Their influence is analyzed from three points of view: 1. flexibility of the model with respect to a parameter that is related to the lowest value of the cost function that can be obtained in the data assimilation experiment that controls this parameter; 2. possibility to improve the model by the parameter's control, i.e. whether the solution with the optimal parameter remains close to observations after the end of control; 3. sensitivity of the model solution to the parameter in a classical sense. That implies the analysis of the sensitivity estimates and their comparison with each other and with the local Lyapunov exponents that characterize the sensitivity of the mode...
Marchuk, G. I.; Zalesny, V. B.
2012-02-01
The problem of modeling the World Ocean circulation with the four-dimensional assimilation of temperature and salinity fields is considered. A mathematical model of the ocean general circulation and a numerical algorithm for its solution are formulated. The model equations are written in a σ coordinate system on the sphere with the North Pole shifted to the point of the continent (60° E, 60.5° N). The model has a flexible numerical structure and consists of two parts: the forward prognostic model and its adjoint analog. The numerical algorithm for solving the forward and adjoint problems is based on the method of multicomponent splitting. This method includes splitting with respect to physical processes and geometric coordinates. Three series of numerical experiments are performed: (1) a test solution to the problem of the four-dimensional variational assimilation, (2) modeling of the World Ocean circulation with the variational assimilation of climatic temperature and salinity fields, and (3) modeling of the World Ocean circulation with the variational assimilation of climatic temperature and salinity fields and the data of Argo buoys. The results of calculations demonstrate the expediency of using the model of World Ocean circulation with the procedure of assimilating observational data for a description of the general structure of thermohaline fields.
Directory of Open Access Journals (Sweden)
Claudia Kratzenstein
2013-07-01
Full Text Available We investigate the Oneshot Optimization strategy introduced by Hamdi and Griewank for the applicability and efficiency to identify parameters in models of the earth's climate system. Parameters of a box model of the North Atlantic Thermohaline Circulation are optimized with respect to the fit of model output to data given by another model of intermediate complexity. Since the model is run into a steady state by a pseudo time-stepping, efficient techniques are necessary to avoid extensive recomputations or storing when using gradient-based local optimization algorithms. The Oneshot approach simultaneously updates state, adjoint and parameter values. For the required partial derivatives, the algorithmic/automatic differentiation tool TAF was used. Numerical results are compared to results obtained by the BFGS-quasi-Newton method.
Oceanic rings and jets as statistical equilibrium states
Venaille, Antoine
2010-01-01
Equilibrium statistical mechanics of two-dimensional flows provides an explanation and a prediction for the self-organization of large scale coherent structures. This theory is applied in this paper to the description of oceanic rings and jets, in the framework of a $1.5$ layer quasi-geostrophic model. The theory predicts the spontaneous formation of regions where the potential vorticity is homogenized, with strong and localized jets at their interface. Mesoscale rings are shown to be close to a statistical equilibrium: the theory accounts for their shape, their drift, and their ubiquity in the ocean, independently of the underlying generation mechanism. At basin scale, inertial states presenting mid basin eastward jets (and then different from the classical Fofonoff solution) are described as marginally unstable states. These states are shown to be marginally unstable for the equilibrium statistical theory. In that case, considering a purely inertial limit is a first step toward more comprehensive out of equ...
Institute of Scientific and Technical Information of China (English)
QIU Ming-yu; LU Wei-song; CHEN Hui-lin; CAI Qin-bo
2007-01-01
Numerical experiments on forcing dissipation and heating response of dipole (unipole) are carried out using global spectral models with quasi-geostrophic barotropic vorticity equations. For each experiment nodel integration is run for 90 days on the condition of three-wave quasi-resonance. The results are given as follows: Under the effects of dipole (unipole) forcing source and basic flow intensity, there exist strong interactions among the three planetary waves and quasi-biweekly and intraseasonal oscillation of the three planetary waves. In the meantime, the changes in the intensity of dipole or unipole forcing source and basic flow have different frequency modulation effects on LFO in the middle and higher latitudes.The results of the stream function field of three quasi-resonant waves evolving with time confirm that the low-frequency oscillation exists in extratropical latitude.
Schubert, Sebastian
2015-01-01
One of the most relevant weather regimes in the mid latitudes atmosphere is the persistent deviation from the approximately zonally symmetric jet stream to the emergence of so-called blocking patterns. Such configurations are usually connected to exceptional local stability properties of the flow which come along with an improved local forecast skills during the phenomenon. It is instead extremely hard to predict onset and decay of blockings. Covariant Lyapunov Vectors (CLVs) offer a suitable characterization of the linear stability of a chaotic flow, since they represent the full tangent linear dynamics by a covariant basis which explores linear perturbations at all time scales. Therefore, we will test whether CLVs feature a signature of the blockings. We examine the CLVs for a quasi-geostrophic beta-plane two-layer model in a periodic channel baroclinically driven by a meridional temperature gradient $\\Delta T$. An orographic forcing enhances the emergence of localized blocked regimes. We detect the blockin...
Study of the Optimal Precursors for Blocking Events
Institute of Scientific and Technical Information of China (English)
JIANG Zhina; LUO Dehai
2005-01-01
The precursors of dipole blocking are obtained by a numerical approach based upon a quasi-geostrophic barotropic planetary- to synoptic-scale interaction model without topography and with a localized synopticscale wave-maker. The optimization problem related to the precursors of blocking is formulated and the nonlinear optimization method is used to examine the optimal synoptic-scale initial field successfully. The results show that the prominent characteristics of the optimal synoptic-scale initial field are that the synoptic-scale wave train structures exist upstream of the incipient blocking. In addition, the large-scale low/high eddy-forcing pattern upstream of the incipient blocking is an essential precondition for the onset of dipole blocking.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on small-scale vortices in Jupiter's atmosphere. Conditional nonlinear optimal perturbations (CNOPs) and linear singular vectors (LSVs) are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter's atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found.The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter's atmosphere and to compare the stability of motions in Jupiter's atmosphere and Earth's atmosphere further.
STUDY ON DYNAMICS OF TROPICAL CISK-ROSSBY WAVES AND MECHANISM OF 30-50 DAY OSCILLATIONS
Institute of Scientific and Technical Information of China (English)
张韧; 余志豪; 蒋全荣
2001-01-01
To add to the growing mature research on the tropical 30-50 day oscillations from a new prospective, the current work bases on dynamic analysis of baroclinic quasi-geostrophic models to discuss dynamic mechanisms for the generation and propagation of CISK-Rossby waves, and to understand restraints and effects of different wave structures and thermodynamic forcing on the 30-50 day oscillations in the tropical atmosphere. Some important properties of the oscillation propagation have been explained and, in detail, with respect to its meridional propagation and vertical "baroclinic" structure. The work has come up with some new opinions and viewpoints. New opinions about the propagation and energy dispersion are to be proved by more observations and study.
Rossby-wave turbulence in a rapidly rotating sphere
Directory of Open Access Journals (Sweden)
N. Schaeffer
2005-01-01
Full Text Available We use a quasi-geostrophic numerical model to study the turbulence of rotating flows in a sphere, with realistic Ekman friction and bulk viscous dissipation. The forcing is caused by the destabilization of an axisymmetric Stewartson shear layer, generated by differential rotation, resulting in a forcing at rather large scales. The equilibrium regime is strongly anisotropic and inhomogeneous but exhibits a steep m-5 spectrum in the azimuthal (periodic direction, at scales smaller than the injection scale. This spectrum has been proposed by Rhines for a Rossby wave turbulence. For some parameter range, we observe a turbulent flow dominated by a large scale vortex located in the shear layer, reminding us of the Great Red Spot of Jupiter.
Computing rare transitions between zonal mid-latitude jets
Simonnet, Eric; Bouchet, Freddy
2016-04-01
Zonal jets are known to naturally emerge from beta-plane turbulence due to the arrest of inverse energy cascade by Rossby waves.Transitions between jets of different wavenumber are indeed observed in particular regimes showing a striking example of bimodality in the context of 2-D turbulence. As the Rayleigh dissipation and stochastic forcing are decreased these transitions become more and more rare. The aim of this talk is to show that it is possible to compute large ensembles of reactive trajectories connecting the different metastable states even at very low probability regimes when direct numerical simulations are not possible. We use an adaptive version of multilevel splitting algorithms on a barotropic quasi geostrophic model of mid-latitude atmosphere. We are able to obtain a detailed statistical description of the high-dimensional phase space as well as the typical transitions. A large-deviation result is also obtained.
Battalio, Michael; Szunyogh, Istvan; Lemmon, Mark
2016-09-01
The energetics of the atmosphere of the northern hemisphere of Mars during the pre-winter solstice period are explored using the Mars Analysis Correction Data Assimilation (MACDA) dataset (v1.0) and the eddy kinetic energy equation, with the quasi-geostrophic omega equation providing vertical velocities. Traveling waves are typically triggered by geopotential flux convergence. The effect of dust on baroclinic instability is examined by comparing a year with a global-scale dust storm (GDS) to two years without a global-scale dust storm. During the non-GDS years, results agree with that of a previous study using a general circulation model simulation. In the GDS year, waves develop a mixed baroclinic/barotropic growth phase before decaying barotropically. Though the total amount of eddy kinetic energy generated by baroclinic energy conversion is lower during the GDS year, the maximum eddy intensity is not diminished. Instead, the number of intense eddies is reduced by about 50%.
DEFF Research Database (Denmark)
Gillet, N.; Jault, D.; Finlay, Chris
2015-01-01
at midlatitudes, and vigorous azimuthal jets in the equatorial belt. The stationary part of the flow predominates on all the spatial scales that we can resolve. We retrieve torsional waves that explain the length-of-day changes at 4 to 9.5 years periods. These waves may be triggered by the nonlinear interaction......We report a calculation of time-dependent quasi-geostrophic core flows for 1940–2010. Inverting recursively for an ensemble of solutions, we evaluate the main source of uncertainties, namely, the model errors arising from interactions between unresolved core surface motions and magnetic fields....... Temporal correlations of these uncertainties are accounted for. The covariance matrix for the flow coefficients is also obtained recursively from the dispersion of an ensemble of solutions. Maps of the flow at the core surface show, upon a planetary-scale gyre, time-dependent large-scale eddies...
Large-scale stationary and turbulent flow over topography
Vallis, G. K.; Roads, J. O.
1984-01-01
The contributions made to the formation of stationary features of flow over topography by linear and nonlinear dynamics were examined with an integrated quasi-geostrophic model with idealized topographic forcing. The simulation was run out to several months and generated time-averaged values which were compared with those obtained with linear theory. Linear predictions were converted to turbulent features through the addition of stationary, nonlinear thermodynamic and transient vorticity fluxes. The turbulence features matched atmospheric data on energy spectra, the direction and magnitude of energy transfers, and the spatial magnitudes involved. Transient flow transferred the majority of energy absorbed by the upscale flow and, by absorbing energy, reduced the energy of stationary flow while retaining resonance signatures. Instability was a pervasive feature of the topographically forced flow except at high wavenumbers. The results confirm that transient eddies are interactive with both asymmetric and zonal flow and cannot be adequately described by linear theory.
Boundary driven shear layer instabilities in a rotating fluid
Schaeffer, N; Schaeffer, Nathanael; Cardin, Philippe
2003-01-01
We study the destabilization of a shear layer, produced by differential rotation of a rotating axisymmetric container. For small forcing, this produces a shear layer, which has been studied by Stewartson and is almost invariant along the rotation axis direction. When the forcing increases, instabilities develop. The way these instabilities grow depends strongly on the geometry of the container. If the depth is constant, the instability develops without breaking the Proudman-Taylor constraint. However, when the depth is not constant (in a spherical shell for instance), the instability has to break the Proudman-Taylor constraint, and thus, the threshold is higher. We develop a quasi-geostrophic two-dimensional model, whose main original feature is to handle the mass conservation correctly, resulting in a divergent two-dimensional flow, and valid for any finite slope. We use it to investigate scalings and asymptotic laws by a simple linear theory and we find an asymmetry between positive and negative differentia...
Efficient Computation of Info-Gap Robustness for Finite Element Models
Energy Technology Data Exchange (ETDEWEB)
Stull, Christopher J. [Los Alamos National Laboratory; Hemez, Francois M. [Los Alamos National Laboratory; Williams, Brian J. [Los Alamos National Laboratory
2012-07-05
A recent research effort at LANL proposed info-gap decision theory as a framework by which to measure the predictive maturity of numerical models. Info-gap theory explores the trade-offs between accuracy, that is, the extent to which predictions reproduce the physical measurements, and robustness, that is, the extent to which predictions are insensitive to modeling assumptions. Both accuracy and robustness are necessary to demonstrate predictive maturity. However, conducting an info-gap analysis can present a formidable challenge, from the standpoint of the required computational resources. This is because a robustness function requires the resolution of multiple optimization problems. This report offers an alternative, adjoint methodology to assess the info-gap robustness of Ax = b-like numerical models solved for a solution x. Two situations that can arise in structural analysis and design are briefly described and contextualized within the info-gap decision theory framework. The treatments of the info-gap problems, using the adjoint methodology are outlined in detail, and the latter problem is solved for four separate finite element models. As compared to statistical sampling, the proposed methodology offers highly accurate approximations of info-gap robustness functions for the finite element models considered in the report, at a small fraction of the computational cost. It is noted that this report considers only linear systems; a natural follow-on study would extend the methodologies described herein to include nonlinear systems.
Investigation of one inverse problem in case of modeling water areas with "liquid" boundaries
Sheloput, Tatiana; Agoshkov, Valery
2015-04-01
In hydrodynamics often appears the problem of modeling water areas (oceans, seas, rivers, etc.) with "liquid" boundaries. "Liquid" boundary means set of those parts of boundary where impermeability condition is broken (for example, straits, bays borders, estuaries, interfaces of oceans). Frequently such effects are ignored: for "liquid" boundaries the same conditions are used as for "solid" ones, "material boundary" approximation is applied [1]. Sometimes it is possible to interpolate the results received from models of bigger areas. Moreover, approximate estimates for boundary conditions are often used. However, those approximations are not always valid. Sometimes errors in boundary condition determination could lead to a significant decrease in the accuracy of the simulation results. In this work one way of considering the problem mentioned above is described. According to this way one inverse problem on reconstruction of boundary function in convection-reaction-diffusion equations which describe transfer of heat and salinity is solved. The work is based on theory of adjoint equations [2] and optimal control, as well as on common methodology of investigation inverse problems [3]. The work contains theoretical investigation and the results of computer simulation applied for the Baltic Sea. Moreover, conditions and restrictions that should be satisfied for solvability of the problem are entered and justified in the work. Submitted work could be applied for the solution of more complicated inverse problems and data assimilation problems in the areas with "liquid" boundaries; also it is a step for developing algorithms on computing level, speed, temperature and salinity that could be applied for real objects. References 1. A. E. Gill. Atmosphere-ocean dynamics. // London: Academic Press, 1982. 2. G. I. Marchuk. Adjoint equations. // Moscow: INM RAS, 2000, 175 p. (in Russian). 3. V.I. Agoshkov. The methods of optimal control and adjoint equations in problems of
Assimilation of geomagnetic observations in dynamical models of the secular variation
International Nuclear Information System (INIS)
Complete text of publication follows. Satellite data contribute to a better description of the secular variation of the main geomagnetic field. To make the best use of that (and upcoming) wealth of data, we consider the possibility to resort to data assimilation, as now routinely used in the fields of meteorology and oceanography. Geomagnetic data assimilation aims at identifying the physics of the Earth's core responsible for the secular variation recorded by satellites and in long-lived, ground observatories. Data assimilation should yield a more accurate forecast of the secular variation, and enable the reanalysis of historical observations. The physics at the heart of our assimilation scheme is based on the assumption that the dynamics responsible for the fast (i.e. interannual) variations of the main magnetic field is quasi-geostrophic. In addition, we describe similarly the magnetic field, in the core interior, using a magnetic flux function, whose dynamics is also two-dimensional. In this presentation, we will focus on the methodological aspects of our assimilation scheme. In particular, we illustrate how the accumulation of successive observations can be used to construct dynamically consistent, time-dependent maps of the magnetic field inside the core.
Implementation and evaluation of an array of chemical solvers in a global chemical transport model
Directory of Open Access Journals (Sweden)
M. Lee
2009-03-01
Full Text Available This paper discusses the implementation and performance of an array of gas-phase chemistry solvers for the state-of-the-science GEOS-Chem global chemical transport model. The implementation is based on the Kinetic PreProcessor (KPP. Two perl parsers automatically generate the needed interfaces between GEOS-Chem and KPP, and allow access to the chemical simulation code without any additional programming effort. This work illustrates the potential of KPP to positively impact global chemical transport modeling by providing additional functionality as follows. (1 The user can select a highly efficient numerical integration method from an array of solvers available in the KPP library. (2 KPP offers extreme flexibility for studies that involve changing the chemical mechanism (e.g., a set of additional reactions is automatically translated into efficient code and incorporated into a modified global model. (3 This work provides immediate access to tangent linear, continuous adjoint, and discrete adjoint chemical models, with applications to sensitivity analysis and data assimilation.
Morales Betancourt, R.; Nenes, A.
2014-05-01
Aerosol indirect effects in climate models strongly depend on the representation of the aerosol activation process. In this study, we assess the process-level differences across activation parameterizations that contribute to droplet number uncertainty by using the adjoints of the Abdul-Razzak and Ghan (2000) and Fountoukis and Nenes (2005) droplet activation parameterizations in the framework of the Community Atmospheric Model version 5.1 (CAM5.1). The adjoint sensitivities of Nd to relevant input parameters are used to (i) unravel the spatially resolved contribution of aerosol number, mass, and chemical composition to changes in Nd between present-day and pre-industrial simulations and (ii) identify the key variables responsible for the differences in Nd fields and aerosol indirect effect estimates when different activation schemes are used within the same modeling framework. The sensitivities are computed online at minimal computational cost. Changes in aerosol number and aerosol mass concentrations were found to contribute to Nd differences much more strongly than chemical composition effects. The main sources of discrepancy between the activation parameterizations considered were the treatment of the water uptake by coarse mode particles, and the sensitivity of the parameterized Nd accumulation mode aerosol geometric mean diameter. These two factors explain the different predictions of Nd over land and over oceans when these parameterizations are employed. Discrepancies in the sensitivity to aerosol size are responsible for an exaggerated response to aerosol volume changes over heavily polluted regions. Because these regions are collocated with areas of deep clouds, their impact on shortwave cloud forcing is amplified through liquid water path changes. The same framework is also utilized to efficiently explore droplet number uncertainty attributable to hygroscopicity parameter of organic aerosol (primary and secondary). Comparisons between the parameterization
Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional non-Abelian spin models
Borisenko, Oleg; Chelnokov, Volodymyr; Cuteri, Francesca; Papa, Alessandro
2016-07-01
It is argued that two-dimensional U(N ) spin models for any N undergo a Berezinskii-Kosterlitz-Thouless (BKT)-like phase transition, similarly to the famous X Y model. This conclusion follows from the Berezinskii-like calculation of the two-point correlation function in U(N ) models, approximate renormalization group analysis, and numerical investigations of the U(2 ) model. It is shown, via Monte Carlo simulations, that the universality class of the U(2 ) model coincides with that of the X Y model. Moreover, preliminary numerical results point out that two-dimensional SU(N ) spin models with the fundamental and adjoint terms and N >4 exhibit two phase transitions of BKT type, similarly to Z (N ) vector models.
Grassi, Alba
2014-01-01
Some matrix models admit, on top of the usual 't Hooft expansion, an M-theory-like expansion, i.e. an expansion at large N but where the rest of the parameters are fixed, instead of scaling with N. These models, which we call M-theoretic matrix models, appear in the localization of Chern-Simons-matter theories, and also in two-dimensional statistical physics. Generically, their partition function receives non-perturbative corrections which are not captured by the 't Hooft expansion. In this paper, we discuss general aspects of these type of matrix integrals and we analyze in detail two different examples. The first one is the matrix model computing the partition function of N=4 supersymmetric Yang-Mills theory in three dimensions with one adjoint hypermultiplet and N_f fundamentals, which has a conjectured M-theory dual, and which we call the N_f matrix model. The second one, which we call the polymer matrix model, computes form factors of the 2d Ising model and is related to the physics of 2d polymers. In bo...
Fusion product of co-adjoint orbits
Chang, Sheldon X.
1998-01-01
The result contained in this paper is an application of a fixed point formula associated with Hamiltonian loop group action. We obtain a G-space which is a geometric dual of the Verlinde's fusion product. Also we obtain a proof of Verlinde formula. The calculation of weights at the fixed point set is based on fundamental properties of root systems of affine Lie algebras. This paper was written in early 1997, the current version has a computer time-stamp 4/4/97.