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.
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.
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.
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...
Adjoint method and runaway electron avalanche
Liu, Chang; Brennan, Dylan P.; Boozer, Allen H.; Bhattacharjee, Amitava
2017-02-01
The adjoint method for the study of runaway electron dynamics in momentum space Liu et al (2016 Phys. Plasmas 23 010702) is rederived using the Green’s function method, for both the runaway probability function (RPF) and the expected loss time (ELT). The RPF and ELT obtained using the adjoint method are presented, both with and without the synchrotron radiation reaction force. The adjoint method is then applied to study the runaway electron avalanche. Both the critical electric field and the growth rate for the avalanche are calculated using this fast and novel approach.
High Order Adjoint Derivatives using ESDIRK Methods for Oil Reservoir Production Optimization
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...
Hekmat, Mohamad Hamed; Mirzaei, Masoud
2015-01-01
In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced.
Double-Difference Measurements in Global Adjoint Tomography
Orsvuran, Ridvan; Yuan, Yanhua; Lei, Wenjie; Bozdag, Ebru; Simons, Frederik J.; Tromp, Jeroen
2017-04-01
The adjoint method efficiently incorporates 3D seismic wave simulations and Fréchet kernels in seismic tomography, and has been successfully applied to exploration and global-scale imaging problems. It is well known that the success of inversions is closely tied to the chosen misfit function. The recently proposed double-difference (DD) method for adjoint inversions (Yuan et al. 2016) minimizes systematic errors in structural inversions related to source parameters, such as origin times, source time functions, etc. Moreover, since the DD method is based on differential measurements between station pairs, bias in structural inversions due to an uneven distribution of stations is also reduced. In this study, our aim is to take advantages of the DD method in real full-waveform inversion problems based on earthquake data. Our main focus is to demonstrate it at the global-scale adjoint tomography. To this end, we closely follow the global adjoint tomography strategies presented in Bozdag et al. (2016) and first consider extending phase misfits, such as multitaper cross-correlation measurements, to the DD approach. The major challenges are to reduce the computational cost of making differential measurements on every station pair and assimilating misfits of all phases in DD measurements. We have initiated the first tests with surface-wave data only. We explore how to incorporate body waves in double-difference adjoint tomography and implement various other misfits, such as instantaneous phase measurements, in the context of global inversions. We discuss how we can implement DD measurements into global adjoint tomography studies in a feasible way and present our initial results.
Adjoint methods for aerodynamic wing design
Grossman, Bernard
1993-01-01
A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.
Tsunami waveform inversion by adjoint methods
Pires, Carlos; Miranda, Pedro M. A.
2001-09-01
An adjoint method for tsunami waveform inversion is proposed, as an alternative to the technique based on Green's functions of the linear long wave model. The method has the advantage of being able to use the nonlinear shallow water equations, or other appropriate equation sets, and to optimize an initial state given as a linear or nonlinear function of any set of free parameters. This last facility is used to perform explicit optimization of the focal fault parameters, characterizing the initial sea surface displacement of tsunamigenic earthquakes. The proposed methodology is validated with experiments using synthetic data, showing the possibility of recovering all relevant details of a tsunami source from tide gauge observations, providing that the adjoint method is constrained in an appropriate manner. It is found, as in other methods, that the inversion skill of tsunami sources increases with the azimuthal and temporal coverage of assimilated tide gauge stations; furthermore, it is shown that the eigenvalue analysis of the Hessian matrix of the cost function provides a consistent and useful methodology to choose the subset of independent parameters that can be inverted with a given dataset of observations and to evaluate the error of the inversion process. The method is also applied to real tide gauge series, from the tsunami of the February 28, 1969, Gorringe Bank earthquake, suggesting some reasonable changes to the assumed focal parameters of that event. It is suggested that the method proposed may be able to deal with transient tsunami sources such as those generated by submarine landslides.
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
Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method
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.
Adjoint method for the optimum planning of industrial pollutant sources
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.
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
Vishnampet, Ramanathan [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Bodony, Daniel J. [Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Freund, Jonathan B., E-mail: jbfreund@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States); Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 (United States)
2015-03-15
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that
Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling
Davis, B. N.; LeVeque, R. J.
2016-12-01
One difficulty in developing numerical methods for tsunami modeling is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain, particularly when tracking a tsunami propagating across the ocean. The open source GeoClaw software deals with this issue by using block-structured adaptive mesh refinement to selectively refine around propagating waves. For problems where only a target area of the total solution is of interest (e.g., one coastal community), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. In this work, we show that solving the time-dependent adjoint equation and using a suitable inner product with the forward solution allows more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and potentially for other tsunami applications beyond adaptive refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source GeoClaw software and present tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement.
STUDY ON THE ADJOINT METHOD IN DATA ASSIMILATION AND THE RELATED PROBLEMS
吕咸青; 吴自库; 谷艺; 田纪伟
2004-01-01
It is not reasonable that one can only use the adjoint of model in data assimilation.The simulated numerical experiment shows that for the tidal model,the result of the adjoint of equation is almost the same as that of the adjoint of model:the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°.The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea.For comparison,the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea.The initial guess values of the boundary conditions are given first,and then are adjusted to acquire the simulated results that are as close as possible to the observations.As the boundary conditions contain 72 values,which should be adjusted and how to adjust them can only be partially solved by adjusting them many times.The satisfied results are hard to acquire even gigantic efforts are done.Here,the automation of the treatment of the open boundary conditions is realized.The method is unique and superior to the traditional methods.It is emphasized that if the adjoint of equation is used,tedious and complicated mathematical deduction can be avoided.Therefore the adjoint of equation should attract much attention.
Approximation of weak adjoints by reverse automatic differentiation of BDF methods
Beigel, Dörte; Wirsching, Leonard; Bock, Hans Georg
2011-01-01
With this contribution, we shed light on the relation between the discrete adjoints of multistep backward differentiation formula (BDF) methods and the solution of the adjoint differential equation. To this end, we develop a functional-analytic framework based on a constrained variational problem and introduce the notion of weak adjoint solutions. We devise a finite element Petrov-Galerkin interpretation of the BDF method together with its discrete adjoint scheme obtained by reverse internal numerical differentiation. We show how the finite element approximation of the weak adjoint is computed by the discrete adjoint scheme and prove its asymptotic convergence in the space of normalized functions of bounded variation. We also obtain asymptotic convergence of the discrete adjoints to the classical adjoints on the inner time interval. Finally, we give numerical results for non-adaptive and fully adaptive BDF schemes. The presented framework opens the way to carry over the existing theory on global error estimat...
The adjoint sensitivity method of global electromagnetic induction for CHAMP magnetic data
Martinec, Zdeněk; Velímský, Jakub
2009-12-01
An existing time-domain spectral-finite element approach for the forward modelling of electromagnetic induction vector data as measured by the CHAMP satellite is, in this paper, supplemented by a new method of computing the sensitivity of the CHAMP electromagnetic induction data to the Earth's mantle electrical conductivity, which we term the adjoint sensitivity method. The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the specification of prescribed boundary conditions. The respective boundary-value data at the satellite's altitude are the X magnetic component measured by the CHAMP vector magnetometer along the satellite track for the forward method and the difference between the measured and predicted Z magnetic component for the adjoint method. The squares of these differences summed up over all CHAMP tracks determine the misfit. The sensitivities of the CHAMP data, that is the partial derivatives of the misfit with respect to mantle conductivity parameters, are then obtained by the scalar product of the forward and adjoint solutions, multiplied by the gradient of the conductivity and integrated over all CHAMP tracks. Such exactly determined sensitivities are checked against numerical differentiation of the misfit, and good agreement is obtained. The attractiveness of the adjoint method lies in the fact that the adjoint sensitivities are calculated for the price of only an additional forward calculation, regardless of the number of conductivity parameters. However, since the adjoint solution proceeds backwards in time, the forward solution must be stored at each time step, leading to memory requirements that are linear with respect to the number of steps undertaken. Having determined the sensitivities, we apply the conjugate gradient method to infer 1-D and 2-D conductivity structures of the Earth based on the CHAMP residual time series (after the subtraction of static field and secular variations
Earthquake Source Modeling using Time-Reversal or Adjoint Methods
Hjorleifsdottir, V.; Liu, Q.; Tromp, J.
2007-12-01
In recent years there have been great advances in earthquake source modeling. Despite the effort, many questions about earthquake source physics remain unanswered. In order to address some of these questions, it is useful to reconstruct what happens on the fault during an event. In this study we focus on determining the slip distribution on a fault plane, or a moment-rate density, as a function of time and space. This is a difficult process involving many trade offs between model parameters. The difficulty lies in the fact that earthquakes are not a controlled experiment, we don't know when and where they will occur, and therefore we have only limited control over what data will be acquired for each event. As a result, much of the advance that can be made, is by extracting more information out of the data that is routinely collected. Here we use a technique that uses 3D waveforms to invert for the slip on a fault plane during rupture. By including 3D wave-forms we can use parts of the wave-forms that are often discarded, as they are altered by structural effects in ways that cannot be accurately predicted using 1D Earth models. However, generating 3D synthetic is computationally expensive. Therefore we turn to an `adjoint' method (Tarantola Geoph.~1984, Tromp et al.~GJI 2005), that reduces the computational cost relative to methods that use Green's function libraries. In it's simplest form an adjoint method for inverting for source parameters can be viewed as a time-reversal experiment performed with a wave-propagation code (McMechan GJRAS 1982). The recorded seismograms are inserted as simultaneous sources at the location of the receiver and the computed wave field (which we call the adjoint wavefield) is recorded on an array around the earthquake location. Here we show, mathematically, that for source inversions for a moment tensor (distributed) source, the time integral of the adjoint strain is the quantity to monitor. We present the results of time
Tape, Carl; Liu, Qinya; Tromp, Jeroen
2007-03-01
We employ adjoint methods in a series of synthetic seismic tomography experiments to recover surface wave phase-speed models of southern California. Our approach involves computing the Fréchet derivative for tomographic inversions via the interaction between a forward wavefield, propagating from the source to the receivers, and an `adjoint' wavefield, propagating from the receivers back to the source. The forward wavefield is computed using a 2-D spectral-element method (SEM) and a phase-speed model for southern California. A `target' phase-speed model is used to generate the `data' at the receivers. We specify an objective or misfit function that defines a measure of misfit between data and synthetics. For a given receiver, the remaining differences between data and synthetics are time-reversed and used as the source of the adjoint wavefield. For each earthquake, the interaction between the regular and adjoint wavefields is used to construct finite-frequency sensitivity kernels, which we call event kernels. An event kernel may be thought of as a weighted sum of phase-specific (e.g. P) banana-doughnut kernels, with weights determined by the measurements. The overall sensitivity is simply the sum of event kernels, which defines the misfit kernel. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, that is, the Fréchet derivative. A non-linear conjugate gradient algorithm is used to iteratively improve the model while reducing the misfit function. We illustrate the construction of the gradient and the minimization algorithm, and consider various tomographic experiments, including source inversions, structural inversions and joint source-structure inversions. Finally, we draw connections between classical Hessian-based tomography and gradient-based adjoint tomography.
Mehdi Delkhosh; Mohammad Delkhosh
2012-01-01
Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011). In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefited from the solution of numerical Self-adjoint equations (Mohynl-Din, 2009; Allame and Azal, 2011;...
Adjoint complement to viscous finite-volume pressure-correction methods
Stück, Arthur; Rung, Thomas
2013-09-01
A hybrid-adjoint Navier-Stokes method for the pressure-based computation of hydrodynamic objective functional derivatives with respect to the shape is systematically derived in three steps: The underlying adjoint partial differential equations and boundary conditions for the frozen-turbulence Reynolds-averaged Navier-Stokes equations are considered in the first step. In step two, the adjoint discretisation is developed from the primal, unstructured finite-volume discretisation, such that adjoint-consistent approximations to the adjoint partial differential equations are obtained following a so-called hybrid-adjoint approach. A unified, discrete boundary description is outlined that supports high- and low-Reynolds number turbulent wall-boundary treatments for both the adjoint boundary condition and the boundary-based gradient formula. The third component focused in the development of the industrial adjoint CFD method is the adjoint counterpart to the primal pressure-correction algorithm. The approach is verified against the direct-differentiation method and an application to internal flow problems is presented.
Comparison of the Monte Carlo adjoint-weighted and differential operator perturbation methods
Kiedrowski, Brian C [Los Alamos National Laboratory; Brown, Forrest B [Los Alamos National Laboratory
2010-01-01
Two perturbation theory methodologies are implemented for k-eigenvalue calculations in the continuous-energy Monte Carlo code, MCNP6. A comparison of the accuracy of these techniques, the differential operator and adjoint-weighted methods, is performed numerically and analytically. Typically, the adjoint-weighted method shows better performance over a larger range; however, there are exceptions.
The state-space approach to the method of adjoints for hybrid guidance loop models
Weiss, M.; Bucco, D.
2009-01-01
A framework is introduced to develop the theory of the Adjoint Method for models including both continuous and discrete dynamics. The basis of this framework consists of the class of impulsive linear dynamical systems. It allows extension of the Adjoint Method to more general models that include mul
Diosady, Laslo; Murman, Scott; Blonigan, Patrick; Garai, Anirban
2017-01-01
Presented space-time adjoint solver for turbulent compressible flows. Confirmed failure of traditional sensitivity methods for chaotic flows. Assessed rate of exponential growth of adjoint for practical 3D turbulent simulation. Demonstrated failure of short-window sensitivity approximations.
Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe
2013-01-01
This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.
Introduction to Adjoint Models
Errico, Ronald M.
2015-01-01
In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.
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.
The adjoint sensitivity method of global electromagnetic induction for CHAMP magnetic data
Z. Martinec; J. Velimsky
2017-01-01
An existing time-domain spectral-finite element approach for the forward modelling of electromagnetic induction vector data as measured by the CHAMP satellite is, in this paper, supplemented by a new method of computing the sensitivity of the CHAMP electromagnetic induction data to the Earth's mantle electrical conductivity, which we term the adjoint sensitivity method. The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the speci...
Yaodeng Chen
2014-01-01
Full Text Available There are two different approaches on how to formulate adjoint numerical model (ANM. Aiming at the disputes arising from the construction methods of ANM, the differences between nonlinear shallow water equation and its adjoint equation are analyzed; the hyperbolicity and homogeneity of the adjoint equation are discussed. Then, based on unstructured meshes and finite volume method, a new adjoint model was advanced by getting numerical model of the adjoint equations directly. Using a gradient check, the correctness of the adjoint model was verified. The results of twin experiments to invert the bottom friction coefficient (Manning’s roughness coefficient indicate that the adjoint model can extract the observation information and produce good quality inversion. The reason of disputes about construction methods of ANM is also discussed in the paper.
Multi-objective optimization strategies using adjoint method and game theory in aerodynamics
Zhili Tang
2006-01-01
There are currently three different game strategies originated in economics:(1) Cooperative games (Pareto front),(2)Competitive games (Nash game) and (3)Hierarchical games (Stackelberg game).Each game achieves different equilibria with different performance,and their players play different roles in the games.Here,we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multicriteria aerodynamic optimization problems.The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments.We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method.The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front.Non-dominated Pareto front solutions are obtained,however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.
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
THE EXISTENCE OF PERIODIC SOLUTIONS TO SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS
无
2010-01-01
In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.
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
Yonghan Choi
2014-01-01
Full Text Available An adjoint sensitivity-based data assimilation (ASDA method is proposed and applied to a heavy rainfall case over the Korean Peninsula. The heavy rainfall case, which occurred on 26 July 2006, caused torrential rainfall over the central part of the Korean Peninsula. The mesoscale convective system (MCS related to the heavy rainfall was classified as training line/adjoining stratiform (TL/AS-type for the earlier period, and back building (BB-type for the later period. In the ASDA method, an adjoint model is run backwards with forecast-error gradient as input, and the adjoint sensitivity of the forecast error to the initial condition is scaled by an optimal scaling factor. The optimal scaling factor is determined by minimising the observational cost function of the four-dimensional variational (4D-Var method, and the scaled sensitivity is added to the original first guess. Finally, the observations at the analysis time are assimilated using a 3D-Var method with the improved first guess. The simulated rainfall distribution is shifted northeastward compared to the observations when no radar data are assimilated or when radar data are assimilated using the 3D-Var method. The rainfall forecasts are improved when radar data are assimilated using the 4D-Var or ASDA method. Simulated atmospheric fields such as horizontal winds, temperature, and water vapour mixing ratio are also improved via the 4D-Var or ASDA method. Due to the improvement in the analysis, subsequent forecasts appropriately simulate the observed features of the TL/AS- and BB-type MCSs and the corresponding heavy rainfall. The computational cost associated with the ASDA method is significantly lower than that of the 4D-Var method.
Pingen, Georg; Evgrafov, Anton; Maute, Kurt
2009-01-01
We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion...
Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir
2012-01-01
are large-scale problems and require specialized numerical algorithms. In this paper, we combine a single shooting optimization algorithm based on sequential quadratic programming (SQP) with explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods and a continuous adjoint method...
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.
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
Bucco, D.; Weiss, M.
2007-01-01
The COVariance and ADjoint Analysis Tool (COVAD) is a specially designed software tool, written for the Matlab/Simulink environment, which allows the user the capability to carry out system analysis and simulation using the adjoint, covariance or Monte Carlo methods. This paper describes phase one o
Bucco, D.; Weiss, M.
2007-01-01
The COVariance and ADjoint Analysis Tool (COVAD) is a specially designed software tool, written for the Matlab/Simulink environment, which allows the user the capability to carry out system analysis and simulation using the adjoint, covariance or Monte Carlo methods. This paper describes phase one
A new method for computing the eigenfunctions and their adjoints of the dynamo operator
Schrinner, M; Jiang, J; Hoyng, P
2009-01-01
We present a new method to determine the eigensolutions of the induction and the dynamo equation in a fluid embedded in vacuum. The magnetic field is expanded in a complete set of functions. The new method is based on the biorthogonality of the adjoint electric current and the vector potential with an inner product defined by a volume integral over the fluid domain. The advantage of this method is that the velocity and the dynamo coefficients of the induction and the dynamo equation do not have to be differentiated and thus even numerically determined tabulated values of the coefficients produce reasonable results. We provide test calculations and compare with published results obtained by the classical treatment based on the biorthogonality of the magnetic field and its adjoint. We especially consider dynamos with mean-field coefficients determined from direct numerical simulations of the geodynamo and compare with initial value calculations and the full MHD simulations.
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.
Topology Optimization of Turbulent Fluid Flow with a Sensitive Porosity Adjoint Method (SPAM)
Philippi, B
2015-01-01
A sensitive porosity adjoint method (SPAM) for optimizing the topology of fluid machines has been proposed. A sensitivity function with respect to the porosity has been developed. In the first step of the optimization process, porous media are introduced into the flow regime according to the sensitivity function. Then the optimized porous media are transformed to solid walls. The turbulent flow in porous media is accounted for by a modified eddy-viscosity based turbulence model. Its influence on the adjoint equations is nevertheless neglected, which refers to the so called frozen turbulence assumption. A test case of application in terms of the turbulent rough wall channel flow shows that a considerable reduction of the objective function can be obtained by this method. The transformation from porous media to solid walls may have important effect on the optimization results.
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.
Grossman, Bernard
1999-01-01
The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based
Aerodynamic Optimization Based on Continuous Adjoint Method for a Flexible Wing
Zhaoke Xu
2016-01-01
Full Text Available Aerodynamic optimization based on continuous adjoint method for a flexible wing is developed using FORTRAN 90 in the present work. Aerostructural analysis is performed on the basis of high-fidelity models with Euler equations on the aerodynamic side and a linear quadrilateral shell element model on the structure side. This shell element can deal with both thin and thick shell problems with intersections, so this shell element is suitable for the wing structural model which consists of two spars, 20 ribs, and skin. The continuous adjoint formulations based on Euler equations and unstructured mesh are derived and used in the work. Sequential quadratic programming method is adopted to search for the optimal solution using the gradients from continuous adjoint method. The flow charts of rigid and flexible optimization are presented and compared. The objective is to minimize drag coefficient meanwhile maintaining lift coefficient for a rigid and flexible wing. A comparison between the results from aerostructural analysis of rigid optimization and flexible optimization is shown here to demonstrate that it is necessary to include the effect of aeroelasticity in the optimization design of a wing.
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.
Adjoint Optimization of a Wing Using the CSRT Method
Straathof, M.H.; Van Tooren, M.J.L.
2011-01-01
This paper will demonstrate the potential of the Class-Shape-Refinement-Transformation (CSRT) method for aerodynamically optimizing three-dimensional surfaces. The CSRT method was coupled to an in-house Euler solver and this combination was used in an optimization framework to optimize the ONERA M6
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
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.
Adjustment of Tsunami Source Parameters By Adjoint Methods
Pires, C.; Miranda, P.
Tsunami waveforms recorded at tide gauges can be used to adjust tsunami source pa- rameters and, indirectly, seismic focal parameters. Simple inversion methods, based on ray-tracing techniques, only used a small fraction of available information. More elab- orate techniques, based on the Green's functions methods, also have some limitations in their scope. A new methodology, using a variational approach, allows for a much more general inversion, which can directly optimize focal parameters of tsunamigenic earthquakes. Idealized synthetic data and an application to the 1969 Gorringe Earth- quake are used to validate the methodology.
Laboure, Vincent M.; McClarren, Ryan G.; Wang, Yaqi
2016-01-01
In this paper, we derive a method for the second-order form of the transport equation that is both globally conservative and compatible with voids, using Continuous Finite Element Methods (CFEM). The main idea is to use the Least-Squares (LS) form of the transport equation in the void regions and the Self-Adjoint Angular Flux (SAAF) form elsewhere. While the SAAF formulation is globally conservative, the LS formulation need a correction in void. The price to pay for this fix is the loss of sy...
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2017-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated.
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2017-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851
Sengupta, T. K.; Bhaumik, S.; Shameem, U.
2011-03-01
A single-parameter family of self-adjoint compact difference (SACD) schemes is developed for discretizing the Laplacian operator in self-adjoint form. Developed implicit scheme is formally second-order accurate (with respect to truncation error) with a free parameter, α which helps control the numerical properties in the spectral plane. The SACD scheme is analyzed in the spectral plane for its resolution properties for both periodic and non-periodic problems using the matrix spectral analysis [T.K. Sengupta, G. Ganeriwal, S. De, Analysis of central and upwind schemes, J. Comput. Phys. 192 (2) (2003) 677-694]. The major objective here is to identify the advantages of the new scheme over the traditional explicit second order CD2 scheme, in discretizing the Laplacian operator in self-adjoint form. This appears in Navier-Stokes equation and in other transport equations and boundary value problems (bvp) expressed in orthogonal co-ordinate systems, either in physical or in transformed plane. We also compare the developed method with the higher order compact schemes for non-uniform grids. To demonstrate the accuracy of SACD scheme we have tested it for: (i) bi-directional wave propagation problem, given by the second order wave equation and (ii) an elliptic bvp, as in the Stommel ocean model for the stream function. These examples help infer the properties of SACD scheme when solving different types of partial differential equations. Most importantly the effects of grid-stretching and choice of value of the free parameter ( α) are investigated here. We also compare the present implicit compact method with explicit compact method known as the higher order compact (HOC) method. Also, the practical applications of the SACD scheme are explored by solving the Navier-Stokes equation for the cases of: (a) a flow inside a lid-driven cavity and (b) the receptivity and instability of an external adverse pressure gradient flow over a flat plate. In the former, unsteadiness of the
Aerodynamic Optimization of the Nose Shape of a Train Using the Adjoint Method
Jorge Munoz-Paniagua
2015-01-01
Full Text Available The adjoint method is used in this paper for the aerodynamic optimization of the nose shape of a train. This method has been extensively applied in aircraft or ground vehicle aerodynamic optimization, but is still in progress in train aerodynamics. Here we consider this innovative optimization method and present its application to reduce the aerodynamic drag when the train is subjected to front wind. The objective of this paper is to demonstrate the effectiveness of the method, highlighting the requirements, limitations and capabilities of it. Furthermore, a significant reduction of the aerodynamic drag in a short number of solver calls is aimed as well. The independence of the computational cost with respect to the number of design variables that define the optimal candidate is stressed as the most interesting characteristic of the adjoint method. This behavior permits a more complete modification of the shape of the train nose because the number of design variables is not a constraint anymore. The information obtained from the sensitivity field permits determining the regions of the geometry where a small modification of the nose shape might introduce a larger improvement of the train performance. A good agreement between this information and the successive geometry modifications is observed here.
Comparison of Observation Impacts in Two Forecast Systems using Adjoint Methods
Gelaro, Ronald; Langland, Rolf; Todling, Ricardo
2009-01-01
An experiment is being conducted to compare directly the impact of all assimilated observations on short-range forecast errors in different operational forecast systems. We use the adjoint-based method developed by Langland and Baker (2004), which allows these impacts to be efficiently calculated. This presentation describes preliminary results for a "baseline" set of observations, including both satellite radiances and conventional observations, used by the Navy/NOGAPS and NASA/GEOS-5 forecast systems for the month of January 2007. In each system, about 65% of the total reduction in 24-h forecast error is provided by satellite observations, although the impact of rawinsonde, aircraft, land, and ship-based observations remains significant. Only a small majority (50- 55%) of all observations assimilated improves the forecast, while the rest degrade it. It is found that most of the total forecast error reduction comes from observations with moderate-size innovations providing small to moderate impacts, not from outliers with very large positive or negative innovations. In a global context, the relative impacts of the major observation types are fairly similar in each system, although regional differences in observation impact can be significant. Of particular interest is the fact that while satellite radiances have a large positive impact overall, they degrade the forecast in certain locations common to both systems, especially over land and ice surfaces. Ongoing comparisons of this type, with results expected from other operational centers, should lead to more robust conclusions about the impacts of the various components of the observing system as well as about the strengths and weaknesses of the methodologies used to assimilate them.
Estimation of Oceanic Eddy Viscosity Profile and Wind Stress Drag Coefficient Using Adjoint Method
Qilin Zhang
2015-01-01
Full Text Available Adjoint method is used to assimilate pseudoobservations to simultaneously estimate the OEVP and the WSDC in an oceanic Ekman layer model. Five groups of experiments are designed to investigate the influences that the optimization algorithms, step-length, inverse integral time of the adjoint model, prescribed vertical distribution of eddy viscosity, and regularization parameter exert on the inversion results. Experimental results show that the best estimation results are obtained with the GD algorithm; the best estimation results are obtained when the step-length is equal to 1 in Group 2; in Group 3, 8 days of inverse integral time yields the best estimation results, and good assimilation efficiency is achieved by increasing iteration steps when the inverse integral time is reduced; in Group 4, the OEVP can be estimated for some specific distributions; however, when the VEVCs increase along with the depth at the bottom of water, the estimation results are relatively poor. For this problem, we use extrapolation method to deal with the VEVCs in layers in which the estimation results are poor; the regularization method with appropriate regularization parameter can indeed improve the experiment result to some extent. In all experiments in Groups 2-3, the WSDCs are inverted successfully within 100 iterations.
Magnetic Field Separation Around Planets Using an Adjoint-Method Approach
Nabert, Christian; Glassmeier, Karl-Heinz; Heyner, Daniel; Othmer, Carsten
The two spacecraft of the BepiColombo mission will reach planet Mercury in 2022. The magnetometers on-board these polar orbiting spacecraft will provide a detailed map of the magnetic field in Mercury's environment. Unfortunately, a separation of the magnetic field into internal and external parts using the classical Gauss-algorithm is not possible due to strong electric currents in the orbit region of the spacecraft. These currents are due to the interaction of the solar wind with Mercury's planetary magnetic field. We use an MHD code to simulate this interaction process. This requires a first choice of Mercury's planetary field which is used and modified until the simulation results fit to the actual measurements. This optimization process is carried out most efficiently using an adjoint-method. The adjoint-method is well known for its low computational cost in order to determine sensitivities required for the minimization. In a first step, the validity of our approach to separate magnetic field contributions into internal and external parts is demonstrated using synthetic generated data. Furthermore, we apply our approach to satellite measurements of the Earth's magnetic field. We can compare the results with the well known planetary field of the Earth to prove practical suitability.
Mani, Karthik
Adjoint methods have found applications in several key areas of computational fluid dynamics (CFD), namely, shape optimization and goal based adaptive solutions. CFD has become an essential tool in the design process by enabling the rapid testing of multiple designs, and currently it is normal practice to use CFD in conjunction with optimization algorithms for design improvement. In the context of shape optimization problems based on CFD, adjoint methods offer the significant advantage of computing sensitivity derivatives of the optimization cost function with respect to the set of design parameters, at a cost that is essentially independent of the number of design parameters. Adjoint methods reduce the cost of obtaining the complete gradient vector at any point in the design space equivalent to that of a single flow solution at the same point in the design space. This immediately enables the use of all gradient based optimization algorithms and lifts any restrictions on the number of design parameters required for the adequate definition of the optimization problem. Adaptive techniques in CFD constitute the other aspect where adjoint methods have have made great inroads. Typical adaptive solutions of the governing flow equations rely on estimating the local error in an evolving solution to target regions of the computational mesh for increased discrete resolution. The main goal of any adaptive solution method is the overall increase in solution accuracy with minimal increase in computational cost. However, targeting local error in the solution does not translate into efficient use of computational resources, since ultimately it is the accurate estimation of boundary integrated functional quantities such as load coefficients that are of importance to the user. Contrary to local error-based methods, adjoint methods allow the adaptation of the computational mesh specifically for the improvement of functionals such as load coefficients. This is achieved by
Numerical Study on Initial Field of Pollution in the Bohai Sea with an Adjoint Method
Chunhui Wang
2013-01-01
Full Text Available Based on the simulation of a marine ecosystem dynamical model in the Bohai Sea, routine monitoring data are assimilated to study the initial field of pollution by using the adjoint method. In order to reduce variables that need to be optimized and make the simulation results more reasonable, an independent grid is selected every four grids both in longitude and latitude, and only the pollutant concentrations of these independent grids needed to be optimized while the other grids were calculated by interpolation method. Based on this method, the stability and reliability of this model were proved by a set of twin experiments. Therefore, this model could be applied in real experiment to simulate the initial field of the total nitrogen (totalN in May, 2009. Moreover, the distribution of totalN in any time step could be calculated by this model, and the monthly mean distribution in May in the Bohai Sea could be obtained.
Data assimilation for massive autonomous systems based on a second-order adjoint method
Ito, Shin-ichi; Nagao, Hiromichi; Yamanaka, Akinori; Tsukada, Yuhki; Koyama, Toshiyuki; Kano, Masayuki; Inoue, Junya
2016-10-01
Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA is now an accepted technique in various scientific fields. One key issue that remains controversial is the implementation of DA in massive simulation models under the constraints of limited computation time and resources. In this paper, we propose an adjoint-based DA method for massive autonomous models that produces optimum estimates and their uncertainties within reasonable computation time and resource constraints. The uncertainties are given as several diagonal elements of an inverse Hessian matrix, which is the covariance matrix of a normal distribution that approximates the target posterior probability density function in the neighborhood of the optimum. Conventional algorithms for deriving the inverse Hessian matrix require O (C N2+N3) computations and O (N2) memory, where N is the number of degrees of freedom of a given autonomous system and C is the number of computations needed to simulate time series of suitable length. The proposed method using a second-order adjoint method allows us to directly evaluate the diagonal elements of the inverse Hessian matrix without computing all of its elements. This drastically reduces the number of computations to O (C ) and the amount of memory to O (N ) for each diagonal element. The proposed method is validated through numerical tests using a massive two-dimensional Kobayashi phase-field model. We confirm that the proposed method correctly reproduces the parameter and initial state assumed in advance, and successfully evaluates the uncertainty of the parameter. Such information regarding uncertainty is valuable, as it can be used to optimize the design of experiments.
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...
Curbelo, Jesus P.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: jperez@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-Graduacao em Modelagem Computacional; Hernandez, Carlos R.G., E-mail: cgh@instec.cu [Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2015-07-01
The spectral Green's function (SGF) method is a numerical method that is free of spatial truncation errors for slab-geometry fixed-source discrete ordinates (S{sub N}) adjoint problems. The method is based on the standard spatially discretized adjoint S{sub N} balance equations and a nonstandard adjoint auxiliary equation expressing the node-average adjoint angular flux, in each discretization node, as a weighted combination of the node-edge outgoing adjoint fluxes. The auxiliary equation contains parameters which act as Green's functions for the cell-average adjoint angular flux. These parameters are determined by means of a spectral analysis which yields the local general solution of the S{sub N} equations within each node of the discretization grid. In this work a number of advances in the SGF adjoint method are presented: the method is extended to adjoint S{sub N} problems considering linearly anisotropic scattering and non-zero prescribed boundary conditions for the forward source-detector problem. Numerical results to typical model problems are considered to illustrate the efficiency and accuracy of the o offered method. (author)
The forward sensitivity and adjoint-state methods of glacial isostatic adjustment
Martinec, Zdeněk; Sasgen, Ingo; Velímský, Jakub
2015-01-01
In this study, a new method for computing the sensitivity of the glacial isostatic adjustment (GIA) forward solution with respect to the Earth's mantle viscosity, the so-called the forward sensitivity method (FSM), and a method for computing the gradient of data misfit with respect to viscosity parameters, the so-called adjoint-state method (ASM), are presented. These advanced formal methods complement each other in the inverse modelling of GIA-related observations. When solving this inverse problem, the first step is to calculate the forward sensitivities by the FSM and use them to fix the model parameters that do not affect the forward model solution, as well as identifying and removing redundant parts of the inferred viscosity structure. Once the viscosity model is optimized in view of the forward sensitivities, the minimization of the data misfit with respect to the viscosity parameters can be carried out by a gradient technique which makes use of the ASM. The aim is this paper is to derive the FSM and ASM in the forms that are closely associated with the forward solver of GIA developed by Martinec. Since this method is based on a continuous form of the forward model equations, which are then discretized by spectral and finite elements, we first derive the continuous forms of the FSM and ASM and then discretize them by the spectral and finite elements used in the discretization of the forward model equations. The advantage of this approach is that all three methods (forward, FSM and ASM) have the same matrix of equations and use the same methodology for the implementation of the time evolution of stresses. The only difference between the forward method and the FSM and ASM is that the different numerical differencing schemes for the time evolution of the Maxwell and generalized Maxwell viscous stresses are applied in the respective methods. However, it requires only a little extra computational time for carrying out the FSM and ASM numerically. An
An adjoint data assimilation method for optimizing frictional parameters on the afterslip area
Kano, Masayuki; Miyazaki, Shin'ichi; Ito, Kosuke; Hirahara, Kazuro
2013-12-01
Afterslip sometimes triggers subsequent earthquakes within a timescale of days to several years. Thus, it may be possible to predict the occurrence of such a triggered earthquake by simulating the spatio-temporal evolution of afterslip with estimated frictional parameters. To demonstrate the feasibility of this idea, we consider a plate interface model where afterslip propagates between two asperities following a rate-and-state friction law, and we adopt an adjoint data assimilation method to optimize frictional parameters. Synthetic observation data are sampled as the slip velocities on the plate interface during 20 days. It is found that: (1) all frictional parameters are optimized if the data sets consists not only of the early phase of afterslip or acceleration, but also of the decaying phase or deceleration; and (2) the prediction of the timing of the triggered earthquake is improved by using adjusted frictional parameters.
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.
Damage Detection of Bridges Using Vibration Data by Adjoint Variable Method
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.
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.
Zahr, M. J.; Persson, P.-O.
2016-12-01
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian-Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge-Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space-time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization. The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier-Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.
Truchet, G.; Leconte, P.; Peneliau, Y.; Santamarina, A.; Malvagi, F.
2014-06-01
Pile-oscillation experiments are performed in the MINERVE reactor at the CEA Cadarache to improve nuclear data accuracy. In order to precisely calculate small reactivity variations (experiments, a reference calculation need to be achieved. This calculation may be accomplished using the continuous-energy Monte Carlo code TRIPOLI-4® by using the eigenvalue difference method. This "direct" method has shown limitations in the evaluation of very small reactivity effects because it needs to reach a very small variance associated to the reactivity in both states. To answer this problem, it has been decided to implement the exact perturbation theory in TRIPOLI-4® and, consequently, to calculate a continuous-energy adjoint flux. The Iterated Fission Probability (IFP) method was chosen because it has shown great results in some other Monte Carlo codes. The IFP method uses a forward calculation to compute the adjoint flux, and consequently, it does not rely on complex code modifications but on the physical definition of the adjoint flux as a phase-space neutron importance. In the first part of this paper, the IFP method implemented in TRIPOLI-4® is described. To illustrate the effciency of the method, several adjoint fluxes are calculated and compared with their equivalent obtained by the deterministic code APOLLO-2. The new implementation can calculate angular adjoint flux. In the second part, a procedure to carry out an exact perturbation calculation is described. A single cell benchmark has been used to test the accuracy of the method, compared with the "direct" estimation of the perturbation. Once again the method based on the IFP shows good agreement for a calculation time far more inferior to the "direct" method. The main advantage of the method is that the relative accuracy of the reactivity variation does not depend on the magnitude of the variation itself, which allows us to calculate very small reactivity perturbations with high precision. Other applications of
MCNP: Multigroup/adjoint capabilities
Wagner, J.C.; Redmond, E.L. II; Palmtag, S.P.; Hendricks, J.S.
1994-04-01
This report discusses various aspects related to the use and validity of the general purpose Monte Carlo code MCNP for multigroup/adjoint calculations. The increased desire to perform comparisons between Monte Carlo and deterministic codes, along with the ever-present desire to increase the efficiency of large MCNP calculations has produced a greater user demand for the multigroup/adjoint capabilities. To more fully utilize these capabilities, we review the applications of the Monte Carlo multigroup/adjoint method, describe how to generate multigroup cross sections for MCNP with the auxiliary CRSRD code, describe how to use the multigroup/adjoint capability in MCNP, and provide examples and results indicating the effectiveness and validity of the MCNP multigroup/adjoint treatment. This information should assist users in taking advantage of the MCNP multigroup/adjoint capabilities.
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...
The adjoint method for general EEG and MEG sensor-based lead field equations
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.
Xiaoyan Zhang
2015-01-01
Full Text Available This study evaluates the impact of Tropospheric Airborne Meteorological Data Reporting (TAMDAR observations on regional 24-hour forecast error reduction over the Continental United States (CONUS domain using adjoint-based forecast sensitivity to observation (FSO method as the diagnostic tool. The relative impact of TAMDAR observations on reducing the forecast error was assessed by conducting the WRFDA FSO experiments for two two-week-long periods, one in January and one in June 2010. These experiments assimilated operational TAMDAR data and other conventional observations, as well as GPS refractivity (GPSREF. FSO results show that rawinsonde soundings (SOUND and TAMDAR exhibit the largest observation impact on 24 h WRF forecast, followed by GeoAMV, aviation routine weather reports (METAR, GPSREF, and synoptic observations (SYNOP. At 0000 and 1200 UTC, TAMDAR has an equivalent impact to SOUND in reducing the 24-hour forecast error. However, at 1800 UTC, TAMDAR has a distinct advantage over SOUND, which has the sparse observation report at these times. In addition, TAMDAR humidity observations at lower levels of the atmosphere (700 and 850 hPa have a significant impact on 24 h forecast error reductions. TAMDAR and SOUND observations present a qualitatively similar observation impact between FSO and Observation System Experiments (OSEs.
Hep, J.; Konecna, A.; Krysl, V.; Smutny, V. [Calculation Dept., Skoda JS plc, Orlik 266, 31606 Plzen (Czech Republic)
2011-07-01
This paper describes the application of effective source in forward calculations and the adjoint method to the solution of fast neutron fluence and activation detector activities in the reactor pressure vessel (RPV) and RPV cavity of a VVER-440 reactor. Its objective is the demonstration of both methods on a practical task. The effective source method applies the Boltzmann transport operator to time integrated source data in order to obtain neutron fluence and detector activities. By weighting the source data by time dependent decay of the detector activity, the result of the calculation is the detector activity. Alternatively, if the weighting is uniform with respect to time, the result is the fluence. The approach works because of the inherent linearity of radiation transport in non-multiplying time-invariant media. Integrated in this way, the source data are referred to as the effective source. The effective source in the forward calculations method thereby enables the analyst to replace numerous intensive transport calculations with a single transport calculation in which the time dependence and magnitude of the source are correctly represented. In this work, the effective source method has been expanded slightly in the following way: neutron source data were performed with few group method calculation using the active core calculation code MOBY-DICK. The follow-up neutron transport calculation was performed using the neutron transport code TORT to perform multigroup calculations. For comparison, an alternative method of calculation has been used based upon adjoint functions of the Boltzmann transport equation. Calculation of the three-dimensional (3-D) adjoint function for each required computational outcome has been obtained using the deterministic code TORT and the cross section library BGL440. Adjoint functions appropriate to the required fast neutron flux density and neutron reaction rates have been calculated for several significant points within the RPV
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.
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.
Anzhou Cao
2013-01-01
Full Text Available Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients of M2 internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs. In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, the M2 internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.
D.L. Henderson; S. Yoo; M. Kowalok; T.R. Mackie; B.R. Thomadsen
2001-10-30
The goal of this project is to investigate the use of the adjoint method, commonly used in the reactor physics community, for the optimization of radiation therapy patient treatment plans. Two different types of radiation therapy are being examined, interstitial brachytherapy and radiotherapy. In brachytherapy radioactive sources are surgically implanted within the diseased organ such as the prostate to treat the cancerous tissue. With radiotherapy, the x-ray source is usually located at a distance of about 1-metere from the patient and focused on the treatment area. For brachytherapy the optimization phase of the treatment plan consists of determining the optimal placement of the radioactive sources, which delivers the prescribed dose to the disease tissue while simultaneously sparing (reducing) the dose to sensitive tissue and organs. For external beam radiation therapy the optimization phase of the treatment plan consists of determining the optimal direction and intensity of beam, which provides complete coverage of the tumor region with the prescribed dose while simultaneously avoiding sensitive tissue areas. For both therapy methods, the optimal treatment plan is one in which the diseased tissue has been treated with the prescribed dose and dose to the sensitive tissue and organs has been kept to a minimum.
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
Martinec, Zdenek; Sasgen, Ingo; Velimsky, Jakub
2014-05-01
In this study, two new methods for computing the sensitivity of the glacial isostatic adjustment (GIA) forward solution with respect to the Earth's mantle viscosity are presented: the forward sensitivity method (FSM) and the adjoint sensitivity method (ASM). These advanced formal methods are based on the time-domain,spectral-finite element method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec (2000). There are many similarities between the forward method and the FSM and ASM for a general physical system. However, in the case of GIA, there are also important differences between the forward and sensitivity methods. The analysis carried out in this study results in the following findings. First, the forward method of GIA is unconditionally solvable, regardless of whether or not a combined ice and ocean-water load contains the first-degree spherical harmonics. This is also the case for the FSM, however, the ASM must in addition be supplemented by nine conditions on the misfit between the given GIA-related data and the forward model predictions to guarantee the existence of a solution. This constrains the definition of data least-squares misfit. Second, the forward method of GIA implements an ocean load as a free boundary-value function over an ocean area with a free geometry. That is, an ocean load and the shape of ocean, the so-called ocean function, are being sought, in addition to deformation and gravity-increment fields, by solving the forward method. The FSM and ASM also apply the adjoint ocean load as a free boundary-value function, but instead over an ocean area with the fixed geometry given by the ocean function determined by the forward method. In other words, a boundary-value problem for the forward method of GIA is free with respect to determining (i) the boundary-value data over an ocean area and (ii) the ocean function itself, while the boundary-value problems for the FSM and ASM are free only with respect to
Haibo Chen
2013-01-01
Full Text Available Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS method and two gradient descent (GD methods (the normal one with Wolfe’s line search and the simplified one are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.
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 ...
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
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.
Self-adjointness of deformed unbounded operators
Much, Albert [Instituto de Ciencias Nucleares, UNAM, México D.F. 04510 (Mexico)
2015-09-15
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel
Nguyen, Nhan; Ardema, Mark
2006-01-01
This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch
Towards Global Adjoint Tomography
Bozdag, E.; Zhu, H.; Peter, D.; Tromp, J.
2012-04-01
Adjoint tomography based on 3D wave simulations provides new opportunities to improve tomographic images for the following reasons: 1) the full non-linearity of wave propagation may be taken into account in the forward problem, 2) 3D background models may be used to compute Fréchet kernels and, 3) seismic models may be updated in an iterative scheme. Our aim is to use this technique based on a spectral element method (Komatitsch & Tromp 2002) to obtain a global Earth model, which is becoming feasible with current computational facilities. To this end, we select 255 global CMT events distributed worldwide having moment magnitudes between 5.8 and 7. As a reference earth model, we use 3D transversely isotropic mantle model S362ANI (Kustowski et al. 2008) with 3D crustal model Crust2.0 (Bassin et al. 2000). In numerical simulations, Moho variations in Crust2.0 are honored if crustal thickness is less than 15 km or greater than 35 km to have a better sampling of the crustal model, particularly very thin oceanic crust. Using the advantages of numerical simulations, our strategy is to invert crustal and mantle structure together to avoid any bias introduced into upper-mantle images due to "crustal corrections", which are commonly used in classical tomography. Prior to the structure inversion, we reinvert global CMT solutions by computing Green functions in the 3D reference model to take into account effects of crustal variations on source parameters. Changes in source parameters are modest, but consistent with reported global CMT errors. In general, inversion results of selected earthquakes indicate a decrease in depth, particularly for ridge events, which can be up to 12 km, and a change in scalar moment of less than 30%. Event locations mostly change by less than 5 km. We use the updated CMT solutions to run forward simulations for adjoint tomography and plan to reinvert source parameters whenever we see a significant improvement in our tomographic model. 3D
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...
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.
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
Virieux, J.; Bretaudeau, F.; Metivier, L.; Brossier, R.
2013-12-01
Simultaneous inversion of seismic velocities and source parameters have been a long standing challenge in seismology since the first attempts to mitigate trade-off between very different parameters influencing travel-times (Spencer and Gubbins 1980, Pavlis and Booker 1980) since the early development in the 1970s (Aki et al 1976, Aki and Lee 1976, Crosson 1976). There is a strong trade-off between earthquake source positions, initial times and velocities during the tomographic inversion: mitigating these trade-offs is usually carried empirically (Lemeur et al 1997). This procedure is not optimal and may lead to errors in the velocity reconstruction as well as in the source localization. For a better simultaneous estimation of such multi-parametric reconstruction problem, one may take benefit of improved local optimization such as full Newton method where the Hessian influence helps balancing between different physical parameter quantities and improving the coverage at the point of reconstruction. Unfortunately, the computation of the full Hessian operator is not easily computed in large models and with large datasets. Truncated Newton (TCN) is an alternative optimization approach (Métivier et al. 2012) that allows resolution of the normal equation H Δm = - g using a matrix-free conjugate gradient algorithm. It only requires to be able to compute the gradient of the misfit function and Hessian-vector products. Traveltime maps can be computed in the whole domain by numerical modeling (Vidale 1998, Zhao 2004). The gradient and the Hessian-vector products for velocities can be computed without ray-tracing using 1st and 2nd order adjoint-state methods for the cost of 1 and 2 additional modeling step (Plessix 2006, Métivier et al. 2012). Reciprocity allows to compute accurately the gradient and the full Hessian for each coordinates of the sources and for their initial times. Then the resolution of the problem is done through two nested loops. The model update Δm is
Adjoint sensitivity analysis of high frequency structures with Matlab
Bakr, Mohamed; Demir, Veysel
2017-01-01
This book covers the theory of adjoint sensitivity analysis and uses the popular FDTD (finite-difference time-domain) method to show how wideband sensitivities can be efficiently estimated for different types of materials and structures. It includes a variety of MATLAB® examples to help readers absorb the content more easily.
Adjoint Error Estimation for Linear Advection
Connors, J M; Banks, J W; Hittinger, J A; Woodward, C S
2011-03-30
An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.
Aerospace Applications of Adjoint Theory
2010-01-01
program. Peterson [12], and later Howe [13] and Tarrant [14), illustrated how the method could be easily applied to the performance analysis of generic...Hill Book Company, New York, NY, 1965. [14] Tarrant , G.A., " The Method of Adjoint Systems and its Application to Guided Missile Noise Studies
High Order Adjoint Derivatives using ESDIRK Methods for Oil Reservoir Production Optimization
Capolei, Andrea; Stenby, Erling Halfdan; Jørgensen, John Bagterp
2012-01-01
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...
Gelaro, Ron; Liu, Emily; Sienkiewicz, Meta
2011-01-01
The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. In this talk, we present results from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. The tool has been running in various off-line configurations for some time, and is scheduled to run as a regular part of the real-time forecast suite beginning in autumn 20 I O. We focus on the impacts of the newest components of the satellite observing system, including AIRS, IASI and GPS. For AIRS and IASI, it is shown that the vast majority of the channels assimilated have systematic positive impacts (of varying magnitudes), although some channels degrade the forecast. Of the latter, most are moisture-sensitive or near-surface channels. The impact of GPS observations in the southern hemisphere is found to be a considerable overall benefit to the system. In addition, the spatial variability of observation impacts reveals coherent patterns of positive and negative impacts that may point to deficiencies in the use of certain observations over, for example, specific surface types. When performed in conjunction with selected observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies appears to pose a major challenge for optimizing the use of the current observational network and
Model adjointization and its cost
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.
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.
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.
Büskens, Christof; Maurer, Helmut
2000-08-01
Parametric nonlinear optimal control problems subject to control and state constraints are studied. Two discretization methods are discussed that transcribe optimal control problems into nonlinear programming problems for which SQP-methods provide efficient solution methods. It is shown that SQP-methods can be used also for a check of second-order sufficient conditions and for a postoptimal calculation of adjoint variables. In addition, SQP-methods lead to a robust computation of sensitivity differentials of optimal solutions with respect to perturbation parameters. Numerical sensitivity analysis is the basis for real-time control approximations of perturbed solutions which are obtained by evaluating a first-order Taylor expansion with respect to the parameter. The proposed numerical methods are illustrated by the optimal control of a low-thrust satellite transfer to geosynchronous orbit and a complex control problem from aquanautics. The examples illustrate the robustness, accuracy and efficiency of the proposed numerical algorithms.
Generalized Uncertainty Principle and Self-Adjoint Operators
Balasubramanian, Venkat; Vagenas, Elias C
2014-01-01
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Generalized uncertainty principle and self-adjoint operators
Balasubramanian, Venkat, E-mail: vbalasu8@uwo.ca [Department of Applied Mathematics, University of Western Ontario London, Ontario N6A 5B7 (Canada); Das, Saurya, E-mail: saurya.das@uleth.ca [Theoretical Physics Group, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4 (Canada); Vagenas, Elias C., E-mail: elias.vagenas@ku.edu.kw [Theoretical Physics Group, Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)
2015-09-15
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Adjoint optimal control problems for the RANS system
Attavino, A.; Cerroni, D.; Da Vià, R.; Manservisi, S.; Menghini, F.
2017-01-01
Adjoint optimal control in computational fluid dynamics has become increasingly popular recently because of its use in several engineering and research studies. However the optimal control of turbulent flows without the use of Direct Numerical Simulation is still an open problem and various methods have been proposed based on different approaches. In this work we study optimal control problems for a turbulent flow modeled with a Reynolds-Averaged Navier-Stokes system. The adjoint system is obtained through the use of a Lagrangian multiplier method by setting as objective of the control a velocity matching profile or an increase or decrease in the turbulent kinetic energy. The optimality system is solved with an in-house finite element code and numerical results are reported in order to show the validity of this approach.
Adjoint affine fusion and tadpoles
Urichuk, Andrew; Walton, Mark A.
2016-06-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Adjoint affine fusion and tadpoles
Urichuk, Andrew
2016-01-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows, and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Adjoint affine fusion and tadpoles
Urichuk, Andrew, E-mail: andrew.urichuk@uleth.ca [Physics and Astronomy Department, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); Walton, Mark A., E-mail: walton@uleth.ca [Physics and Astronomy Department, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste (Italy)
2016-06-15
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
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.
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.
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.
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.
ADGEN: ADjoint GENerator for computer models
Worley, B.A.; Pin, F.G.; Horwedel, J.E.; Oblow, E.M.
1989-05-01
This paper presents the development of a FORTRAN compiler and an associated supporting software library called ADGEN. ADGEN reads FORTRAN models as input and produces and enhanced version of the input model. The enhanced version reproduces the original model calculations but also has the capability to calculate derivatives of model results of interest with respect to any and all of the model data and input parameters. The method for calculating the derivatives and sensitivities is the adjoint method. Partial derivatives are calculated analytically using computer calculus and saved as elements of an adjoint matrix on direct assess storage. The total derivatives are calculated by solving an appropriate adjoint equation. ADGEN is applied to a major computer model of interest to the Low-Level Waste Community, the PRESTO-II model. PRESTO-II sample problem results reveal that ADGEN correctly calculates derivatives of response of interest with respect to 300 parameters. The execution time to create the adjoint matrix is a factor of 45 times the execution time of the reference sample problem. Once this matrix is determined, the derivatives with respect to 3000 parameters are calculated in a factor of 6.8 that of the reference model for each response of interest. For a single 3000 for determining these derivatives by parameter perturbations. The automation of the implementation of the adjoint technique for calculating derivatives and sensitivities eliminates the costly and manpower-intensive task of direct hand-implementation by reprogramming and thus makes the powerful adjoint technique more amenable for use in sensitivity analysis of existing models. 20 refs., 1 fig., 5 tabs.
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...
Adjoint based sensitivity analysis of a reacting jet in crossflow
Sashittal, Palash; Sayadi, Taraneh; Schmid, Peter
2016-11-01
With current advances in computational resources, high fidelity simulations of reactive flows are increasingly being used as predictive tools in various industrial applications. In order to capture the combustion process accurately, detailed/reduced chemical mechanisms are employed, which in turn rely on various model parameters. Therefore, it would be of great interest to quantify the sensitivities of the predictions with respect to the introduced models. Due to the high dimensionality of the parameter space, methods such as finite differences which rely on multiple forward simulations prove to be very costly and adjoint based techniques are a suitable alternative. The complex nature of the governing equations, however, renders an efficient strategy in finding the adjoint equations a challenging task. In this study, we employ the modular approach of Fosas de Pando et al. (2012), to build a discrete adjoint framework applied to a reacting jet in crossflow. The developed framework is then used to extract the sensitivity of the integrated heat release with respect to the existing combustion parameters. Analyzing the sensitivities in the three-dimensional domain provides insight towards the specific regions of the flow that are more susceptible to the choice of the model.
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.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Optimization Design of Transonic Winglet Based on Discrete Adjoint Method%基于伴随算子的翼尖小翼优化设计
杨洋; 刘学强; 覃宁
2012-01-01
Aerodynamic optimization design of transonic winglet is presented in this paper. The Osher scheme is used to solve the Navier- Stokes equations to obtain the aerodynamic coefficients. The turbulence model is k - ω model. A discrete adjoint solver is used to calculate efficiently the gradients, which make it possible to optimize for a large number of design variables. The coefficient design method is used for original design. The results show that the optimization of winglet can improve to 5. 8% ,and validate this method%采用基于伴随算子的优化设计方法,对跨音速翼尖小翼进行了优化设计.其中,采用基于多块结构网格的流场解算器计算气动力.解算器的空间离散采用Osher格式,湍流模型采用k-ω两方程模型.优化设计结果表明,采用优化设计后的翼尖小翼,能改善机翼的气动特性,在巡航状态下翼尖小翼能增加机翼的升阻比5.8％,从数值计算的角度表明了方法的有效性.
Eigenvalues of singular differential operators by finite difference methods. II.
Baxley, J. V.
1972-01-01
Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.
Nonlinear self-adjointness and conservation laws
Ibragimov, N H, E-mail: nib@bth.se [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)
2011-10-28
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation u{sub t} - {Delta}u = 0 becomes strictly self-adjoint after multiplying by u{sup -1}. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems. (fast track communication)
Adjoint string breaking in the pseudoparticle approach
Szasz, Christian
2008-01-01
We apply the pseudoparticle approach to SU(2) Yang-Mills theory and perform a detailed study of the potential between two static charges for various representations. Whereas for charges in the fundamental representation we find a linearly rising confining potential, we clearly observe string breaking, when considering charges in the adjoint representation. We also demonstrate Casimir scaling and compute gluelump masses for different spin and parity. Numerical results are in qualitative agreement with lattice results.
Tanaka, Ken'ichiro; Murashige, Sunao
2012-01-01
We present the convergence rates and the explicit error bounds of Hill's method, which is a numerical method for computing the spectra of ordinary differential operators with periodic coefficients. This method approximates the operator by a finite dimensional matrix. On the assumption that the operator is selfadjoint, it is shown that, under some conditions, we can obtain the convergence rates of eigenvalues with respect to the dimension and the explicit error bounds. Numerical examples demon...
Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver
Paige, Cody
The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward mode ADjoint is a combination of an adjoint sensitivity analysis method with a forward mode automatic differentiation (AD) and is a modification of the reverse mode ADjoint method proposed by Mader et al.[1]. A colouring acceleration technique is presented to reduce the computational cost increase associated with forward mode AD. The forward mode AD facilitates the implementation of the laminar Navier-Stokes (NS) equations. The forward mode ADjoint method is applied to a three-dimensional computational fluid dynamics solver. The resulting Euler and viscous ADjoint sensitivities are compared to the reverse mode Euler ADjoint derivatives and a complex-step method to demonstrate the reduced computational cost and accuracy. Both comparisons demonstrate the benefits of the colouring method and the practicality of using a forward mode AD. [1] Mader, C.A., Martins, J.R.R.A., Alonso, J.J., and van der Weide, E. (2008) ADjoint: An approach for the rapid development of discrete adjoint solvers. AIAA Journal, 46(4):863-873. doi:10.2514/1.29123.
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...
Tanaka, Ken'ichiro
2012-01-01
We present the convergence rates and the explicit error bounds of Hill's method, which is a numerical method for computing the spectra of ordinary differential operators with periodic coefficients. This method approximates the operator by a finite dimensional matrix. On the assumption that the operator is selfadjoint, it is shown that, under some conditions, we can obtain the convergence rates of eigenvalues with respect to the dimension and the explicit error bounds. Numerical examples demonstrate that we can verify these conditions using Gershgorin's theorem for some real problems. Main theorems are proved using the Dunford integrals which project an eigenvector to the corresponding eigenspace.
Optimal Multistage Algorithm for Adjoint Computation
Aupy, Guillaume; Herrmann, Julien; Hovland, Paul; Robert, Yves
2016-01-01
We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.
On adjoint symmetry equations, integrating factors and solutions of nonlinear ODEs
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.
Global adjoint tomography: first-generation model
Bozdağ, Ebru; Peter, Daniel; Lefebvre, Matthieu; Komatitsch, Dimitri; Tromp, Jeroen; Hill, Judith; Podhorszki, Norbert; Pugmire, David
2016-12-01
We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named `Titan', a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematically reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used `crustal corrections'. We used data from 253 earthquakes in the magnitude range 5.8 ≤ Mw ≤ 7.0. We started inversions by combining ˜30 s body-wave data with ˜60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ˜17 s body waves with ˜45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the resolution
Global adjoint tomography: first-generation model
Bozdağ, Ebru
2016-09-23
We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named \\'Titan\\', a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematically reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used \\'crustal corrections\\'. We used data from 253 earthquakes in the magnitude range 5.8 ≤ M ≤ 7.0. We started inversions by combining ~30 s body-wave data with ~60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ~17 s body waves with ~45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Quasi self-adjoint nonlinear wave equations
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.s, E-mail: torrisi@dmi.unict.i, E-mail: tracina@dmi.unict.i [Dipartimento di Matematica e Informatica, University of Catania (Italy)
2010-11-05
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)
Challenges in adjoint-based well location optimization when using well models
Ashoori, E.; Jansen, J.D.
2015-01-01
There is a general consensus that the most efficient method for large-scale well location optimization is gradient-based with gradients computed with an adjoint formulation. Handels et al. (2007) (later published in journal form as Zandvliet et al., 2008), were the first to use the adjoint method fo
Kano, Masayuki; Miyazaki, Shin'ichi; Ishikawa, Yoichi; Hiyoshi, Yoshihisa; Ito, Kosuke; Hirahara, Kazuro
2015-10-01
Data assimilation is a technique that optimizes the parameters used in a numerical model with a constraint of model dynamics achieving the better fit to observations. Optimized parameters can be utilized for the subsequent prediction with a numerical model and predicted physical variables are presumably closer to observations that will be available in the future, at least, comparing to those obtained without the optimization through data assimilation. In this work, an adjoint data assimilation system is developed for optimizing a relatively large number of spatially inhomogeneous frictional parameters during the afterslip period in which the physical constraints are a quasi-dynamic equation of motion and a laboratory derived rate and state dependent friction law that describe the temporal evolution of slip velocity at subduction zones. The observed variable is estimated slip velocity on the plate interface. Before applying this method to the real data assimilation for the afterslip of the 2003 Tokachi-oki earthquake, a synthetic data assimilation experiment is conducted to examine the feasibility of optimizing the frictional parameters in the afterslip area. It is confirmed that the current system is capable of optimizing the frictional parameters A-B, A and L by adopting the physical constraint based on a numerical model if observations capture the acceleration and decaying phases of slip on the plate interface. On the other hand, it is unlikely to constrain the frictional parameters in the region where the amplitude of afterslip is less than 1.0 cm d-1. Next, real data assimilation for the 2003 Tokachi-oki earthquake is conducted to incorporate slip velocity data inferred from time dependent inversion of Global Navigation Satellite System time-series. The optimized values of A-B, A and L are O(10 kPa), O(102 kPa) and O(10 mm), respectively. The optimized frictional parameters yield the better fit to the observations and the better prediction skill of slip
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
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.
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...
Adjoint Functors and Representation Dimensions
Chang Chang XI
2006-01-01
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
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 ...
Analysis on observing optimization for the wind-driven circulation by an adjoint approach
王东晓; 吴国雄; 朱江; 兰健
2000-01-01
The adjoint approach is a variational method which is often applied to data assimilation widely in meteorology and oceanography. It is used for analyses on observing optimization for the wind-driven Sverdrup circulation. The adjoint system developed by Thacker and Long (1992), which is based on the GFDL Byran-Cox model, includes three components, i. e. the forward model, the adjoint model and the optimal algorithm. The GFDL Byran-Cox model was integrated for a long time driven by a batch of ideal wind stresses whose meridional component is set to null and zonal component is a sine function of latitudes in a rectangle box with six vertical levels and 2 by 2 degree horizontal resolution. The results are regarded as a "real" representative of the wind-driven Sverdrup circulation, from which the four dimensional fields are allowed to be sampled in several ways, such as sampling at the different levels or along the different vertical sections. To set the different samples, the fields of temperature, salinity
Adjoint-based approach to Enhancing Mixing in Rayleigh-Taylor Turbulence
Kord, Ali; Capecelatro, Jesse
2016-11-01
A recently developed adjoint method for multi-component compressible flow is used to measure sensitivity of the mixing rate to initial perturbations in Rayleigh-Taylor (RT) turbulence. Direct numerical simulations (DNS) of RT instabilities are performed at moderate Reynolds numbers. The DNS are used to provide an initial prediction, and the corresponding space-time discrete-exact adjoint provides a sensitivity gradient for a specific quantity of interest (QoI). In this work, a QoI is defined based on the time-integrated scalar field to quantify the mixing rate. Therefore, the adjoint solution is used to measure sensitivity of this QoI to a set of initial perturbations, and inform a gradient-based line search to optimize mixing. We first demonstrate the adjoint approach in the linear regime and compare the optimized initial conditions to the expected values from linear stability analysis. The adjoint method is then used in the high Reynolds number limit where theory is no longer valid. Finally, chaos is known to contaminate the accuracy of the adjoint gradient in turbulent flows when integrated over long time horizons. We assess the influence of chaos on the accuracy of the adjoint gradient to guide the work of future studies on adjoint-based sensitivity of turbulent mixing. PhD Student, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI.
Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology
Rallabhandi, Siriam K.; Diskin, Boris; Nielsen, Eric J.
2012-01-01
This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.
Adjoint analysis of mixed continuous/discrete systems in simulink
Bucco, D.; Weiss, M.
2010-01-01
The adjoint simulation method is a well established and efficient tool for gaining insight and understanding of key parameters affecting the behaviour and performance of a guided missile homing system. Traditionally, the method has been employed by various missile companies during the preliminary an
Adjoint analysis of mixed continuous/discrete systems in simulink
Bucco, D.; Weiss, M.
2010-01-01
The adjoint simulation method is a well established and efficient tool for gaining insight and understanding of key parameters affecting the behaviour and performance of a guided missile homing system. Traditionally, the method has been employed by various missile companies during the preliminary
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
Tamás Fülöp
2007-11-01
Full Text Available For a class of singular potentials, including the Coulomb potential (in three and less dimensions and $V(x = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the self-adjoint version chosen. The article discusses how the self-adjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different self-adjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations.
Two different hematocrit detection methods: Different methods, different results?
Schuepbach Reto A
2010-03-01
Full Text Available Abstract Background Less is known about the influence of hematocrit detection methodology on transfusion triggers. Therefore, the aim of the present study was to compare two different hematocrit-assessing methods. In a total of 50 critically ill patients hematocrit was analyzed using (1 blood gas analyzer (ABLflex 800 and (2 the central laboratory method (ADVIA® 2120 and compared. Findings Bland-Altman analysis for repeated measurements showed a good correlation with a bias of +1.39% and 2 SD of ± 3.12%. The 24%-hematocrit-group showed a correlation of r2 = 0.87. With a kappa of 0.56, 22.7% of the cases would have been transfused differently. In the-28%-hematocrit group with a similar correlation (r2 = 0.8 and a kappa of 0.58, 21% of the cases would have been transfused differently. Conclusions Despite a good agreement between the two methods used to determine hematocrit in clinical routine, the calculated difference of 1.4% might substantially influence transfusion triggers depending on the employed method.
An 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.
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.
Toward regional-scale adjoint tomography in the deep earth
Masson, Y.; Romanowicz, B. A.
2013-12-01
Thanks to the development of efficient numerical computation methods, such as the Spectral Element Method (SEM) and to the increasing power of computer clusters, it is now possible to obtain regional-scale images of the Earth's interior using adjoint-tomography (e.g. Tape, C., et al., 2009). As for now, these tomographic models are limited to the upper layers of the earth, i.e., they provide us with high-resolution images of the crust and the upper part of the mantle. Given the gigantic amount of calculation it represents, obtaing similar models at the global scale (i.e. images of the entire Earth) seems out of reach at the moment. Furthermore, it's likely that the first generation of such global adjoint tomographic models will have a resolution significantly smaller than the current regional models. In order to image regions of interests in the deep Earth, such as plumes, slabs or large low shear velocity provinces (LLSVPs), while keeping the computation tractable, we are developing new tools that will allow us to perform regional-scale adjoint-tomography at arbitrary depths. In a recent study (Masson et al., 2013), we showed that a numerical equivalent of the time reversal mirrors used in experimental acoustics permits to confine the wave propagation computations (i.e. using SEM simulations) inside the region to be imaged. With this ability to limit wave propagation modeling inside a region of interest, obtaining the adjoint sensitivity kernels needed for tomographic imaging is only two steps further. First, the local wavefield modeling needs to be coupled with field extrapolation techniques in order to obtain synthetic seismograms at the surface of the earth. These seismograms will account for the 3D structure inside the region of interest in a quasi-exact manner. We will present preliminary results where the field-extrapolation is performed using Green's function computed in a 1D Earth model thanks to the Direct Solution Method (DSM). Once synthetic seismograms
Eigenvalues of singular differential operators by finite difference methods. I.
Baxley, J. V.
1972-01-01
Approximation of the eigenvalues of certain self-adjoint operators defined by a formal differential operator in a Hilbert space. In general, two problems are studied. The first is the problem of defining a suitable Hilbert space operator that has eigenvalues. The second problem concerns the finite difference operators to be used.
Andrews, Arlyn; Kawa, Randy; Zhu, Zhengxin; Burris, John; Abshire, Jim
2004-01-01
A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.
Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle
Peplow, Douglas E. [ORNL; Mosher, Scott W [ORNL; Evans, Thomas M [ORNL
2012-08-01
For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.
McGovern, Jonathan; Rutt, Ian; Murray, Tavi; Utke, Jean
2013-04-01
Studying the future behaviour of the Greenland Ice Sheet is important considering the ice sheet has a sea-level equivalent of 7 metres and the rate of mass loss from it is increasing (Velicogna, 2009). Examining the modelled response of the Greenland Ice Sheet to changes in forcing parameters can give insight into how it will behave in the future. The response of the ice sheet to specific changes in forcing parameters is referred to as the sensitivity. Being able to obtain model sensitivities in as little computation time as possible would be useful for examining the future response of the Greenland Ice Sheet. Adjoint models allow sensitivities to be obtained more efficiently than the conventional way, when considering spatially varying parameters. Conventionally, such sensitivities are obtained by perturbing a parameter at every grid point in turn and calculating the sensitivity at every grid point. Adjoint sensitivities, though, are calculated in a single step. This reduces the computational cost when obtaining sensitivities over large model domains. The adjoint method also has the advantage that it gives the exact value of the model sensitivity, rather than a finite difference approximation to it. We present the adjoint of a finite difference, shallow ice, thermomechanical ice sheet model with basal sliding, applied to the Greenland Ice Sheet. This adjoint model is obtained using the OpenAD automatic differentiation tool (Utke, 2006), which is open source. The adjoint model is validated by comparing adjoint and forward model sensitivities over 100 years. This work builds on the work of Heimbach (2009). We use the adjoint model to examine the sensitivity of the model to changes in basal sliding. About half the mass loss from the Greenland Ice Sheet occurs from surface runoff and half from dynamic mass loss (Broeke, 2009). Melt-water from Greenland Ice Sheet supra-glacial lakes can percolate to the bed through moulins. The melt-water that reaches the bed can then
GPU-accelerated adjoint algorithmic differentiation
Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe
2016-03-01
Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the ;tape;. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.
Radiation source reconstruction with known geometry and materials using the adjoint
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)
Verdugo, Francesc; Parés, Núria; Díez, Pedro
2014-08-01
This article presents a space-time adaptive strategy for transient elastodynamics. The method aims at computing an optimal space-time discretization such that the computed solution has an error in the quantity of interest below a user-defined tolerance. The methodology is based on a goal-oriented error estimate that requires accounting for an auxiliary adjoint problem. The major novelty of this paper is using modal analysis to obtain a proper approximation of the adjoint solution. The idea of using a modal-based description was introduced in a previous work for error estimation purposes. Here this approach is used for the first time in the context of adaptivity. With respect to the standard direct time-integration methods, the modal solution of the adjoint problem is highly competitive in terms of computational effort and memory requirements. The performance of the proposed strategy is tested in two numerical examples. The two examples are selected to be representative of different wave propagation phenomena, one being a 2D bulky continuum and the second a 2D domain representing a structural frame.
Local fibred right adjoints are polynomial
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...
On the adjoint operator in photoacoustic tomography
Arridge, Simon R.; Betcke, Marta M.; Cox, Ben T.; Lucka, Felix; Treeby, Brad E.
2016-11-01
Photoacoustic tomography (PAT) is an emerging biomedical imaging from coupled physics technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.
Monopole condensation in two-flavour Adjoint QCD
Cossu, G; Di Giacomo, A; Lacagnina, G; Pica, C
2008-01-01
In QCD with adjoint fermions (aQCD) the deconfining transition takes place at a lower temperature than the chiral transition. We study the two transitions by use of the Polyakov Loop, the monopole order parameter and the chiral condensate. The deconfining transition is first order, the chiral is a crossover. The order parameters for confinement are not affected by the chiral transition. We conclude that the degrees of freedom relevant to confinement are different from those describing chiral symmetry.
Determining scaling laws from geodynamic simulations using adjoint gradients.
Reuber, Georg; Kaus, Boris; Popov, Anton
2016-04-01
Whereas significant progress has been made in modelling of lithospheric and crustal scale processes in recent years, it often remains a challenge to understand which of the many model parameters is of key importance for a particular simulation. Determining this is usually done by manually changing the model input parameters and performing new simulations. For a few cases, such as for crustal-scale folding instabilities (with viscous rheologies, e.g. [1]) or for Rayleigh-Taylor instabilities, one can use existing scaling laws to obtain such insights. Yet, for a more general case, it is not straightforward to do this (apart from running many simulations). Here, we test a different approach which computes gradients of the model parameters using adjoint based methods, which has the advantage that we can test the influence of an independent number of parameters on the system by computing and analysing the covariance matrix and the gradient of the parameter space. This method might give us the chance to get insights on which parameters affect for example subduction processes and how strong the system depends on their influence. [1] Fernandez, N., & Kaus, B. J. (2014). Fold interaction and wavelength selection in 3D models of multilayer detachment folding. Tectonophysics, 632, 199-217.
Adjoint Tomography of Taiwan Region: From Travel-Time Toward Waveform Inversion
Huang, H. H.; Lee, S. J.; Tromp, J.
2014-12-01
The complicated tectonic environment such as Taiwan region can modulate the seismic waveform severely and hamper the discrimination and the utilization of later phases. Restricted to the use of only first arrivals of P- and S-wave, the travel-time tomographic models of Taiwan can simulate the seismic waveform barely to a frequency of 0.2 Hz to date. While it has been sufficient for long-period studies, e.g. source inversion, this frequency band is still far from the applications to the community and high-resolution studies. To achieve a higher-frequency simulation, more data and the considerations of off-path and finite-frequency effects are necessary. Based on the spectral-element and the adjoint method recently developed, we prepared 94 MW 3.5-6.0 earthquakes with well-defined location and focal mechanism solutions from Real-Time Moment Tensor Monitoring System (RMT), and preformed an iterative gradient-based inversion employing waveform modeling and finite-frequency measurements of adjoint method. By which the 3-D sensitivity kernels are taken into account realistically and the full waveform information are naturally sought, without a need of any phase pick. A preliminary model m003 using 10-50 sec data was demonstrated and compared with previous travel-time models. The primary difference appears in the mountainous area, where the previous travel-time model may underestimate the S-wave speed in the upper crust, but overestimates in the lower crust.
A general nonlinear inverse transport algorithm using forward and adjoint flux computations
Norton, S.J. [Oak Ridge National Lab., TN (United States)
1997-04-01
Iterative approaches to the nonlinear inverse transport problem are described, which give rise to the structure that best predicts a set of transport observations. Such methods are based on minimizing a global error functional measuring the discrepancy between predicted and observed transport data. Required for this minimization is the functional gradient (Frechet derivative) of the global error evaluated with respect to a set of unknown material parameters (specifying boundary locations, scattering cross sections, etc.) which are to be determined. It is shown how this functional gradient is obtained from numerical solutions to the forward and adjoint transport problems computed once per iteration. This approach is not only far more efficient, but also more accurate, than a finite-difference method for computing the gradient of the global error. The general technique can be applied to inverse-transport problems of all descriptions, provided only that solutions to the forward and adjoint problems can be found numerically. As an illustration, two inverse problems are treated: the reconstruction of an anisotropic scattering function in a one-dimensional homogeneous slab and the two-dimensional imaging of a spatially-varying scattering cross section.
Coupling of MASH-MORSE Adjoint Leakages with Space- and Time-Dependent Plume Radiation Sources
Slater, C.O.
2001-04-20
reduce computational times. The second source calculation uses a point kernel like method to calculate directional fluences at points surrounding user-specified detector and structure locations and folds those fluences with MASH-MORSE adjoint leakages to calculate free-field and shielded fluences and dose rates and the indicated protection factors. Both source calculation methods were tested for determining dose rates at specified locations within a two-story concrete building. For two early time steps, results from the second method are 50 to 60% higher than those from the first method, but the protection factors differ by only a few percent. This indicates that the free-field and shielded fluence spectra are similar and differ mainly in magnitude. Other comparisons were made, and from the comparisons there was a perceived underprediction by TORT. That underprediction can be attributed to the coarse mesh and quadrature used in the calculations. The second method, while not rigorously correct, requires much less computer time for a reasonably good estimate of the shielded dose rates within a structure.
Adjoint-Based Uncertainty Quantification with MCNP
Seifried, Jeffrey E. [Univ. of California, Berkeley, CA (United States)
2011-09-01
This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence in the simulation is acquired.
The Roots of Adjoint Polynomial of the Graphs Contain Triangles
YECheng-fu
2004-01-01
We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.
On a difference scheme for nonlocal heat transfer boundary-value problem
Akhymbek, Meiram E.; Sadybekov, Makhmud A.
2016-08-01
In this paper, we propose a new method of solving nonlocal problems for the heat equation with finite difference method. The main important feature of these problems is their non-self-adjointness. This non-self-adjointness causes major difficulties in their analytical and numerical solving. The problems, which boundary conditions do not possess strong regularity, are less studied. The scope of study of the paper justifies possibility of building a stable difference scheme with weights for abovementioned type of problems.
Brezillon, Joël; Dwight, Richard P.
2009-01-01
Within the next few years, numerical shape optimization based on high fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimization problems, and the adjoint approach - which allows fast and accurate evaluations of the gradients with respect to the design parameters - is seen as a promising strategy. After describing the theory of the viscous discrete adjoint method and its impleme...
Brezillon, J.; Dwight, R.P.
2009-01-01
Within the next few years, numerical shape optimization based on high fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimization problems, and the adjoint approach - which allows fast and accurate evaluations of the gradients with respect to the design parameters - is seen as a promising strategy. After describing the theory of the viscous discrete adjoint method and its impleme...
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.
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...
Dual of QCD with One Adjoint Fermion
Mojaza, Matin; Nardecchia, Marco; Pica, Claudio;
2011-01-01
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the...
Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions
Akgun, Mehmet A.; Haftka, Raphael T.
2000-01-01
The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local
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.
Monopole condensation in two-flavour Adjoint QCD
Cossu, G; Di Giacomo, Adriano; Lacagnina, G; Pica, C
2006-01-01
Two distinct phase transitions occur at different temperatures in QCD with adjoint fermions (aQCD): deconfinement and chiral symmetry restoration. In this model, quarks do no explicitely break the center Z(3) symmetry and therefore the Polyakov loop is a good order parameter for the deconfinement transition. We study monopole condensation by inspecting the expectation value of an operator which creates a monopole. Such a quantity is expected to be an order parameter for the deconfinement transition as in the case of fundamental fermions.
An adjoint-based approach for finding invariant solutions of Navier-Stokes equations
Farazmand, Mohammad
2015-01-01
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and traveling wave solutions of the Navier--Stokes equations. Using the adjoint equations, arbitrary initial conditions evolve to the vicinity of a (relative) equilibrium at which point a few Newton-type iterations yield the desired (relative) equilibrium solution. We apply this adjoint-based method to a chaotic two-dimensional Kolmogorov flow. A convergence rate of 100% is observed, leading to the discovery of 21 new steady state and traveling wave solutions at Reynolds number Re=40. Some of the new invariant solutions have spatially localized structures that were previously believed to only exist on domains with large aspect ratios. We show that one of the newly found steady state solutions underpins the temporal intermittencies, i.e., high energy dissipation episodes of the flo...
Humbird, Kelli D.; McClarren, Ryan G.
2017-03-01
Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a mathematically related set of adjoint equations. The information contained in the equations can be combined to produce sensitivity information in a computationally efficient manner. In this work, sensitivity analyses are performed on systems described by flux-limited radiative diffusion using the adjoint approach. The sensitivities computed are shown to agree with standard perturbation theory and require significantly less computational time. The adjoint approach saves the computational cost of one forward solve per sensitivity, making the method attractive when multiple sensitivities are of interest.
Advances in Global Adjoint Tomography -- Massive Data Assimilation
Ruan, Y.; Lei, W.; Bozdag, E.; Lefebvre, M. P.; Smith, J. A.; Krischer, L.; Tromp, J.
2015-12-01
Azimuthal anisotropy and anelasticity are key to understanding a myriad of processes in Earth's interior. Resolving these properties requires accurate simulations of seismic wave propagation in complex 3-D Earth models and an iterative inversion strategy. In the wake of successes in regional studies(e.g., Chen et al., 2007; Tape et al., 2009, 2010; Fichtner et al., 2009, 2010; Chen et al.,2010; Zhu et al., 2012, 2013; Chen et al., 2015), we are employing adjoint tomography based on a spectral-element method (Komatitsch & Tromp 1999, 2002) on a global scale using the supercomputer ''Titan'' at Oak Ridge National Laboratory. After 15 iterations, we have obtained a high-resolution transversely isotropic Earth model (M15) using traveltime data from 253 earthquakes. To obtain higher resolution images of the emerging new features and to prepare the inversion for azimuthal anisotropy and anelasticity, we expanded the original dataset with approximately 4,220 additional global earthquakes (Mw5.5-7.0) --occurring between 1995 and 2014-- and downloaded 300-minute-long time series for all available data archived at the IRIS Data Management Center, ORFEUS, and F-net. Ocean Bottom Seismograph data from the last decade are also included to maximize data coverage. In order to handle the huge dataset and solve the I/O bottleneck in global adjoint tomography, we implemented a python-based parallel data processing workflow based on the newly developed Adaptable Seismic Data Format (ASDF). With the help of the data selection tool MUSTANG developed by IRIS, we cleaned our dataset and assembled event-based ASDF files for parallel processing. We have started Centroid Moment Tensors (CMT) inversions for all 4,220 earthquakes with the latest model M15, and selected high-quality data for measurement. We will statistically investigate each channel using synthetic seismograms calculated in M15 for updated CMTs and identify problematic channels. In addition to data screening, we also modified
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
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.
YANG YiDu; CHEN Zhen
2008-01-01
This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T. Under the condition that the approximate operator Th converges to T in norm, it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems, and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.
雷靖; 白雪玲
2012-01-01
The paper considers the optimal disturbance rejection problem for continuous-time systems with state, control, and measurement delays. Firstly, the conditions of system transformation are analyzed and the approach is proposed , based on which the original system is transformed into one without delays. Then combining the system and the exosystem to an augmented system, the optimal disturbance rejection control problem is converted to an optimal state regulator problem. The necessity is proved by using Pontryagin minimum principle and the sufficiency is proved applying dynamic programming. The physical unrealization problem of disturbance vector and optimal performance index is solved by defining an adjoint vector. Finally, numerical simulations are made to compare the system responses using some different control laws. The effectiveness and simplicity of the designed control law are demonstrated.%研究包含有状态、控制和测量延时连续系统的最优扰动抑制问题.首先分析并提出了系统转换的方法,将原系统转化为无延时项的连续系统.然后将该系统与扰动系统联立为增广系统,并将最优扰动抑制问题转化为最优状态调节器问题.运用Pontryagin极小值原理证明最优控制的必要性,运用动态规划法证明其充分性；通过定义伴随向量解决了扰动向量和最优性能指标物理不可实现的问题.最后运用数据仿真将几种不同控制律作用下的系统响应作比较,验证所设计控制律的有效性及简易性.
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
Chiral transition of fundamental and adjoint quarks
Capdevilla, R.M. [Instituto de Física Teórica, UNESP – Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070 São Paulo, SP (Brazil); Doff, A., E-mail: agomes@utfpr.edu.br [Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR (Brazil); Natale, A.A., E-mail: natale@ift.unesp.br [Instituto de Física Teórica, UNESP – Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070 São Paulo, SP (Brazil); Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil)
2014-01-20
The chiral symmetry breaking transition of quarks in the fundamental and adjoint representation is studied in a model where the gap equation contains two contributions, one containing a confining propagator and another corresponding to the exchange of one-dressed dynamically massive gluons. When quarks are in the fundamental representation the confinement effect dominates the chiral symmetry breaking while the gluon exchange is suppressed due to the dynamical gluon mass effect in the propagator and in the coupling constant. In this case the chiral and deconfinement transition temperatures are approximately the same. For quarks in the adjoint representation, due to the larger Casimir eigenvalue, the gluon exchange is operative and the chiral transition happens at a larger temperature than the deconfinement one.
Dual of QCD with One Adjoint Fermion
Mojaza, Matin; Pica, Claudio; Sannino, Francesco
2011-01-01
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the anomalous dimension of the Dirac fermion mass operator to be less than one in the conformal window.
Chiral phases of fundamental and adjoint quarks
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.
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.
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.
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.
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
Confining vs. conformal scenario for SU(2) with 2 adjoint fermions. Mesonic spectrum
Pica, Claudio; Del Debbio, Luigi; Lucini, Biagio;
2010-01-01
The Minimal Walking Technicolor (MWT) model, based on the SU(2) gauge group with two Dirac adjoint fermions, is expected to lie close to the lower boundary of the conformal window. As such, it is believed to possess a dynamics different enough from QCD to be a viable candidate for a Technicolor t...
Miyoshi, Takayuki
2017-10-04
A three-dimensional seismic wave speed model in the Kanto region of Japan was developed using adjoint tomography for application in the effective reproduction of observed waveforms. Starting with a model based on previous travel time tomographic results, we inverted the waveforms obtained at seismic broadband stations from 140 local earthquakes in the Kanto region to obtain the P- and S-wave speeds Vp and Vs. Additionally, all centroid times of the source solutions were determined before the structural inversion. The synthetic displacements were calculated using the spectral-element method (SEM) in which the Kanto region was parameterized using 16 million grid points. The model parameters Vp and Vs were updated iteratively by Newton’s method using the misfit and Hessian kernels until the misfit between the observed and synthetic waveforms was minimized. Computations of the forward and adjoint simulations were conducted on the K computer in Japan. The optimized SEM code required a total of 6720 simulations using approximately 62,000 node hours to obtain the final model after 16 iterations. The proposed model reveals several anomalous areas with extremely low-Vs values in comparison with those of the initial model. These anomalies were found to correspond to geological features, earthquake sources, and volcanic regions with good data coverage and resolution. The synthetic waveforms obtained using the newly proposed model for the selected earthquakes showed better fit than the initial model to the observed waveforms in different period ranges within 5–30 s. This result indicates that the model can accurately predict actual waveforms.
Liu, Yaning; Niu, Fenglin; Chen, Min; Yang, Wencai
2017-03-01
We construct a new 3-D shear wave speed model of the crust and the uppermost mantle beneath Northeast China using the ambient noise adjoint tomography method. Without intermediate steps of measuring phase dispersion, the adjoint tomography inverts for shear wave speeds of the crust and uppermost mantle directly from 6-40 s waveforms of Empirical Green's functions (EGFs) of Rayleigh waves, which are derived from interferometry of two years of ambient noise data recorded by the 127 Northeast China Extended Seismic Array stations. With an initial 3-D model derived from traditional asymptotic surface wave tomography method, adjoint tomography refines the 3-D model by iteratively minimizing the frequency-dependent traveltime misfits between EGFs and synthetic Green's functions measured in four period bands: 6-15 s, 10-20 s, 15-30 s, and 20-40 s. Our new model shows shear wave speed anomalies that are spatially correlated with known tectonic units such as the Great Xing'an range and the Changbaishan mountain range. The new model also reveals low wave speed conduits in the mid-lower crust and the uppermost mantle with a wave speed reduction indicative of partial melting beneath the Halaha, Xilinhot-Abaga, and Jingpohu volcanic complexes, suggesting that the Cenozoic volcanism in the area has a deep origin. Overall, the adjoint tomographic images show more vertically continuous velocity anomalies with larger amplitudes due to the consideration of the finite frequency and 3-D effects.
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
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
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.
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.
Parameter and state estimation with a time-dependent adjoint marine ice sheet model
D. N. Goldberg
2013-06-01
Full Text Available To date, assimilation of observations into large-scale ice models has consisted predominantly of time-independent inversions of surface velocities for basal traction, bed elevation, or ice stiffness, and has relied primarily on analytically-derived adjoints of diagnostic ice velocity models. To overcome limitations of such "snapshot" inversions, i.e. their inability to assimilate time-dependent data, or to produce initial states with minimum artificial drift and suitable for time-dependent simulations, we have developed an adjoint of a time-dependent parallel glaciological flow model. The model implements a hybrid shallow shelf-shallow ice stress balance, involves a prognostic equation for ice thickness evolution, and can represent the floating, fast-sliding, and frozen bed regimes of a marine ice sheet. The adjoint is generated by a combination of analytic methods and the use of algorithmic differentiation (AD software. Several experiments are carried out with idealized geometries and synthetic observations, including inversion of time-dependent surface elevations for past thicknesses, and simultaneous retrieval of basal traction and topography from surface data. Flexible generation of the adjoint for a range of independent uncertain variables is exemplified through sensitivity calculations of grounded ice volume to changes in basal melting of floating and basal sliding of grounded ice. The results are encouraging and suggest the feasibility, using real observations, of improved ice sheet state estimation and comprehensive transient sensitivity assessments.
Adjoint analysis of the source and path sensitivities of basin-guided waves
Day, Steven M.; Roten, Daniel; Olsen, Kim B.
2012-05-01
Simulations of earthquake rupture on the southern San Andreas Fault (SAF) reveal large amplifications in the San Gabriel and Los Angeles Basins (SGB and LAB) apparently associated with long-range path effects. Geometrically similar excitation patterns can be recognized repeatedly in different SAF simulations (e.g. Love wave-like energy with predominant period around 4 s, channelled southwestwardly from the SGB into LAB), yet the amplitudes with which these distinctive wavefield patterns are excited change, depending upon source details (slip distribution, direction and velocity of rupture). We describe a method for rapid calculation of the sensitivity of such predicted wavefield features to perturbations of the source kinematics, using a time-reversed (adjoint) wavefield simulation. The calculations are analogous to those done in adjoint tomography, and the same time-reversed calculation also yields path-sensitivity kernels that give further insight into the excitation mechanism. For rupture on the southernmost 300 km of SAF, LAB excitation is greatest for slip concentrated between the northern Coachella Valley and the transverse ranges, propagating to the NE and with rupture velocities between 3250 and 3500 m s-1 along that fault segment; that is, within or slightly above the velocity range (between Rayleigh and S velocities) that is energetically precluded in the limit of a sharp rupture front, highlighting the potential value of imposing physical constraints (such as from spontaneous rupture models) on source parametrizations. LAB excitation is weak for rupture to the SW and for ruptures in either direction located north of the transverse transverse ranges, whereas Ventura Basin (VTB) is preferentially excited by NE ruptures situated north of the transverse ranges. Path kernels show that LAB excitation is mediated by surface waves deflected by the velocity contrast along the southern margin of the transverse ranges, having most of their energy in basement rock
Self-adjointness of the Gaffney Laplacian on Vector Bundles
Bandara, Lashi, E-mail: lashi.bandara@chalmers.se [Chalmers University of Technology and University of Gothenburg, Mathematical Sciences (Sweden); Milatovic, Ognjen, E-mail: omilatov@unf.edu [University of North Florida, Department of Mathematics and Statistics (United States)
2015-12-15
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
Al-Hashimi, M.H., E-mail: hashimi@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Salman, M., E-mail: msalman@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Shalaby, A., E-mail: amshalab@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Physics Department, Faculty of Science, Mansoura University (Egypt); Wiese, U.-J., E-mail: wiese@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA (United States)
2013-10-15
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
On the product of the self-adjoint operators
Wulf Rehder
1982-01-01
Full Text Available A proof is given for the fact that the product of two self-adjoint operators, one of which is also positive, is again self-adjoint if and only if the product is normal. This theorem applies, in particular, if one operator is an orthogonal projection. In general, the positivity requirement cannot be dropped.
Haydock's recursive solution of self-adjoint problems. Discrete spectrum
Moroz, Alexander
2014-12-01
Haydock's recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber's quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock's recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials {pn(E) } in energy variable E. The polynomials {pn(E) } are orthonormal with respect to the density of states n0(E) and energy eigenstate | E > is the generating function of {pn(E) } . The generality of Haydock's recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.
Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator
Weir, John
2008-01-01
We prove that the eigenvalues of a certain highly non-self-adjoint operator correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many eigenvalues which accumulate only at infinity.
Adjoint 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.
Imaging the Italian Lithosphere based on Adjoint Tomography
Magnoni, F.; Casarotti, E.; Komatitsch, D.; Melini, D.; Michelini, A.; Piersanti, A.; Tape, C.; Tromp, J.
2016-12-01
We exploit the powerful European computational resources awarded to our PRACE project IMAGINE_IT ("3D full-wave tomographic IMAGINg of the Entire ITalian lithosphere") to develop a reference, high-resolution 3D seismic wavespeed model for the Italian lithosphere. The inversion procedure consists of iterative improvements of an initial 3D traveltime tomographic model of the region constrained by a large number of full, high-quality observed seismic waveforms. The final model images the regional structure at unprecedented resolution ( 10 s) minimizing the misfit between recorded and synthetic data. Numerical wavefield simulations at high frequency are performed using a spectral-element method (code SPECFEM3D) that allows us to implement all complexities that characterize the studied region (lateral heterogeneity, topography, attenuation). This method is then efficiently combined with an adjoint technique to perform the 3D full-wave tomographic inversion. The Italian peninsula is characterized by very heterogeneous features resulting from complex tectonic evolution of the region mainly dominated by the interaction of Tyrrhenian, Adria and European plates. Our inversion includes 163 earthquakes that occurred in Italy and neighboring areas between 2005 and 2014, and a dense seismological network of 400 seismic recording stations. We perform 25 iterations of our iterative tomographic inversion process, as well as moment tensor inversions for the considered events. The resolution capabilities of our model are also explored based on point spread function analyses and calculation of the approximate Hessian. Thanks to our project IMAGINE_IT, at present the first application of adjoint tomography for the whole Italian region, we are able to constrain Vp as well as Vs at unprecedented resolution; the complex plate relationships start to be accurately modeled, and other inferences on the Italian geodynamical evolution or on fluid (such as CO2) distribution become possible.
Non-variational approximation of discrete eigenvalues of self-adjoint operators
Boulton, Lyonell
2005-01-01
We establish sufficiency conditions in order to achieve approximation to discrete eigenvalues of self-adjoint operators in the second-order projection method suggested recently by Levitin and Shargorodsky, [math.SP/0212087]. We find explicit estimates for the eigenvalue error and study in detail two concrete model examples. Our results show that, unlike the majority of the standard methods, second-order projection strategies combine non-pollution and approximation at a very high level of gene...
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.
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.
Kraft, S.; Puel, G.; Aubry, D.; Funfschilling, C.
2016-12-01
For the calibration of multi-body models of railway vehicles, the identification of the model parameters from on-track measurement is required. This involves the solution of an inverse problem by minimising the misfit function which describes the distance between model and measurement using optimisation methods. The application of gradient-based optimisation methods is advantageous but necessitates an efficient approach for the computation of the gradients considering the large number of model parameters and the costly evaluation of the forward model. This work shows that the application of the adjoint state approach to the nonlinear vehicle-track multi-body system is suitable, reducing on the one hand the computational cost and increasing on the other hand the precision of the gradients. Gradients from the adjoint state method are computed for vehicle models and validated taking into account measurement noise.
Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables
Nielsen, Eric J.; Kleb, William L.
2005-01-01
A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.
Nielsen, Eric J.; Kleb, William L.
2005-01-01
A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.
Morimoto, Kenichi; Kinoshita, Hidenori; Suzuki, Yuji
2016-11-01
In the present study, an adjoint-based shape-optimization method has been developed for designing extended heat transfer surfaces in conjugate heat transfer problems. Here we specifically consider heat conduction-dominated solidification problem under different thermal boundary conditions: (i) the isothermal condition, and (ii) the conjugate condition with thermal coupling between the solidified liquid and the solid wall inside the domain bounded by the extended heat transfer surface. In the present shape-optimization scheme, extended heat transfer surfaces are successively refined in a local way based on the variational information of a cost functional with respect to the shape modification. In the computation of the developed scheme, a meshless method is employed for dealing with the complex boundary shape. For high-resolution analyses with boundary-fitted node arrangement, we have introduced a bubble-mesh method combined with a high-efficiency algorithm for searching neighboring bubbles within a cut-off distance. The present technique can be easily applied to convection problems including high Reynolds number flow. We demonstrate, for the isothermal boundary condition, that the present optimization leads to tree-like fin shapes, which achieve the temperature field with global similarity for different initial fin shapes. We will also show the computational results for the conjugate condition, which would regularize the present optimization due to the fin-efficiency effect.
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.
Adjoint Networks with Inverting and Noninverting Current Conveyors
J. Cajka; T. Dostal; Vrba, K.
2000-01-01
Four types of second-generation current conveyors are shown. The realisation of the above conveyors using differential voltage current conveyors (VDCC) is presented. Two examples illustrate the building of adjoint networks containing second-generation current conveyors.
Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation
Yaşar, Emrullah; San, Sait; Özkan, Yeşim Sağlam
2016-01-01
In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.
Adjoint gradient-based approach for aerodynamic optimization of transport aircraft
Ilic, Caslav
2013-01-01
Aerodynamic design of transport aircraft has been steadily improved over past several decades, to the point where today highly-detailed shape control is needed to achieve further improvements. Aircraft manufacturers are therefore increasingly looking into formal optimization methods, driving high-fidelity CFD analysis of finely-parametrized candidate designs. We present an adjoint gradient-based approach for maximizing the aerodynamic performance index relevant to cruise-climb mission segment...
Self-Adjointness Criterion for Operators in Fock Spaces
Falconi, Marco, E-mail: marco.falconi@univ-rennes1.fr [Université de Rennes I, IRMAR and Centre Henri Lebesgue (France)
2015-12-15
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.
Optimizing Spectral Wave Estimates with Adjoint-Based Sensitivity Maps
2014-02-18
forecasts of nearshore wave conditions are important to a diverse constituency, including vacation destinations such as Miami Beach or San Diego, coastal...a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 18 FEB 2014 2. REPORT TYPE 3. DATES...Sensitivity maps for wave spectra For any type of adjoint, sensitivity maps may be constructed from adjoint output to track the response of system properties
Heimbach, P.; Bugnion, V.
2008-12-01
We present a new and original approach to understanding the sensitivity of the Greenland ice sheet to key model parameters and environmental conditions. At the heart of this approach is the use of an adjoint ice sheet model. MacAyeal (1992) introduced adjoints in the context of applying control theory to estimate basal sliding parameters (basal shear stress, basal friction) of an ice stream model which minimize a least-squares model vs. observation misfit. Since then, this method has become widespread to fit ice stream models to the increasing number and diversity of satellite observations, and to estimate uncertain model parameters. However, no attempt has been made to extend this method to comprehensive ice sheet models. Here, we present a first step toward moving beyond limiting the use of control theory to ice stream models. We have generated an adjoint of the three-dimensional thermo-mechanical ice sheet model SICOPOLIS of Greve (1997). The adjoint was generated using the automatic differentiation (AD) tool TAF. TAF generates exact source code representing the tangent linear and adjoint model of the parent model provided. Model sensitivities are given by the partial derivatives of a scalar-valued model diagnostic or "cost function" with respect to the controls, and can be efficiently calculated via the adjoint. An effort to generate an efficient adjoint with the newly developed open-source AD tool OpenAD is also under way. To gain insight into the adjoint solutions, we explore various cost functions, such as local and domain-integrated ice temperature, total ice volume or the velocity of ice at the margins of the ice sheet. Elements of our control space include initial cold ice temperatures, surface mass balance, as well as parameters such as appear in Glen's flow law, or in the surface degree-day or basal sliding parameterizations. Sensitivity maps provide a comprehensive view, and allow a quantification of where and to which variables the ice sheet model is
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.
Universal Racah matrices and adjoint knot polynomials: Arborescent knots
Mironov, A.; Morozov, A.
2016-04-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.
Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
Mironov, A
2015-01-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SU_N) and Kauffman (SO_N) polynomials. For E_8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6x6 case. The adjoint polynomials do not distinguish between mutant...
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.
CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine
Lasse Mueller
2017-09-01
Full Text Available The adjoint method is considered as the most efficient approach to compute gradients with respect to an arbitrary number of design parameters. However, one major challenge of adjoint-based shape optimization methods is the integration into a computer-aided design (CAD workflow for practical industrial cases. This paper presents an adjoint-based framework that uses a tailored shape parameterization to satisfy geometric constraints due to mechanical and manufacturing requirements while maintaining the shape in a CAD representation. The system employs a sequential quadratic programming (SQP algorithm and in-house developed libraries for the CAD and grid generation as well as a 3D Navier–Stokes flow and adjoint solver. The developed method is applied to a multipoint optimization of a turbocharger radial turbine aiming at maximizing the total-to-static efficiency at multiple operating points while constraining the output power and the choking mass flow of the machine. The optimization converged in a few design cycles in which the total-to-static efficiency could be significantly improved over a wide operating range. Additionally, the imposed aerodynamic constraints with strict convergence tolerances are satisfied and several geometric constraints are inherently respected due to the parameterization of the turbine. In particular, radial fibered blades are used to avoid bending stresses in the turbine blades due to centrifugal forces. The methodology is a step forward towards robustness and consistency of gradient-based optimization for practical industrial cases, as it maintains the optimal shape in CAD representation. As shown in this paper, this avoids shape approximations and allows manufacturing constraints to be included.
2008-01-01
This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.
Seismic structure of the European crust and upper mantle based on adjoint tomography
Zhu, Hejun
We use adjoint tomography to estimate three-dimensional variations in seismic parameters within the crust and upper mantle beneath Europe and the North Atlantic Ocean. Spectral-element and adjoint methods are used to numerically calculate synthetic seismograms and sensitivity kernels in three-dimensional Earth models. Combined with gradient- based optimization algorithms, e.g., preconditioned conjugate-gradient and L-BFGS methods, we iteratively update seismic models of Earth's interior. A three-stage inversion strategy is designed to estimate variations in elastic wavespeeds, anelastic attenuation and radial & azimuthal anisotropy. In stage one, frequency-dependent phase differences between observed and simulated seismograms are used to determine a new radially anisotropic wavespeed model for the European crust and upper mantle, namely EU30. Long-wavelength structures in EU30 compare favorably with previous body- and surface-wave tomographic models. Some hitherto unidentified features naturally emerge from the smooth starting model. In stage two, frequency-dependent amplitude differences combined with remaining phase anomalies are used to simultaneously constrain elastic and anelastic structures. A new anelastic model, named EU50, is constructed in this stage. We observe several notable features, such as enhanced attenuation within the mantle transition zone beneath the North Atlantic Ocean. In the first two stages, long-period surface waves and short-period body waves in three-component seismograms are combined to simultaneously constrain shallow and deep structures. In stage three, frequency-dependent phase and amplitude anomalies of three-component surface waves are used to construct a radially and azimuthally anisotropic model EU60. We find that the direction of the fast axis is closely tied to the tectonic evolution in this region, such as extension along the North Atlantic Ridge, trench retreat in the Mediterranean, and counterclockwise rotation of the
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.
Nabert, Christian; Othmer, Carsten; Glassmeier, Karl-Heinz
2017-05-01
The interaction of the solar wind with a planetary magnetic field causes electrical currents that modify the magnetic field distribution around the planet. We present an approach to estimating the planetary magnetic field from in situ spacecraft data using a magnetohydrodynamic (MHD) simulation approach. The method is developed with respect to the upcoming BepiColombo mission to planet Mercury aimed at determining the planet's magnetic field and its interior electrical conductivity distribution. In contrast to the widely used empirical models, global MHD simulations allow the calculation of the strongly time-dependent interaction process of the solar wind with the planet. As a first approach, we use a simple MHD simulation code that includes time-dependent solar wind and magnetic field parameters. The planetary parameters are estimated by minimizing the misfit of spacecraft data and simulation results with a gradient-based optimization. As the calculation of gradients with respect to many parameters is usually very time-consuming, we investigate the application of an adjoint MHD model. This adjoint MHD model is generated by an automatic differentiation tool to compute the gradients efficiently. The computational cost for determining the gradient with an adjoint approach is nearly independent of the number of parameters. Our method is validated by application to THEMIS (Time History of Events and Macroscale Interactions during Substorms) magnetosheath data to estimate Earth's dipole moment.
Convergence analysis of combinations of different methods
Kang, Y. [Clarkson Univ., Potsdam, NY (United States)
1994-12-31
This paper provides a convergence analysis for combinations of different numerical methods for solving systems of differential equations. The author proves that combinations of two convergent linear multistep methods or Runge-Kutta methods produce a new convergent method of which the order is equal to the smaller order of the two original methods.
Brezillon, J.; Dwight, R.P.
2009-01-01
Within the next few years, numerical shape optimization based on high fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimization problems, and the adjoint approach - which allows fast
Simon, Moritz
2014-11-14
© 2014, Springer Science+Business Media New York. With the target of optimizing CO
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.
汪量子; 姚栋; 王侃
2012-01-01
A method of using iterated fission probability to estimate the adjoint fluence during particles simulation, and using it as the weighting function to calculate kinetics parameters βell and A in Monte Carlo codes, was introduced in this paper. Implements of this method in continuous energy Monte Carlo code MCNP and multi-group Monte Carlo code MCMG are both elaborated. Verification results show that, with regardless additional computing cost, using this method, the adjoint fluence accounted by MCMG matches well with the result computed by ANISN, and the kinetics parameters calculated by MCNP agree very well with benchmarks. This method is proved to be reliable, and the function of calculating kinetics parameters in Monte Carlo codes is carried out effectively, which could be the basement for Monte Carlo codes' utility in the analysis of nuclear reactors' transient behavior.%文章介绍了在蒙特卡罗程序中,使用反复裂变几率的统计结果作为共轭通量的估计,并作为权重函数计算动力学参数βeff和Λ的方法,阐释了在连续能量蒙特卡罗程序MCNP和多群蒙特卡罗程序MCMG中实现这种方法的过程.数值校验结果表明:在几乎不带来附加计算量的同时,在MCMG中使用该方法统计得到的共轭通量与ANISN的共轭通量计算结果符合较好,在MCNP中使用该方法计算得到的中子动力学参数与基准测量结果符合较好.在蒙特卡罗程序中实现了高效率计算中子动力学参数的功能,为蒙特卡罗程序进一步用于反应堆动态行为的分析奠定了基础.
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.
Komatitsch, Dimitri; Xie, Zhinan; Bozdaǧ, Ebru; Sales de Andrade, Elliott; Peter, Daniel; Liu, Qinya; Tromp, Jeroen
2016-09-01
We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.
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...
An adjoint-based scheme for eigenvalue error improvement
Merton, S.R.; Smedley-Stevenson, R.P., E-mail: Simon.Merton@awe.co.uk, E-mail: Richard.Smedley-Stevenson@awe.co.uk [AWE plc, Berkshire (United Kingdom); Pain, C.C.; El-Sheikh, A.H.; Buchan, A.G., E-mail: c.pain@imperial.ac.uk, E-mail: a.el-sheikh@imperial.ac.uk, E-mail: andrew.buchan@imperial.ac.uk [Department of Earth Science and Engineering, Imperial College, London (United Kingdom)
2011-07-01
A scheme for improving the accuracy and reducing the error in eigenvalue calculations is presented. Using a rst order Taylor series expansion of both the eigenvalue solution and the residual of the governing equation, an approximation to the error in the eigenvalue is derived. This is done using a convolution of the equation residual and adjoint solution, which is calculated in-line with the primal solution. A defect correction on the solution is then performed in which the approximation to the error is used to apply a correction to the eigenvalue. The method is shown to dramatically improve convergence of the eigenvalue. The equation for the eigenvalue is shown to simplify when certain normalizations are applied to the eigenvector. Two such normalizations are considered; the rst of these is a fission-source type of normalisation and the second is an eigenvector normalisation. Results are demonstrated on a number of demanding elliptic problems using continuous Galerkin weighted nite elements. Moreover, the correction scheme may also be applied to hyperbolic problems and arbitrary discretization. This is not limited to spatial corrections and may be used throughout the phase space of the discrete equation. The applied correction not only improves fidelity of the calculation, it allows assessment of the reliability of numerical schemes to be made and could be used to guide mesh adaption algorithms or to automate mesh generation schemes. (author)
Generalized rectangular finite difference beam propagation method.
Sujecki, Slawomir
2008-08-10
A method is proposed that allows for significant improvement of the numerical efficiency of the standard finite difference beam propagation algorithm. The advantages of the proposed method derive from the fact that it allows for an arbitrary selection of the preferred direction of propagation. It is demonstrated that such flexibility is particularly useful when studying the properties of obliquely propagating optical beams. The results obtained show that the proposed method achieves the same level of accuracy as the standard finite difference beam propagation method but with lower order Padé approximations and a coarser finite difference mesh.
Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations
Júlio Cesar Santos Sampaio
2014-01-01
Full Text Available The concepts of strictly, quasi, weak, and nonlinearly self-adjoint differential equations are revisited. A nonlinear self-adjoint classification of a class of equations with second and third order is carried out.
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.
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.
Searching for Standard Model Adjoint Scalars with Diboson Resonance Signatures
Carpenter, Linda M
2015-01-01
We explore the phenomenology of scalar fields in the adjoint representation of SM gauge groups. We write a general set of dimension 5 effective operators in which SM adjoint scalars couple to pairs of standard model bosons. Using these effective operators, we explore new possible decay channels of a scalar color octet into a gluon and a Z boson/ gluon and a photon. We recast several analyses from Run I of the LHC to find constraints on an a scalar octet decaying into these channels, and we project the discovery potential of color octets in our gluon+photon channel for the 14 TeV run of LHC.
On the Adjoint of a Strongly Continuous Semigroup
Diómedes Bárcenas
2008-01-01
Full Text Available Using some techniques from vector integration, we prove the weak measurability of the adjoint of strongly continuous semigroups which factor through Banach spaces without isomorphic copy of l1; we also prove the strong continuity away from zero of the adjoint if the semigroup factors through Grothendieck spaces. These results are used, in particular, to characterize the space of strong continuity of {T**(t}t≥0, which, in addition, is also characterized for abstract L- and M-spaces. As a corollary, it is proven that abstract L-spaces with no copy of l1 are finite-dimensional.
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids
Christ, Michael
2010-01-01
It was proved independently by Foschi and Hundertmark, Zharnitsky that Gaussians extremize the adjoint Fourier restriction inequality for L^2 functions on the paraboloid in the two lowest-dimesional cases. Here we prove that Gaussians are critical points for the L^p to L^q adjoint Fourier restriction inequalities if and only if p=2. Also, Gaussians are critial points for the L^2 to L^r_t L^q_x Strichartz inequalities for all admissible pairs (r,q) in (1,infinity)^2.
On the wavelet optimized finite difference method
Jameson, Leland
1994-01-01
When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.
Compressions of maximal dissipative and self-adjoint linear relations and of dilations
Azizov, T.Ya.; Dijksma, A.; Wanjala, G.
2013-01-01
In this paper we generalize results from Stenger (1968) [30], Nudelman (2011) [28] and Azizov and Dijksma (2012) [7] to maximal dissipative and self-adjoint linear relations and discuss related results for nonnegative self-adjoint extensions of nonnegative symmetric linear relations and self-adjoint
Time-dependent problems and difference methods
Gustafsson, Bertil; Oliger, Joseph
2013-01-01
Praise for the First Edition "". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations."" -SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-de
Different partial volume correction methods lead to different conclusions
Greve, Douglas N; Salat, David H; Bowen, Spencer L
2016-01-01
A cross-sectional group study of the effects of aging on brain metabolism as measured with (18)F-FDG-PET was performed using several different partial volume correction (PVC) methods: no correction (NoPVC), Meltzer (MZ), Müller-Gärtner (MG), and the symmetric geometric transfer matrix (SGTM) usin...
Reuther, James; Jameson, Antony; Alonso, Juan Jose; Rimlinger, Mark J.; Saunders, David
1997-01-01
An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat
Adjoint-based optimization of a foam EOR process
Namdar Zanganeh, M.; Kraaijevanger, J.F.B.M.; Buurman, H.W.; Jansen, J.D.; Rossen, W.R.
2012-01-01
We apply adjoint-based optimization to a Surfactant-Alternating-Gas foam process using a linear foam model introducing gradual changes in gas mobility and a nonlinear foam model giving abrupt changes in gas mobility as function of oil and water saturations and surfactant concentration. For the
Non-self-adjoint hamiltonians defined by Riesz bases
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.
Nefness of adjoint bundles for ample vector bundles
Hidetoshi Maeda
1995-11-01
Full Text Available Let E be an ample vector bundle of rank >1 on a smooth complex projective variety X of dimension n. This paper gives a classification of pairs (X,E whose adjoint bundles K_X+det E are not nef in the case when r=n-2.
On self-adjointness of singular Floquet Hamiltonians
Duclos, Pierre; Jensen, Arne
2010-01-01
Schrödinger equations with time-dependent interactions are studied. We investigate how to define the Floquet Hamiltonian as a self-adjoint operator, when the interaction is singular in time or space. Using these results we establish the existence of a bounded propagator, by applying a result given...
Large-volume results in SU(2) with adjoint fermions
Del Debbio, Luigi; Pica, Claudio; Patella, Agostino; Rago, Antonio; Roman, Sabin
2014-01-01
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, and extrapolate to thermodynamic limit when possible.
Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"
Ammonia emissions parameters in North America can be refined in order to improve the evaluation of modeled concentrations against observations. Here, we seek to do so by developing and applying the GEOS-Chem adjoint nested over North America to conductassimilation of observations...
Large-volume results in SU(2) with adjoint fermions
Del Debbio, Luigi; Lucini, Biagio; Pica, Claudio;
2013-01-01
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, an...
Finite volume effects in SU(2) with two adjoint fermions
Del Debbio, Luigi; Lucini, Biagio; Patella, Agostino;
2011-01-01
Many evidences from lattice simulations support the idea that SU(2) with two Dirac flavors in the adjoint representation (also called Minimal Walking Technicolor) is IR conformal. A possible way to see this is through the behavior of the spectrum of the mass-deformed theory. When fermions are mas...
Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey
2015-04-01
The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each
Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation
Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David
1996-01-01
This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.
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...
Maintenance Approaches for Different Production Methods
Mungani, Dzivhuluwani Simon
2013-11-01
Full Text Available Various production methods are used in industry to manufacture or produce a variety of products needed by industry and consumers. The nature of a product determines which production method is most suitable or cost-effective. A continuous process is typically used to produce large volumes of liquids or gases. Batch processing is often used for small volumes, such as pharmaceutical products. This paper discusses a research project to determine the relationship between maintenance approaches and production methods. A survey was done to determine to what extent three maintenance approaches reliability-centred maintenance (RCM, total productive maintenance (TPM, and business-centred maintenance (BCM are used for three different processing methods (continuous process, batch process, and a production line method.
An update in monopole condensation in two-flavour Adjoint QCD
Lacagnina, G; D'Elia, M; Di Giacomo, A; Pica, C
2007-01-01
QCD with fermions in the adjoint representation (aQCD) is a model for which a deconfinement and a chiral phase transition take place at different temperatures. In this work, we present a study of the deconfinement transition in the dual superconductor picture based on the evaluation of an operator which carries magnetic charge. The expectation value of this operator signals monopole condensation and is an order parameter for deconfinement as in the case of fermions in the fundamental representation. We find a sharp first order deconfinement transition. We also study the effects of the chiral transition on the monopole order parameter and find them negligible.
Adjusting Teaching Methods with Different Students
Jian Zhao
2000-01-01
@@ Teaching Chinese as a second language can draw upon certain assumptions and methods that are applicable to the student whatever his or her first language might be. But there are also significant features which vary among different student groups, for example, English and Japanese students.The more years that I teach Chinese to these two groups, the more I find these features of increasing focus and interest. In this article, I would like to describe the major differences in learning Chinese among students from these two groups. My focus will be placed on how to take advantage of these differences and adopt appropriate teaching approaches.
Adjoint sensitivity of global cloud droplet number to aerosol and dynamical parameters
V. A. Karydis
2012-10-01
Full Text Available We present the development of the adjoint of a comprehensive cloud droplet formation parameterization for use in aerosol-cloud-climate interaction studies. The adjoint efficiently and accurately calculates the sensitivity of cloud droplet number concentration (CDNC to all parameterization inputs (e.g., updraft velocity, water uptake coefficient, aerosol number and hygroscopicity with a single execution. The adjoint is then integrated within three dimensional (3-D aerosol modeling frameworks to quantify the sensitivity of CDNC formation globally to each parameter. Sensitivities are computed for year-long executions of the NASA Global Modeling Initiative (GMI Chemical Transport Model (CTM, using wind fields computed with the Goddard Institute for Space Studies (GISS Global Circulation Model (GCM II', and the GEOS-Chem CTM, driven by meteorological input from the Goddard Earth Observing System (GEOS of the NASA Global Modeling and Assimilation Office (GMAO. We find that over polluted (pristine areas, CDNC is more sensitive to updraft velocity and uptake coefficient (aerosol number and hygroscopicity. Over the oceans of the Northern Hemisphere, addition of anthropogenic or biomass burning aerosol is predicted to increase CDNC in contrast to coarse-mode sea salt which tends to decrease CDNC. Over the Southern Oceans, CDNC is most sensitive to sea salt, which is the main aerosol component of the region. Globally, CDNC is predicted to be less sensitive to changes in the hygroscopicity of the aerosols than in their concentration with the exception of dust where CDNC is very sensitive to particle hydrophilicity over arid areas. Regionally, the sensitivities differ considerably between the two frameworks and quantitatively reveal why the models differ considerably in their indirect forcing estimates.
Fourth order difference methods for hyperbolic IBVP's
Gustafsson, Bertil; Olsson, Pelle
1994-01-01
Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.
郑召文; 刘宝圣
2012-01-01
本文讨论了极限圆型Hamilton算子乘积的自伴性，利用Calkin方法及奇异Hamilton系统自伴扩张的一般构造理论，给出了在极限圆型时判定Hamilton算子乘积自伴的一个充要条件．%In this paper, the self-adjointness of the product of two Hamiltonian op- erators under the limit circle case is considered. Using the Calkin method and the construction of self-adjoint extension for singular Hamiltonian systems, the necessary and sufficient conditions which make the product of two Hamiltonian operators under the limit circle case being a self-adjoint operator are obtained.
Mapping Emissions that Contribute to Air Pollution Using Adjoint Sensitivity Analysis
Bastien, L. A. J.; Mcdonald, B. C.; Brown, N. J.; Harley, R.
2014-12-01
The adjoint of the Community Multiscale Air Quality model (CMAQ) is used to map emissions that contribute to air pollution at receptors of interest. Adjoint tools provide an efficient way to calculate the sensitivity of a model response to a large number of model inputs, a task that would require thousands of simulations using a more traditional forward sensitivity approach. Initial applications of this technique, demonstrated here, are to benzene and directly-emitted diesel particulate matter, for which atmospheric reactions are neglected. Emissions of these pollutants are strongly influenced by light-duty gasoline vehicles and heavy-duty diesel trucks, respectively. We study air quality responses in three receptor areas where populations have been identified as especially susceptible to, and adversely affected by air pollution. Population-weighted air basin-wide responses for each pollutant are also evaluated for the entire San Francisco Bay area. High-resolution (1 km horizontal grid) emission inventories have been developed for on-road motor vehicle emission sources, based on observed traffic count data. Emission estimates represent diurnal, day of week, and seasonal variations of on-road vehicle activity, with separate descriptions for gasoline and diesel sources. Emissions that contribute to air pollution at each receptor have been mapped in space and time using the adjoint method. Effects on air quality of both relative (multiplicative) and absolute (additive) perturbations to underlying emission inventories are analyzed. The contributions of local versus upwind sources to air quality in each receptor area are quantified, and weekday/weekend and seasonal variations in the influence of emissions from upwind areas are investigated. The contribution of local sources to the total air pollution burden within the receptor areas increases from about 40% in the summer to about 50% in the winter due to increased atmospheric stagnation. The effectiveness of control
Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach
Aguilar, José G.; Magri, Luca; Juniper, Matthew P.
2017-07-01
Strict pollutant emission regulations are pushing gas turbine manufacturers to develop devices that operate in lean conditions, with the downside that combustion instabilities are more likely to occur. Methods to predict and control unstable modes inside combustion chambers have been developed in the last decades but, in some cases, they are computationally expensive. Sensitivity analysis aided by adjoint methods provides valuable sensitivity information at a low computational cost. This paper introduces adjoint methods and their application in wave-based low order network models, which are used as industrial tools, to predict and control thermoacoustic oscillations. Two thermoacoustic models of interest are analyzed. First, in the zero Mach number limit, a nonlinear eigenvalue problem is derived, and continuous and discrete adjoint methods are used to obtain the sensitivities of the system to small modifications. Sensitivities to base-state modification and feedback devices are presented. Second, a more general case with non-zero Mach number, a moving flame front and choked outlet, is presented. The influence of the entropy waves on the computed sensitivities is shown.
Implicit finite difference methods on composite grids
Mastin, C. Wayne
1987-01-01
Techniques for eliminating time lags in the implicit finite-difference solution of partial differential equations are investigated analytically, with a focus on transient fluid dynamics problems on overlapping multicomponent grids. The fundamental principles of the approach are explained, and the method is shown to be applicable to both rectangular and curvilinear grids. Numerical results for sample problems are compared with exact solutions in graphs, and good agreement is demonstrated.
Measurements and Terminology of Different Measure Methods
FANG Fang; ZHANG Wei-yuan; ZHANG Wen-bin
2005-01-01
Body measuring is very important for garment sizing and pattern making. In this paper, we study the difference of the landmarks between the traditional method and 3D scanner and we also select the 19 circumference measurements,29 height and length measurements, 18 breadth and depth measurements and 3 other measurements, which are quite important in fashion body measuring, to compare the terminology of them in these two measuring method. 3D scanners seem better than the traditional method on these aspects, which are the number of measurements, speed,privacy and data accuracy, but they are limited on measuring posture. And there is no uniform standard for the scanners and the definitions of the measurements in the scanners are diversified.
The Complex-Step-Finite-Difference method
Abreu, Rafael; Stich, Daniel; Morales, Jose
2015-07-01
We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.
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.
Mitigation of Engine Inlet Distortion Through Adjoint-Based Design
Ordaz, Irian; Rallabhandi, Sriram; Nielsen, Eric J.; Diskin, Boris
2017-01-01
The adjoint-based design capability in FUN3D is extended to allow efficient gradient- based optimization and design of concepts with highly integrated aero-propulsive systems. A circumferential distortion calculation, along with the derivatives needed to perform adjoint-based design, have been implemented in FUN3D. This newly implemented distortion calculation can be used not only for design but also to drive the existing mesh adaptation process and reduce the error associated with the fan distortion calculation. The design capability is demonstrated by the shape optimization of an in-house aircraft concept equipped with an aft fuselage propulsor. The optimization objective is the minimization of flow distortion at the aerodynamic interface plane of this aft fuselage propulsor.
Three-Dimensional Turbulent RANS Adjoint-Based Error Correction
Park, Michael A.
2003-01-01
Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.
Nonself-adjoint semicrossed products by abelian semigroups
Fuller, Adam Hanley
2011-01-01
Let $\\mathcal{S}$ be the semigroup $\\mathcal{S}=\\sum^{\\oplus k}_{i=1}\\Sc{S}_i$, where for each $i\\in I$, $\\mathcal{S}_i$ is a countable subsemigroup of the additive semigroup $\\B{R}_+$ containing 0. We consider representations of $\\mathcal{S}$ as contractions $\\{T_s\\}_{s\\in\\mathcal{S}}$ on a Hilbert space with the Nica-covariance property: $T_s^*T_t=T_tT_s^*$ whenever $t\\wedge s=0$. We show that all such representations have a unique minimal isometric Nica-covariant dilation. This result is used to help analyse the nonself-adjoint semicrossed product algebras formed from Nica-covariant representations of the action of $\\mathcal{S}$ on an operator algebra $\\mathcal{A}$ by completely contractive endomorphisms. We conclude by calculating the $C^*$-envelope of the isometric nonself-adjoint semicrossed product algebra (in the sense of Kakariadis and Katsoulis).
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.
Higher order self-adjoint operators with polynomial coefficients
Hassan Azad
2017-01-01
Full Text Available We study algebraic and analytic aspects of self-adjoint operators of order four or higher with polynomial coefficients. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain many examples up to order 8; similar examples can be constructed for all even order operators. In particular, a complete classification of all order 4 operators is given.
Arrangements, multiderivations, and adjoint quotient map of type ADE
Yoshinaga, Masahiko
2010-01-01
The first part of this paper is a survey on algebro-geometric aspects of sheaves of logarithmic vector fields of hyperplane arrangements. In the second part we prove that the relative de Rham cohomology (of degree two) of ADE-type adjoint quotient map is naturally isomorphic to the module of certain multiderivations. The isomorphism is obtained by the Gauss-Manin derivative of the Kostant-Kirillov form.
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.
Effective condition number for finite difference method
Li, Zi-Cai; Chien, Cheng-Sheng; Huang, Hung-Tsai
2007-01-01
For solving the linear algebraic equations Ax=b with the symmetric and positive definite matrix A, from elliptic equations, the traditional condition number in the 2-norm is defined by Cond.=[lambda]1/[lambda]n, where [lambda]1 and [lambda]n are the maximal and minimal eigenvalues of the matrix A, respectively. The condition number is used to provide the bounds of the relative errors from the perturbation of both A and b. Such a Cond. can only be reached by the worst situation of all rounding errors and all b. For the given b, the true relative errors may be smaller, or even much smaller than the Cond., which is called the effective condition number in Chan and Foulser [Effectively well-conditioned linear systems, SIAM J. Sci. Statist. Comput. 9 (1988) 963-969] and Christiansen and Hansen [The effective condition number applied to error analysis of certain boundary collocation methods, J. Comput. Appl. Math. 54(1) (1994) 15-36]. In this paper, we propose the new computational formulas for effective condition number Cond_eff, and define the new simplified effective condition number Cond_E. For the latter, we only need the eigenvector corresponding to the minimal eigenvalue of A, which can be easily obtained by the inverse power method. In this paper, we also apply the effective condition number for the finite difference method for Poisson's equation. The difference grids are not supposed to be quasiuniform. Under a non-orthogonality assumption, the effective condition number is proven to be O(1) for the homogeneous boundary conditions. Such a result is extraordinary, compared with the traditional , where hmin is the minimal meshspacing of the difference grids used. For the non-homogeneous Neumann and Dirichlet boundary conditions, the effective condition number is proven to be O(h-1/2) and , respectively, where h is the maximal meshspacing of the difference grids. Numerical experiments are carried out to verify the analysis made.
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...
Evaluation of toothbrush disinfection via different methods.
Basman, Adil; Peker, Ilkay; Akca, Gulcin; Alkurt, Meryem Toraman; Sarikir, Cigdem; Celik, Irem
2016-01-01
The aim of this study was to compare the efficacy of using a dishwasher or different chemical agents, including 0.12% chlorhexidine gluconate, 2% sodium hypochlorite (NaOCl), a mouthrinse containing essential oils and alcohol, and 50% white vinegar, for toothbrush disinfection. Sixty volunteers were divided into five experimental groups and one control group (n = 10). Participants brushed their teeth using toothbrushes with standard bristles, and they disinfected the toothbrushes according to instructed methods. Bacterial contamination of the toothbrushes was compared between the experimental groups and the control group. Data were analyzed by Kruskal-Wallis and Duncan's multiple range tests, with 95% confidence intervals for multiple comparisons. Bacterial contamination of toothbrushes from individuals in the experimental groups differed from those in the control group (p method for elimination of all tested bacterial species was 50% white vinegar, followed in order by 2% NaOCl, mouthrinse containing essential oils and alcohol, 0.12% chlorhexidine gluconate, dishwasher use, and tap water (control). The results of this study show that the most effective method for disinfecting toothbrushes was submersion in 50% white vinegar, which is cost-effective, easy to access, and appropriate for household use.
Evaluation of toothbrush disinfection via different methods
Adil BASMAN
2016-01-01
Full Text Available The aim of this study was to compare the efficacy of using a dishwasher or different chemical agents, including 0.12% chlorhexidine gluconate, 2% sodium hypochlorite (NaOCl, a mouthrinse containing essential oils and alcohol, and 50% white vinegar, for toothbrush disinfection. Sixty volunteers were divided into five experimental groups and one control group (n = 10. Participants brushed their teeth using toothbrushes with standard bristles, and they disinfected the toothbrushes according to instructed methods. Bacterial contamination of the toothbrushes was compared between the experimental groups and the control group. Data were analyzed by Kruskal–Wallis and Duncan's multiple range tests, with 95% confidence intervals for multiple comparisons. Bacterial contamination of toothbrushes from individuals in the experimental groups differed from those in the control group (p < 0.05. The most effective method for elimination of all tested bacterial species was 50% white vinegar, followed in order by 2% NaOCl, mouthrinse containing essential oils and alcohol, 0.12% chlorhexidine gluconate, dishwasher use, and tap water (control. The results of this study show that the most effective method for disinfecting toothbrushes was submersion in 50% white vinegar, which is cost-effective, easy to access, and appropriate for household use.
Hybrid Active Noise Control using Adjoint LMS Algorithms
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.
Infrared conformality and bulk critical points: SU(2) with heavy adjoint quarks
Lucini, Biagio; Rago, Antonio; Rinaldi, Enrico
2013-01-01
The lattice phase structure of a gauge theory can be a serious obstruction to Monte Carlo studies of its continuum behaviour. This issue is particularly delicate when numerical studies are performed to determine whether a theory is in a (near-)conformal phase. In this work we investigate the heavy mass limit of the SU(2) gauge theory with Nf=2 adjoint fermions and its lattice phase diagram, showing the presence of a critical point ending a line of first order bulk phase transition. The relevant gauge observables and the low-lying spectrum are monitored in the vicinity of the critical point with very good control over different systematic effects. The scaling properties of masses and susceptibilities open the possibility that the effective theory at criticality is a scalar theory in the universality class of the four-dimensional Gaussian model. This behaviour is clearly different from what is observed for SU(2) gauge theory with two dynamical adjoint fermions, whose (near-)conformal numerical signature is henc...
Detecting sulphate aerosol geoengineering with different methods
Lo, Y. T. Eunice; Charlton-Perez, Andrew J.; Lott, Fraser C.; Highwood, Eleanor J.
2016-12-01
Sulphate aerosol injection has been widely discussed as a possible way to engineer future climate. Monitoring it would require detecting its effects amidst internal variability and in the presence of other external forcings. We investigate how the use of different detection methods and filtering techniques affects the detectability of sulphate aerosol geoengineering in annual-mean global-mean near-surface air temperature. This is done by assuming a future scenario that injects 5 Tg yr‑1 of sulphur dioxide into the stratosphere and cross-comparing simulations from 5 climate models. 64% of the studied comparisons would require 25 years or more for detection when no filter and the multi-variate method that has been extensively used for attributing climate change are used, while 66% of the same comparisons would require fewer than 10 years for detection using a trend-based filter. This highlights the high sensitivity of sulphate aerosol geoengineering detectability to the choice of filter. With the same trend-based filter but a non-stationary method, 80% of the comparisons would require fewer than 10 years for detection. This does not imply sulphate aerosol geoengineering should be deployed, but suggests that both detection methods could be used for monitoring geoengineering in global, annual mean temperature should it be needed.
Learning phacoemulsification. Results of different teaching methods.
Hennig Albrecht
2004-01-01
Full Text Available We report the learning curves of three eye surgeons converting from sutureless extracapsular cataract extraction to phacoemulsification using different teaching methods. Posterior capsule rupture (PCR as a per-operative complication and visual outcome of the first 100 operations were analysed. The PCR rate was 4% and 15% in supervised and unsupervised surgery respectively. Likewise, an uncorrected visual acuity of > or = 6/18 on the first postoperative day was seen in 62 (62% of patients and in 22 (22% in supervised and unsupervised surgery respectively.
Adjoint inversion modeling of Asian dust emission using lidar observations
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
Nasser, Mohamed M. S.; Murid, Ali H. M.; Sangawi, Ali W. K.
2013-01-01
This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a boundary integral equation with the adjoint generalized Neumann kernel for the derivative of the boundary...
Development and Applications of the FV3 GEOS-5 Adjoint Modeling System
Holdaway, Daniel; Kim, Jong G.; Lin, Shian-Jiann; Errico, Ron; Gelaro, Ron; Kent, James; Coy, Larry; Doyle, Jim; Goldstein, Alex
2017-01-01
GMAO has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR. In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system.
Efficient discretization in finite difference method
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
Efficiency of different methods for seeding grasslands
Vesna Očić
2009-12-01
Full Text Available In Croatia, the economic effects of different grassland sowing methods are still insufficiently explored. In order to detect the difference between grassland sowing methods a three-year field trialswere performed to determine the production and economic value of grasslands sown by: direct seeding into corn stubble field with row distance of 18 cm (DSK18 or ii 9 cm (DSK9, iii conventional seeding (KS, iv sod-seeding in existing grassland (RPTDS and v natural grassland as control (KPT. In the whole research period the highest average green mass productivity was achieved by conventional seeding (38.84 t/ha, while the lowest green mass yield had natural grassland and sod-seeded natural grassland (10.92 and 11.63 t/ha of green mass. Observed per unit of area, difference in production values ranged from 3276 kn, which was achieved with natural grass to 17.478 kn/ha, which was achieved by conventional seeding. Looking at the production efficiency, direct seeding into corn stubble field with row distance of 9 cm (3.17 has the largest coefficient, while natural grassland is on the economy border with coefficient 1.00. Relations between invested and obtained, which was measured with value of Gross Margin, is in range from 6 kn/ha (natural grassland to 11.420 kn/ha, which was achieved by conventional seeding. Looking at the production of hay, conventional seeding with 7.11 t/ha of hay had the maximum productivity, while the natural grassland and sod-seeded natural grassland had the lowest production (2.87 and 2.86 t/ha.
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.
Global Adjoint Tomography: Combining Big Data with HPC Simulations
Bozdag, E.; Lefebvre, M. P.; Lei, W.; Peter, D. B.; Smith, J. A.; Komatitsch, D.; Tromp, J.
2014-12-01
The steady increase in data quality and the number of global seismographic stations have substantially grown the amount of data available for construction of Earth models. Meanwhile, developments in the theory of wave propagation, numerical methods and HPC systems have enabled unprecedented simulations of seismic wave propagation in realistic 3D Earth models which lead the extraction of more information from data, ultimately culminating in the use of entire three-component seismograms.Our aim is to take adjoint tomography further to image the entire planet which is one of the extreme cases in seismology due to its intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. We have started low resolution (T > 27 s, soon will be > 17 s) global inversions with 253 earthquakes for a transversely isotropic crust and mantle model on Oak Ridge National Laboratory's Cray XK7 "Titan" system. Recent improvements in our 3D solvers, such as the GPU version of the SPECFEM3D_GLOBE package, will allow us perform higher-resolution (T > 9 s) and longer-duration (~180 m) simulations to take the advantage of high-frequency body waves and major-arc surface waves to improve imbalanced ray coverage as a result of uneven distribution of sources and receivers on the globe. Our initial results after 10 iterations already indicate several prominent features reported in high-resolution continental studies, such as major slabs (Hellenic, Japan, Bismarck, Sandwich, etc.) and enhancement in plume structures (the Pacific superplume, the Hawaii hot spot, etc.). Our ultimate goal is to assimilate seismic data from more than 6,000 earthquakes within the magnitude range 5.5 ≤ Mw ≤ 7.0. To take full advantage of this data set on ORNL's computational resources, we need a solid framework for managing big data sets during pre-processing (e.g., data requests and quality checks), gradient calculations, and post-processing (e
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.
Spak, S.; Henze, D. K.; Carmichael, G. R.
2013-12-01
The science and policy communities both need common metrics that clearly, comprehensively, and intuitively communicate the relative sensitivities of air quality and climate to emissions control strategies, include emissions and process uncertainties, and minimize the range of error that is transferred to the metric. This is particularly important because most emissions control policies impact multiple short-lived climate forcing agents, and non-linear climate and health responses in space and time limit the accuracy and policy value of simple emissions-based calculations. Here we describe and apply new second-order elasticity metrics to support the direct comparison of emissions control policies for air quality and health co-benefits analyses using adjoint chemical transport and chemistry-climate models. Borrowing an econometric concept, the simplest elasticities in the atmospheric system are the percentage changes in concentrations due to a percentage change in the emissions. We propose a second-order elasticity metric, the Emissions Reduction Efficiency, which supports comparison across compounds, to long-lived climate forcing agents like CO2, and to other air quality impacts, at any temporal or spatial scale. These adjoint-based metrics (1) possess a single uncertainty range; (2) allow for the inclusion of related health and other impacts effects within the same framework; (3) take advantage of adjoint and forward sensitivity models; and (4) are easily understood. Using global simulations with the adjoint of GEOS-Chem, we apply these metrics to identify spatial and sectoral variability in the climate and health co-benefits of sectoral emissions controls on black carbon, sulfur dioxide, and PM2.5. We find spatial gradients in optimal control strategies on every continent, along with differences among megacities.
On the Norm Convergence of the Self-Adjoint Trotter–Kato Product Formula with Error Bound
Takashi Ichinose; Hideo Tamura
2002-02-01
The norm convergence of the Trotter–Kato product formula with error bound is shown for the semigroup generated by that operator sum of two nonnegative self-adjoint operators and which is self-adjoint.
Self-adjoint Extensions for the Neumann Laplacian and Applications
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.
Bimetric Gravity From Adjoint Frame Field In Four Dimensions
Guo, Zhi-Qiang
2015-01-01
We provide a novel model of gravity by using adjoint frame fields in four dimensions. It has a natural interpretation as a gravitational theory of a complex metric field, which describes interactions between two real metrics. The classical solutions establish three appealing features. The spherical symmetric black hole solution has an additional hair, which includes the Schwarzschild solution as a special case. The de Sitter solution is realized without introducing a cosmological constant. The constant flat background breaks the Lorentz invariance spontaneously, although the Lorentz breaking effect can be localized to the second metric while the first metric still respects the Lorentz invariance.
Large-N reduction with adjoint Wilson fermions
Bringoltz, Barak; Sharpe, Stephen R
2012-01-01
We analyze the large-N behavior of SU(N) lattice gauge theories with adjoint fermions by studying volume-reduced models, as pioneered by Eguchi and Kawai. We perform simulations on a single-site lattice for Nf = 1 and Nf = 2 Wilson Dirac fermions with values of N up to 53. We show for both values of Nf that in the large-N limit there is a finite region, containing both light and heavy fermions, of unbroken center symmetry where the theory exhibits volume independence. Using large-N reduction we attempt to calculate physical quantities such as the string tension and meson masses.
Mass anomalous dimension in SU(2) with two adjoint fermions
Bursa, Francis; Keegan, Liam; Pica, Claudio; Pickup, Thomas
2009-01-01
We study SU(2) lattice gauge theory with two flavours of Dirac fermions in the adjoint representation. We measure the running of the coupling in the Schroedinger Functional (SF) scheme and find it is consistent with the existence of an infrared fixed point (IRFP). We discuss how systematic errors affect the evidence for an IRFP. We present the first measurement of the running of the mass in the SF scheme. Assuming the existence of a fixed point, we can deduce the anomalous dimension at the fixed point. At the current level of accuracy, we can estimate 0.05 < gamma < 0.56 at the IRFP.
QCD thermodynamics from 3d adjoint Higgs model
Karsch, Frithjof; Patkós, András; Petreczky, P; Szép, Z; Szep, Zs.
1998-01-01
The screening masses of hot SU(N) gauge theory, defined as poles of the corresponding propagators are studied in 3d adjoint Higgs model, considered as an effective theory of QCD, using coupled gap equations and lattice Monte-Carlo simulations (for N=2). Using so-called lambda gauges non-perturbative evidence for gauge independence of the pole masses within this class of gauges is given. A possible application of the screening masses for the resummation of the free energy is discussed.
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.
Adaptive boundaryless finite-difference method.
Lopez-Mago, Dorilian; Gutiérrez-Vega, Julio C
2013-02-01
The boundaryless beam propagation method uses a mapping function to transform the infinite real space into a finite-size computational domain [Opt. Lett.21, 4 (1996)]. This leads to a bounded field that avoids the artificial reflections produced by the computational window. However, the method suffers from frequency aliasing problems, limiting the physical region to be sampled. We propose an adaptive boundaryless method that concentrates the higher density of sampling points in the region of interest. The method is implemented in Cartesian and cylindrical coordinate systems. It keeps the same advantages of the original method but increases accuracy and is not affected by frequency aliasing.
On rational R-matrices with adjoint SU(n) symmetry
Stronks, Laurens; Schuricht, Dirk
2016-01-01
Using the representation theory of Yangians we construct the rational R-matrix which takes values in the adjoint representation of SU(n). From this we derive an integrable SU(n) spin chain with lattice spins transforming under the adjoint representation. However, the resulting Hamiltonian is found to be non-Hermitian.
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2000-07-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)
Habte, Aron [National Renewable Energy Laboratory, Golden CO 80401 USA; Sengupta, Manajit [National Renewable Energy Laboratory, Golden CO 80401 USA; Andreas, Afshin [National Renewable Energy Laboratory, Golden CO 80401 USA; Reda, Ibrahim [National Renewable Energy Laboratory, Golden CO 80401 USA; Robinson, Justin [GroundWork Renewables Inc., Logan UT 84321 USA
2016-10-07
Accurate solar radiation measured by radiometers depends on instrument performance specifications, installation method, calibration procedure, measurement conditions, maintenance practices, location, and environmental conditions. This study addresses the effect of different calibration methodologies and resulting differences provided by radiometric calibration service providers such as the National Renewable Energy Laboratory (NREL) and manufacturers of radiometers. Some of these methods calibrate radiometers indoors and some outdoors. To establish or understand the differences in calibration methodologies, we processed and analyzed field-measured data from radiometers deployed for 10 months at NREL's Solar Radiation Research Laboratory. These different methods of calibration resulted in a difference of +/-1% to +/-2% in solar irradiance measurements. Analyzing these differences will ultimately assist in determining the uncertainties of the field radiometer data and will help develop a consensus on a standard for calibration. Further advancing procedures for precisely calibrating radiometers to world reference standards that reduce measurement uncertainties will help the accurate prediction of the output of planned solar conversion projects and improve the bankability of financing solar projects.
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.
On the Self-adjointness of the Product Operators of Two mth-Order Differential Operators on [0, +∞)
Jian Ye AN; Jiong SUN
2004-01-01
In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, +∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.
Self-adjoint oscillator operator from a modified factorization
Reyes, Marco A. [Departamento de Fisica, DCI Campus Leon, Universidad de Guanajuato, Apdo. Postal E143, 37150 Leon, Gto. (Mexico); Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Gutierrez, M. Ranferi [Departamento de Fisica, DCI Campus Leon, Universidad de Guanajuato, Apdo. Postal E143, 37150 Leon, Gto. (Mexico)
2011-05-30
By using an alternative factorization, we obtain a self-adjoint oscillator operator of the form L{sub δ}=d/(dx) (p{sub δ}(x)d/(dx) )-((x{sup 2})/(p{sub δ}(x)) +p{sub δ}(x)-1), where p{sub δ}(x)=1+δe{sup -x{sup 2}}, with δ element of (-1,∞) an arbitrary real factorization parameter. At positive values of δ, this operator interpolates between the quantum harmonic oscillator Hamiltonian for δ=0 and a scaled Hermite operator at high values of δ. For the negative values of δ, the eigenfunctions look like deformed quantum mechanical Hermite functions. Possible applications are mentioned. -- Highlights: → We present a generalization of the Mielnik factorization. → We study the case of linear relationship between the factorization coefficients. → We introduce a new one-parameter self-adjoint oscillator operator. → We show its properties depending on the values of the parameter.
Adjoint $SU(5)$ GUT model with $T_{7}$ flavor symmetry
Arbeláez, Carolina; Kovalenko, Sergey; Schmidt, Iván
2015-01-01
We propose an adjoint $SU(5)$ GUT model with a $T_{7}$ family symmetry and an extra $Z_{2}\\otimes Z_{2}^{\\prime }\\otimes Z_{3}\\otimes Z_{4}\\otimes Z_{12}$ discrete group, that successfully describes the prevailing Standard Model (SM) fermion mass and mixing pattern. The observed hierarchy of the charged fermion masses and the quark mixing angles arises from the $Z_{3}\\otimes Z_{4}\\otimes Z_{12}$ symmetry breaking, which occurs near the GUT scale. The light active neutrino masses are generated by type I and type III seesaw mechanisms mediated by the fermionic $SU(5)$ singlet and the adjoint $\\mathbf{24}$-plet. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be $m_{\\beta \\beta }=$ 4 and 50 meV for the normal and the inverted neutrino spectrum, respectively. We construct several benchmark scenarios, which lead to $SU(5)$ gauge coupling unification and are compatible with the known phenomenological constraints originating from the lightness of neutrinos, prot...
Adjoint-Based Forecast Error Sensitivity Diagnostics in Data Assimilation
Langland, R.; Daescu, D.
2016-12-01
We present an up-to-date review of the adjoint-data assimilation system (DAS) approach to evaluate the forecast sensitivity to error covariance parameters and provide guidance to flow-dependent adaptive covariance tuning (ACT) procedures. New applications of the forecast sensitivity to observation error covariance (FSR) are investigated including the sensitivity to observation error correlations and a priori first-order assessment to the error correlation impact on the forecasts. Issues related to ambiguities in the a posteriori estimation to the observation error covariance (R) and background error covariance (B) are discussed. A synergistic framework to adaptive covariance tuning is considered that combines R-estimates derived from a posteriori covariance diagnosis and FSR derivative information. The evaluation of the forecast sensitivity to the innovation-weight coefficients is introduced as a computationally-feasible approach to account for the characteristics of both R- and B-parameters and perform direct tuning of the DAS gain operator (K). Theoretical aspects are discussed and recent results are provided with the adjoint versions of the Naval Research Laboratory Atmospheric Variational Data Assimilation System-Accelerated Representer (NAVDAS-AR).
Adaptive finite difference methods in fluid dynamics
Berger, Marsha J.
1987-01-01
An adaptive method to solve partial differential equations in fluid mechanics is presented. The approach requires internal boundary conditions that must be conservative, data structures for keeping track of several layers of fine grid patches, error estimation, and heuristics for automatic grid generation. In practical calculations gains in computer efficiency up to 10 over nonadaptive methods are observed. The whole procedure takes 3000 lines of FORTRAN code.
Barbone, Paul E; Rivas, Carlos E [College of Engineering, Boston University, Boston, MA (United States); Harari, Isaac; Albocher, Uri [Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv (Israel); Oberai, Assad A; Goenzen, Sevan [Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Inst., Troy, NY (United States)], E-mail: barbone@bu.edu, E-mail: harari@eng.tau.ac.il, E-mail: oberaa@rpi.edu
2008-11-01
We describe a novel variational formulation of the inverse elasticity problem given interior data. The strong form of this problem is governed by equations of pure advective transport. To address this problem, we generalize the adjoint-weighted variational equation (AWE) formulation, originally developed for flow of a passive scalar. Here, we shall study the properties of the AWE formulation in the context of inverse plane stress elasticity imaging. We show that the solution of the AWE formulation is equivalent to that of the strong form when both are well posed. We prove that the Galerkin discretization of the AWE formulation leads to a stable, convergent numerical method, and prove optimal rates of convergence.
Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity
Li, Dunzhu; Gurnis, Michael; Stadler, Georg
2017-01-01
We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature- and strain rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a preconditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.
Spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavors
Bergner, Georg; Giudice, Pietro; Münster, Gernot; Montvay, Istvan; Piemonte, Stefano
2017-08-01
In this work we present the results of our investigation of SU(2) gauge theory with two Dirac fermions in the adjoint representation (aQCD2), which belongs to the class of strongly interacting gauge theories that are of basic interest for extensions of the Standard Model. We have done numerical lattice simulations of this theory at two different values of the gauge coupling and several fermion masses. Our results include the particle spectrum and the mass anomalous dimension. The spectrum contains new exotic fermion-gluon states and flavor-singlet mesons. The mass anomalous dimension is determined from the scaling of the masses and the mode number. The remnant dependence of the universal mass ratios and mass anomalous dimension on the gauge coupling indicates the relevance of scaling corrections, such that earlier estimations for the universal fixed point value of the mass anomalous dimension are incomplete without their inclusion.
The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours
Bergner, Georg; Montvay, Istvan; Münster, Gernot; Piemonte, Stefano
2016-01-01
In this work we present the results of our investigation of SU(2) gauge theory with two Dirac fermions in the adjoint representation, also known as Minimal Walking Technicolour. We have done numerical lattice simulations of this theory at two different values of the gauge coupling and several fermion masses. Our results include the particle spectrum and the mass anomalous dimension. The spectrum contains so far unconsidered states, a fermion-gluon state and flavour singlet mesons. The mass anomalous dimension is determined from the scaling of the masses and the mode number. The remnant dependence of the universal mass ratios and mass anomalous dimension on the gauge coupling indicates the relevance of scaling corrections.
Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks
Catterall, Simon; Sannino, Francesco; Schneible, Joe
2008-01-01
We report on numerical simulations of SU(2) lattice gauge theory with two flavors of light dynamical quarks in the adjoint of the gauge group. The dynamics of this theory is thought to be very different from QCD -- the theory exhibiting conformal or near conformal behavior in the infrared. We make a high resolution survey of the phase diagram of this model in the plane of the bare coupling and quark mass on lattices of size 8^3 \\times 16. Our simulations reveal a line of first order phase transitions extending from beta=0 to beta=beta_c \\sim 2.0. For beta > beta_c the line is no longer first order but continues as the locus of minimum meson mass. For beta > 2.0 we observe the critical pion and rho masses to be light, independent of bare coupling and approximately degenerate. We discuss possible interpretations of these observations and corresponding continuum limits.
Comparison of several finite-difference methods
Biringen, S.; Saati, A.
1990-01-01
The present numerical study establishes that, with the MacCormack and 'two-four' methods, the solution accuracy obtainable in problems involving wave propagation, shock-wave and contact discontinuities, and viscous effects, will be strongly dependent on Courant number. The application of flux correction to the MacCormack and two-four methods is noted to significantly attenuate dispersion errors; the ensuing solutions capture the discontinuities in the shock-tube problem with improved accuracy and resolution, and are free of dispersion errors for the viscous Burgers' equation.
Developing shock-capturing difference methods
TU Guo-hua; YUAN Xiang-jiang; LU Li-peng
2007-01-01
A new shock-capturing method is proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes are projected along characteristic directions. Secondly, the amplitudes of the characteristic decompositions are carefully controlled by limiters to prevent non-physical oscillations. Lastly, the schemes are converted into conservative forms, and the oscillation-free shock-capturing schemes are acquired. Two explicit upwind schemes (2nd-order and 3rd-order) and three compact upwind schemes (3rd-order, 5th-order and 7th-order) are modified by the method for hyperbolic systems and the modified schemes are checked on several one-dimensional and two-dimensional test cases. Some numerical solutions of the schemes are compared with those of a WENO scheme and a MP scheme as well as a compact-WENO scheme. The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly.
Abstract Level Parallelization of Finite Difference Methods
Edwin Vollebregt
1997-01-01
Full Text Available A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”. The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automaticcode generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channel programming paradigm (e.g., message passing. This is important because message passing, unfortunately, still is the only approach that leads to acceptable performance for many more unstructured or irregular problems on parallel computers that have non-uniform memory access times. It will be shown that the use of index sets and stencils greatly simplifies the determination of which data must be exchanged between different computing processes.
Central differences, Euler numbers and symbolic methods
Dowker, J S
2013-01-01
I relate some coefficients encountered when computing the functional determinants on spheres to the central differentials of nothing. In doing this I use some historic works, in particular transcribing the elegant symbolic formalism of Jeffery (1861) into central difference form which has computational advantages for Euler numbers, as discovered by Shovelton (1915). I derive sum rules for these, and for the central differentials, the proof of which involves an interesting expression for powers of sech x as multiple derivatives. I present a more general, symbolic treatment of central difference calculus which allows known, and unknown, things to be obtained in an elegant and compact fashion gaining, at no cost, the expansion of the powers of the inverse sinh, a basic central function. Systematic use is made of the operator 2 asinh(D/2). Umbral calculus is employed to compress the operator formalism. For example the orthogonality/completeness of the factorial numbers, of the first and second kinds, translates, ...
Different methods for volatile sampling in mammals.
Kücklich, Marlen; Möller, Manfred; Marcillo, Andrea; Einspanier, Almuth; Weiß, Brigitte M; Birkemeyer, Claudia; Widdig, Anja
2017-01-01
Previous studies showed that olfactory cues are important for mammalian communication. However, many specific compounds that convey information between conspecifics are still unknown. To understand mechanisms and functions of olfactory cues, olfactory signals such as volatile compounds emitted from individuals need to be assessed. Sampling of animals with and without scent glands was typically conducted using cotton swabs rubbed over the skin or fur and analysed by gas chromatography-mass spectrometry (GC-MS). However, this method has various drawbacks, including a high level of contaminations. Thus, we adapted two methods of volatile sampling from other research fields and compared them to sampling with cotton swabs. To do so we assessed the body odor of common marmosets (Callithrix jacchus) using cotton swabs, thermal desorption (TD) tubes and, alternatively, a mobile GC-MS device containing a thermal desorption trap. Overall, TD tubes comprised most compounds (N = 113), with half of those compounds being volatile (N = 52). The mobile GC-MS captured the fewest compounds (N = 35), of which all were volatile. Cotton swabs contained an intermediate number of compounds (N = 55), but very few volatiles (N = 10). Almost all compounds found with the mobile GC-MS were also captured with TD tubes (94%). Hence, we recommend TD tubes for state of the art sampling of body odor of mammals or other vertebrates, particularly for field studies, as they can be easily transported, stored and analysed with high performance instruments in the lab. Nevertheless, cotton swabs capture compounds which still may contribute to the body odor, e.g. after bacterial fermentation, while profiles from mobile GC-MS include only the most abundant volatiles of the body odor.
Different methods for volatile sampling in mammals
Möller, Manfred; Marcillo, Andrea; Einspanier, Almuth; Weiß, Brigitte M.
2017-01-01
Previous studies showed that olfactory cues are important for mammalian communication. However, many specific compounds that convey information between conspecifics are still unknown. To understand mechanisms and functions of olfactory cues, olfactory signals such as volatile compounds emitted from individuals need to be assessed. Sampling of animals with and without scent glands was typically conducted using cotton swabs rubbed over the skin or fur and analysed by gas chromatography-mass spectrometry (GC-MS). However, this method has various drawbacks, including a high level of contaminations. Thus, we adapted two methods of volatile sampling from other research fields and compared them to sampling with cotton swabs. To do so we assessed the body odor of common marmosets (Callithrix jacchus) using cotton swabs, thermal desorption (TD) tubes and, alternatively, a mobile GC-MS device containing a thermal desorption trap. Overall, TD tubes comprised most compounds (N = 113), with half of those compounds being volatile (N = 52). The mobile GC-MS captured the fewest compounds (N = 35), of which all were volatile. Cotton swabs contained an intermediate number of compounds (N = 55), but very few volatiles (N = 10). Almost all compounds found with the mobile GC-MS were also captured with TD tubes (94%). Hence, we recommend TD tubes for state of the art sampling of body odor of mammals or other vertebrates, particularly for field studies, as they can be easily transported, stored and analysed with high performance instruments in the lab. Nevertheless, cotton swabs capture compounds which still may contribute to the body odor, e.g. after bacterial fermentation, while profiles from mobile GC-MS include only the most abundant volatiles of the body odor. PMID:28841690
Adjoint Inversion for Extended Earthquake Source Kinematics From Very Dense Strong Motion Data
Ampuero, J. P.; Somala, S.; Lapusta, N.
2010-12-01
Addressing key open questions about earthquake dynamics requires a radical improvement of the robustness and resolution of seismic observations of large earthquakes. Proposals for a new generation of earthquake observation systems include the deployment of “community seismic networks” of low-cost accelerometers in urban areas and the extraction of strong ground motions from high-rate optical images of the Earth's surface recorded by a large space telescope in geostationary orbit. Both systems could deliver strong motion data with a spatial density orders of magnitude higher than current seismic networks. In particular, a “space seismometer” could sample the seismic wave field at a spatio-temporal resolution of 100 m, 1 Hz over areas several 100 km wide with an amplitude resolution of few cm/s in ground velocity. The amount of data to process would be immensely larger than what current extended source inversion algorithms can handle, which hampers the quantitative assessment of the cost-benefit trade-offs that can guide the practical design of the proposed earthquake observation systems. We report here on the development of a scalable source imaging technique based on iterative adjoint inversion and its application to the proof-of-concept of a space seismometer. We generated synthetic ground motions for M7 earthquake rupture scenarios based on dynamic rupture simulations on a vertical strike-slip fault embedded in an elastic half-space. A range of scenarios include increasing levels of complexity and interesting features such as supershear rupture speed. The resulting ground shaking is then processed accordingly to what would be captured by an optical satellite. Based on the resulting data, we perform source inversion by an adjoint/time-reversal method. The gradient of a cost function quantifying the waveform misfit between data and synthetics is efficiently obtained by applying the time-reversed ground velocity residuals as surface force sources, back
Analyzing of coffee quality with different methods
Rajković Miloš B.
2004-01-01
Full Text Available The results obtained by the analysis of the samples of coffee mostly consumed on our market showed that the coffee quality corresponds to the values as given in the Law of Health Food. It was not found that any of the parameters which determine food quality exceeded permitted values. Content of heavy metals and aflatoxines is below permitted values. The least content of caffeine was determined in a coffee sample roasted in the private roaster’s shop, and only in it the presence of coffee surrogates/substitutes was not proved. The obtained results of the coffee analysis showed that the coffees of most popular producers are very equal, and results of caffeine analysis are even more equal. This indicates the most probable fact that coffee is of the same origin, and that later, on during production, a different mixture was made, which affects the final product and gives aroma and taste to the liquid.
Self-adjoint integral operator for bounded nonlocal transport
Maggs, J. E.; Morales, G. J.
2016-11-01
An integral operator is developed to describe nonlocal transport in a one-dimensional system bounded on both ends by material walls. The "jump" distributions associated with nonlocal transport are taken to be Lévy α -stable distributions, which become naturally truncated by the bounding walls. The truncation process results in the operator containing a self-consistent, convective inward transport term (pinch). The properties of the integral operator as functions of the Lévy distribution parameter set [α ,γ ] and the wall conductivity are presented. The integral operator continuously recovers the features of local transport when α =2 . The self-adjoint formulation allows for an accurate description of spatial variation in the Lévy parameters in the nonlocal system. Spatial variation in the Lévy parameters is shown to result in internally generated flows. Examples of cold-pulse propagation in nonlocal systems illustrate the capabilities of the methodology.
Finite volume effects in SU(2) with two adjoint fermions
Patella, Agostino; Lucini, Biagio; Pica, Claudio; Rago, Antonio
2011-01-01
Many evidences from lattice simulations support the idea that SU(2) with two Dirac flavors in the adjoint representation (also called Minimal Walking Technicolor) is IR conformal. A possible way to see this is through the behavior of the spectrum of the mass-deformed theory. When fermions are massive, a mass-gap is generated and the theory is confined. IR-conformality is recovered in the chiral limit: masses of particles vanish in the chiral limit, while their ratios stay finite. In order to trust this analysis one has to relay on the infinite volume extrapolation. We will discuss the finite volume effects on the mesonic spectrum, investigated by varying the size of the lattice and by changing the boundary conditions for the fields.
Adjoint Assimilation in Marine Ecosystem Models and an Example of Application
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.
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.
Self-adjoint extensions of the Pauli equation in the presence of a magnetic monopole
Karat, E R; Karat, Edwin R; Schulz, Michael B
1996-01-01
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of a magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation.
Self-adjointness and conservation laws of a generalized Burgers equation
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.se, E-mail: torrisi@dmi.unict.it, E-mail: tracina@dmi.unict.it [Dipartimento di Matematica e Informatica, University of Catania, Catania (Italy)
2011-04-08
A (2 + 1)-dimensional generalized Burgers equation is considered. Having written this equation as a system of two dependent variables, we show that it is quasi self-adjoint and find a nontrivial additional conservation law.
Almost commuting self-adjoint matrices: The real and self-dual cases
Loring, Terry A.; Sørensen, Adam P. W.
2016-08-01
We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover, we prove that the same holds with self-dual in place of symmetric and also for paths of self-adjoint matrices. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin’s famous theorem on almost commuting matrices. Similarly, the self-dual case gives a version for matrices over the quaternions. To prove these results, we develop a theory of semiprojectivity for real C*-algebras and also examine various definitions of low-rank for real C*-algebras.
Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential
Aleksandr Mikhailovich Kholkin
2016-01-01
Full Text Available A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained.
The Relation of Finite Element and Finite Difference Methods
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians
Galapon, E A
2002-01-01
We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each characteristic time operator generates an uncountable class of self- adjoint operators canonically conjugate with the same Hamiltonian.
Adjoint-Free Variational Data Assimilation into a Regional Wave Model
2015-07-01
linearized model is localized both in space and time. Holthuijsen et al. (1997) explored a similar technique using a limited number of nonlocal ...Adjoint-Free Variational Data Assimilation into a Regional Wave Model GLEB PANTELEEV University of Alaska Fairbanks, Fairbanks, Alaska, and National...wave prediction model [Wave Model (WAM)]. The algorithm employs the adjoint-free technique and was tested in a series of data assimilation experiments
ORIGINAL ARTICLE Fitted-Stable Finite Difference Method for ...
Gemechis
A fitted-stable central difference method is presented for solving singularly perturbed two point ... with exact solutions. The error bound and convergence of the proposed method has also ... explicit method involving the reduction of order for ...
A Method of Controlling Synchronization in Different Systems
陈骏; 刘曾荣
2003-01-01
A new control method to synchronize between two different systems is proposed and the mathematical proof of this method is provided. Moreover, numerical simulation validates the efficiency of the proposed method.
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...
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.
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
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.
Conformal vs confining scenario in SU(2) with adjoint fermions
Del Debbio, L; Patella, A; Pica, C; Rago, A
2009-01-01
The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling $\\beta = 4/g_0^2 = 2.25$ for values of the bare fermion mass $m_0$ that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near-)conformal and the confining scenario is outlined.
Smith, J. A.; Peter, D. B.; Tromp, J.; Komatitsch, D.; Lefebvre, M. P.
2015-12-01
We present both SPECFEM3D_Cartesian and SPECFEM3D_GLOBE open-source codes, representing high-performance numerical wave solvers simulating seismic wave propagation for local-, regional-, and global-scale application. These codes are suitable for both forward propagation in complex media and tomographic imaging. Both solvers compute highly accurate seismic wave fields using the continuous Galerkin spectral-element method on unstructured meshes. Lateral variations in compressional- and shear-wave speeds, density, as well as 3D attenuation Q models, topography and fluid-solid coupling are all readily included in both codes. For global simulations, effects due to rotation, ellipticity, the oceans, 3D crustal models, and self-gravitation are additionally included. Both packages provide forward and adjoint functionality suitable for adjoint tomography on high-performance computing architectures. We highlight the most recent release of the global version which includes improved performance, simultaneous MPI runs, OpenCL and CUDA support via an automatic source-to-source transformation library (BOAST), parallel I/O readers and writers for databases using ADIOS and seismograms using the recently developed Adaptable Seismic Data Format (ASDF) with built-in provenance. This makes our spectral-element solvers current state-of-the-art, open-source community codes for high-performance seismic wave propagation on arbitrarily complex 3D models. Together with these solvers, we provide full-waveform inversion tools to image the Earth's interior at unprecedented resolution.
Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation
Boujo, E.; Noiray, N.
2017-04-01
We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations-for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker-Planck equation is solved to compute Kramers-Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.
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,...
Vincent M. Laboure; Yaqi Wang; Mark D. DeHart
2016-05-01
In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment, in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutions (MMS) and find the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.
Mixed Methods and Action Research: similar or different?
2011-01-01
This article attempts to analyse and compare ELT studies grounded solely in mixed methods and ELT action research studies based on a mixed methods approach in order to identify to what degree action research studies combining different methods in a single study comply with the principles of rigorous mixed methods study.
Klasen, D.
2003-07-01
In recent years high resolution data have become available due to the deployment of satellite born instruments observing the state of a large number of stratospheric constituents with unprecedentedly high horizontal and vertical resolution. These measurements are valuable for accessing the state of the atmosphere and for helping to develop guidelines for its preservation as a protection layer for terrestrial life. Nevertheless, the measurements alone offer limited direct information. They require interpretation and combination with other information sources to accurately describe the state of the atmosphere. By combining measurements with atmospheric models, the measurements' scatter in time and space can be mitigated and their interpretation improved. A chemistry-transport model (CTM) version of the Cologne model of the middle atmosphere (COMMA) has been developed to model transport and chemical transformation of atmospheric trace gases. In this thesis, the method of four-dimensional variational data assimilation is used to realize the above-mentioned combination in a mathematically rigorous way. The goal is to identify the most probable chemical state of the atmosphere using all available information. As chemistry-transport modelling is an initial value problem, those initial conditions are sought which result in best compliance of the model state with available information during the time period considered. As a measure of compliance, a cost function is specified, whose gradient is needed for minimising the cost function, and which can be obtained by means of an adjoint model. To this end, the adjoint code to the CTM was developed. As a last building block of the data assimilation system, the L-BFGS algorithm for the minimization of the cost function was added. The adjoint model of the middle atmosphere of Cologne CTM (AMMOC-CTM) data-assimilation system thereby developed was tested by applying it to data measured by the cryogenic infrared spectrometer and
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 ...
Zhou, Wei
1993-01-01
In the high accurate measurement of periodic signals, the greatest common factor frequency and its characteristics have special functions. A method of time difference measurement - the time difference method by dual 'phase coincidence points' detection is described. This method utilizes the characteristics of the greatest common factor frequency to measure time or phase difference between periodic signals. It can suit a very wide frequency range. Measurement precision and potential accuracy of several picoseconds were demonstrated with this new method. The instrument based on this method is very simple, and the demand for the common oscillator is low. This method and instrument can be used widely.
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.
Development of Variational Data Assimilation Methods for the MoSST Geodynamo Code
Egbert, G. D.; Erofeeva, S.; Kuang, W.; Tangborn, A.; Dimitrova, L. L.
2013-12-01
A range of different approaches to data assimilation for Earth's geodynamo are now being pursued, from sequential schemes based on approximate covariances of various degrees of sophistication, to variational methods for models of varying degrees of physical completeness. While variational methods require development of adjoint (and possible tangent linear) variants on the forward code---a challenging programming task for a fully self-consistent modern dynamo code---this approach may ultimately offer significant advantages. For example, adjoint based variational approaches allow initial, boundary, and forcing terms to be explicitly adjusted to combine data from modern and historical eras into dynamically consistent maps of core state, including flow, buoyancy and magnetic fields. Here we describe development of tangent linear and adjoint codes for the Modular Scalable Self-consistent Three-dimensional (MoSST) geodynamo simulator, and present initial results from simple synthetic data assimilation experiments. Our approach has been to develop the exact linearization and adjoint of the actual discrete functions represented by the computer code. To do this we use a 'divide-and-concur' approach: the code is decomposed as the sequential action of a series of linear and non-linear procedures on specified inputs. Non-linear procedures are first linearized about a pre-computed input background state (derived by running the non-linear forward model), and a tangent linear time-step code is developed. For small perturbations of initial state the linearization appears to remain valid for times comparable to the secular variation time-scale. Adjoints for each linear (or linearized) procedure were then developed and tested separately (for symmetry), and then merged into adjoint procedures of increasing complexity. We have completed development of the adjoint for a serial version of the MoSST code, explore time limits of forward operator linearization, and discuss next steps
Compact finite difference method for American option pricing
Zhao, Jichao; Davison, Matt; Corless, Robert M.
2007-09-01
A compact finite difference method is designed to obtain quick and accurate solutions to partial differential equation problems. The problem of pricing an American option can be cast as a partial differential equation. Using the compact finite difference method this problem can be recast as an ordinary differential equation initial value problem. The complicating factor for American options is the existence of an optimal exercise boundary which is jointly determined with the value of the option. In this article we develop three ways of combining compact finite difference methods for American option price on a single asset with methods for dealing with this optimal exercise boundary. Compact finite difference method one uses the implicit condition that solutions of the transformed partial differential equation be nonnegative to detect the optimal exercise value. This method is very fast and accurate even when the spatial step size h is large (h[greater-or-equal, slanted]0.1). Compact difference method two must solve an algebraic nonlinear equation obtained by Pantazopoulos (1998) at every time step. This method can obtain second order accuracy for space x and requires a moderate amount of time comparable with that required by the Crank Nicolson projected successive over relaxation method. Compact finite difference method three refines the free boundary value by a method developed by Barone-Adesi and Lugano [The saga of the American put, 2003], and this method can obtain high accuracy for space x. The last two of these three methods are convergent, moreover all the three methods work for both short term and long term options. Through comparison with existing popular methods by numerical experiments, our work shows that compact finite difference methods provide an exciting new tool for American option pricing.
Comparison of Thermal Properties Measured by Different Methods
Sundberg, Jan [Geo Innova AB, Linkoeping (Sweden); Kukkonen, Ilmo [Geological Survey of Finland, Helsinki (Finland); Haelldahl, Lars [Hot Disk AB, Uppsala (Sweden)
2003-04-01
A strategy for a thermal site descriptive model of bedrock is under development at SKB. In the model different kinds of uncertainties exist. Some of these uncertainties are related to the potential errors in the methods used for determining thermal properties of rock. In two earlier investigations thermal properties of rock samples were analysed according to the TPS method (transient plane source). Thermal conductivity and thermal diffusivity were determined using the TPS method. For a comparison, the same samples have been measured at the Geological Survey of Finland (GSF), using different laboratory methods. In this later investigation, the thermal conductivity was determined using the divided-bar method and the specific heat capacity using a calorimetric method. The mean differences between the results of different methods are relatively low but the results of individual samples show large variations. The thermal conductivity measured by the divided bar method gives for most samples slightly higher values, in average about 3%, than the TPS method. The specific heat capacity measured by the calorimetric method gives lower values, in average about 2%, than the TPS method. Consequently, the thermal diffusivity calculated from thermal conductivity and specific heat capacity gives higher values, in average about 6%, than the TPS method. Reasons for the differences are estimated mainly to be dependent on differences between the samples, errors in the temperature dependence of specific heat and in the transformation from volumetric to specific heat. The TPS measurements are performed using two pieces (sub-samples) of rock. Only one of these two sub-samples was measured using the divided bar method and the calorimetric method. Further, sample preparation involved changes in the size of some of the samples. The mean differences between the results of different methods are within the margins of error reported by the measuring laboratories. However, systematic errors in
Light adjoint quarks in the instanton-dyon liquid model. IV.
Liu, Yizhuang; Shuryak, Edward; Zahed, Ismail
2016-11-01
We discuss the instanton-dyon liquid model with Nf Majorana quark flavors in the adjoint representation of color S Uc(2 ) at finite temperature. We briefly recall the index theorem on S1×R3 for twisted adjoint fermions in a Bogomolny-Prasad-Sommerfeld (BPS) dyon background of arbitrary holonomy and use the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction to derive the adjoint antiperiodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with Nf light and antiperiodic adjoint quarks. We develop the model in details by mapping the theory on a three-dimensional quantum effective theory with adjoint quarks with manifest S U (Nf)×Z4 Nf symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for Nf=1 . For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through S U (Nf)×Z4 Nf→O (Nf). As the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.
Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
Liu, Yizhuang; Zahed, Ismail
2016-01-01
We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $SU_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective theory with adjoint quarks with manifest $SU(N_f)\\times Z_{4N_f}$ symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for $N_f=1$. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through $SU(N_f)\\times Z_{4N...
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
A Solution to Study Different Homing Methods Using a PLC
Mihai Rață
2014-09-01
Full Text Available In a positioning control with stepper motors it is very important to know zero location. For this purpose it is necessary a homing command. This paper presents a solution that allows the study of different methods implemented to find a home position (also called: zero point and to observe the differences between these methods.
A COMPARISON OF DIFFERENT CONTRACTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES
Bingsheng He; Xiang Wang; Junfeng Yang
2009-01-01
It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.
T. Ziehn
2011-11-01
Full Text Available Accurate modelling of the carbon cycle strongly depends on the parametrization of its underlying processes. The Carbon Cycle Data Assimilation System (CCDAS can be used as an estimator algorithm to derive posterior parameter values and uncertainties for the Biosphere Energy Transfer and Hydrology scheme (BETHY. However, the simultaneous optimization of all process parameters can be challenging, due to the complexity and non-linearity of the BETHY model. Therefore, we propose a new concept that uses ensemble runs and the adjoint optimization approach of CCDAS to derive the full probability density function (PDF for posterior soil carbon parameters and the net carbon flux at the global scale. This method allows us to optimize only those parameters that can be constrained best by atmospheric carbon dioxide (CO_{2} data. The prior uncertainties of the remaining parameters are included in a consistent way through ensemble runs, but are not constrained by data. The final PDF for the optimized parameters and the net carbon flux are then derived by superimposing the individual PDFs for each ensemble member. We find that the optimization with CCDAS converges much faster, due to the smaller number of processes involved. Faster convergence also gives us much increased confidence that we find the global minimum in the reduced parameter space.
Poirier, Vincent
Mesh deformation schemes play an important role in numerical aerodynamic optimization. As the aerodynamic shape changes, the computational mesh must adapt to conform to the deformed geometry. In this work, an extension to an existing fast and robust Radial Basis Function (RBF) mesh movement scheme is presented. Using a reduced set of surface points to define the mesh deformation increases the efficiency of the RBF method; however, at the cost of introducing errors into the parameterization by not recovering the exact displacement of all surface points. A secondary mesh movement is implemented, within an adjoint-based optimization framework, to eliminate these errors. The proposed scheme is tested within a 3D Euler flow by reducing the pressure drag while maintaining lift of a wing-body configured Boeing-747 and an Onera-M6 wing. As well, an inverse pressure design is executed on the Onera-M6 wing and an inverse span loading case is presented for a wing-body configured DLR-F6 aircraft.
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.
Forward and adjoint radiance Monte Carlo models for quantitative photoacoustic imaging
Hochuli, Roman; Powell, Samuel; Arridge, Simon; Cox, Ben
2015-03-01
In quantitative photoacoustic imaging, the aim is to recover physiologically relevant tissue parameters such as chromophore concentrations or oxygen saturation. Obtaining accurate estimates is challenging due to the non-linear relationship between the concentrations and the photoacoustic images. Nonlinear least squares inversions designed to tackle this problem require a model of light transport, the most accurate of which is the radiative transfer equation. This paper presents a highly scalable Monte Carlo model of light transport that computes the radiance in 2D using a Fourier basis to discretise in angle. The model was validated against a 2D finite element model of the radiative transfer equation, and was used to compute gradients of an error functional with respect to the absorption and scattering coefficient. It was found that adjoint-based gradient calculations were much more robust to inherent Monte Carlo noise than a finite difference approach. Furthermore, the Fourier angular discretisation allowed very efficient gradient calculations as sums of Fourier coefficients. These advantages, along with the high parallelisability of Monte Carlo models, makes this approach an attractive candidate as a light model for quantitative inversion in photoacoustic imaging.
Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland
2014-01-01
an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D...... in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems...... with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and the main domain only, thus avoiding the need to solve a backward wave propagation problem inside the CFS-UPML, which is known to be highly...
Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony
1996-01-01
This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.
Mass anomalous dimension of Adjoint QCD at large N from twisted volume reduction
Pérez, Margarita García; Keegan, Liam; Okawa, Masanori
2015-01-01
In this work we consider the $SU(N)$ gauge theory with two Dirac fermions in the adjoint representation, in the limit of large $N$. In this limit the infinite-volume physics of this model can be studied by means of the corresponding twisted reduced model defined on a single site lattice. Making use of this strategy we study the reduced model for various values of $N$ up to 289. By analyzing the eigenvalue distribution of the adjoint Dirac operator we test the conformality of the theory and extract the corresponding mass anomalous dimension.
Psychological traits underlying different killing methods among Malaysian male murderers.
Kamaluddin, Mohammad Rahim; Shariff, Nadiah Syariani; Nurfarliza, Siti; Othman, Azizah; Ismail, Khaidzir H; Mat Saat, Geshina Ayu
2014-04-01
Murder is the most notorious crime that violates religious, social and cultural norms. Examining the types and number of different killing methods that used are pivotal in a murder case. However, the psychological traits underlying specific and multiple killing methods are still understudied. The present study attempts to fill this gap in knowledge by identifying the underlying psychological traits of different killing methods among Malaysian murderers. The study adapted an observational cross-sectional methodology using a guided self-administered questionnaire for data collection. The sampling frame consisted of 71 Malaysian male murderers from 11 Malaysian prisons who were selected using purposive sampling method. The participants were also asked to provide the types and number of different killing methods used to kill their respective victims. An independent sample t-test was performed to establish the mean score difference of psychological traits between the murderers who used single and multiple types of killing methods. Kruskal-Wallis tests were carried out to ascertain the psychological trait differences between specific types of killing methods. The results suggest that specific psychological traits underlie the type and number of different killing methods used during murder. The majority (88.7%) of murderers used a single method of killing. Multiple methods of killing was evident in 'premeditated' murder compared to 'passion' murder, and revenge was a common motive. Examples of multiple methods are combinations of stabbing and strangulation or slashing and physical force. An exception was premeditated murder committed with shooting, when it was usually a single method, attributed to the high lethality of firearms. Shooting was also notable when the motive was financial gain or related to drug dealing. Murderers who used multiple killing methods were more aggressive and sadistic than those who used a single killing method. Those who used multiple methods or
The Roots of Adjoint Polynomial of the Graphs Contain Triangles%一类含三角形图的伴随多项式的根
冶成福
2004-01-01
We denote h(G, x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles.By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Adjoint-tomography for a Local Surface Structure: Methodology and a Blind Test
Kubina, Filip; Michlik, Filip; Moczo, Peter; Kristek, Jozef; Stripajova, Svetlana
2017-04-01
We have developed a multiscale full-waveform adjoint-tomography method for local surface sedimentary structures with complicated interference wavefields. The local surface sedimentary basins and valleys are often responsible for anomalous earthquake ground motions and corresponding damage in earthquakes. In many cases only relatively small number of records of a few local earthquakes is available for a site of interest. Consequently, prediction of earthquake ground motion at the site has to include numerical modeling for a realistic model of the local structure. Though limited, the information about the local structure encoded in the records is important and irreplaceable. It is therefore reasonable to have a method capable of using the limited information in records for improving a model of the local structure. A local surface structure and its interference wavefield require a specific multiscale approach. In order to verify our inversion method, we performed a blind test. We obtained synthetic seismograms at 8 receivers for 2 local sources, complete description of the sources, positions of the receivers and material parameters of the bedrock. We considered the simplest possible starting model - a homogeneous halfspace made of the bedrock. Using our inversion method we obtained an inverted model. Given the starting model, synthetic seismograms simulated for the inverted model are surprisingly close to the synthetic seismograms simulated for the true structure in the target frequency range up to 4.5 Hz. We quantify the level of agreement between the true and inverted seismograms using the L2 and time-frequency misfits, and, more importantly for earthquake-engineering applications, also using the goodness-of-fit criteria based on the earthquake-engineering characteristics of earthquake ground motion. We also verified the inverted model for other source-receiver configurations not used in the inversion.
Evaluation of Three Different Osteosynthesis Methods for Mandibular Angle Fractures
Pereira-Filho, Valfrido Antonio; Oliveira, Luis Fernando de Gorla; Reis, José Maurício Dos Santos Nunes;
2016-01-01
The aim of this study was to evaluate the mechanical behavior of different rigid fixation methods in mandible angle fractures. Three different plates were tested: one 4-hole grid miniplate, one 8-hole curved grid miniplate, and one 4-hole straight miniplate.For the loading tests, 30 polyurethane ...
Explicit finite difference methods for the delay pseudoparabolic equations.
Amirali, I; Amiraliyev, G M; Cakir, M; Cimen, E
2014-01-01
Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.
Explicit finite-difference lattice Boltzmann method for curvilinear coordinates.
Guo, Zhaoli; Zhao, T S
2003-06-01
In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is treated implicitly. In the present method, the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently. As a result, an explicit finite-difference lattice Boltzmann method for curvilinear coordinates is obtained. The scheme is applied to a two-dimensional Poiseuille flow, an unsteady Couette flow, a lid-driven cavity flow, and a steady flow around a circular cylinder. The numerical results are in good agreement with the results of previous studies. Extensions to other lattice Boltzmann models based on nonuniform meshes are also discussed.
Chebyshev Finite Difference Method for Fractional Boundary Value Problems
Boundary
2015-09-01
Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative
High order spectral difference lattice Boltzmann method for incompressible hydrodynamics
Li, Weidong
2017-09-01
This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.
Large-N reduction of SU(N) Yang-Mills theory with massive adjoint overlap fermions
Hietanen, A
2010-01-01
We study four dimensional large-N SU(N) Yang-Mills theory coupled to adjoint overlap fermions on a single site lattice. Lattice simulations along with perturbation theory show that the bare quark mass has to be taken to zero as one takes the continuum limit in order to be in the physically relevant center-symmetric phase. But, it seems that it is possible to take the continuum limit with any renormalized quark mass and still be in the center-symmetric physics. We have also conducted a study of the correlations between Polyakov loop operators in different directions and obtained the range for the Wilson mass parameter that enters the overlap Dirac operator.
Crawford, Charles G.; Martin, Jeffrey D.
2017-07-21
In October 2012, the U.S. Geological Survey (USGS) began measuring the concentration of the pesticide fipronil and three of its degradates (desulfinylfipronil, fipronil sulfide, and fipronil sulfone) by a new laboratory method using direct aqueous-injection liquid chromatography tandem mass spectrometry (DAI LC–MS/MS). This method replaced the previous method—in use since 2002—that used gas chromatography/mass spectrometry (GC/MS). The performance of the two methods is not comparable for fipronil and the three degradates. Concentrations of these four chemical compounds determined by the DAI LC–MS/MS method are substantially lower than the GC/MS method. A method was developed to correct for the difference in concentrations obtained by the two laboratory methods based on a methods comparison field study done in 2012. Environmental and field matrix spike samples to be analyzed by both methods from 48 stream sites from across the United States were sampled approximately three times each for this study. These data were used to develop a relation between the two laboratory methods for each compound using regression analysis. The relations were used to calibrate data obtained by the older method to the new method in order to remove any biases attributable to differences in the methods. The coefficients of the equations obtained from the regressions were used to calibrate over 16,600 observations of fipronil, as well as the three degradates determined by the GC/MS method retrieved from the USGS National Water Information System. The calibrated values were then compared to over 7,800 observations of fipronil and to the three degradates determined by the DAI LC–MS/MS method also retrieved from the National Water Information System. The original and calibrated values from the GC/MS method, along with measures of uncertainty in the calibrated values and the original values from the DAI LC–MS/MS method, are provided in an accompanying data release.
Analysis of surface asperity flattening based on two different methods
Li, Hejie; Öchsner, Andreas; Ni, Guowei; Wei, Dongbin; Jiang, Zhengyi
2016-11-01
The stress state is an important parameter in metal forming processes, which significantly influences the strain state and microstructure of products, affecting their surface qualities. In order to make the metal products have a good surface quality, the surface stress state must be optimised. In this study, two classical methods, the upper bound method and the crystal plasticity finite element method, were investigated. The differences between the two methods were discussed in regard to the model, the velocity field, and the strain field. Then the related surface roughness is deduced.
An Effective Method for Seeking Conservation Laws of Partial Differential Equations
QIN Mao-Chang; MEI Feng-Xiang; FAN Gui-Hong
2006-01-01
This paper introduces an effective method for seeking localconservation laws of general partial differential equations (PDEs). The well-known variational principle does not involve in this method. Alternatively, the conservation laws can be derived from symmetries, which include the symmetries of the associated linearized equation of the PDEs,and the adjoint symmetries of the adjoint equation of the PDEs.
Time-dependent optimal heater control using finite difference method
Li, Zhen Zhe; Heo, Kwang Su; Choi, Jun Hoo; Seol, Seoung Yun [Chonnam National Univ., Gwangju (Korea, Republic of)
2008-07-01
Thermoforming is one of the most versatile and economical process to produce polymer products. The drawback of thermoforming is difficult to control thickness of final products. Temperature distribution affects the thickness distribution of final products, but temperature difference between surface and center of sheet is difficult to decrease because of low thermal conductivity of ABS material. In order to decrease temperature difference between surface and center, heating profile must be expressed as exponential function form. In this study, Finite Difference Method was used to find out the coefficients of optimal heating profiles. Through investigation, the optimal results using Finite Difference Method show that temperature difference between surface and center of sheet can be remarkably minimized with satisfying temperature of forming window.
Differential and difference equations a comparison of methods of solution
Maximon, Leonard C
2016-01-01
This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associat...
CFD-based method of determining form factor k for different ship types and different drafts
Wang, Jinbao; Yu, Hai; Zhang, Yuefeng; Xiong, Xiaoqing
2016-09-01
The value of form factor k at different drafts is important in predicting full-scale total resistance and speed for different types of ships. In the ITTC community, most organizations predict form factor k using a low-speed model test. However, this method is problematic for ships with bulbous bows and transom. In this article, a Computational Fluid Dynamics (CFD)-based method is introduced to obtain k for different type of ships at different drafts, and a comparison is made between the CFD method and the model test. The results show that the CFD method produces reasonable k values. A grid generating method and turbulence model are briefly discussed in the context of obtaining a consistent k using CFD.
CFD-Based Method of Determining Form Factor k for Different Ship Types and Different Drafts
Xiaoqing Xiong
2016-01-01
The value of form factor k at different drafts is important in predicting full-scale total resistance and speed for different types of ships. In the ITTC community, most organizations predict form factor k using a low-speed model test. However, this method is problematic for ships with bulbous bows and transom. In this article, a Computational Fluid Dynamics (CFD)-based method is introduced to obtain k for different type of ships at different drafts, and a comparison is made between the CFD method and the model test. The results show that the CFD method produces reasonable k values. A grid generating method and turbulence model are briefly discussed in the context of obtaining a consistent k using CFD.
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
Self-adjoint extensions of Coulomb systems in 1,2 and 3 dimensions
de Oliveira, Cesar R
2008-01-01
We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in $R^n$, n = 1, 2, 3. We characterize their self-adjoint extensions and, in the unidimensional case, present a discussion of controversies in the literature, particularly the question of the permeability of the origin. Potentials given by fundamental solutions of Laplace equation are also briefly considered.
Blind range influence on guidance loop performance: An adjoint-based analysis
Bucco, D.; Weiss, M.
2013-01-01
In this paper, we investigate the use of adjoint simulation for assessing the miss distance performance of a generic guidance system under the influence of a blind range condition. The term "blind range" refers to that final portion of the missile trajectory for which sensor data are not available.
Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Shondin, Yuri
2007-01-01
The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization of a generalized Nevanlinna function.
Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Shondin, Yuri
2007-01-01
The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization of a generalized Nevanlinna function.
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
FRANCOIS, MARIANNE M. [Los Alamos National Laboratory; DENDY, EDWARD D. [Los Alamos National Laboratory; LOWRIE, ROBERT B. [Los Alamos National Laboratory; LIVESCU, DANIEL [Los Alamos National Laboratory; STEINKAMP, MICHAEL J. [Los Alamos National Laboratory
2007-01-11
The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.
Economic Consequences of DifferentLean Percentage Estimation Methods
Zdravko Tolušić
2003-06-01
Full Text Available The economic effects of the choice of two different lean percentage estimation methods and terminal sire breed were investigated on 53 pig carcasses divided in two groups. In the 1st group were progeny of Pietrain used as terminal sire (n=25 and in 2nd the progeny of Large White terminal sire. It was found that the breed of terminal sire haven.t had influence on cold carcass weight and fat thickness measured for TP method of lean percentage estimation. Inclusion of Pietrain as terminal sire had influence on MLD thickness measured for TP and INS methods which was significantly higher, while fat thickness measured for instrumental method was significantly lower (p<0.01. Carcasses of the same group had higher lean percentage estimated by TP and INS methods (p<0.05 and p<0.01, resp.. Also, different methods of lean percentage estimation resulted in different classification of the carcasses into SEUROP classes. The choice of the lean percentage estimation method had no significant effect on the price of the carcasses from 2nd group which had Large White as terminal sire, while in pig carcasses from the 1st group (Pietrain as terminal sire, the choice of lean percentage method of estimation determined the price of the carcasses, and by this also economic surplus (or loss of the producers. It is concluded that both methods are equally applicable in the case of Large White crossbreeds, while caution should be taken in the case of pig carcasses originated from Pietrain as terminal sire because carcasses of such pigs reached higher prices when estimated by instrumental method.
Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model
Oluwaseun Egbelowo
2017-05-01
Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.
A comparison of four different block bootstrap methods
Boris Radovanov
2014-12-01
Full Text Available The paper contains a description of four different block bootstrap methods, i.e., non-overlapping block bootstrap, overlapping block bootstrap (moving block bootstrap, stationary block bootstrap and subsampling. Furthermore, the basic goal of this paper is to quantify relative efficiency of each mentioned block bootstrap procedure and then to compare those methods. To achieve the goal, we measure mean square errors of estimation variance returns. The returns are calculated from 1250 daily observations of Serbian stock market index values BELEX15 from April 2009 to April 2014. Thereby, considering the effects of potential changes in decisions according to variations in the sample length and purposes of the use, this paper introduces stability analysis which contains robustness testing of the different sample size and the different block length. Testing results indicate some changes in bootstrap method efficiencies when altering the sample size or the block length.
Vibro-acoustic design sensitivity analysis using the wave-based method
Koo, Kunmo; Pluymers, Bert; Desmet, Wim; Wang, Semyung
2011-08-01
Conventional element-based methods, such as the finite element method (FEM) and boundary element method (BEM), require mesh refinements at higher frequencies in order to converge. Therefore, their applications are limited to low frequencies. Compared to element-based methods, the wave-based method (WBM) adopts exact solutions of the governing differential equation instead of simple polynomials to describe the dynamic response variables within the subdomains. As such, the WBM does not require a finer division of subdomains as the frequency increases in order to exhibit high computational efficiency. In this paper, the design sensitivity formulation of a semi-coupled structural-acoustic problem is implemented using the WBM. Here, the results of structural harmonic analyses are imported as the boundary conditions for the acoustic domain, which consists of multiple wave-based subdomains. The cross-sectional area of each beam element is considered as a sizing design variable. Then, the adjoint variable method (AVM) is used to efficiently compute the sensitivity. The adjoint variable is obtained from structural reanalysis using an adjoint load composed of the system matrix and an evaluation of the wave functions of each boundary. The proposed sensitivity formulation is subsequently applied to a two-dimensional (2D) vehicle model. Finally, the sensitivity results are compared to the finite difference sensitivity results, which show good agreement.
Comparison between different synchronization methods of identical chaotic systems
Haeri, Mohammad [Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9363 Tehran (Iran, Islamic Republic of)]. E-mail: haeri@sina.sharif.edu; Khademian, Behzad [Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9363 Tehran (Iran, Islamic Republic of)
2006-08-15
This paper studies and compares three nonadaptive (bidirectional, unidirectional, and sliding mode) and two adaptive (active control and backstepping) synchronization methods on the synchronizing of four pairs of identical chaotic systems (Chua's circuit, Roessler system, Lorenz system, and Lue system). Results from computer simulations are presented in order to illustrate the effectiveness of the methods and to compare them based on different criteria.
Combined Method of Datum Transformation Between Different Coordinate Systems
无
2002-01-01
The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy to that with high accuracy cannot guarantee a high precision of transformation.In this paper,a combined method of similarity transformation and regressive approximating is presented.The local error accumulation and distortion are taken into consideration and the precision of coordinate system is improved by using the recommended method.
Semidiscrete central difference method in time for determining surface temperatures
Zhi Qian
2005-01-01
the data. Eldén (1995 has used a difference method for solving this problem, but he did not obtain the convergence at x=0. In this paper, we gave a logarithmic stability of the approximation solution at x=0 under a stronger a priori assumption ‖u(0,t‖p≤E with p>1/2. A numerical example shows that the computational effect of this method is satisfactory.
Estimation of citicoline sodium in tablets by difference spectrophotometric method
Sagar Suman Panda
2013-01-01
Full Text Available Aim: The present work deals with development and validation of a novel, precise, and accurate spectrophotometric method for the estimation of citicoline sodium (CTS in tablets. This spectrophotometric method is based on the principle that CTS shows two different forms that differs in the absorption spectra in basic and acidic medium. Materials and Methods: The present work was being carried out on Shimadzu 1800 Double Beam UV-visible spectrophotometer. Difference spectra were generated using 10 mm quartz cells over the range of 200-400 nm. Solvents used were 0.1 M NaOH and 0.1 M HCl. Results: The maxima and minima in the difference spectra of CTS were found to be 239 nm and 283 nm, respectively. Amplitude was calculated from the maxima and minima of spectrum. The drug follows linearity in the range of 1-50 μ/ml (R 2 = 0.999. The average % recovery from the tablet formulation was found to be 98.47%. The method was validated as per International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use: ICH Q2(R1 Validation of Analytical Procedures: Text and Methodology guidelines. Conclusion: This method is simple and inexpensive. Hence it can be applied for determination of the drug in pharmaceutical dosage forms.
Study on color difference estimation method of medicine biochemical analysis
Wang, Chunhong; Zhou, Yue; Zhao, Hongxia; Sun, Jiashi; Zhou, Fengkun
2006-01-01
The biochemical analysis in medicine is an important inspection and diagnosis method in hospital clinic. The biochemical analysis of urine is one important item. The Urine test paper shows corresponding color with different detection project or different illness degree. The color difference between the standard threshold and the test paper color of urine can be used to judge the illness degree, so that further analysis and diagnosis to urine is gotten. The color is a three-dimensional physical variable concerning psychology, while reflectance is one-dimensional variable; therefore, the estimation method of color difference in urine test can have better precision and facility than the conventional test method with one-dimensional reflectance, it can make an accurate diagnose. The digital camera is easy to take an image of urine test paper and is used to carry out the urine biochemical analysis conveniently. On the experiment, the color image of urine test paper is taken by popular color digital camera and saved in the computer which installs a simple color space conversion (RGB -> XYZ -> L *a *b *)and the calculation software. Test sample is graded according to intelligent detection of quantitative color. The images taken every time were saved in computer, and the whole illness process will be monitored. This method can also use in other medicine biochemical analyses that have relation with color. Experiment result shows that this test method is quick and accurate; it can be used in hospital, calibrating organization and family, so its application prospect is extensive.
Finite-Difference Frequency-Domain Method in Nanophotonics
Ivinskaya, Aliaksandra
is often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwell’s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers...... is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes...
Structural features of carbon materials synthesized by different methods
Streletskii, O. A.; Ivanenko, I. P.; Khvostov, V. V.; Savchenko, N. F.; Nishchak, O. Yu.; Aleksandrov, A. F.
2016-10-01
This paper presents the results of investigations of three types of carbon structures synthesized by different methods, such as arc discharge plasma enhanced chemical vapor deposition of carbon in a magnetic field, chemical dehydrohalogenation of the poly(vinyl chloride)/poly(vinylidene chloride) precursor, and pulsed plasma ion assisted deposition. It has been found that the samples prepared by different methods have a common feature, i.e., the presence of three-dimensional clusters based on sp 2- or sp 3-bonds surrounded by quasi-one-dimensional carbon chains. It has been shown that the structure of carbon materials changes depending on the synthesis conditions.
Preliminary comparison of different reduction methods of graphene oxide
Yu Shang; Dong Zhang; Yanyun Liu; Chao Guo
2015-02-01
The reduction of graphene oxide (GO) is a promising route to bulk produce graphene-based sheets. Different reduction processes result in reduced graphene oxide (RGO) with different properties. In this paper three reduction methods, chemical, thermal and electrochemical reduction, were compared on three aspects including morphology and structure, reduction degree and electrical conductivity by means of scanning electron microscopy (SEM), X-ray diffraction(XRD), the Fourier transform infrared spectroscopy (FT-IR) spectrum, X-ray photoelectron spectroscopy (XPS) and four-point probe conductivity measurement. Understanding the different characteristics of different RGO by preliminary comparison is helpful in tailoring the characteristics of graphene materials for diverse applications and developing a simple, green, and efficient method for the mass production of graphene.
Zhu, Rong-Ying; Mu, Li-Chun; Zhang, Yan
2005-06-01
To observe therapeutic effects of different therapeutic methods for treatment of peripheral facial paralysis at different stages. In the treatment group, 26 cases at acute stage were treated by acupuncture at corresponding acupoints at the healthy side, 15 cases at resting stage by acupuncture at the affected side with shallow needling method, and 2 cases at restoration stage by routine acupuncture and moxibustion, and their therapeutic effects were compared with the control group of 36 cases who were treated by routine acupuncture and moxibustion. The acupoints selected in the two groups were same. The cured-markedly effective rate was 97.7% in the treatment group and 75.0% in the control group with a very significant difference between the two groups (P acupuncture methods at different stages are better than routine acupuncture method in treatment of peripheral facial paralysis.
Solution of Higher-Order ODEs Using Backward Difference Method
Mohamed Bin Suleiman
2011-01-01
Full Text Available The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher-order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis.
Palatine tonsil volume estimation using different methods after tonsillectomy.
Sağıroğlu, Ayşe; Acer, Niyazi; Okuducu, Hacı; Ertekin, Tolga; Erkan, Mustafa; Durmaz, Esra; Aydın, Mesut; Yılmaz, Seher; Zararsız, Gökmen
2016-06-15
This study was carried out to measure the volume of the palatine tonsil in otorhinolaryngology outpatients with complaints of adenotonsillar hypertrophy and chronic tonsillitis who had undergone tonsillectomy. To date, no study has investigated palatine tonsil volume using different methods and compared with subjective tonsil size in the literature. For this purpose, we used three different methods to measure palatine tonsil volume. The correlation of each parameter with tonsil size was assessed. After tonsillectomy, palatine tonsil volume was measured by Archimedes, Cavalieri and Ellipsoid methods. Mean right-left palatine tonsil volumes were calculated as 2.63 ± 1.34 cm(3) and 2.72 ± 1.51 cm(3) by the Archimedes method, 3.51 ± 1.48 cm(3) and 3.37 ± 1.36 cm(3) by the Cavalieri method, and 2.22 ± 1.22 cm(3) and 2.29 ± 1.42 cm(3) by the Ellipsoid method, respectively. Excellent agreement was found among the three methods of measuring volumetric techniques according to Bland-Altman plots. In addition, tonsil grade was correlated significantly with tonsil volume.
The review and results of different methods for facial recognition
Le, Yifan
2017-09-01
In recent years, facial recognition draws much attention due to its wide potential applications. As a unique technology in Biometric Identification, facial recognition represents a significant improvement since it could be operated without cooperation of people under detection. Hence, facial recognition will be taken into defense system, medical detection, human behavior understanding, etc. Several theories and methods have been established to make progress in facial recognition: (1) A novel two-stage facial landmark localization method is proposed which has more accurate facial localization effect under specific database; (2) A statistical face frontalization method is proposed which outperforms state-of-the-art methods for face landmark localization; (3) It proposes a general facial landmark detection algorithm to handle images with severe occlusion and images with large head poses; (4) There are three methods proposed on Face Alignment including shape augmented regression method, pose-indexed based multi-view method and a learning based method via regressing local binary features. The aim of this paper is to analyze previous work of different aspects in facial recognition, focusing on concrete method and performance under various databases. In addition, some improvement measures and suggestions in potential applications will be put forward.
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.
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
Hyperbolic function method for solving nonlinear differential-different equations
Zhu Jia-Min
2005-01-01
An algorithm is devised to obtained exact travelling wave solutions of differential-different equations by means of hyperbolic function. For illustration, we apply the method to solve the discrete nonlinear (2+1)-dimensional Toda lattice equation and the discretized nonlinear mKdV lattice equation, and successfully constructed some explicit and exact travelling wave solutions.
Efficient interface conditions for the finite difference beam propagation method
Hoekstra, Hugo; Krijnen, Gijsbertus J.M.; Lambeck, Paul
1992-01-01
It is shown that by adapting the refractive indexes in the vicinity of interfaces, the 2-D beam propagation method based on the finite-difference (FDBPM) scheme can be made much more effective. This holds especially for TM modes propagating in structures with high-index contrasts, such as surface
Generational (age) differences in nursing students' preferences for teaching methods.
Walker, Jean T; Martin, Tina; White, Jill; Elliott, Rowena; Norwood, Anne; Mangum, Carl; Haynie, Lisa
2006-09-01
A generational age transformation is occurring in nursing classrooms across the United States. Nurse educators need to prepare for the different values and expectations of students from Generation X and the newly emerging Generation Y in the educational environment. This quantitative, descriptive research begins to examine the preferences and expectations of these generations regarding teaching methods.
Experimental Study for the Different Methods of Generating Millimeter Waves
Aamer Jamal Albaghdadi
2014-08-01
Full Text Available In this paper a analytical comparison and experimental implementation of different methods used in generating a low phase noise millimeter wave signals is presented. Four techniques were experimented and compared, Multiplication, phase lock loop (PLL, Injection locking (IL, and Injection locking with phase lock loop (ILPLL. The comparison and experimental results of a laboratory discussed.
Fourth-Order Difference Methods for Hyperbolic IBVPs
Gustafsson, Bertil; Olsson, Pelle
1995-03-01
In this paper we consider fourth-order difference approximations of initial-boundary value problems for hyperbolic partial differential equations. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics; the second one is used for modeling shocks and rarefaction waves. The time discretization is done with a third-order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second-order viscosity. In case of the non-linear Burgers' equation we use a flux splitting technique that results in an energy estimate for certain difference approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth-order methods with a standard second-order one and with a third-order TVD method. The results show that the fourth-order methods are the only ones that give good results for all the considered test problems.
More than Method?: A Discussion of Paradigm Differences within Mixed Methods Research
Harrits, Gitte Sommer
2011-01-01
This article challenges the idea that mixed methods research (MMR) constitutes a coherent research paradigm and explores how different research paradigms exist within MMR. Tracing paradigmatic differences at the level of methods, ontology, and epistemology, two MMR strategies are discussed: nested analysis, recently presented by the American…
More than Method?: A Discussion of Paradigm Differences within Mixed Methods Research
Harrits, Gitte Sommer
2011-01-01
This article challenges the idea that mixed methods research (MMR) constitutes a coherent research paradigm and explores how different research paradigms exist within MMR. Tracing paradigmatic differences at the level of methods, ontology, and epistemology, two MMR strategies are discussed: nested analysis, recently presented by the American…
The mimetic finite difference method for elliptic problems
Veiga, Lourenço Beirão; Manzini, Gianmarco
2014-01-01
This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.
Temperature profiles of different cooling methods in porcine pancreas procurement.
Weegman, Bradley P; Suszynski, Thomas M; Scott, William E; Ferrer Fábrega, Joana; Avgoustiniatos, Efstathios S; Anazawa, Takayuki; O'Brien, Timothy D; Rizzari, Michael D; Karatzas, Theodore; Jie, Tun; Sutherland, David E R; Hering, Bernhard J; Papas, Klearchos K
2014-01-01
Porcine islet xenotransplantation is a promising alternative to human islet allotransplantation. Porcine pancreas cooling needs to be optimized to reduce the warm ischemia time (WIT) following donation after cardiac death, which is associated with poorer islet isolation outcomes. This study examines the effect of four different cooling Methods on core porcine pancreas temperature (n = 24) and histopathology (n = 16). All Methods involved surface cooling with crushed ice and chilled irrigation. Method A, which is the standard for porcine pancreas procurement, used only surface cooling. Method B involved an intravascular flush with cold solution through the pancreas arterial system. Method C involved an intraductal infusion with cold solution through the major pancreatic duct, and Method D combined all three cooling Methods. Surface cooling alone (Method A) gradually decreased core pancreas temperature to pancreas temperature profiles during procurement and histopathology scores. These data may also have implications on human pancreas procurement as use of an intraductal infusion is not common practice. © 2014 John Wiley & Sons A/S Published by John Wiley & Sons Ltd.
Comparison of three different methods of total carbon dioxide measurement.
Kilborn, Susan H.; Bonnett, Brenda N.; Pook, Harold A.
1995-01-01
The objective of this study was to compare total carbon dioxide (TCO(2)) levels measured by three different methods. Two hundred jugular venous blood samples from dogs admitted to the Veterinary Teaching Hospital, Ontario Veterinary College with various clinical disorders were analyzed by the Radiometer blood gas analyzer (BGA) and the Coulter DACOS analyzer. In 70 of these samples, TCO(2) was also measured by the Kodak Ektachem DTE chemistry analyzer. Comparison of the agreement between methods revealed intraclass correlation coefficients (ICC) of 0.63, 0.79, and 0.82 for the DACOS-Ektachem, DACOS-BGA and Ektachem-BGA comparisons, respectively. Evaluation of the effect of storage time on TCO(2) content of stored serum samples measured on the DACOS analyzer revealed a decrease of almost 2 mmol/L and a decrease in the intraclass correlation coefficient values between the DACOS analyzer and other methods after 7 hours storage time. The results of this observational study revealed lower agreement between the three methods in this study than previously reported between other methods of TCO(2) measurement. Possible reasons for the lower than expected agreement in this study included changes in DACOS values because of storage and differences in methodologies between the methods.
Impact of Different Obesity Assessment Methods after Acute Coronary Syndromes
Caroline N. M. Nunes
2014-07-01
Full Text Available Background: Abdominal obesity is an important cardiovascular risk factor. Therefore, identifying the best method for measuring waist circumference (WC is a priority. Objective: To evaluate the eight methods of measuring WC in patients with acute coronary syndrome (ACS as a predictor of cardiovascular complications during hospitalization. Methods: Prospective study of patients with ACS. The measurement of WC was performed by eight known methods: midpoint between the last rib and the iliac crest (1, point of minimum circumference (2; immediately above the iliac crest (3, umbilicus (4, one inch above the umbilicus (5, one centimeter above the umbilicus (6, smallest rib and (7 the point of greatest circumference around the waist (8. Complications included: angina, arrhythmia, heart failure, cardiogenic shock, hypotension, pericarditis and death. Logistic regression tests were used for predictive factors. Results: A total of 55 patients were evaluated. During the hospitalization period, which corresponded on average to seven days, 37 (67% patients had complications, with the exception of death, which was not observed in any of the cases. Of these complications, the only one that was associated with WC was angina, and with every cm of WC increase, the risk for angina increased from 7.5 to 9.9%, depending on the measurement site. It is noteworthy the fact that there was no difference between the different methods of measuring WC as a predictor of angina. Conclusion: The eight methods of measuring WC are also predictors of recurrent angina after acute coronary syndromes.
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.
R. H. Moore
2013-04-01
Full Text Available We use the Global Modelling Initiative (GMI chemical transport model with a cloud droplet parameterisation adjoint to quantify the sensitivity of cloud droplet number concentration to uncertainties in predicting CCN concentrations. Published CCN closure uncertainties for six different sets of simplifying compositional and mixing state assumptions are used as proxies for modelled CCN uncertainty arising from application of those scenarios. It is found that cloud droplet number concentrations (Nd are fairly insensitive to the number concentration (Na of aerosol which act as CCN over the continents (∂lnNd/∂lnNa ~10–30%, but the sensitivities exceed 70% in pristine regions such as the Alaskan Arctic and remote oceans. This means that CCN concentration uncertainties of 4–71% translate into only 1–23% uncertainty in cloud droplet number, on average. Since most of the anthropogenic indirect forcing is concentrated over the continents, this work shows that the application of Köhler theory and attendant simplifying assumptions in models is not a major source of uncertainty in predicting cloud droplet number or anthropogenic aerosol indirect forcing for the liquid, stratiform clouds simulated in these models. However, it does highlight the sensitivity of some remote areas to pollution brought into the region via long-range transport (e.g., biomass burning or from seasonal biogenic sources (e.g., phytoplankton as a source of dimethylsulfide in the southern oceans. Since these transient processes are not captured well by the climatological emissions inventories employed by current large-scale models, the uncertainties in aerosol-cloud interactions during these events could be much larger than those uncovered here. This finding motivates additional measurements in these pristine regions, for which few observations exist, to quantify the impact (and associated uncertainty of transient aerosol processes on cloud properties.
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.
Aparna Zagabathuni
2016-12-01
Full Text Available A suspension of particles below 100 nm in size, usually termed as nanofluid, often shows a notable enhancement in thermal conductivity, when measured by the transient hot-wire method. In contrast, when the conductivity of the same nanofluid is measured by the laser flash method, the enhancement reported is about one order of magnitude lower. This difference has been quantitatively resolved for the first time on the basis of the collision-mediated heat transfer model for nanofluids proposed earlier by our research group. Based on the continuum simulation coupled with stochastic analysis, the present theoretical prediction agrees well with the experimental observations from different measuring methods reported in the literature, and fully accounts for the different results from the two measuring methods mentioned above. This analysis also gives an indication that the nanofluids are unlikely to be effective for heat transfer in microchannels.
Zagabathuni, Aparna; Ghosh, Sudipto; Pabi, Shyamal Kumar
2016-01-01
A suspension of particles below 100 nm in size, usually termed as nanofluid, often shows a notable enhancement in thermal conductivity, when measured by the transient hot-wire method. In contrast, when the conductivity of the same nanofluid is measured by the laser flash method, the enhancement reported is about one order of magnitude lower. This difference has been quantitatively resolved for the first time on the basis of the collision-mediated heat transfer model for nanofluids proposed earlier by our research group. Based on the continuum simulation coupled with stochastic analysis, the present theoretical prediction agrees well with the experimental observations from different measuring methods reported in the literature, and fully accounts for the different results from the two measuring methods mentioned above. This analysis also gives an indication that the nanofluids are unlikely to be effective for heat transfer in microchannels.
A parallel fast multipole method for elliptic difference equations
Liska, Sebastian
2014-01-01
A new fast multipole formulation for solving elliptic PDEs on unbounded domains and its parallel implementation are presented. This method formally discretizes the PDE on an infinite Cartesian grid, and then solves the corresponding difference equations. In the analog to solving continuous inhomogeneous differential equations using Green's functions, the proposed method uses the fundamental solution of the discrete operator on an infinite grid, or lattice Green's function. Fast solutions O(N) are achieved by using a kernel-independent interpolation-based fast multipole method. Unlike other fast multipole algorithms, our approach exploits the regularity of the underlying Cartesian grid and the efficiency of FFTs to reduce the computation time. Our parallel implementation allows communications and computations to be overlapped and requires minimal global synchronization. The accuracy, efficiency, and parallel performance of the method are demonstrated through numerical experiments on the discrete 3D Poisson equ...
Localization of metastases from medullary thyroid carcinoma using different methods
Cabezas, R.C.; Berna, L.; Estorch, M.; Carrio, I.; Garcia-Ameijeiras, A.
1989-01-01
We analyzed the efficiency of three different noninvasive methods in the localization of recurrent medullary thyroid carcinoma (MTC). Nine patients (six females and three males) with biochemical evidence of disease after primary surgery were subjected to {sup 131}I anti-carcinoembryonic antigen (anti-CEA) antibody, {sup 131}I meta-iodo-benzylguanidine (MIBG), and computed tomography. Another female patient, in biochemical remission for six years after initial surgery, was also studied using the same methods. Three of the ten patients had negative results with all three methods (including the patient in remission). The other seven patients showed abnormal uptake of labeled anti-CEA antibody in various localizations; only two of these patients had a corresponding pathological image by computed tomography and only one by {sup 131}I MIBG. These preliminary results suggest that {sup 131}I anti-CEA scanning may be the most sensitive noninvasive method for the localization of MTC recurrences.
Adaptive Image Restoration and Segmentation Method Using Different Neighborhood Sizes
Chengcheng Li
2003-04-01
Full Text Available The image restoration methods based on the Bayesian's framework and Markov random fields (MRF have been widely used in the image-processing field. The basic idea of all these methods is to use calculus of variation and mathematical statistics to average or estimate a pixel value by the values of its neighbors. After applying this averaging process to the whole image a number of times, the noisy pixels, which are abnormal values, are filtered out. Based on the Tea-trade model, which states that the closer the neighbor, more contribution it makes, almost all of these methods use only the nearest four neighbors for calculation. In our previous research [1, 2], we extended the research on CLRS (image restoration and segmentation by using competitive learning algorithm to enlarge the neighborhood size. The results showed that the longer neighborhood range could improve or worsen the restoration results. We also found that the autocorrelation coefficient was an important factor to determine the proper neighborhood size. We then further realized that the computational complexity increased dramatically along with the enlargement of the neighborhood size. This paper is to further the previous research and to discuss the tradeoff between the computational complexity and the restoration improvement by using longer neighborhood range. We used a couple of methods to construct the synthetic images with the exact correlation coefficients we want and to determine the corresponding neighborhood size. We constructed an image with a range of correlation coefficients by blending some synthetic images. Then an adaptive method to find the correlation coefficients of this image was constructed. We restored the image by applying different neighborhood CLRS algorithm to different parts of the image according to its correlation coefficient. Finally, we applied this adaptive method to some real-world images to get improved restoration results than by using single
Impact of Different Obesity Assessment Methods after Acute Coronary Syndromes
Nunes, Caroline N. M.; Minicucci, Marcos F.; Farah, Elaine; Fusco, Daniéliso; Azevedo, Paula S.; Paiva, Sergio A. R.; Zornoff, Leonardo A. M., E-mail: lzornoff@cardiol.br [Faculdade de Medicina de Botucatu, Botucatu, SP (Brazil)
2014-07-15
Abdominal obesity is an important cardiovascular risk factor. Therefore, identifying the best method for measuring waist circumference (WC) is a priority. To evaluate the eight methods of measuring WC in patients with acute coronary syndrome (ACS) as a predictor of cardiovascular complications during hospitalization. Prospective study of patients with ACS. The measurement of WC was performed by eight known methods: midpoint between the last rib and the iliac crest (1), point of minimum circumference (2); immediately above the iliac crest (3), umbilicus (4), one inch above the umbilicus (5), one centimeter above the umbilicus (6), smallest rib and (7) the point of greatest circumference around the waist (8). Complications included: angina, arrhythmia, heart failure, cardiogenic shock, hypotension, pericarditis and death. Logistic regression tests were used for predictive factors. A total of 55 patients were evaluated. During the hospitalization period, which corresponded on average to seven days, 37 (67%) patients had complications, with the exception of death, which was not observed in any of the cases. Of these complications, the only one that was associated with WC was angina, and with every cm of WC increase, the risk for angina increased from 7.5 to 9.9%, depending on the measurement site. It is noteworthy the fact that there was no difference between the different methods of measuring WC as a predictor of angina. The eight methods of measuring WC are also predictors of recurrent angina after acute coronary syndromes.
Comparison of different diagnostic methods in infants with Cholestasis
Seyed Mohsen Dehghani; Mahmood Haghighat; Mohammad Hadi Imanieh; Bita Geramizadeh
2006-01-01
AIM: To evaluate different methods in differentiating idiopathic neonatal hepatitis from biliary atresia.METHODS: Sixty-five infants with cholestatic jaundice and final diagnosis of idiopathic neonatal hepatitis and biliary atresia were studied prospectively from September 2003 to March 2006. A thorough history and physical examination were undertaken and the liver enzymes were examined. All cases underwent abdominal ultrasonography, hepatobiliary scintigraphy,and percutaneous liver biopsy. The accuracy, sensitivity,specificity and predictive values of these various methods were compared.RESULTS: There were 34 girls and 31 boys, among them 46 subjects had idiopathic neonatal hepatitis (age,61 ± 17 d) and 19 had biliary atresia (age, 64 ± 18 d).The mean age at onset of jaundice was significantly lower in cases of biliary atresia when compared to idiopathic neonatal hepatitis cases (9 ± 13 d vs 20 ± 21 d;P = 0.032). The diagnostic accuracy of different methods was as follows: liver biopsy, 96.9%; clinical evaluation,70.8%; ultrasonography, 69.2%; hepatobiliary scintigraphy, 58.5%; and liver enzymes, 50.8%.CONCLUSION: Our results indicate that clinical evaluation by an experienced pediatric hepatologist and a biopsy of the liver are considered as the most reliable methods to differentiate idiopathic neonatal hepatitis and biliary atresia.
Field evaluation of broiler gait score using different sampling methods
AFS Cordeiro
2009-09-01
Full Text Available Brazil is today the world's largest broiler meat exporter; however, in order to keep this position, it must comply with welfare regulations while maintaining low production costs. Locomotion problems restrain bird movements, limiting their access to drinking and feeding equipment, and therefore their survival and productivity. The objective of this study was to evaluate locomotion deficiency in broiler chickens reared under stressful temperature conditions using three different sampling methods of birds from three different ages. The experiment consisted in determining the gait score of 28, 35, 42 and 49-day-old broilers using three different known gait scoring methods: M1, birds were randomly selected, enclosed in a circle, and then stimulated to walk out of the circle; M2, ten birds were randomly selected and gait scored; and M3, birds were randomly selected, enclosed in a circle, and then observed while walking away from the circle without stimulus to walking. Environmental temperature, relative humidity, and light intensity inside the poultry houses were recorded. No evidence of interaction between scoring method and age was found however, both method and age influenced gait score. Gait score was found to be lower at 28 days of age. The evaluation using the ten randomly selected birds within the house was the method that presented the less reliable results. Gait score results when birds were stimulated to walk were lower than when they were not simulated, independently of age. The gait scores obtained with the three tested methods and ages were higher than those considered acceptable. The highest frequency of normal gait score (0 represented 50% of the flock. These results may be related to heat stress during rearing. Average gait score incresead with average ambient temperature, relative humidity, and light intensity. The evaluation of gait score to detect locomotion problems of broilers under rearing conditions seems subjective and
Perkó, Z.
2015-01-01
This thesis presents novel adjoint and spectral methods for the sensitivity and uncertainty (S&U) analysis of multi-physics problems encountered in the field of reactor physics. The first part focuses on the steady state of reactors and extends the adjoint sensitivity analysis methods well establish
Perkó, Z.
2015-01-01
This thesis presents novel adjoint and spectral methods for the sensitivity and uncertainty (S&U) analysis of multi-physics problems encountered in the field of reactor physics. The first part focuses on the steady state of reactors and extends the adjoint sensitivity analysis methods well
Acoustic radiation force analysis using finite difference time domain method.
Grinenko, A; Wilcox, P D; Courtney, C R P; Drinkwater, B W
2012-05-01
Acoustic radiation force exerted by standing waves on particles is analyzed using a finite difference time domain Lagrangian method. This method allows the acoustic radiation force to be obtained directly from the solution of nonlinear fluid equations, without any assumptions on size or geometry of the particles, boundary conditions, or acoustic field amplitude. The model converges to analytical results in the limit of small particle radii and low field amplitudes, where assumptions within the analytical models apply. Good agreement with analytical and numerical models based on solutions of linear scattering problems is observed for compressible particles, whereas some disagreement is detected when the compressibility of the particles decreases.
Combining different methods improves assessment of competence in colonoscopy
Konge, Lars; Svendsen, Morten Bo Søndergaard; Preisler, Louise
2017-01-01
score calculations were used to explore different combinations of the measures. RESULTS: Twenty physicians were included in the study. The reliability (Cronbach's alpha) were 0.92, 0.57, 0.87 and 0.55 for the subjective score assessed under direct observation, time to cecum, distance between operator......'s hands and colonoscopy progression score, respectively. Equal weight (=25%) to all four methods resulted in a reliability of 0.91 and optimal weighting of the methods (55%, 10%, 25% and 10%, respectively) resulted in a maximum reliability of 0.95. CONCLUSION: Combining subjective expert ratings...
Finn, John M., E-mail: finn@lanl.gov [T-5, Applied Mathematics and Plasma Physics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2015-03-15
Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012
张慧; 刘兴祥; 冯学利
2011-01-01
We study the weak adjoint matrix and m- weak adjoint matrix＇s eigenvalues,eigenvectors and their corresponding eigenvalues eigenvector＇relationship.%研究了弱伴随矩阵、m重弱伴随矩阵的特征值、特征向量与其对应矩阵的特征值、特征向量的关系。
Convergence of a finite difference method for combustion model problems
YING; Long'an
2004-01-01
We study a finite difference scheme for a combustion model problem. A projection scheme near the combustion wave, and the standard upwind finite difference scheme away from the combustion wave are applied. Convergence to weak solutions with a combustion wave is proved under the normal Courant-Friedrichs-Lewy condition. Some conditions on the ignition temperature are given to guarantee the solution containing a strong detonation wave or a weak detonation wave. Convergence to strong detonation wave solutions for the random projection method is also proved.
Passage to the Differences for the BDF's Methods
Abdelouahab Salmi
2006-01-01
Full Text Available In this study, we give an improvement to the backward differentiation formula (BDF. We use a formula for the differences that permits us to determine the new coefficients αi^ and γi ^in function of the classical coefficients αi and γi of this method. Our proposed approach decreases the error and the cost of computation. Numerical results for concrete problems are given to support the theory.
High Order Finite Difference Methods for Multiscale Complex Compressible Flows
Sjoegreen, Bjoern; Yee, H. C.
2002-01-01
The classical way of analyzing finite difference schemes for hyperbolic problems is to investigate as many as possible of the following points: (1) Linear stability for constant coefficients; (2) Linear stability for variable coefficients; (3) Non-linear stability; and (4) Stability at discontinuities. We will build a new numerical method, which satisfies all types of stability, by dealing with each of the points above step by step.
Finite difference methods for the solution of unsteady potential flows
Caradonna, F. X.
1985-01-01
A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.
Refinement of thermal imager minimum resolvable temperature difference calculating method
Kolobrodov, V. G.; Mykytenko, V. I.
2015-11-01
Calculating methods, which accurately predict minimum resolvable temperature difference (MRTD), are of significant interest for many years. The article deals with improvement the accuracy of determining the thermal imaging system MRTD by elaboration the visual perception model. We suggest MRTD calculating algorithm, which is based on a reliable approximation of the human visual system modulation transfer function (MTF) proposed by N. Nill. There was obtained a new expression for the bandwidth evaluation, which is independent of angular size of the Foucault bar target.
Computational electrodynamics the finite-difference time-domain method
Taflove, Allen
2005-01-01
This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.
A finite-difference method for transonic airfoil design.
Steger, J. L.; Klineberg, J. M.
1972-01-01
This paper describes an inverse method for designing transonic airfoil sections or for modifying existing profiles. Mixed finite-difference procedures are applied to the equations of transonic small disturbance theory to determine the airfoil shape corresponding to a given surface pressure distribution. The equations are solved for the velocity components in the physical domain and flows with embedded shock waves can be calculated. To facilitate airfoil design, the method allows alternating between inverse and direct calculations to obtain a profile shape that satisfies given geometric constraints. Examples are shown of the application of the technique to improve the performance of several lifting airfoil sections. The extension of the method to three dimensions for designing supercritical wings is also indicated.
Parallel finite-difference time-domain method
Yu, Wenhua
2006-01-01
The finite-difference time-domain (FTDT) method has revolutionized antenna design and electromagnetics engineering. This book raises the FDTD method to the next level by empowering it with the vast capabilities of parallel computing. It shows engineers how to exploit the natural parallel properties of FDTD to improve the existing FDTD method and to efficiently solve more complex and large problem sets. Professionals learn how to apply open source software to develop parallel software and hardware to run FDTD in parallel for their projects. The book features hands-on examples that illustrate the power of parallel FDTD and presents practical strategies for carrying out parallel FDTD. This detailed resource provides instructions on downloading, installing, and setting up the required open source software on either Windows or Linux systems, and includes a handy tutorial on parallel programming.
Face recognition by combining eigenface method with different wavelet subbands
MA Yan; LI Shun-bao
2006-01-01
@@ A method combining eigenface with different wavelet subbands for face recognition is proposed.Each training image is decomposed into multi-subbands for extracting their eigenvector sets and projection vectors.In the recognition process,the inner product distance between the projection vectors of the test image and that of the training image are calculated.The training image,corresponding to the maximum distance under the given threshold condition,is considered as the final result.The experimental results on the ORL and YALE face database show that,compared with the eigenface method directly on the image domain or on a single wavelet subband,the recognition accuracy using the proposed method is improved by 5% without influencing the recognition speed.
A Review on Different Virtual Learning Methods in Pharmacy Education
Amin Noori
2015-10-01
Full Text Available Virtual learning is a type of electronic learning system based on the web. It models traditional in- person learning by providing virtual access to classes, tests, homework, feedbacks and etc. Students and teachers can interact through chat rooms or other virtual environments. Web 2.0 services are usually used for this method. Internet audio-visual tools, multimedia systems, a disco CD-ROMs, videotapes, animation, video conferencing, and interactive phones can all be used to deliver data to the students. E-learning can occur in or out of the classroom. It is time saving with lower costs compared to traditional methods. It can be self-paced, it is suitable for distance learning and it is flexible. It is a great learning style for continuing education and students can independently solve their problems but it has its disadvantages too. Thereby, blended learning (combination of conventional and virtual education is being used worldwide and has improved knowledge, skills and confidence of pharmacy students.The aim of this study is to review, discuss and introduce different methods of virtual learning for pharmacy students.Google scholar, Pubmed and Scupus databases were searched for topics related to virtual, electronic and blended learning and different styles like computer simulators, virtual practice environment technology, virtual mentor, virtual patient, 3D simulators, etc. are discussed in this article.Our review on different studies on these areas shows that the students are highly satisfied withvirtual and blended types of learning.
Comparing different methods for estimating radiation dose to the conceptus
Lopez-Rendon, X.; Dedulle, A. [KU Leuven, Department of Imaging and Pathology, Division of Medical Physics and Quality Assessment, Herestraat 49, box 7003, Leuven (Belgium); Walgraeve, M.S.; Woussen, S.; Zhang, G. [University Hospitals Leuven, Department of Radiology, Leuven (Belgium); Bosmans, H. [KU Leuven, Department of Imaging and Pathology, Division of Medical Physics and Quality Assessment, Herestraat 49, box 7003, Leuven (Belgium); University Hospitals Leuven, Department of Radiology, Leuven (Belgium); Zanca, F. [KU Leuven, Department of Imaging and Pathology, Division of Medical Physics and Quality Assessment, Herestraat 49, box 7003, Leuven (Belgium); GE Healthcare, Buc (France)
2017-02-15
To compare different methods available in the literature for estimating radiation dose to the conceptus (D{sub conceptus}) against a patient-specific Monte Carlo (MC) simulation and a commercial software package (CSP). Eight voxel models from abdominopelvic CT exams of pregnant patients were generated. D{sub conceptus} was calculated with an MC framework including patient-specific longitudinal tube current modulation (TCM). For the same patients, dose to the uterus, D{sub uterus}, was calculated as an alternative for D{sub conceptus}, with a CSP that uses a standard-size, non-pregnant phantom and a generic TCM curve. The percentage error between D{sub uterus} and D{sub conceptus} was studied. Dose to the conceptus and percent error with respect to D{sub conceptus} was also estimated for three methods in the literature. The percentage error ranged from -15.9% to 40.0% when comparing MC to CSP. When comparing the TCM profiles with the generic TCM profile from the CSP, differences were observed due to patient habitus and conceptus position. For the other methods, the percentage error ranged from -30.1% to 13.5% but applicability was limited. Estimating an accurate D{sub conceptus} requires a patient-specific approach that the CSP investigated cannot provide. Available methods in the literature can provide a better estimation if applicable to patient-specific cases. (orig.)
Long term performance of different radon remedial methods in Sweden
Clavensjoe, B
2002-01-01
The object of this project was to investigate the long time effectiveness of different radon remedial methods. The ten years project started 1991. From start the investigation comprised of 105 dwellings (91 single-family houses and 14 flats in multi-family buildings). In all of the dwellings remedial measures were carried out in the eighties. Before and immediately after the reduction the local measured the radon concentrations. New measurements of the radon concentrations have been made every third year; in 1991, 1994, 1997 and in 2000. Twelve different radon remedial methods and method combinations were used. The radon sources were building materials as well as sub-soils. In all of the dwellings the radon concentrations were measured by nuclear track films during 3 months (January-March) measurements and in half of them the air change rates by passive tracer gas methods. The results of the 2000 and the 1991 (within brackets) studies showed that the radon concentration was up to 200 Bq/m sup 3 in 54 (54) sin...
Comparative analysis of different methods for graphene nanoribbon synthesis
Tošić Dragana D.
2013-01-01
Full Text Available Graphene nanoribbons (GNRs are thin strips of graphene that have captured the interest of scientists due to their unique structure and promising applications in electronics. This paper presents the results of a comparative analysis of morphological properties of graphene nanoribbons synthesized by different methods. Various methods have been reported for graphene nanoribons synthesis. Lithography methods usually include electron-beam (e-beam lithography, atomic force microscopy (AFM lithography, and scanning tunnelling microscopy (STM lithography. Sonochemical and chemical methods exist as well, namely chemical vapour deposition (CVD and anisotropic etching. Graphene nanoribbons can also be fabricated from unzipping carbon nanotubes (CNTs. We propose a new highly efficient method for graphene nanoribbons production by gamma irradiation of graphene dispersed in cyclopentanone (CPO. Surface morphology of graphene nanoribbons was visualized with atomic force and transmission electron microscopy. It was determined that dimensions of graphene nanoribbons are inversely proportional to applied gamma irradiation dose. It was established that the narrowest nanoribbons were 10-20 nm wide and 1 nm high with regular and smooth edges. In comparison to other synthesis methods, dimensions of graphene nanoribbons synthesized by gamma irradiation are slightly larger, but the yield of nanoribbons is much higher. Fourier transform infrared spectroscopy was used for structural analysis of graphene nanoribbons. Results of photoluminescence spectroscopy revealed for the first time that synthesized nanoribbons showed photoluminescence in the blue region of visible light in contrast to graphene nanoribbons synthesized by other methods. Based on disclosed facts, we believe that our synthesis method has good prospects for potential future mass production of graphene nanoribbons with uniform size, as well as for future investigations of carbon nanomaterials for
Comparison of different microsurgery methods for trigeminal neuralgia
Zihang Xie; Lin Chen; Yan Wang; Zhiqiang Cui; Shijie Wang; Qiang Ao; Yuqi Zhang; Huancong Zuo
2016-01-01
Objective: To study the influence of different microsurgical methods on surgical outcomes and complications, and to improve the surgical outcomes for trigeminal neuralgia. Methods: The clinical data of 109 patients with trigeminal neuralgia, who were treated with microsurgery, were analyzed retrospectively. All patients were divided into 3 groups according to surgical modality: the trigeminal neuralgia decompression group (TND group, 19 patients), the TND and rhizotomy group (rhizotomy group, 55 patients), and the TND and selective lesioning group (lesioning group, 35 patients). The mid-term and short-term effects of microsurgery, and the occurrences of com-plications, were compared between the 3 groups. Results: There were no statistical differences in the frequency of complications between the 3 groups (P > 0.05). Eighty-four patients were followed up for 6 to 33 months. The rate of pain disappearance was found to be 94.4% in the TND group, and 100% in both the rhizotomy and lesioning groups; thus, no significant differences were found between these 3 groups (P > 0.05). Additionally, 50% of the patients in the rhizotomy group and 3.6% of the patients in the lesioning group had facial numbness while no patients were affected with facial numbness in the TND group, and the differences between these 3 groups were significant (P < 0.05). Conclusions: Microsurgery is effective and safe for trigeminal neuralgia. The use of TND, in combination with selective lesioning, ensures therapeutic efficacy and improves the quality of life in postoperative patients.
Humbird, Kelli D.; McClarren, Ryan G.
2016-01-01
Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a mathematically related set of adjoint equations. The information contained in the equations can be combined to produce sensitivity information in a computationally efficient manner. In this work, sensitivity analyses are performed on systems described by flux-limited ...
[Fetal responses to different methods of electrocution of pregnant sows].
Peisker, Nina; Preissel, Anne-Kathrin; Ritzmann, Mathias; Schuster, Tibor; Thomes, Rainer; Henke, Julia
2008-01-01
The fetal stress responses in sows euthanized by electrical current during their second and last trimester of pregnancy (G1 and G2) were evaluated. Three methods of euthanasia of pregnant sows generally applicable to cases of epizootic or emergency slaughter were investigated: 1. conventional application of electrical current to the head and heart (HH); 2. application of electrical current to the head, heart and the uterus (HHU); 3. application of electrical current to the head, heart and from the upper body to the vagina (HHV). Fetuses were delivered by cesarean section at intervals of 3 to 4 minutes and remained attached to the sow by the umbilical cord. Fetal vitality, reflexes, heart rate, blood pressure, rectal body temperature, intracardial arteriovenous pCO2, pH and lactic acid were monitored for a period of 30 minutes. No method was found to kill the fetal pigs immediately. In fetuses at G1 there were no significant differences between the HH and HHU and HHV methods. Fetuses at G2 showed a significantly faster decrease in heart rate and blood pressure as well as a shorter period of time for the absence of fetal body movements and reflexes for the HHT method, compared to the other methods. Since it is not yet known to what extent the fetal pig experiences pain and suffering, the prolonged process of dying for the in utero fetus due to hypoxia which includes struggling and gasps is inconsistent with criteria for humane euthanasia and animal welfare.
Comparative Study of Rice Morphogenesis wit Different Cultivation Methods
2012-01-01
[Objective] The aim of this study was to compare the morphological char- acteristics of rice (Oryza sativa L.) with different cultivation methods and investigate the dynamics of organ growth and development characteristics of different rice culti- vars. [Method] Based on continuous field observation and destructive sampling over a growing season, detailed organ morphological data were obtained including leaf length, node number, plant height, tiller number, leaf angle, leaf area and specific leaf weight, to compare organ morphological differences among 4 rice cultivars of Baidao (indica), Jinnanfeng (japonica), 9325 (japonica) and 9915 (japonica) with 3 cultivation methods of field planting in Weigang, pot planting in Weigang, and field planting in Jiangpu. [Result] Maximum leaf length of each node gradually increased at the early growth stage and decreased at the later growth stage, the relationship between maximum leaf length and node position can be described by the equations y=a,,-~ and y=ax+b; node number, growth duration, leaf length and plant height of pot planting rice in Weigang were smaller than that of the other two field planting meth- ods; the relationship between plant height and sunshine duration, plant height and GDD (growing degree days) can be described by the equation y=ax+b, 19.23 ℃.d of GDD (≥10 ≥-d) and 8.12 h of sunshine duration were required to increase 1 cm of plant height; plant height, tiller number, and leaf area of Baidao were higher than that of the other 3 laponica rice cultivars, but the specific leaf weight and leaf angle were smaller. [Conclusion] Comparison of morphological characteristic differ- ences among rice cultivars is an important way to select water-saving and drought- tolerant rice varieties. In this study, the experimental results can be integrated into a rice functional-architectural model to simulate rice organ growth dynamics in a three- dimensional space, thereby providing reference for selecting water
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.
Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems
Asner, Liya
2012-01-01
We consider time-dependent parabolic problem s coupled across a common interface which we formulate using a Lagrange multiplier construction and solve by applying a monolithic solution technique. We derive an adjoint-based a posteriori error representation for a quantity of interest given by a linear functional of the solution. We establish the accuracy of our error representation formula through numerical experimentation and investigate the effect of error in the adjoint solution. Crucially, the error representation affords a distinction between temporal and spatial errors and can be used as a basis for a blockwise time-space refinement strategy. Numerical tests illustrate the efficacy of the refinement strategy by capturing the distinctive behavior of a localized traveling wave solution. The saddle point systems considered here are equivalent to those arising in the mortar finite element technique for parabolic problems. © 2012 Society for Industrial and Applied Mathematics.
Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas
Rallabhandi, Sriram K.
2013-01-01
This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent area cost functionals are discussed and further refined using ground loudness based objectives.
Essential self-adjointness of n-dimensional Dirac operators with a variable mass term
Kalf, Hubert; Yamada, Osanobu
2001-06-01
We give some results about the essential self-adjointness of the Dirac operator H=∑j=1nαj pj+m(x) αn+1+V(x) IN (N=2 [(n+1)/2]), on [C0∞(Rn{0})]N, where the αj (j=1,2,…,n) are Dirac matrices and m(x) and V(x) are real-valued functions. We are mainly interested in a singularity of V(x) and m(x) near the origin which preserves the essential self-adjointness of H. As a result, if m=m(r) is spherically symmetric or m(x)≡V(x), then we can permit a singularity of m and V which is stronger than that of the Coulomb potential.
Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
Catterall, Simon; /Syracuse U.; Galvez, Richard; /Syracuse U.; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2010-08-26
We report on the results of numerical simulations of SU(N) lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with {Lambda} sites in each direction in the large-N limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of {Lambda}, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume 2{sup 4}. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit N {yields} {infinity}, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.
Neutrino masses in SU(5) x U(1){sub F} with adjoint flavons
Nardi, Enrico [INFN, Laboratori Nazionali di Frascati, C.P. 13, Frascati (Italy); IFT-UAM/CSIC, Madrid (Spain); Universidad Autonoma de Madrid, Departamento de Fisica Teorica, Madrid (Spain); Restrepo, Diego; Velasquez, Mauricio [Universidad de Antioquia, Instituto de Fisica, Medellin (Colombia)
2012-03-15
We present a SU(5) x U(1){sub F} supersymmetric model for neutrino masses and mixings that implements the seesaw mechanism by means of the heavy SU(2) singlets and triplets states contained in three adjoints of SU(5). We discuss how Abelian U(1){sub F} symmetries can naturally yield non-hierarchical light neutrinos even when the heavy states are strongly hierarchical, and how it can also ensure that R-parity arises as an exact accidental symmetry. By assigning two flavons that break U(1){sub F} to the adjoint representation of SU(5) and assuming universality for all the fundamental couplings, the coefficients of the effective Yukawa and Majorana mass operators become calculable in terms of group theoretical quantities. There is a single free parameter in the model, however, at leading order the structure of the light neutrinos mass matrix is determined in a parameter independent way. (orig.)
Cotton-textile wastewater management: investigating different treatment methods.
Georgiou, D; Aivasidis, A
2012-01-01
The cotton-textile industry consumes significant amounts of water during manufacturing, creating high volumes of wastewater needing treatment. The organic-load concentration of cotton-textile wastewater is equivalent to a medium-strength municipal wastewater; the color of the water, however, remains a significant environmental issue. This research, in cooperation with a cotton-textile manufacturer, investigated different treatment methods and different combinations of methods to identify the most cost-effective approaches to treating textile wastewater. Although activated-sludge is economical, it can only be used as part of an integrated wastewater management system because it cannot decolorize wastewater. Coagulation/flocculation methods are able to decolorize cotton-wastewater; however, this process creates high amounts of wastewater solids, thus significantly increasing total treatment costs. Chemical oxidation is an environmentally friendly technique that can only be used as a polishing step because of high operating costs. Anaerobic digestion in a series of fixed-bed bioreactors with immobilized methanogens using acetic acid as a substrate and a pH-control agent followed by activated-sludge treatment was found to be the most cost-effective and environmentally safe cotton-textile wastewater management approach investigated.
Using different methods to assess the discomfort during car driving.
Ravnik, David; Otáhal, Stanislav; Dodic Fikfak, Metoda
2008-03-01
This study investigated the discomfort caused by car driving. Discomfort estimates were achieved by self-administered questionnaire, measured by different testing methods, and through the goniometry of principal angles. Data from a total of 200 non-professional drivers who fulfilled the questionnaire was analysed. 118 subjects were analysed by goniometry and 30 drivers were assessed using the OWAS (Ovaco orking Posture Analysis), RULA (Rapid Upper Limb Assessment), and CORLETT tests. The aim of this paper was to assess the appearance of the discomfort and to find some correlations between drivers' postures. Results suggest that different levels of discomfort are perceived in different body regions when driving cars. Differences appear mostly between the genders concerning the discomfort. With the questionnaire and the different estimation techniques, it is possible to identify 'at risk' drivers and ensure urgent attention when necessary. It can be concluded that the questionnare and the CORLETT test are good in predicting location of discomfort. TheB org CRI10scale is good indicator of the level of the discomfort, while OWAS and RULA can appraise the body posture to predict discomfort appearance. According to the goniometry data, the drivers posture could be one of the contributing factors in appearing of discomfort.
Evaluation of the positional difference between two common geocoding methods.
Duncan, Dustin T; Castro, Marcia C; Blossom, Jeffrey C; Bennett, Gary G; Gortmaker, Steven L
2011-05-01
Geocoding, the process of matching addresses to geographic coordinates, is a necessary first step when using geographical information systems (GIS) technology. However, different geocoding methodologies can result in different geographic coordinates. The objective of this study was to compare the positional (i.e. longitude/latitude) difference between two common geocoding methods, i.e. ArcGIS (Environmental System Research Institute, Redlands, CA, USA) and Batchgeo (freely available online at http://www.batchgeo.com). Address data came from the YMCA-Harvard After School Food and Fitness Project, an obesity prevention intervention involving children aged 5-11 years and their families participating in YMCA-administered, after-school programmes located in four geographically diverse metropolitan areas in the USA. Our analyses include baseline addresses (n = 748) collected from the parents of the children in the after school sites. Addresses were first geocoded to the street level and assigned longitude and latitude coordinates with ArcGIS, version 9.3, then the same addresses were geocoded with Batchgeo. For this analysis, the ArcGIS minimum match score was 80. The resulting geocodes were projected into state plane coordinates, and the difference in longitude and latitude coordinates were calculated in meters between the two methods for all data points in each of the four metropolitan areas. We also quantified the descriptions of the geocoding accuracy provided by Batchgeo with the match scores from ArcGIS. We found a 94% match rate (n = 705), 2% (n = 18) were tied and 3% (n = 25) were unmatched using ArcGIS. Forty-eight addresses (6.4%) were not matched in ArcGIS with a match score ≥80 (therefore only 700 addresses were included in our positional difference analysis). Six hundred thirteen (87.6%) of these addresses had a match score of 100. Batchgeo yielded a 100% match rate for the addresses that ArcGIS geocoded. The median for longitude and latitude coordinates
Evaluation of Different Methods of Sperm Immunization in Mice
H Moatamed
2005-07-01
Full Text Available Introduction: Antifertility effects of naturally occuring antisperm antibody (ASA in infertile couples and studies on experimental immunization of various animals with sperm antigens represent ASA as an immunocontraceptive target. The effects of different factors on sperm immunogenecity and ASA production have been studied and different results have been reported. In this study, whole sperm immunization was evaluated. Methods: In this experimental study, whole mice sperm with different adjuvants i.e. complete Freund’s adjuvant (CFA, incomplete Freund’s adjuvant (ICFA, cholera toxin subunit-β (CTS-β were administrated to mice by different routes; Intramuscular (IM, Subcutaneous (SC, Intranasal (IN, Intra peritoneal (IP, Intrarectal (IR, Intravaginal (IVA and oral. Control groups were inoculated with phosphate buffer saline (PBS plus corresponding adjuvant. Immunization was carried out on day 0,7,14,28 and ASA titers were detected by indirect immunofluorescence (IFA technique. The results were compared between control and experimental groups by Mann Whitney and Fisher exact tests. Results: The number of positive mice for ASA in IM, IN and SC experimental and control groups were significantly different (P=0.01, P=0.01, P=0.04 respectively. However, there were no significant differences between the IR, IVA, and oral experimental and control groups. No differences were observed between ASA in vaginal washing of all groups. Due to high mortality, the IP group was excluded from the study. Conclusion: It can be concluded that whole sperm antigen can induce immune response in female mice by IM, SC and IN routes, but not through IAV, IR and oral administration routes.
Different methods for the induction of labour in outpatient settings
Dowswell, Therese; Kelly, Anthony J; Livio, Stefania; Norman, Jane E; Alfirevic, Zarko
2014-01-01
Background Induction of labour is carried out for a variety of indications and using a range of pharmacological, mechanical and other methods. For women at low risk, some methods of induction of labour may be suitable for use in outpatient settings. Objectives To examine pharmacological and mechanical interventions to induce labour in outpatient settings in terms of feasibility, effectiveness, maternal satisfaction, healthcare costs and, where information is available, safety. The review complements existing reviews on labour induction examining effectiveness and safety. Search methods We searched the Cochrane Pregnancy and Childbirth Group’s Trials Register (December 2009) and reference lists of retrieved studies. Selection criteria We included randomised controlled trials examining outpatient cervical ripening or induction of labour with pharmacological agents or mechanical methods. Data collection and analysis Two authors independently extracted data and assessed eligible papers for risk of bias. We checked all data after entry into review manager software. Main results We included 28 studies with 2616 women examining different methods of induction of labour where women received treatment at home or were sent home after initial treatment and monitoring in hospital. Studies examined vaginal and intracervical PGE2, vaginal and oral misoprostol, isosorbide mononitrate, mifepristone, oestrogens, and acupuncture. Overall, the results demonstrate that outpatient induction of labour is feasible and that important adverse events are rare. There was no strong evidence that agents used to induce labour in outpatient settings had an impact (positive or negative) on maternal or neonatal health. There was some evidence that, compared to placebo or no treatment, induction agents reduced the need for further interventions to induce labour, and shortened the interval from intervention to birth. We were unable to pool results on outcomes relating to progress in labour as
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.
On Lipschitz Perturbations of a Self-Adjoint Strongly Positive Operator
Dinu Teodorescu
2013-01-01
Full Text Available In this paper we study semilinear equations of the form Au+λF(u=f, where A is a linear self-adjoint operator, satisfying a strong positivity condition, and F is a nonlinear Lipschitz operator. As applications we develop Krasnoselskii and Ky Fan type approximation results for certain pair of maps and to illustrate the usability of the obtained results, the existence of solution of an integral equation is provided.
Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics
Strauss, Y; Machnes, S; Horwitz, L P
2011-01-01
In [J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its expectation value decreases monotonically for any initial state. In this paper we study some of this operator's properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.
Ibragimov, Nail H
2011-01-01
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.
On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces
Sobhy El-Sayed Ibrahim
2003-01-01
order, with complex coefficients and its formal adjoint Mp+ on any finite number of intervals Ip=(ap,bp, p=1,…, N, are considered in the setting of the direct sums of Lwp2(ap,bp-spaces of functions defined on each of the separate intervals. And a number of results concerning the location of the point spectra and regularity fields of general differential operators generated by such expressions are obtained.
First results for SU(2) Yang-Mills with one adjoint Dirac Fermion
Athenodorou, Andreas; Bergner, Georg; Lucini, Biagio; Patella, Agostino
2013-01-01
We present a first exploratory study of SU(2) gauge theory with one Dirac flavour in the adjoint representation. We provide initial results for the spectroscopy and the anomalous dimension for the chiral condensate. Our investigation indicates that the theory is conformal or near-conformal, with an anomalous dimension of order one. A discussion of the relevance of these findings in relation to walking technicolor scenarios is also presented.
Running of the coupling and quark mass in SU(2) with two adjoint fermions
Bursa, Francis; Keegan, Liam; Pica, Claudio; Pickup, Thomas
2009-01-01
We simulate SU(2) gauge theory with two massless Dirac fermions in the adjoint representation. We calculate the running of the Schroedinger Functional coupling and the renormalised quark mass over a wide range of length scales. The running of the coupling is consistent with the existence of an infrared fixed point (IRFP), and we find 0.07 < gamma < 0.56 at the IRFP, depending on the value of the critical coupling.
Comparative analysis of different methods for image enhancement
吴笑峰; 胡仕刚; 赵瑾; 李志明; 李劲; 唐志军; 席在芳
2014-01-01
Image enhancement technology plays a very important role to improve image quality in image processing. By enhancing some information and restraining other information selectively, it can improve image visual effect. The objective of this work is to implement the image enhancement to gray scale images using different techniques. After the fundamental methods of image enhancement processing are demonstrated, image enhancement algorithms based on space and frequency domains are systematically investigated and compared. The advantage and defect of the above-mentioned algorithms are analyzed. The algorithms of wavelet based image enhancement are also deduced and generalized. Wavelet transform modulus maxima (WTMM) is a method for detecting the fractal dimension of a signal, it is well used for image enhancement. The image techniques are compared by using the mean (μ), standard deviation (s), mean square error (MSE) and PSNR (peak signal to noise ratio). A group of experimental results demonstrate that the image enhancement algorithm based on wavelet transform is effective for image de-noising and enhancement. Wavelet transform modulus maxima method is one of the best methods for image enhancement.
Assessment of disinfection of hospital surfaces using different monitoring methods
Adriano Menis Ferreira
2015-06-01
Full Text Available OBJECTIVE: to assess the efficiency of cleaning/disinfection of surfaces of an Intensive Care Unit.METHOD: descriptive-exploratory study with quantitative approach conducted over the course of four weeks. Visual inspection, bioluminescence adenosine triphosphate and microbiological indicators were used to indicate cleanliness/disinfection. Five surfaces (bed rails, bedside tables, infusion pumps, nurses' counter, and medical prescription table were assessed before and after the use of rubbing alcohol at 70% (w/v, totaling 160 samples for each method. Non-parametric tests were used considering statistically significant differences at p<0.05.RESULTS: after the cleaning/disinfection process, 87.5, 79.4 and 87.5% of the surfaces were considered clean using the visual inspection, bioluminescence adenosine triphosphate and microbiological analyses, respectively. A statistically significant decrease was observed in the disapproval rates after the cleaning process considering the three assessment methods; the visual inspection was the least reliable.CONCLUSION: the cleaning/disinfection method was efficient in reducing microbial load and organic matter of surfaces, however, these findings require further study to clarify aspects related to the efficiency of friction, its frequency, and whether or not there is association with other inputs to achieve improved results of the cleaning/disinfection process.
ESR studies on flint with a difference-spectrum method
Walther, R.; Zilles, D.
Dating of fired flints with ESR is often difficult because of disturbing signals in the ESR spectrum. Flint samples from the archaeological sites 'San Quintin de Mediona' (NE Spain) and 'Berigoule' (in the south of France) were used for studies on the Al centre in heated material. Our samples measured at 100 K show the Al signal with very weak hyperfine structure and an unidentified disturbing signal, similar to the spectra described by Porat and Schwarcz (1991). We tested a new method for subtracting the spectrum of a disturbing signal from the Al spectrum (as an alternative procedure to the method proposed by Porat and Schwarcz, 1991), using different measurement temperatures. The DE determination with these filtered Al spectra was carried out and was compared with the usual procedure on one flint sample. For comparison with the ESR results we measured TL on some of the samples.
Accurate finite difference methods for time-harmonic wave propagation
Harari, Isaac; Turkel, Eli
1994-01-01
Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.
Finite difference methods for coupled flow interaction transport models
Shelly McGee
2009-04-01
Full Text Available Understanding chemical transport in blood flow involves coupling the chemical transport process with flow equations describing the blood and plasma in the membrane wall. In this work, we consider a coupled two-dimensional model with transient Navier-Stokes equation to model the blood flow in the vessel and Darcy's flow to model the plasma flow through the vessel wall. The advection-diffusion equation is coupled with the velocities from the flows in the vessel and wall, respectively to model the transport of the chemical. The coupled chemical transport equations are discretized by the finite difference method and the resulting system is solved using the additive Schwarz method. Development of the model and related analytical and numerical results are presented in this work.
Acute effect of different stretching methods on isometric muscle strength
Gabriel Vasconcellos de Lima Costa e Silva
2014-03-01
This study investigated the acute effect of static stretching methods (SS and proprioceptive neuromuscular facilitation (PNF on the static muscle strength (SMS. Eleven young male subjects with strength training experience, performed 3 tests with a 48h interval between them, randomly selected, where each one subject carried out all procedures: a hand grip without stretching; b hand grip preceded by static stretching of wrist flexors muscles; c hand grip preceded by PNF stretching of wrist flexors muscles. The Shapiro-Wilk test verified the normality of data, and a one-way ANOVA with repeated measures, followed by Tukey’s post hoc test, evaluated the differences between the groups. The significance was set at p 0.05. In conclusion, both stretching methods had caused negative effects on isometric strength, reducing its levels.
A review of current finite difference rotor flow methods
Caradonna, F. X.; Tung, C.
1986-01-01
Rotary-wing computational fluid dynamics is reaching a point where many three-dimensional, unsteady, finite-difference codes are becoming available. This paper gives a brief review of five such codes, which treat the small disturbance, conservative and nonconservative full-potential, and Euler flow models. A discussion of the methods of applying these codes to the rotor environment (including wake and trim considerations) is followed by a comparison with various available data. These data include tests of advancing lifting and nonlifting, and hovering model rotors with significant supercritical flow regions. The codes are also compared for computational efficiency.
The efficiency study of different purification methods for liquid scintillator
Hu, Wei; Yu, Boxiang; Zhang, Xuan; Zhou, Li; Cai, Xiao; Sun, Lijun
2016-01-01
JUNO is an experiment aimed at detecting neutrino mass hierarchy. The innermost part of the JUNO detector is formed by 20,000 tons of liquid scintillator which should have very low level of radioactive materials, such as 238U, 232Th, and 40K. Since the radioactive level of raw LAB(the solvent of LS)cannot reach so stringent requirements of JUNO, the purification for LAB plays an extremely important role in LS production. This article studies the efficiency of several different purification methods for LS, like distillation, water extraction and Al2O3 purification.
COMPARATIVE EFFECTIVENESS OF DIFFERENT METHODS OF CANDIDAL DYSBACTERIOSIS THERAPY
S.V. Nikolaeva
2009-01-01
Full Text Available The study of effectiveness of different methods of microbiological disorders correction in children after 3 years old with candidal dysbacteriosis are presented in this article. The study compared probiotical sour milk-made stuff («Actimel» and sour milk-made stuff, not fortified with probiotical cultures («Rastishka» and traditional kefir. It was shown that an inclusion of probiotical sour milkmade stuff in diet of children with candidal dysbacteriosis results in normalization of lacto- and bifidobacteria level and decreasing of Candida level.Key words: children, candidal dysbacteriosis, probiotics.(Voprosy sovremennoi pediatrii — Current Pediatrics. 2009;8(6:31-35
A comparative analysis of different DEM interpolation methods
P.V. Arun
2013-12-01
Full Text Available Visualization of geospatial entities generally entails Digital Elevation Models (DEMs that are interpolated to establish three dimensional co-ordinates for the entire terrain. The accuracy of generated terrain model depends on the interpolation mechanism adopted and hence it is needed to investigate the comparative performance of different approaches in this context. General interpolation techniques namely Inverse Distance Weighted, kriging, ANUDEM, Nearest Neighbor, and Spline approaches have been compared. Differential ground field survey has been conducted to generate reference DEM as well as specific set of test points for comparative evaluation. We have also investigated the suitability of Shuttle Radar Topographic Mapper Digital Elevation Mapper for Indian terrain by comparing it with the Survey of India (SOI Digital Elevation Model (DEM. Contours were generated at different intervals for comparative analysis and found SRTM as more suitable. The terrain sensitivity of various methods has also been analyzed with reference to the study area.
Jacobs, Christian T; Kramer, Stephan C; Funke, Simon W
2016-01-01
Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation of high-resolution and ideally 3D transient models is generally a very computationally expensive problem. As a result, existing work on the adjoint optimisation of tidal turbine placement has been mostly limited to steady-state simulations in which very high, non-physical values of the background viscosity are required to ensure that a steady-state solution exists. However, such compromises may affect the reliability of the modelled turbines, their wakes and interactions, and thus bring into question the validity of the co...
SUSY SU(5) with singlet plus adjoint matter and A{sub 4} family symmetry
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.
Probing Seesaw in an Adjoint SUSY SU(5) Model at LHC
Awasthi, Ram Lal; Mitra, Manimala
2010-01-01
The SU(5) GUT model extended with fermions in the adjoint $24_F$ representation predicts triplet fermions in the 100 GeV mass range, opening up the possibility of testing seesaw at LHC. However, once the model is supersymmerized, the triplet fermion mass is constrained to be close to the GUT scale for the gauge couplings to unify. We propose an extension of the SUSY SU(5) model where type II seesaw can be tested at LHC. In this model we add a matter chiral field in the adjoint $\\hat{24}_F$ representation and Higgs chiral superfields in the symmetric $\\hat{15}_H$ and $\\hat{\\bar{15}}_H$ representations. We call this the symmetric adjoint SUSY SU(5) model. The triplet scalar and triplet fermion masses in this model are predicted to be in the 100 GeV and $10^{13}$ GeV range respectively, while the mass of the singlet fermion remains unconstrained. This gives a type I plus type II plus type III seesaw mass term for the neutrinos. The triplet scalars with masses $\\sim 100$ GeV range can be produced at the LHC. We b...
Scocco, Paola; Brusaferro, Andrea; Catorci, Andrea
2012-07-01
Although the Geographical Information System (GIS), which integrates computerized drawing computer assisted design (CAD) and relational databases (data base management system (DBMS)), is best known for applications in geographical and planning cartography, it can also use many kinds of information concerning the territory. A multidisciplinary project was initiated since 5 years a multidisciplinary study was initiated to use GIS to integrate environmental and ecological data with findings on animal health, ethology, and anatomy. This study is chiefly aimed at comparing two different methods for measuring the absorptive surface of rumen papillae. To this scope, 21 female sheep (Ovis aries) on different alimentary regimes (e.g., milk and forage mixed diet, early herbaceous diet, dry hay diet, and fresh hay diet at the maximum of pasture flowering and at the maximum of pasture dryness) were used; after slaughtering, 20 papillae were randomly removed from each sample collected from four indicator regions of rumen wall, placed near a metric reference and digitally photographed. The images were developed with the ArcGIS™ software to calculate the area of rumen papillae by means of GIS and to measure their mid-level width and length to calculate the papillae area as previously performed with a different method. Spatial measurements were analyzed using univariate and multivariate methods. This work demonstrates that the GIS methodology can be efficiently used for measuring the absorptive surface of rumen papillae. In addition, GIS demonstrated to be a rapid, precise, and objective tool when compared with previously used method.
Radial anisotropy of the North American upper mantle based on adjoint tomography with USArray
Zhu, Hejun; Komatitsch, Dimitri; Tromp, Jeroen
2017-10-01
We use seismic data from USArray to image the upper mantle underneath the United States based on a so-called `adjoint tomography', an iterative full waveform inversion technique. The inversion uses data from 180 regional earthquakes recorded by 4516 seismographic stations, resulting in 586 185 frequency-dependent measurements. Three-component short-period body waves and long-period surface waves are combined to simultaneously constrain deep and shallow structures. The transversely isotropic model US22 is the result of 22 pre-conditioned conjugate-gradient iterations. Approximate Hessian maps and point-spread function tests demonstrate good illumination of the study region and limited trade-offs among different model parameters. We observe a distinct wave-speed contrast between the stable eastern US and the tectonically active western US. This boundary is well correlated with the Rocky Mountain Front. Stable cratonic regions are characterized by fast anomalies down to 250-300 km, reflecting the thickness of the North American lithosphere. Several fast anomalies are observed beneath the North American lithosphere, suggesting the possibility of lithospheric delamination. Slow wave-speed channels are imaged beneath the lithosphere, which might indicate weak asthenosphere. Beneath the mantle transition zone of the central US, an elongated north-south fast anomaly is observed, which might be the ancient subducted Farallon slab. The tectonically active western US is dominated by prominent slow anomalies with magnitudes greater than -6 per cent down to approximately 250 km. No continuous lower to upper mantle upwellings are observed beneath Yellowstone. In addition, our results confirm previously observed differences between oceans and continents in the anisotropic parameter ξ = (βh/βv)2. A slow wave-speed channel with ξ > 1 is imaged beneath the eastern Pacific at depths from 100 to 200 km, reflecting horizontal shear within the asthenosphere. Underneath continental
A new method for precursory information extraction: Slope-difference information method
无
2001-01-01
A new method for precursory information extraction, i.e.,slope-difference information method is proposed in the paper for the daily-mean-value precursory data sequence. Taking Tangshan station as an example, the calculation of full-time-domain leveling data is made, which is tested and compared with several other methods. The results indicate that the method is very effective for extracting short-term precursory information from the daily mean values after the optimization is made. Therefore, it is valuable for popularization and application.
Use of different investigation methods of soil for forensic purpose
Kristina Štibelj
2012-06-01
Full Text Available With its specific background and methods, geology may help forensic scientists considerably when doingresearches and analyses. Based on the procedures used in the National Forensic Laboratory, we have beenresearching and comparing 15 soil samples from different locations. We divided them into 3 groups, of which eachcomprised one pair of samples of the same location. By comparing colour, density and mineral composition in thesoil samples, we tried to determine which two samples originated from the same location. We were comparingthe results of individually used research methods and tried to evaluate which provide the best sample matches.Furthermore, we were comparing how the mineral composition of the samples and their bedrock match. The bestmatch was achieved by applying the method of X-ray powder diffraction, which clearly showed identical samplescollected from the same location. When measuring density, the values varied according to the location site, fromwhich the comparative and conflicting samples were taken. The change of density was observed in the distanceof less than one meter. For the field of forensic science the exact location of sample collection is of crucial importance.The proximity of sample collecting has considerable impact on density, as longer distances do not providecomparative results, whereas a short distance may present us with highly matching samples, the method which iswidely considered applicable in forensic science. By applying the method of X-ray powder it is possible to acquirecomparative results at the distance of several meters; in forensic science, however, this does not provide acceptableresults for defining the identity of the location.
Meat Quality of Chicken Breast Subjected to Different Thawing Methods
MR Oliveira
2015-06-01
Full Text Available Freezing is one of the methods to preserve and guarantee the quality of meat until it reaches the consumer. Even though freezing is classified as a mild form of preservation, it causes meat changes resulting from the formation of ice crystals that subsequently affect the tenderness and functionality of meat. The aim of this study was to evaluate the physicochemical and structural characteristics of chicken half breast submitted to fast freezing (-36 °C for 2 hours and thawed by five different methods (under refrigeration, in a microwave, in a oven with air circulation, placed in cold water, or at room temperature. After thawing, the following parameters were evaluated: moisture content, drip loss (syneresis, water activity (aw, and shear force. Samples were also histologically evaluated by light microscopy. The results indicated that, despite being submitted to fast freezing, thawing affected (p <0.05 most of the physicochemical and structural properties of the meat, except for aw. Thawing in cold water (packed in low-density polyethylene bags and placed in cold water at approximately 10 °C for 2 hours and 15 minutes presented the best results due to lesser damage to the cell structure, as shown by the lower drip loss, higher moisture content, and greater tenderness of the samples compared to those thawed using the other methods. Histological examination showed that muscle fiber structural features and organization were maintained. Thawing at low temperatures seems to cause less damage to the meat structure and allows maintaining of its properties. It was concluded that the meat quality is not related only with the freezing method, but also with the method and conditions used in thawing.
SIMULATION OF POLLUTANTS IN RIVER SYSTEMS USING FINITE DIFFERENCE METHOD
ZAHEER Iqbal; CUI Guang Bai
2002-01-01
This paper using finite difference scheme for the numerical solution of advection-dispersion equation develops a one-dimensional water quality model. The model algorithm has some modification over other steady state models including QUAL2E, which have been used steady state implementation of implicit backward-difference numerical scheme. The computer program in the developed model contains a special unsteady state implementation of four point implicit upwind numerical schemes using double sweep method. The superiority of this method in the modeling procedure results the simulation efficacy under simplified conditions of effluent discharge from point and non-point sources. The model is helpful for eye view assessment of degree of interaction between model variables for strategic planning purposes. The model has been applied for the water quality simulation of the Hanjiang River basin using flow computation model. Model simulation results have shown the pollutants prediction, dispersion and impact on the existing water quality.Model test shows the model validity comparing with other sophisticated models. Sensitivity analysis was performed to overview the most sensitive parameters followed by calibration and verification process.
Physiologic responses of grizzly bears to different methods of capture.
Cattet, Marc R; Christison, Katina; Caulkett, Nigel A; Stenhouse, Gordon B
2003-07-01
The physiologic effects of two methods of capture, chemical immobilization of free-ranging (FR) bears by remote injection from a helicopter and physical restraint (PR) by leg-hold snare prior to chemical immobilization, were compared in 46 grizzly bears (Ursus arctos) handled during 90 captures between 1999 and 2001. Induction dosages and times were greater for FR bears than PR bears, a finding consistent with depletion of, or decreased sensitivity to, catecholamines. Free-ranging bears also had higher rectal temperatures 15 min following immobilization and temperatures throughout handling that correlated positively with induction time. Physically restrained bears had higher white blood cell counts, with more neutrophils and fewer lymphocytes and eosinophils, than did FR bears. This white blood cell profile was consistent with a stress leukogram, possibly affected by elevated levels of serum cortisol. Serum concentrations of alanine aminotransferase, aspartate aminotransferase, and creatine kinase were higher in PR bears that suggested muscle injury. Serum concentrations of sodium and chloride also were higher in PR bears and attributed to reduced body water volume through water deprivation and increased insensible water loss. Overall, different methods of capture resulted in different patterns of physiologic disturbance. Reducing pursuit and drug induction times should help to minimize increase in body temperature and alteration of acid-base balance in bears immobilized by remote injection. Minimizing restraint time and ensuring snare-anchoring cables are short should help to minimize loss of body water and prevent serious muscle injury in bears captured by leg-hold snare.
Evaluation of the positional difference between two common geocoding methods
Dustin T. Duncan
2011-05-01
Full Text Available Geocoding, the process of matching addresses to geographic coordinates, is a necessary first step when using geographical information systems (GIS technology. However, different geocoding methodologies can result in different geographic coordinates. The objective of this study was to compare the positional (i.e. longitude/latitude difference between two common geocoding methods, i.e. ArcGIS (Environmental System Research Institute, Redlands, CA, USA and Batchgeo (freely available online at http://www.batchgeo.com. Address data came from the YMCA-Harvard After School Food and Fitness Project, an obesity prevention intervention involving children aged 5-11 years and their families participating in YMCAadministered, after-school programmes located in four geographically diverse metropolitan areas in the USA. Our analyses include baseline addresses (n = 748 collected from the parents of the children in the after school sites. Addresses were first geocoded to the street level and assigned longitude and latitude coordinates with ArcGIS, version 9.3, then the same addresses were geocoded with Batchgeo. For this analysis, the ArcGIS minimum match score was 80. The resulting geocodes were projected into state plane coordinates, and the difference in longitude and latitude coordinates were calculated in meters between the two methods for all data points in each of the four metropolitan areas. We also quantified the descriptions of the geocoding accuracy provided by Batchgeo with the match scores from ArcGIS. We found a 94% match rate (n = 705, 2% (n = 18 were tied and 3% (n = 25 were unmatched using ArcGIS. Forty-eight addresses (6.4% were not matched in ArcGIS with a match score ≥80 (therefore only 700 addresses were included in our positional difference analysis. Six hundred thirteen (87.6% of these addresses had a match score of 100. Batchgeo yielded a 100% match rate for the addresses that ArcGIS geocoded. The median for longitude and latitude
Assessment of disinfection of hospital surfaces using different monitoring methods.
Ferreira, Adriano Menis; de Andrade, Denise; Rigotti, Marcelo Alessandro; de Almeida, Margarete Teresa Gottardo; Guerra, Odanir Garcia; dos Santos Junior, Aires Garcia
2015-01-01
to assess the efficiency of cleaning/disinfection of surfaces of an Intensive Care Unit. descriptive-exploratory study with quantitative approach conducted over the course of four weeks. Visual inspection, bioluminescence adenosine triphosphate and microbiological indicators were used to indicate cleanliness/disinfection. Five surfaces (bed rails, bedside tables, infusion pumps, nurses' counter, and medical prescription table) were assessed before and after the use of rubbing alcohol at 70% (w/v), totaling 160 samples for each method. Non-parametric tests were used considering statistically significant differences at pdisinfection process, 87.5, 79.4 and 87.5% of the surfaces were considered clean using the visual inspection, bioluminescence adenosine triphosphate and microbiological analyses, respectively. A statistically significant decrease was observed in the disapproval rates after the cleaning process considering the three assessment methods; the visual inspection was the least reliable. the cleaning/disinfection method was efficient in reducing microbial load and organic matter of surfaces, however, these findings require further study to clarify aspects related to the efficiency of friction, its frequency, and whether or not there is association with other inputs to achieve improved results of the cleaning/disinfection process.
Assessment of hip dysplasia and osteoarthritis: Variability of different methods
Troelsen, Anders; Elmengaard, Brian; Soeballe, Kjeld (Orthopedic Research Unit, Univ. Hospital of Aarhus, Aarhus (Denmark)), e-mail: a_troelsen@hotmail.com; Roemer, Lone (Dept. of Radiology, Univ. Hospital of Aarhus, Aarhus (Denmark)); Kring, Soeren (Dept. of Orthopedic Surgery, Aabenraa Hospital, Aabenraa (Denmark))
2010-03-15
Background: Reliable assessment of hip dysplasia and osteoarthritis is crucial in young adults who may benefit from joint-preserving surgery. Purpose: To investigate the variability of different methods for diagnostic assessment of hip dysplasia and osteoarthritis. Material and Methods: By each of four observers, two assessments were done by vision and two by angle construction. For both methods, the intra- and interobserver variability of center-edge and acetabular index angle assessment were analyzed. The observers' ability to diagnose hip dysplasia and osteoarthritis were assessed. All measures were compared to those made on computed tomography scan. Results: Intra- and interobserver variability of angle assessment was less when angles were drawn compared with assessment by vision, and the observers' ability to diagnose hip dysplasia improved when angles were drawn. Assessment of osteoarthritis in general showed poor agreement with findings on computed tomography scan. Conclusion: We recommend that angles always should be drawn for assessment of hip dysplasia on pelvic radiographs. Given the inherent variability of diagnostic assessment of hip dysplasia, a computed tomography scan could be considered in patients with relevant hip symptoms and a center-edge angle between 20 deg and 30 deg. Osteoarthritis should be assessed by measuring the joint space width or by classifying the Toennis grade as either 0-1 or 2-3
Antioxidant activity of wine assessed by different in vitro methods
Di Lorenzo Chiara
2017-01-01
Full Text Available Epidemiological studies have suggested that a diet rich in antioxidant compounds could help in counteracting the effects of reactive oxygen species, reducing the risk factors for chronic diseases. The moderate consumption of wine, especially red wine, has been associated with the reduction in mortalities from cardiovascular diseases. One of the possible reasons for the protective effect of wine can be identified in the high content of polyphenols (mainly flavonoids, which have significant antioxidant activity. Even though several in vitro tests have been developed for the measure of the antioxidant property, no method has showed a satisfactory correlation with the in vivo situation. On these bases, the aim of this study was the application and comparison of different in vitro methods to assess the antioxidant activity of red, rosé and white wines. The methods were: 1 Folin-Cocalteau's assay for the quantification of total polyphenol content; 2 the DPPH (1,1-diphenyl-2-picrylhydrazyl spectrophotometric assay and the Trolox Equivalent Antioxidant Capacity (TEAC spectrophotometric assay for measuring the antioxidant activity of samples; 3 High Performance Thin Layer Chromatography for separation of phenolic substances and assessment of the associated antioxidant activity; 4 electrochemical detection by using a biosensor. Although all the approaches show some limitations, this battery of tests offers a more reliable body of data on the antioxidant activity of vine derivatives.
Three Different Methods of Estimating LAI in a Small Watershed
Speckman, H. N.; Ewers, B. E.; Beverly, D.
2015-12-01
Leaf area index (LAI) is a critical input of models that improve predictive understanding of ecology, hydrology, and climate change. Multiple techniques exist to quantify LAI, most of which are labor intensive, and all often fail to converge on similar estimates. . Recent large-scale bark beetle induced mortality greatly altered LAI, which is now dominated by younger and more metabolically active trees compared to the pre-beetle forest. Tree mortality increases error in optical LAI estimates due to the lack of differentiation between live and dead branches in dense canopy. Our study aims to quantify LAI using three different LAI methods, and then to compare the techniques to each other and topographic drivers to develop an effective predictive model of LAI. This study focuses on quantifying LAI within a small (~120 ha) beetle infested watershed in Wyoming's Snowy Range Mountains. The first technique estimated LAI using in-situ hemispherical canopy photographs that were then analyzed with Hemisfer software. The second LAI estimation technique was use of the Kaufmann 1982 allometrerics from forest inventories conducted throughout the watershed, accounting for stand basal area, species composition, and the extent of bark beetle driven mortality. The final technique used airborne light detection and ranging (LIDAR) first DMS returns, which were used to estimating canopy heights and crown area. LIDAR final returns provided topographical information and were then ground-truthed during forest inventories. Once data was collected, a fractural analysis was conducted comparing the three methods. Species composition was driven by slope position and elevation Ultimately the three different techniques provided very different estimations of LAI, but each had their advantage: estimates from hemisphere photos were well correlated with SWE and snow depth measurements, forest inventories provided insight into stand health and composition, and LIDAR were able to quickly and
Kuś, Tomasz; Bartlett, Rodney J.
2008-09-01
The doublet and quartet excited states of the formyl radical have been studied by the equation-of-motion (EOM) coupled cluster (CC) method. The Sz spin-conserving singles and doubles (EOM-EE-CCSD) and singles, doubles, and triples (EOM-EE-CCSDT) approaches, as well as the spin-flipped singles and doubles (EOM-SF-CCSD) method have been applied, subject to unrestricted Hartree-Fock (HF), restricted open-shell HF, and quasirestricted HF references. The structural parameters, vertical and adiabatic excitation energies, and harmonic vibrational frequencies have been calculated. The issue of the reference function choice for the spin-flipped (SF) method and its impact on the results has been discussed using the experimental data and theoretical results available. The results show that if the appropriate reference function is chosen so that target states differ from the reference by only single excitations, then EOM-EE-CCSD and EOM-SF-CCSD methods give a very good description of the excited states. For the states that have a non-negligible contribution of the doubly excited configurations one is able to use the SF method with such a reference function, that in most cases the performance of the EOM-SF-CCSD method is better than that of the EOM-EE-CCSD approach.
PURE CULTURE METHOD: GIARDIA LAMBLIA FROM DIFFERENT STOOL SAMPLES
H.A YOUSEFI
2000-03-01
Full Text Available Introduction. Giardiasis is one of the health problems in the world including Iran. To determine the biochemical and biological problems and also identification of various strains, it is essential to obtain pure culture and then mass production of Giardia lamblia. The goal of this study was to isolate this protozoa purely.
Methods. Giardia lamblia cysts were isolated from 50 stool samples by use of floating of a four - layer of sucrose method. The cysts were transfered to an inducing solution. Subsequently, they were cultured in a modified culture medium (TYIS-33. Following excystation of trophozoite and its multiplication, the parasite was caltured and purified.
Findings. Excitation of trophozoite was observed in 40 samples (80 percent from which 22 samples (55 percent yielded pure culture. The doubling time was approximately 13hr and the peak of parasite was observed between third and fourth days.
Conclusion. The proliferation and growth rate of Giardia lamblia have enabled us to use this method widely. Cystein and ascorbic acid which are present in the induction solution, have a key role in excystation of trophozoite. Purification and passage of samples has facilitated the culture of this parasite in vitro. Therefore this method has yielded better results in comparison with other studies. This is probably due to a decrease in the amount of bovine bile or using different strains of Giardia lamblia in the present study.
Estimation of water percolation by different methods using TDR
Alisson Jadavi Pereira da Silva
2014-02-01
Full Text Available Detailed knowledge on water percolation into the soil in irrigated areas is fundamental for solving problems of drainage, pollution and the recharge of underground aquifers. The aim of this study was to evaluate the percolation estimated by time-domain-reflectometry (TDR in a drainage lysimeter. We used Darcy's law with K(θ functions determined by field and laboratory methods and by the change in water storage in the soil profile at 16 points of moisture measurement at different time intervals. A sandy clay soil was saturated and covered with plastic sheet to prevent evaporation and an internal drainage trial in a drainage lysimeter was installed. The relationship between the observed and estimated percolation values was evaluated by linear regression analysis. The results suggest that percolation in the field or laboratory can be estimated based on continuous monitoring with TDR, and at short time intervals, of the variations in soil water storage. The precision and accuracy of this approach are similar to those of the lysimeter and it has advantages over the other evaluated methods, of which the most relevant are the possibility of estimating percolation in short time intervals and exemption from the predetermination of soil hydraulic properties such as water retention and hydraulic conductivity. The estimates obtained by the Darcy-Buckingham equation for percolation levels using function K(θ predicted by the method of Hillel et al. (1972 provided compatible water percolation estimates with those obtained in the lysimeter at time intervals greater than 1 h. The methods of Libardi et al. (1980, Sisson et al. (1980 and van Genuchten (1980 underestimated water percolation.
Comparison of two different methods of detecting residual caries
Kütük, Zeynep Bilge; Ergin, Esra; Yalçın Çakır, Filiz; Gürgan, Sevil
2017-01-01
Objectives The aim of this study was to investigate the ability of the fluorescence-aided caries excavation (FACE) device to detect residual caries by comparing conventional methods in vivo. Materials and Methods A total of 301 females and 202 males with carious teeth participated in this study. The cavity preparations were done by grade 4 (Group 1, 154 teeth), grade 5 (Group 2, 176 teeth), and postgraduate (Group 3, 173 teeth) students. After caries excavation using a handpiece and hand instruments, the presence of residual caries was evaluated by 2 investigators who were previously calibrated for visual-tactile assessment with and without magnifying glasses and trained in the use of a FACE device. The tooth number, cavity type, and presence or absence of residual caries were recorded. The data were analyzed using the Chi-square test, the Fisher's Exact test, or the McNemar test as appropriate. Kappa statistics was used for calibration. In all tests, the level of significance was set at p = 0.05. Results Almost half of the cavities prepared were Class II (Class I, 20.9%; Class II, 48.9%; Class III, 20.1%; Class IV, 3.4%; Class V, 6.8%). Higher numbers of cavities left with caries were observed in Groups 1 and 2 than in Group 3 for all examination methods. Significant differences were found between visual inspection with or without magnifying glasses and inspection with a FACE device for all groups (p < 0.001). More residual caries were detected through inspection with a FACE device (46.5%) than through either visual inspection (31.8%) or inspection with a magnifying glass (37.6%). Conclusions Within the limitations of this study, the FACE device may be an effective method for the detection of residual caries. PMID:28194364